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mirror of https://gitlab.com/scemama/qp_plugins_scemama.git synced 2024-12-22 20:34:05 +01:00

Merge gitlab.com:scemama/qp_plugins_scemama

Conflicts:
	devel/svdwf/Evar_TruncSVD.irp.f
This commit is contained in:
Abdallah Ammar 2021-07-28 17:28:31 +02:00
commit 4385cb2991
255 changed files with 13876 additions and 393 deletions

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@ -10,22 +10,66 @@ doc: Calculated |FCI| energy + |PT2|
interface: ezfio
size: (determinants.n_states)
[cisd_guess]
type: logical
doc: If true, the CASSCF starts with a CISD wave function
interface: ezfio,provider,ocaml
default: True
[state_following_casscf]
type: logical
type: logical
doc: If |true|, the CASSCF will try to follow the guess CI vector and orbitals
interface: ezfio,provider,ocaml
default: False
[diag_hess_cas]
type: logical
doc: If |true|, only the DIAGONAL part of the hessian is retained for the CASSCF
interface: ezfio,provider,ocaml
default: False
[hess_cv_cv]
type: logical
doc: If |true|, the core-virtual - core-virtual part of the hessian is computed
interface: ezfio,provider,ocaml
default: True
[level_shift_casscf]
type: Positive_float
doc: Energy shift on the virtual MOs to improve SCF convergence
interface: ezfio,provider,ocaml
default: 0.005
[fast_2rdm]
type: logical
doc: If true, the two-rdm are computed with a fast algo
interface: ezfio,provider,ocaml
default: True
[criterion_casscf]
type: character*(32)
doc: choice of the criterion for the convergence of the casscf: can be energy or gradients or e_pt2
interface: ezfio, provider, ocaml
default: e_pt2
[thresh_casscf]
type: Threshold
doc: Threshold on the convergence of the CASCF energy.
interface: ezfio,provider,ocaml
default: 1.e-06
[pt2_min_casscf]
type: Threshold
doc: Minimum value of the pt2_max parameter for the CIPSI in the CASSCF iterations.
interface: ezfio,provider,ocaml
default: 1.e-04
[n_big_act_orb]
type: integer
doc: Number of active orbitals from which the active space is considered as large, and therefore pt2_min_casscf is activated.
interface: ezfio,provider,ocaml
default: 16
[adaptive_pt2_max]
type: logical
doc: If |true|, the pt2_max value in the CIPSI iterations will automatically adapt, otherwise it is fixed at the value given in the EZFIO folder
interface: ezfio,provider,ocaml
default: True

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@ -2,3 +2,4 @@ cipsi
selectors_full
generators_cas
two_body_rdm
dav_general_mat

1
devel/casscf/TODO Normal file
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@ -0,0 +1 @@
it recomputes the gradients and hessian also with only one determinant, useless and confusing

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@ -4,17 +4,19 @@ program casscf
! TODO : Put the documentation of the program here
END_DOC
call reorder_orbitals_for_casscf
no_vvvv_integrals = .True.
touch no_vvvv_integrals
pt2_max = 0.02
SOFT_TOUCH no_vvvv_integrals pt2_max
! no_vvvv_integrals = .True.
! touch no_vvvv_integrals
n_det_max_full = 500
touch n_det_max_full
pt2_relative_error = 0.02
touch pt2_relative_error
call run_stochastic_cipsi
call run
end
subroutine run
implicit none
double precision :: energy_old, energy
double precision :: energy_old, energy, pt2_max_before, ept2_before,delta_E
logical :: converged,state_following_casscf_save
integer :: iteration
converged = .False.
@ -25,34 +27,79 @@ subroutine run
state_following_casscf_save = state_following_casscf
state_following_casscf = .True.
touch state_following_casscf
ept2_before = 0.d0
if(adaptive_pt2_max)then
pt2_max = 0.005
SOFT_TOUCH pt2_max
endif
do while (.not.converged)
call run_stochastic_cipsi
energy_old = energy
energy = eone+etwo+ecore
pt2_max_before = pt2_max
call write_time(6)
call write_int(6,iteration,'CAS-SCF iteration')
call write_double(6,energy,'CAS-SCF energy')
call write_double(6,energy_improvement, 'Predicted energy improvement')
call write_int(6,iteration,'CAS-SCF iteration = ')
call write_double(6,energy,'CAS-SCF energy = ')
if(n_states == 1)then
double precision :: E_PT2, PT2
call ezfio_get_casscf_energy_pt2(E_PT2)
call ezfio_get_casscf_energy(PT2)
PT2 -= E_PT2
call write_double(6,E_PT2,'E + PT2 energy = ')
call write_double(6,PT2,' PT2 = ')
call write_double(6,pt2_max,' PT2_MAX = ')
endif
converged = dabs(energy_improvement) < thresh_scf
pt2_max = dabs(energy_improvement / pt2_relative_error)
print*,''
call write_double(6,norm_grad_vec2,'Norm of gradients = ')
call write_double(6,norm_grad_vec2_tab(1), ' Core-active gradients = ')
call write_double(6,norm_grad_vec2_tab(2), ' Core-virtual gradients = ')
call write_double(6,norm_grad_vec2_tab(3), ' Active-virtual gradients = ')
print*,''
call write_double(6,energy_improvement, 'Predicted energy improvement = ')
if(criterion_casscf == "energy")then
converged = dabs(energy_improvement) < thresh_scf
else if (criterion_casscf == "gradients")then
converged = norm_grad_vec2 < thresh_scf
else if (criterion_casscf == "e_pt2")then
delta_E = dabs(E_PT2 - ept2_before)
converged = dabs(delta_E) < thresh_casscf
endif
ept2_before = E_PT2
if(adaptive_pt2_max)then
pt2_max = dabs(energy_improvement / (pt2_relative_error))
pt2_max = min(pt2_max, pt2_max_before)
if(n_act_orb.ge.n_big_act_orb)then
pt2_max = max(pt2_max,pt2_min_casscf)
endif
endif
print*,''
call write_double(6,pt2_max, 'PT2_MAX for next iteration = ')
mo_coef = NewOrbs
mo_occ = occnum
mo_occ = occnum
call save_mos
iteration += 1
N_det = max(N_det/2 ,N_states)
psi_det = psi_det_sorted
psi_coef = psi_coef_sorted
read_wf = .True.
call clear_mo_map
SOFT_TOUCH mo_coef N_det pt2_max psi_det psi_coef
if(iteration .gt. 3)then
state_following_casscf = state_following_casscf_save
touch state_following_casscf
if(.not.converged)then
iteration += 1
N_det = max(N_det/8 ,N_states)
psi_det = psi_det_sorted
psi_coef = psi_coef_sorted
read_wf = .True.
call clear_mo_map
SOFT_TOUCH mo_coef N_det psi_det psi_coef
if(adaptive_pt2_max)then
SOFT_TOUCH pt2_max
endif
if(iteration .gt. 3)then
state_following_casscf = state_following_casscf_save
soft_touch state_following_casscf
endif
endif
enddo
end

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@ -0,0 +1,45 @@
subroutine davidson_diag_sx_mat(N_st, u_in, energies)
implicit none
integer, intent(in) :: N_st
double precision, intent(out) :: u_in(nMonoEx+1,n_states_diag), energies(N_st)
integer :: i,j,N_st_tmp, dim_in, sze, N_st_diag_in
integer, allocatable :: list_guess(:)
double precision, allocatable :: H_jj(:)
logical :: converged
N_st_diag_in = n_states_diag
provide SXmatrix
sze = nMonoEx+1
dim_in = sze
allocate(H_jj(sze), list_guess(sze))
H_jj(1) = 0.d0
N_st_tmp = 1
list_guess(1) = 1
do j = 2, nMonoEx+1
H_jj(j) = SXmatrix(j,j)
if(H_jj(j).lt.0.d0)then
list_guess(N_st_tmp) = j
N_st_tmp += 1
endif
enddo
if(N_st_tmp .ne. N_st)then
print*,'Pb in davidson_diag_sx_mat'
print*,'N_st_tmp .ne. N_st'
print*,N_st_tmp, N_st
stop
endif
print*,'Number of possibly interesting states = ',N_st
print*,'Corresponding diagonal elements of the SX matrix '
u_in = 0.d0
do i = 1, min(N_st, N_st_diag_in)
! do i = 1, N_st
j = list_guess(i)
print*,'i,j',i,j
print*,'SX(i,i) = ',H_jj(j)
u_in(j,i) = 1.d0
enddo
call davidson_general(u_in,H_jj,energies,dim_in,sze,N_st,N_st_diag_in,converged,SXmatrix)
print*,'energies = ',energies
end

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@ -47,17 +47,21 @@ BEGIN_PROVIDER [real*8, P0tuvx, (n_act_orb,n_act_orb,n_act_orb,n_act_orb) ]
endif
P0tuvx= 0.d0
do istate=1,N_states
do x = 1, n_act_orb
do v = 1, n_act_orb
do u = 1, n_act_orb
do t = 1, n_act_orb
! 1 1 2 2 1 2 1 2
P0tuvx(t,u,v,x) = state_av_act_2_rdm_spin_trace_mo(t,v,u,x)
enddo
enddo
if(fast_2rdm)then
do istate=1,N_states
do x = 1, n_act_orb
do v = 1, n_act_orb
do u = 1, n_act_orb
do t = 1, n_act_orb
! 1 1 2 2 1 2 1 2
P0tuvx(t,u,v,x) = state_av_act_2_rdm_spin_trace_mo(t,v,u,x)
enddo
enddo
enddo
enddo
enddo
enddo
else
P0tuvx = P0tuvx_peter
endif
END_PROVIDER

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@ -0,0 +1,150 @@
use bitmasks
BEGIN_PROVIDER [real*8, P0tuvx_peter, (n_act_orb,n_act_orb,n_act_orb,n_act_orb) ]
BEGIN_DOC
! the second-order density matrix in the basis of the starting MOs
! matrices are state averaged
!
! we use the spin-free generators of mono-excitations
! E_pq destroys q and creates p
! D_pq = <0|E_pq|0> = D_qp
! P_pqrs = 1/2 <0|E_pq E_rs - delta_qr E_ps|0>
!
END_DOC
implicit none
integer :: t,u,v,x,mu,nu,istate,ispin,jspin,ihole,ipart,jhole,jpart
integer :: ierr
real*8 :: phase1,phase11,phase12,phase2,phase21,phase22
integer :: nu1,nu2,nu11,nu12,nu21,nu22
integer :: ierr1,ierr2,ierr11,ierr12,ierr21,ierr22
real*8 :: cI_mu(N_states),term
integer(bit_kind), dimension(N_int,2) :: det_mu, det_mu_ex
integer(bit_kind), dimension(N_int,2) :: det_mu_ex1, det_mu_ex11, det_mu_ex12
integer(bit_kind), dimension(N_int,2) :: det_mu_ex2, det_mu_ex21, det_mu_ex22
if (bavard) then
write(6,*) ' providing density matrix P0'
endif
P0tuvx_peter = 0.d0
! first loop: we apply E_tu, once for D_tu, once for -P_tvvu
do mu=1,n_det
call det_extract(det_mu,mu,N_int)
do istate=1,n_states
cI_mu(istate)=psi_coef(mu,istate)
end do
do t=1,n_act_orb
ipart=list_act(t)
do u=1,n_act_orb
ihole=list_act(u)
! apply E_tu
call det_copy(det_mu,det_mu_ex1,N_int)
call det_copy(det_mu,det_mu_ex2,N_int)
call do_spinfree_mono_excitation(det_mu,det_mu_ex1 &
,det_mu_ex2,nu1,nu2,ihole,ipart,phase1,phase2,ierr1,ierr2)
! det_mu_ex1 is in the list
if (nu1.ne.-1) then
do istate=1,n_states
term=cI_mu(istate)*psi_coef(nu1,istate)*phase1
! and we fill P0_tvvu
do v=1,n_act_orb
P0tuvx_peter(t,v,v,u)-=term
end do
end do
end if
! det_mu_ex2 is in the list
if (nu2.ne.-1) then
do istate=1,n_states
term=cI_mu(istate)*psi_coef(nu2,istate)*phase2
do v=1,n_act_orb
P0tuvx_peter(t,v,v,u)-=term
end do
end do
end if
end do
end do
end do
! now we do the double excitation E_tu E_vx |0>
do mu=1,n_det
call det_extract(det_mu,mu,N_int)
do istate=1,n_states
cI_mu(istate)=psi_coef(mu,istate)
end do
do v=1,n_act_orb
ipart=list_act(v)
do x=1,n_act_orb
ihole=list_act(x)
! apply E_vx
call det_copy(det_mu,det_mu_ex1,N_int)
call det_copy(det_mu,det_mu_ex2,N_int)
call do_spinfree_mono_excitation(det_mu,det_mu_ex1 &
,det_mu_ex2,nu1,nu2,ihole,ipart,phase1,phase2,ierr1,ierr2)
! we apply E_tu to the first resultant determinant, thus E_tu E_vx |0>
if (ierr1.eq.1) then
do t=1,n_act_orb
jpart=list_act(t)
do u=1,n_act_orb
jhole=list_act(u)
call det_copy(det_mu_ex1,det_mu_ex11,N_int)
call det_copy(det_mu_ex1,det_mu_ex12,N_int)
call do_spinfree_mono_excitation(det_mu_ex1,det_mu_ex11&
,det_mu_ex12,nu11,nu12,jhole,jpart,phase11,phase12,ierr11,ierr12)
if (nu11.ne.-1) then
do istate=1,n_states
P0tuvx_peter(t,u,v,x)+=cI_mu(istate)*psi_coef(nu11,istate)&
*phase11*phase1
end do
end if
if (nu12.ne.-1) then
do istate=1,n_states
P0tuvx_peter(t,u,v,x)+=cI_mu(istate)*psi_coef(nu12,istate)&
*phase12*phase1
end do
end if
end do
end do
end if
! we apply E_tu to the second resultant determinant
if (ierr2.eq.1) then
do t=1,n_act_orb
jpart=list_act(t)
do u=1,n_act_orb
jhole=list_act(u)
call det_copy(det_mu_ex2,det_mu_ex21,N_int)
call det_copy(det_mu_ex2,det_mu_ex22,N_int)
call do_spinfree_mono_excitation(det_mu_ex2,det_mu_ex21&
,det_mu_ex22,nu21,nu22,jhole,jpart,phase21,phase22,ierr21,ierr22)
if (nu21.ne.-1) then
do istate=1,n_states
P0tuvx_peter(t,u,v,x)+=cI_mu(istate)*psi_coef(nu21,istate)&
*phase21*phase2
end do
end if
if (nu22.ne.-1) then
do istate=1,n_states
P0tuvx_peter(t,u,v,x)+=cI_mu(istate)*psi_coef(nu22,istate)&
*phase22*phase2
end do
end if
end do
end do
end if
end do
end do
end do
! we average by just dividing by the number of states
do x=1,n_act_orb
do v=1,n_act_orb
do u=1,n_act_orb
do t=1,n_act_orb
P0tuvx_peter(t,u,v,x)*=0.5D0/dble(N_states)
end do
end do
end do
end do
END_PROVIDER

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@ -8,15 +8,31 @@ BEGIN_PROVIDER [ integer, nMonoEx ]
nMonoEx=n_core_inact_orb*n_act_orb+n_core_inact_orb*n_virt_orb+n_act_orb*n_virt_orb
END_PROVIDER
BEGIN_PROVIDER [integer, n_c_a_prov]
&BEGIN_PROVIDER [integer, n_c_v_prov]
&BEGIN_PROVIDER [integer, n_a_v_prov]
implicit none
n_c_a_prov = n_core_inact_orb * n_act_orb
n_c_v_prov = n_core_inact_orb * n_virt_orb
n_a_v_prov = n_act_orb * n_virt_orb
END_PROVIDER
BEGIN_PROVIDER [integer, excit, (2,nMonoEx)]
&BEGIN_PROVIDER [character*3, excit_class, (nMonoEx)]
&BEGIN_PROVIDER [integer, list_idx_c_a, (3,n_c_a_prov) ]
&BEGIN_PROVIDER [integer, list_idx_c_v, (3,n_c_v_prov) ]
&BEGIN_PROVIDER [integer, list_idx_a_v, (3,n_a_v_prov) ]
&BEGIN_PROVIDER [integer, mat_idx_c_a, (n_core_inact_orb,n_act_orb)
&BEGIN_PROVIDER [integer, mat_idx_c_v, (n_core_inact_orb,n_virt_orb)
&BEGIN_PROVIDER [integer, mat_idx_a_v, (n_act_orb,n_virt_orb)
BEGIN_DOC
! a list of the orbitals involved in the excitation
END_DOC
implicit none
integer :: i,t,a,ii,tt,aa,indx
integer :: i,t,a,ii,tt,aa,indx,indx_tmp
indx=0
indx_tmp = 0
do ii=1,n_core_inact_orb
i=list_core_inact(ii)
do tt=1,n_act_orb
@ -25,9 +41,15 @@ END_PROVIDER
excit(1,indx)=i
excit(2,indx)=t
excit_class(indx)='c-a'
indx_tmp += 1
list_idx_c_a(1,indx_tmp) = indx
list_idx_c_a(2,indx_tmp) = ii
list_idx_c_a(3,indx_tmp) = tt
mat_idx_c_a(ii,tt) = indx
end do
end do
indx_tmp = 0
do ii=1,n_core_inact_orb
i=list_core_inact(ii)
do aa=1,n_virt_orb
@ -36,9 +58,15 @@ END_PROVIDER
excit(1,indx)=i
excit(2,indx)=a
excit_class(indx)='c-v'
indx_tmp += 1
list_idx_c_v(1,indx_tmp) = indx
list_idx_c_v(2,indx_tmp) = ii
list_idx_c_v(3,indx_tmp) = aa
mat_idx_c_v(ii,aa) = indx
end do
end do
indx_tmp = 0
do tt=1,n_act_orb
t=list_act(tt)
do aa=1,n_virt_orb
@ -47,6 +75,11 @@ END_PROVIDER
excit(1,indx)=t
excit(2,indx)=a
excit_class(indx)='a-v'
indx_tmp += 1
list_idx_a_v(1,indx_tmp) = indx
list_idx_a_v(2,indx_tmp) = tt
list_idx_a_v(3,indx_tmp) = aa
mat_idx_a_v(tt,aa) = indx
end do
end do
@ -60,7 +93,9 @@ END_PROVIDER
END_PROVIDER
BEGIN_PROVIDER [real*8, gradvec2, (nMonoEx)]
BEGIN_PROVIDER [real*8, gradvec2, (nMonoEx)]
&BEGIN_PROVIDER [real*8, norm_grad_vec2]
&BEGIN_PROVIDER [real*8, norm_grad_vec2_tab, (3)]
BEGIN_DOC
! calculate the orbital gradient <Psi| H E_pq |Psi> from density
! matrices and integrals; Siegbahn et al, Phys Scr 1980
@ -69,13 +104,14 @@ BEGIN_PROVIDER [real*8, gradvec2, (nMonoEx)]
implicit none
integer :: i,t,a,indx
real*8 :: gradvec_it,gradvec_ia,gradvec_ta
real*8 :: norm_grad
indx=0
norm_grad_vec2_tab = 0.d0
do i=1,n_core_inact_orb
do t=1,n_act_orb
indx+=1
gradvec2(indx)=gradvec_it(i,t)
norm_grad_vec2_tab(1) += gradvec2(indx)*gradvec2(indx)
end do
end do
@ -83,6 +119,7 @@ BEGIN_PROVIDER [real*8, gradvec2, (nMonoEx)]
do a=1,n_virt_orb
indx+=1
gradvec2(indx)=gradvec_ia(i,a)
norm_grad_vec2_tab(2) += gradvec2(indx)*gradvec2(indx)
end do
end do
@ -90,17 +127,23 @@ BEGIN_PROVIDER [real*8, gradvec2, (nMonoEx)]
do a=1,n_virt_orb
indx+=1
gradvec2(indx)=gradvec_ta(t,a)
norm_grad_vec2_tab(3) += gradvec2(indx)*gradvec2(indx)
end do
end do
norm_grad=0.d0
norm_grad_vec2=0.d0
do indx=1,nMonoEx
norm_grad+=gradvec2(indx)*gradvec2(indx)
norm_grad_vec2+=gradvec2(indx)*gradvec2(indx)
end do
norm_grad=sqrt(norm_grad)
write(6,*)
write(6,*) ' Norm of the orbital gradient (via D, P and integrals): ', norm_grad
write(6,*)
do i = 1, 3
norm_grad_vec2_tab(i) = dsqrt(norm_grad_vec2_tab(i))
enddo
norm_grad_vec2=sqrt(norm_grad_vec2)
if(bavard)then
write(6,*)
write(6,*) ' Norm of the orbital gradient (via D, P and integrals): ', norm_grad_vec2
write(6,*)
endif
END_PROVIDER

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@ -1,303 +1,5 @@
use bitmasks
BEGIN_PROVIDER [real*8, hessmat, (nMonoEx,nMonoEx)]
BEGIN_DOC
! calculate the orbital hessian 2 <Psi| E_pq H E_rs |Psi>
! + <Psi| E_pq E_rs H |Psi> + <Psi| E_rs E_pq H |Psi> by hand,
! determinant per determinant, as for the gradient
!
! we assume that we have natural active orbitals
END_DOC
implicit none
integer :: indx,ihole,ipart
integer :: jndx,jhole,jpart
character*3 :: iexc,jexc
real*8 :: res
if (bavard) then
write(6,*) ' providing Hessian matrix hessmat '
write(6,*) ' nMonoEx = ',nMonoEx
endif
do indx=1,nMonoEx
do jndx=1,nMonoEx
hessmat(indx,jndx)=0.D0
end do
end do
do indx=1,nMonoEx
ihole=excit(1,indx)
ipart=excit(2,indx)
iexc=excit_class(indx)
do jndx=indx,nMonoEx
jhole=excit(1,jndx)
jpart=excit(2,jndx)
jexc=excit_class(jndx)
call calc_hess_elem(ihole,ipart,jhole,jpart,res)
hessmat(indx,jndx)=res
hessmat(jndx,indx)=res
end do
end do
END_PROVIDER
subroutine calc_hess_elem(ihole,ipart,jhole,jpart,res)
BEGIN_DOC
! eq 19 of Siegbahn et al, Physica Scripta 1980
! we calculate 2 <Psi| E_pq H E_rs |Psi>
! + <Psi| E_pq E_rs H |Psi> + <Psi| E_rs E_pq H |Psi>
! average over all states is performed.
! no transition between states.
END_DOC
implicit none
integer :: ihole,ipart,ispin,mu,istate
integer :: jhole,jpart,jspin
integer :: mu_pq, mu_pqrs, mu_rs, mu_rspq, nu_rs,nu
real*8 :: res
integer(bit_kind), allocatable :: det_mu(:,:)
integer(bit_kind), allocatable :: det_nu(:,:)
integer(bit_kind), allocatable :: det_mu_pq(:,:)
integer(bit_kind), allocatable :: det_mu_rs(:,:)
integer(bit_kind), allocatable :: det_nu_rs(:,:)
integer(bit_kind), allocatable :: det_mu_pqrs(:,:)
integer(bit_kind), allocatable :: det_mu_rspq(:,:)
real*8 :: i_H_psi_array(N_states),phase,phase2,phase3
real*8 :: i_H_j_element
allocate(det_mu(N_int,2))
allocate(det_nu(N_int,2))
allocate(det_mu_pq(N_int,2))
allocate(det_mu_rs(N_int,2))
allocate(det_nu_rs(N_int,2))
allocate(det_mu_pqrs(N_int,2))
allocate(det_mu_rspq(N_int,2))
integer :: mu_pq_possible
integer :: mu_rs_possible
integer :: nu_rs_possible
integer :: mu_pqrs_possible
integer :: mu_rspq_possible
res=0.D0
! the terms <0|E E H |0>
do mu=1,n_det
! get the string of the determinant
call det_extract(det_mu,mu,N_int)
do ispin=1,2
! do the monoexcitation pq on it
call det_copy(det_mu,det_mu_pq,N_int)
call do_signed_mono_excitation(det_mu,det_mu_pq,mu_pq &
,ihole,ipart,ispin,phase,mu_pq_possible)
if (mu_pq_possible.eq.1) then
! possible, but not necessarily in the list
! do the second excitation
do jspin=1,2
call det_copy(det_mu_pq,det_mu_pqrs,N_int)
call do_signed_mono_excitation(det_mu_pq,det_mu_pqrs,mu_pqrs&
,jhole,jpart,jspin,phase2,mu_pqrs_possible)
! excitation possible
if (mu_pqrs_possible.eq.1) then
call i_H_psi(det_mu_pqrs,psi_det,psi_coef,N_int &
,N_det,N_det,N_states,i_H_psi_array)
do istate=1,N_states
res+=i_H_psi_array(istate)*psi_coef(mu,istate)*phase*phase2
end do
end if
! try the de-excitation with opposite sign
call det_copy(det_mu_pq,det_mu_pqrs,N_int)
call do_signed_mono_excitation(det_mu_pq,det_mu_pqrs,mu_pqrs&
,jpart,jhole,jspin,phase2,mu_pqrs_possible)
phase2=-phase2
! excitation possible
if (mu_pqrs_possible.eq.1) then
call i_H_psi(det_mu_pqrs,psi_det,psi_coef,N_int &
,N_det,N_det,N_states,i_H_psi_array)
do istate=1,N_states
res+=i_H_psi_array(istate)*psi_coef(mu,istate)*phase*phase2
end do
end if
end do
end if
! exchange the notion of pq and rs
! do the monoexcitation rs on the initial determinant
call det_copy(det_mu,det_mu_rs,N_int)
call do_signed_mono_excitation(det_mu,det_mu_rs,mu_rs &
,jhole,jpart,ispin,phase2,mu_rs_possible)
if (mu_rs_possible.eq.1) then
! do the second excitation
do jspin=1,2
call det_copy(det_mu_rs,det_mu_rspq,N_int)
call do_signed_mono_excitation(det_mu_rs,det_mu_rspq,mu_rspq&
,ihole,ipart,jspin,phase3,mu_rspq_possible)
! excitation possible (of course, the result is outside the CAS)
if (mu_rspq_possible.eq.1) then
call i_H_psi(det_mu_rspq,psi_det,psi_coef,N_int &
,N_det,N_det,N_states,i_H_psi_array)
do istate=1,N_states
res+=i_H_psi_array(istate)*psi_coef(mu,istate)*phase2*phase3
end do
end if
! we may try the de-excitation, with opposite sign
call det_copy(det_mu_rs,det_mu_rspq,N_int)
call do_signed_mono_excitation(det_mu_rs,det_mu_rspq,mu_rspq&
,ipart,ihole,jspin,phase3,mu_rspq_possible)
phase3=-phase3
! excitation possible (of course, the result is outside the CAS)
if (mu_rspq_possible.eq.1) then
call i_H_psi(det_mu_rspq,psi_det,psi_coef,N_int &
,N_det,N_det,N_states,i_H_psi_array)
do istate=1,N_states
res+=i_H_psi_array(istate)*psi_coef(mu,istate)*phase2*phase3
end do
end if
end do
end if
!
! the operator E H E, we have to do a double loop over the determinants
! we still have the determinant mu_pq and the phase in memory
if (mu_pq_possible.eq.1) then
do nu=1,N_det
call det_extract(det_nu,nu,N_int)
do jspin=1,2
call det_copy(det_nu,det_nu_rs,N_int)
call do_signed_mono_excitation(det_nu,det_nu_rs,nu_rs &
,jhole,jpart,jspin,phase2,nu_rs_possible)
! excitation possible ?
if (nu_rs_possible.eq.1) then
call i_H_j(det_mu_pq,det_nu_rs,N_int,i_H_j_element)
do istate=1,N_states
res+=2.D0*i_H_j_element*psi_coef(mu,istate) &
*psi_coef(nu,istate)*phase*phase2
end do
end if
end do
end do
end if
end do
end do
! state-averaged Hessian
res*=1.D0/dble(N_states)
end subroutine calc_hess_elem
BEGIN_PROVIDER [real*8, hessmat2, (nMonoEx,nMonoEx)]
BEGIN_DOC
! explicit hessian matrix from density matrices and integrals
! of course, this will be used for a direct Davidson procedure later
! we will not store the matrix in real life
! formulas are broken down as functions for the 6 classes of matrix elements
!
END_DOC
implicit none
integer :: i,j,t,u,a,b,indx,jndx,bstart,ustart,indx_shift
real*8 :: hessmat_itju
real*8 :: hessmat_itja
real*8 :: hessmat_itua
real*8 :: hessmat_iajb
real*8 :: hessmat_iatb
real*8 :: hessmat_taub
if (bavard) then
write(6,*) ' providing Hessian matrix hessmat2 '
write(6,*) ' nMonoEx = ',nMonoEx
endif
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(hessmat2,n_core_inact_orb,n_act_orb,n_virt_orb,nMonoEx) &
!$OMP PRIVATE(i,indx,jndx,j,ustart,t,u,a,bstart,indx_shift)
!$OMP DO
do i=1,n_core_inact_orb
do t=1,n_act_orb
indx = t + (i-1)*n_act_orb
jndx=indx
do j=i,n_core_inact_orb
if (i.eq.j) then
ustart=t
else
ustart=1
end if
do u=ustart,n_act_orb
hessmat2(jndx,indx)=hessmat_itju(i,t,j,u)
jndx+=1
end do
end do
do j=1,n_core_inact_orb
do a=1,n_virt_orb
hessmat2(jndx,indx)=hessmat_itja(i,t,j,a)
jndx+=1
end do
end do
do u=1,n_act_orb
do a=1,n_virt_orb
hessmat2(jndx,indx)=hessmat_itua(i,t,u,a)
jndx+=1
end do
end do
end do
end do
!$OMP END DO NOWAIT
indx_shift = n_core_inact_orb*n_act_orb
!$OMP DO
do a=1,n_virt_orb
do i=1,n_core_inact_orb
indx = a + (i-1)*n_virt_orb + indx_shift
jndx=indx
do j=i,n_core_inact_orb
if (i.eq.j) then
bstart=a
else
bstart=1
end if
do b=bstart,n_virt_orb
hessmat2(jndx,indx)=hessmat_iajb(i,a,j,b)
jndx+=1
end do
end do
do t=1,n_act_orb
do b=1,n_virt_orb
hessmat2(jndx,indx)=hessmat_iatb(i,a,t,b)
jndx+=1
end do
end do
end do
end do
!$OMP END DO NOWAIT
indx_shift += n_core_inact_orb*n_virt_orb
!$OMP DO
do a=1,n_virt_orb
do t=1,n_act_orb
indx = a + (t-1)*n_virt_orb + indx_shift
jndx=indx
do u=t,n_act_orb
if (t.eq.u) then
bstart=a
else
bstart=1
end if
do b=bstart,n_virt_orb
hessmat2(jndx,indx)=hessmat_taub(t,a,u,b)
jndx+=1
end do
end do
end do
end do
!$OMP END DO
!$OMP END PARALLEL
do jndx=1,nMonoEx
do indx=1,jndx-1
hessmat2(indx,jndx) = hessmat2(jndx,indx)
enddo
enddo
END_PROVIDER
real*8 function hessmat_itju(i,t,j,u)
BEGIN_DOC
! the orbital hessian for core/inactive -> active, core/inactive -> active
@ -654,3 +356,184 @@ BEGIN_PROVIDER [real*8, hessdiag, (nMonoEx)]
!$OMP END PARALLEL
END_PROVIDER
BEGIN_PROVIDER [double precision, hessmat, (nMonoEx,nMonoEx)]
implicit none
integer :: i,j,t,u,a,b
integer :: indx,indx_tmp, jndx, jndx_tmp
integer :: ustart,bstart
real*8 :: hessmat_itju
real*8 :: hessmat_itja
real*8 :: hessmat_itua
real*8 :: hessmat_iajb
real*8 :: hessmat_iatb
real*8 :: hessmat_taub
! c-a c-v a-v
! c-a | X X X
! c-v | X X
! a-v | X
provide mo_two_e_integrals_in_map
hessmat = 0.d0
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(hessmat,n_c_a_prov,list_idx_c_a,n_core_inact_orb,n_act_orb,mat_idx_c_a) &
!$OMP PRIVATE(indx_tmp,indx,i,t,j,u,ustart,jndx)
!$OMP DO
!!!! < Core-active| H |Core-active >
! Core-active excitations
do indx_tmp = 1, n_c_a_prov
indx = list_idx_c_a(1,indx_tmp)
i = list_idx_c_a(2,indx_tmp)
t = list_idx_c_a(3,indx_tmp)
! Core-active excitations
do j = 1, n_core_inact_orb
if (i.eq.j) then
ustart=t
else
ustart=1
end if
do u=ustart,n_act_orb
jndx = mat_idx_c_a(j,u)
hessmat(jndx,indx) = hessmat_itju(i,t,j,u)
hessmat(indx,jndx) = hessmat(jndx,indx)
enddo
enddo
enddo
!$OMP END DO NOWAIT
!$OMP END PARALLEL
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(hessmat,n_c_a_prov,n_c_v_prov,list_idx_c_a,list_idx_c_v) &
!$OMP PRIVATE(indx_tmp,jndx_tmp,indx,i,t,j,a,jndx)
!$OMP DO
!!!! < Core-active| H |Core-VIRTUAL >
! Core-active excitations
do indx_tmp = 1, n_c_a_prov
indx = list_idx_c_a(1,indx_tmp)
i = list_idx_c_a(2,indx_tmp)
t = list_idx_c_a(3,indx_tmp)
! Core-VIRTUAL excitations
do jndx_tmp = 1, n_c_v_prov
jndx = list_idx_c_v(1,jndx_tmp)
j = list_idx_c_v(2,jndx_tmp)
a = list_idx_c_v(3,jndx_tmp)
hessmat(jndx,indx) = hessmat_itja(i,t,j,a)
hessmat(indx,jndx) = hessmat(jndx,indx)
enddo
enddo
!$OMP END DO NOWAIT
!$OMP END PARALLEL
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(hessmat,n_c_a_prov,n_a_v_prov,list_idx_c_a,list_idx_a_v) &
!$OMP PRIVATE(indx_tmp,jndx_tmp,indx,i,t,u,a,jndx)
!$OMP DO
!!!! < Core-active| H |ACTIVE-VIRTUAL >
! Core-active excitations
do indx_tmp = 1, n_c_a_prov
indx = list_idx_c_a(1,indx_tmp)
i = list_idx_c_a(2,indx_tmp)
t = list_idx_c_a(3,indx_tmp)
! ACTIVE-VIRTUAL excitations
do jndx_tmp = 1, n_a_v_prov
jndx = list_idx_a_v(1,jndx_tmp)
u = list_idx_a_v(2,jndx_tmp)
a = list_idx_a_v(3,jndx_tmp)
hessmat(jndx,indx) = hessmat_itua(i,t,u,a)
hessmat(indx,jndx) = hessmat(jndx,indx)
enddo
enddo
!$OMP END DO NOWAIT
!$OMP END PARALLEL
if(hess_cv_cv)then
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(hessmat,n_c_v_prov,list_idx_c_v,n_core_inact_orb,n_virt_orb,mat_idx_c_v) &
!$OMP PRIVATE(indx_tmp,indx,i,a,j,b,bstart,jndx)
!$OMP DO
!!!!! < Core-VIRTUAL | H |Core-VIRTUAL >
! Core-VIRTUAL excitations
do indx_tmp = 1, n_c_v_prov
indx = list_idx_c_v(1,indx_tmp)
i = list_idx_c_v(2,indx_tmp)
a = list_idx_c_v(3,indx_tmp)
! Core-VIRTUAL excitations
do j = 1, n_core_inact_orb
if (i.eq.j) then
bstart=a
else
bstart=1
end if
do b=bstart,n_virt_orb
jndx = mat_idx_c_v(j,b)
hessmat(jndx,indx) = hessmat_iajb(i,a,j,b)
hessmat(indx,jndx) = hessmat(jndx,indx)
enddo
enddo
enddo
!$OMP END DO NOWAIT
!$OMP END PARALLEL
endif
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(hessmat,n_c_v_prov,n_a_v_prov,list_idx_c_v,list_idx_a_v) &
!$OMP PRIVATE(indx_tmp,jndx_tmp,indx,i,a,t,b,jndx)
!$OMP DO
!!!! < Core-VIRTUAL | H |Active-VIRTUAL >
! Core-VIRTUAL excitations
do indx_tmp = 1, n_c_v_prov
indx = list_idx_c_v(1,indx_tmp)
i = list_idx_c_v(2,indx_tmp)
a = list_idx_c_v(3,indx_tmp)
! Active-VIRTUAL excitations
do jndx_tmp = 1, n_a_v_prov
jndx = list_idx_a_v(1,jndx_tmp)
t = list_idx_a_v(2,jndx_tmp)
b = list_idx_a_v(3,jndx_tmp)
hessmat(jndx,indx) = hessmat_iatb(i,a,t,b)
hessmat(indx,jndx) = hessmat(jndx,indx)
enddo
enddo
!$OMP END DO NOWAIT
!$OMP END PARALLEL
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(hessmat,n_a_v_prov,list_idx_a_v,n_act_orb,n_virt_orb,mat_idx_a_v) &
!$OMP PRIVATE(indx_tmp,indx,t,a,u,b,bstart,jndx)
!$OMP DO
!!!! < Active-VIRTUAL | H |Active-VIRTUAL >
! Active-VIRTUAL excitations
do indx_tmp = 1, n_a_v_prov
indx = list_idx_a_v(1,indx_tmp)
t = list_idx_a_v(2,indx_tmp)
a = list_idx_a_v(3,indx_tmp)
! Active-VIRTUAL excitations
do u=t,n_act_orb
if (t.eq.u) then
bstart=a
else
bstart=1
end if
do b=bstart,n_virt_orb
jndx = mat_idx_a_v(u,b)
hessmat(jndx,indx) = hessmat_taub(t,a,u,b)
hessmat(indx,jndx) = hessmat(jndx,indx)
enddo
enddo
enddo
!$OMP END DO NOWAIT
!$OMP END PARALLEL
END_PROVIDER

View File

@ -0,0 +1,310 @@
use bitmasks
BEGIN_PROVIDER [real*8, hessmat_old, (nMonoEx,nMonoEx)]
BEGIN_DOC
! calculate the orbital hessian 2 <Psi| E_pq H E_rs |Psi>
! + <Psi| E_pq E_rs H |Psi> + <Psi| E_rs E_pq H |Psi> by hand,
! determinant per determinant, as for the gradient
!
! we assume that we have natural active orbitals
END_DOC
implicit none
integer :: indx,ihole,ipart
integer :: jndx,jhole,jpart
character*3 :: iexc,jexc
real*8 :: res
if (bavard) then
write(6,*) ' providing Hessian matrix hessmat_old '
write(6,*) ' nMonoEx = ',nMonoEx
endif
do indx=1,nMonoEx
do jndx=1,nMonoEx
hessmat_old(indx,jndx)=0.D0
end do
end do
do indx=1,nMonoEx
ihole=excit(1,indx)
ipart=excit(2,indx)
iexc=excit_class(indx)
do jndx=indx,nMonoEx
jhole=excit(1,jndx)
jpart=excit(2,jndx)
jexc=excit_class(jndx)
call calc_hess_elem(ihole,ipart,jhole,jpart,res)
hessmat_old(indx,jndx)=res
hessmat_old(jndx,indx)=res
end do
end do
END_PROVIDER
subroutine calc_hess_elem(ihole,ipart,jhole,jpart,res)
BEGIN_DOC
! eq 19 of Siegbahn et al, Physica Scripta 1980
! we calculate 2 <Psi| E_pq H E_rs |Psi>
! + <Psi| E_pq E_rs H |Psi> + <Psi| E_rs E_pq H |Psi>
! average over all states is performed.
! no transition between states.
END_DOC
implicit none
integer :: ihole,ipart,ispin,mu,istate
integer :: jhole,jpart,jspin
integer :: mu_pq, mu_pqrs, mu_rs, mu_rspq, nu_rs,nu
real*8 :: res
integer(bit_kind), allocatable :: det_mu(:,:)
integer(bit_kind), allocatable :: det_nu(:,:)
integer(bit_kind), allocatable :: det_mu_pq(:,:)
integer(bit_kind), allocatable :: det_mu_rs(:,:)
integer(bit_kind), allocatable :: det_nu_rs(:,:)
integer(bit_kind), allocatable :: det_mu_pqrs(:,:)
integer(bit_kind), allocatable :: det_mu_rspq(:,:)
real*8 :: i_H_psi_array(N_states),phase,phase2,phase3
real*8 :: i_H_j_element
allocate(det_mu(N_int,2))
allocate(det_nu(N_int,2))
allocate(det_mu_pq(N_int,2))
allocate(det_mu_rs(N_int,2))
allocate(det_nu_rs(N_int,2))
allocate(det_mu_pqrs(N_int,2))
allocate(det_mu_rspq(N_int,2))
integer :: mu_pq_possible
integer :: mu_rs_possible
integer :: nu_rs_possible
integer :: mu_pqrs_possible
integer :: mu_rspq_possible
res=0.D0
! the terms <0|E E H |0>
do mu=1,n_det
! get the string of the determinant
call det_extract(det_mu,mu,N_int)
do ispin=1,2
! do the monoexcitation pq on it
call det_copy(det_mu,det_mu_pq,N_int)
call do_signed_mono_excitation(det_mu,det_mu_pq,mu_pq &
,ihole,ipart,ispin,phase,mu_pq_possible)
if (mu_pq_possible.eq.1) then
! possible, but not necessarily in the list
! do the second excitation
do jspin=1,2
call det_copy(det_mu_pq,det_mu_pqrs,N_int)
call do_signed_mono_excitation(det_mu_pq,det_mu_pqrs,mu_pqrs&
,jhole,jpart,jspin,phase2,mu_pqrs_possible)
! excitation possible
if (mu_pqrs_possible.eq.1) then
call i_H_psi(det_mu_pqrs,psi_det,psi_coef,N_int &
,N_det,N_det,N_states,i_H_psi_array)
do istate=1,N_states
res+=i_H_psi_array(istate)*psi_coef(mu,istate)*phase*phase2
end do
end if
! try the de-excitation with opposite sign
call det_copy(det_mu_pq,det_mu_pqrs,N_int)
call do_signed_mono_excitation(det_mu_pq,det_mu_pqrs,mu_pqrs&
,jpart,jhole,jspin,phase2,mu_pqrs_possible)
phase2=-phase2
! excitation possible
if (mu_pqrs_possible.eq.1) then
call i_H_psi(det_mu_pqrs,psi_det,psi_coef,N_int &
,N_det,N_det,N_states,i_H_psi_array)
do istate=1,N_states
res+=i_H_psi_array(istate)*psi_coef(mu,istate)*phase*phase2
end do
end if
end do
end if
! exchange the notion of pq and rs
! do the monoexcitation rs on the initial determinant
call det_copy(det_mu,det_mu_rs,N_int)
call do_signed_mono_excitation(det_mu,det_mu_rs,mu_rs &
,jhole,jpart,ispin,phase2,mu_rs_possible)
if (mu_rs_possible.eq.1) then
! do the second excitation
do jspin=1,2
call det_copy(det_mu_rs,det_mu_rspq,N_int)
call do_signed_mono_excitation(det_mu_rs,det_mu_rspq,mu_rspq&
,ihole,ipart,jspin,phase3,mu_rspq_possible)
! excitation possible (of course, the result is outside the CAS)
if (mu_rspq_possible.eq.1) then
call i_H_psi(det_mu_rspq,psi_det,psi_coef,N_int &
,N_det,N_det,N_states,i_H_psi_array)
do istate=1,N_states
res+=i_H_psi_array(istate)*psi_coef(mu,istate)*phase2*phase3
end do
end if
! we may try the de-excitation, with opposite sign
call det_copy(det_mu_rs,det_mu_rspq,N_int)
call do_signed_mono_excitation(det_mu_rs,det_mu_rspq,mu_rspq&
,ipart,ihole,jspin,phase3,mu_rspq_possible)
phase3=-phase3
! excitation possible (of course, the result is outside the CAS)
if (mu_rspq_possible.eq.1) then
call i_H_psi(det_mu_rspq,psi_det,psi_coef,N_int &
,N_det,N_det,N_states,i_H_psi_array)
do istate=1,N_states
res+=i_H_psi_array(istate)*psi_coef(mu,istate)*phase2*phase3
end do
end if
end do
end if
!
! the operator E H E, we have to do a double loop over the determinants
! we still have the determinant mu_pq and the phase in memory
if (mu_pq_possible.eq.1) then
do nu=1,N_det
call det_extract(det_nu,nu,N_int)
do jspin=1,2
call det_copy(det_nu,det_nu_rs,N_int)
call do_signed_mono_excitation(det_nu,det_nu_rs,nu_rs &
,jhole,jpart,jspin,phase2,nu_rs_possible)
! excitation possible ?
if (nu_rs_possible.eq.1) then
call i_H_j(det_mu_pq,det_nu_rs,N_int,i_H_j_element)
do istate=1,N_states
res+=2.D0*i_H_j_element*psi_coef(mu,istate) &
*psi_coef(nu,istate)*phase*phase2
end do
end if
end do
end do
end if
end do
end do
! state-averaged Hessian
res*=1.D0/dble(N_states)
end subroutine calc_hess_elem
BEGIN_PROVIDER [real*8, hessmat_peter, (nMonoEx,nMonoEx)]
BEGIN_DOC
! explicit hessian matrix from density matrices and integrals
! of course, this will be used for a direct Davidson procedure later
! we will not store the matrix in real life
! formulas are broken down as functions for the 6 classes of matrix elements
!
END_DOC
implicit none
integer :: i,j,t,u,a,b,indx,jndx,bstart,ustart,indx_shift
real*8 :: hessmat_itju
real*8 :: hessmat_itja
real*8 :: hessmat_itua
real*8 :: hessmat_iajb
real*8 :: hessmat_iatb
real*8 :: hessmat_taub
if (bavard) then
write(6,*) ' providing Hessian matrix hessmat_peter '
write(6,*) ' nMonoEx = ',nMonoEx
endif
provide mo_two_e_integrals_in_map
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(hessmat_peter,n_core_inact_orb,n_act_orb,n_virt_orb,nMonoEx) &
!$OMP PRIVATE(i,indx,jndx,j,ustart,t,u,a,bstart,indx_shift)
!$OMP DO
! (DOUBLY OCCUPIED ---> ACT )
do i=1,n_core_inact_orb
do t=1,n_act_orb
indx = t + (i-1)*n_act_orb
jndx=indx
! (DOUBLY OCCUPIED ---> ACT )
do j=i,n_core_inact_orb
if (i.eq.j) then
ustart=t
else
ustart=1
end if
do u=ustart,n_act_orb
hessmat_peter(jndx,indx)=hessmat_itju(i,t,j,u)
jndx+=1
end do
end do
! (DOUBLY OCCUPIED ---> VIRTUAL)
do j=1,n_core_inact_orb
do a=1,n_virt_orb
hessmat_peter(jndx,indx)=hessmat_itja(i,t,j,a)
jndx+=1
end do
end do
! (ACTIVE ---> VIRTUAL)
do u=1,n_act_orb
do a=1,n_virt_orb
hessmat_peter(jndx,indx)=hessmat_itua(i,t,u,a)
jndx+=1
end do
end do
end do
end do
!$OMP END DO NOWAIT
indx_shift = n_core_inact_orb*n_act_orb
!$OMP DO
! (DOUBLY OCCUPIED ---> VIRTUAL)
do a=1,n_virt_orb
do i=1,n_core_inact_orb
indx = a + (i-1)*n_virt_orb + indx_shift
jndx=indx
! (DOUBLY OCCUPIED ---> VIRTUAL)
do j=i,n_core_inact_orb
if (i.eq.j) then
bstart=a
else
bstart=1
end if
do b=bstart,n_virt_orb
hessmat_peter(jndx,indx)=hessmat_iajb(i,a,j,b)
jndx+=1
end do
end do
! (ACT ---> VIRTUAL)
do t=1,n_act_orb
do b=1,n_virt_orb
hessmat_peter(jndx,indx)=hessmat_iatb(i,a,t,b)
jndx+=1
end do
end do
end do
end do
!$OMP END DO NOWAIT
indx_shift += n_core_inact_orb*n_virt_orb
!$OMP DO
! (ACT ---> VIRTUAL)
do a=1,n_virt_orb
do t=1,n_act_orb
indx = a + (t-1)*n_virt_orb + indx_shift
jndx=indx
! (ACT ---> VIRTUAL)
do u=t,n_act_orb
if (t.eq.u) then
bstart=a
else
bstart=1
end if
do b=bstart,n_virt_orb
hessmat_peter(jndx,indx)=hessmat_taub(t,a,u,b)
jndx+=1
end do
end do
end do
end do
!$OMP END DO
!$OMP END PARALLEL
do jndx=1,nMonoEx
do indx=1,jndx-1
hessmat_peter(indx,jndx) = hessmat_peter(jndx,indx)
enddo
enddo
END_PROVIDER

View File

@ -1,4 +1,5 @@
BEGIN_PROVIDER [real*8, SXmatrix, (nMonoEx+1,nMonoEx+1)]
BEGIN_PROVIDER [real*8, SXmatrix, (nMonoEx+1,nMonoEx+1)]
&BEGIN_PROVIDER [integer, n_guess_sx_mat ]
implicit none
BEGIN_DOC
! Single-excitation matrix
@ -16,24 +17,34 @@ BEGIN_PROVIDER [real*8, SXmatrix, (nMonoEx+1,nMonoEx+1)]
SXmatrix(1,i+1)=gradvec2(i)
SXmatrix(1+i,1)=gradvec2(i)
end do
do i=1,nMonoEx
do j=1,nMonoEx
SXmatrix(i+1,j+1)=hessmat2(i,j)
SXmatrix(j+1,i+1)=hessmat2(i,j)
end do
end do
if(diag_hess_cas)then
do i = 1, nMonoEx
SXmatrix(i+1,i+1) = hessdiag(i)
enddo
else
do i=1,nMonoEx
do j=1,nMonoEx
SXmatrix(i+1,j+1)=hessmat(i,j)
SXmatrix(j+1,i+1)=hessmat(i,j)
end do
end do
endif
do i = 1, nMonoEx
SXmatrix(i+1,i+1) += level_shift_casscf
enddo
n_guess_sx_mat = 1
do i = 1, nMonoEx
if(SXmatrix(i+1,i+1).lt.0.d0 )then
n_guess_sx_mat += 1
endif
enddo
if (bavard) then
do i=2,nMonoEx
write(6,*) ' diagonal of the Hessian : ',i,hessmat2(i,i)
write(6,*) ' diagonal of the Hessian : ',i,hessmat(i,i)
end do
end if
END_PROVIDER
BEGIN_PROVIDER [real*8, SXeigenvec, (nMonoEx+1,nMonoEx+1)]
@ -42,11 +53,32 @@ END_PROVIDER
BEGIN_DOC
! Eigenvectors/eigenvalues of the single-excitation matrix
END_DOC
call lapack_diag(SXeigenval,SXeigenvec,SXmatrix,nMonoEx+1,nMonoEx+1)
if(nMonoEx+1.gt.n_det_max_full)then
if(bavard)then
print*,'Using the Davidson algorithm to diagonalize the SXmatrix'
endif
double precision, allocatable :: u_in(:,:),energies(:)
allocate(u_in(nMonoEx+1,n_states_diag),energies(n_guess_sx_mat))
call davidson_diag_sx_mat(n_guess_sx_mat, u_in, energies)
integer :: i,j
SXeigenvec = 0.d0
SXeigenval = 0.d0
do i = 1, n_guess_sx_mat
SXeigenval(i) = energies(i)
do j = 1, nMonoEx+1
SXeigenvec(j,i) = u_in(j,i)
enddo
enddo
else
if(bavard)then
print*,'Diagonalize the SXmatrix with Jacobi'
endif
call lapack_diag(SXeigenval,SXeigenvec,SXmatrix,nMonoEx+1,nMonoEx+1)
endif
if (bavard) then
write(6,*) ' SXdiag : lowest 5 eigenvalues '
write(6,*) ' SXdiag : lowest eigenvalues '
write(6,*) ' 1 - ',SXeigenval(1),SXeigenvec(1,1)
if(nmonoex.gt.0)then
if(n_guess_sx_mat.gt.0)then
write(6,*) ' 2 - ',SXeigenval(2),SXeigenvec(1,2)
write(6,*) ' 3 - ',SXeigenval(3),SXeigenvec(1,3)
write(6,*) ' 4 - ',SXeigenval(4),SXeigenvec(1,4)
@ -77,8 +109,8 @@ END_PROVIDER
best_vector_ovrlp_casscf = -1000
do i=1,nMonoEx+1
if (SXeigenval(i).lt.0.D0) then
if (abs(SXeigenvec(1,i)).gt.best_overlap_casscf) then
best_overlap_casscf=abs(SXeigenvec(1,i))
if (dabs(SXeigenvec(1,i)).gt.best_overlap_casscf) then
best_overlap_casscf=dabs(SXeigenvec(1,i))
best_vector_ovrlp_casscf = i
end if
end if

View File

@ -45,12 +45,12 @@
imono = max_overlap(i)
iorb = excit(1,imono)
jorb = excit(2,imono)
if (excit_class(imono) == "c-a" .and.hessmat2(imono,imono).gt.0.d0)then ! core --> active rotation
if (excit_class(imono) == "c-a" .and.hessmat(imono,imono).gt.0.d0)then ! core --> active rotation
n_orb_swap += 1
orb_swap(1,n_orb_swap) = iorb ! core
orb_swap(2,n_orb_swap) = jorb ! active
index_orb_swap(n_orb_swap) = imono
else if (excit_class(imono) == "a-v" .and.hessmat2(imono,imono).gt.0.d0)then ! active --> virtual rotation
else if (excit_class(imono) == "a-v" .and.hessmat(imono,imono).gt.0.d0)then ! active --> virtual rotation
n_orb_swap += 1
orb_swap(1,n_orb_swap) = jorb ! virtual
orb_swap(2,n_orb_swap) = iorb ! active

View File

@ -0,0 +1,6 @@
[dmc_delta_h]
type: double precision
doc: Dressing matrix obtained from DMC
size: (determinants.n_det)
interface: ezfio, provider

3
devel/dmc_dress/NEED Normal file
View File

@ -0,0 +1,3 @@
selectors_full
generators_full
davidson_dressed

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@ -0,0 +1,4 @@
=========
dmc_dress
=========

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@ -0,0 +1,19 @@
program diagonalize_h
implicit none
BEGIN_DOC
! Program that extracts the lowest states of the Hamiltonian dressed by the QMC
! dressing vector stored in :option:`dmc_dressing dmc_delta_h`
!
END_DOC
read_wf = .True.
touch read_wf
call routine
call save_wavefunction_general(N_det,N_states,psi_det_sorted,size(psi_coef_sorted,1),psi_coef_sorted)
end
subroutine routine
implicit none
psi_coef(1:N_det,1) = ci_eigenvectors_dressed(1:N_det,1)
print*,'N_det = ',N_det
SOFT_TOUCH psi_coef
end

View File

@ -0,0 +1,24 @@
BEGIN_PROVIDER [ double precision, dressing_column_h, (N_det,N_states) ]
&BEGIN_PROVIDER [ double precision, dressing_column_s, (N_det,N_states) ]
implicit none
BEGIN_DOC
! \Delta_{state-specific}. \Psi
END_DOC
integer :: i,ii,k,j, l
double precision :: f, tmp
double precision, external :: u_dot_v
logical, external :: detEq
dressing_column_h(:,:) = 0.d0
dressing_column_s(:,:) = 0.d0
l = dressed_column_idx(1)
do j = 1, n_det
dressing_column_h(j,1) = 0.5d0*dmc_delta_h(j)
dressing_column_h(l,1) -= 0.5d0 * psi_coef(j,1) * dmc_delta_h(j) /psi_coef(l,1)
enddo
END_PROVIDER

View File

@ -0,0 +1,6 @@
[energy]
type: double precision
doc: Calculated Selected |FCI| energy
interface: ezfio
size: (determinants.n_states)

3
devel/fci_complete/NEED Normal file
View File

@ -0,0 +1,3 @@
davidson_undressed
hartree_fock
determinants

View File

@ -0,0 +1,4 @@
===
mpn
===

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@ -0,0 +1,8 @@
program fci_complete
call generate_fci_space
call diagonalize_ci
end

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@ -0,0 +1,85 @@
subroutine generate_fci_space
use bitmasks
implicit none
BEGIN_DOC
! Generates the complete FCI space
END_DOC
integer :: i, sze, ncore
integer(bit_kind) :: o(N_int,2)
integer(bit_kind) :: u, coremask
ncore = 0
coremask = 0_bit_kind
do i=1,mo_num
if (trim(mo_class(i)) == 'Core') then
ncore += 1
coremask = ibset(coremask,i-1)
endif
enddo
o(1,1) = iand(full_ijkl_bitmask(1),not(coremask))
o(1,2) = 0_bit_kind
integer :: norb
norb = mo_num
do i=1,mo_num
if (trim(mo_class(i)) == 'Deleted') then
norb -= 1
o(1,1) = ibclr(o(1,1) ,i-1)
endif
enddo
if (norb > 64) then
stop 'No more than 64 MOs'
endif
call configuration_to_dets_size(act_bitmask,n_det_alpha_unique,elec_alpha_num-ncore,N_int)
TOUCH n_det_alpha_unique
integer :: k,n,m, t, t1, t2
k=0
n = elec_alpha_num
m = norb - n
n = n
u = shiftl(1_bit_kind,n) -1
do while (u < shiftl(1_bit_kind,n+m))
if (iand(coremask, u) == coremask) then
k = k+1
psi_det_alpha_unique(1,k) = u
endif
t = ior(u,u-1)
t1 = t+1
IRP_IF WITHOUT_TRAILZ
t2 = shiftr((iand(not(t),t1)-1), popcnt(ieor(u,u-1)))
IRP_ELSE
t2 = shiftr((iand(not(t),t1)-1), trailz(u)+1)
IRP_ENDIF
u = ior(t1,t2)
enddo
call configuration_to_dets_size(act_bitmask,n_det_beta_unique,elec_beta_num-ncore,N_int)
TOUCH n_det_beta_unique
k=0
n = elec_beta_num
m = norb - n
u = shiftl(1_bit_kind,n) -1
do while (u < shiftl(1_bit_kind,n+m))
if (iand(coremask, u) == coremask) then
k = k+1
psi_det_beta_unique(1,k) = u
endif
t = ior(u,u-1)
t1 = t+1
t2 = shiftr((iand(not(t),t1)-1), trailz(u)+1)
u = ior(t1,t2)
enddo
call generate_all_alpha_beta_det_products
print *, 'Ndet = ', N_det
end

View File

@ -40,7 +40,11 @@ subroutine generate_fci_space
endif
t = ior(u,u-1)
t1 = t+1
IRP_IF WITHOUT_TRAILZ
t2 = shiftr((iand(not(t),t1)-1), popcnt(ieor(u,u-1)))
IRP_ELSE
t2 = shiftr((iand(not(t),t1)-1), trailz(u)+1)
IRP_ENDIF
u = ior(t1,t2)
enddo
@ -59,7 +63,11 @@ subroutine generate_fci_space
endif
t = ior(u,u-1)
t1 = t+1
IRP_IF WITHOUT_TRAILZ
t2 = shiftr((iand(not(t),t1)-1), popcnt(ieor(u,u-1)))
IRP_ELSE
t2 = shiftr((iand(not(t),t1)-1), trailz(u)+1)
IRP_ENDIF
u = ior(t1,t2)
enddo

View File

@ -6,16 +6,13 @@ program e_curve
integer, allocatable :: iorder(:)
double precision , allocatable :: norm_sort(:)
double precision :: e_0(N_states)
PROVIDE mo_two_e_integrals_in_map
PROVIDE mo_two_e_integrals_in_map mo_one_e_integrals
nab = n_det_alpha_unique+n_det_beta_unique
allocate ( norm_sort(0:nab), iorder(0:nab) )
double precision, allocatable :: u_t(:,:), v_t(:,:), s_t(:,:)
double precision, allocatable :: u_0(:,:), v_0(:,:)
allocate(u_t(N_states,N_det),v_t(N_states,N_det),s_t(N_states,N_det))
allocate(u_0(N_states,N_det),v_0(N_states,N_det))
norm_sort(0) = 0.d0
@ -24,19 +21,20 @@ program e_curve
norm_sort(i) = det_alpha_norm(i)
iorder(i) = i
enddo
do i=1,n_det_beta_unique
norm_sort(i+n_det_alpha_unique) = det_beta_norm(i)
iorder(i+n_det_alpha_unique) = -i
enddo
call dsort(norm_sort(1),iorder(1),nab)
if (.not.read_wf) then
stop 'Please set read_wf to true'
endif
PROVIDE psi_bilinear_matrix_values nuclear_repulsion
PROVIDE psi_bilinear_matrix_values nuclear_repulsion
print *, ''
print *, '=============================='
print *, 'Energies at different cut-offs'
@ -47,16 +45,21 @@ program e_curve
print *, '=========================================================='
double precision :: thresh
integer(bit_kind), allocatable :: det_i(:,:), det_j(:,:)
integer :: na, nb
thresh = 1.d-10
na = n_det_alpha_unique
nb = n_det_beta_unique
do j=0,nab
i = iorder(j)
if (i<0) then
nb -= 1
do k=1,n_det
if (psi_bilinear_matrix_columns(k) == -i) then
psi_bilinear_matrix_values(k,1) = 0.d0
endif
enddo
else
na -= 1
do k=1,n_det
if (psi_bilinear_matrix_rows(k) == i) then
psi_bilinear_matrix_values(k,1) = 0.d0
@ -67,27 +70,11 @@ program e_curve
cycle
endif
u_0 = psi_bilinear_matrix_values(1:N_det,1:N_states)
v_t = 0.d0
s_t = 0.d0
call dtranspose( &
u_0, &
size(u_0, 1), &
u_t, &
size(u_t, 1), &
N_det, N_states)
call H_S2_u_0_nstates_openmp_work(v_t,s_t,u_t,N_states,N_det,1,N_det,0,1)
call dtranspose( &
v_t, &
size(v_t, 1), &
v_0, &
size(v_0, 1), &
N_states, N_det)
double precision, external :: u_dot_u, u_dot_v
do i=1,N_states
e_0(i) = u_dot_v(v_t(1,i),u_0(1,i),N_det)/u_dot_u(u_0(1,i),N_det)
do k=1,N_states
psi_coef(1:N_det,k) = psi_bilinear_matrix_values(1:N_det,k)
call dset_order(psi_coef(1,k),psi_bilinear_matrix_order_reverse,N_det)
enddo
TOUCH psi_det psi_coef
m = 0
do k=1,n_det
@ -100,10 +87,18 @@ program e_curve
exit
endif
E = E_0(1) + nuclear_repulsion
norm = u_dot_u(u_0(1,1),N_det)
print '(E9.1,2X,I8,2X,F10.2,2X,F10.8,2X,F12.6)', thresh, m, &
dble( elec_alpha_num**3 + elec_alpha_num**2 * (nab-1) ) / &
dble( elec_alpha_num**3 + elec_alpha_num**2 * (j-1)), norm, E
double precision :: cost0, cost
cost0 = elec_alpha_num**3 + elec_beta_num**3
cost = (na-1) * elec_alpha_num**2 + &
(nb-1) * elec_beta_num**2 + &
elec_alpha_num**3 + elec_beta_num**3
cost = cost/cost0
double precision :: u_dot_u
norm = dsqrt(u_dot_u(psi_coef(1,1),N_det))
print '(E9.1,2X,I8,2X,F10.2,2X,F10.8,2X,F15.10)', thresh, m, &
cost, norm, psi_energy(1)
thresh = thresh * dsqrt(10.d0)
enddo
print *, '=========================================================='

View File

@ -0,0 +1,75 @@
program e_curve
use bitmasks
implicit none
integer :: i,j,k, kk, nab, m, l
double precision :: norm, E, hij, num, ci, cj
double precision :: e_0(N_states)
double precision, allocatable :: psi_save(:)
PROVIDE mo_two_e_integrals_in_map mo_one_e_integrals
if (.not.read_wf) then
stop 'Please set read_wf to true'
endif
PROVIDE psi_bilinear_matrix nuclear_repulsion
PROVIDE psi_coef_sorted psi_det psi_coef
print *, ''
print *, '=============================='
print *, 'Energies at different cut-offs'
print *, '=============================='
print *, ''
print *, '=========================================================='
print '(A8,2X,A8,2X,A12,2X,A10,2X,A12)', 'Thresh.', 'Ndet', 'Cost', 'Norm', 'E'
print *, '=========================================================='
double precision :: thresh
integer(bit_kind), allocatable :: det_i(:,:), det_j(:,:)
thresh = 1.d-10
integer :: n_det_prime
nab = n_det_alpha_unique+n_det_beta_unique
allocate(psi_save(1:N_det))
psi_save(1:N_det) = psi_coef(1:N_det,1)
do while (thresh < 1.d0)
norm = 0.d0
n_det_prime = n_det
do k=1,n_det
psi_coef(k,1) = psi_save(k)
if (dabs(psi_coef(k,1)) < thresh) then
psi_coef(k,1) = 0.d0
n_det_prime -= 1
endif
norm = norm + psi_coef(k,1)**2
enddo
TOUCH psi_coef psi_det
norm = norm/dsqrt(norm)
psi_coef(:,1) = psi_coef(:,1)/norm
integer :: na, nb
na = 0
do k=1,n_det_alpha_unique
if (det_alpha_norm(k) > 0.d0) then
na += 1
endif
enddo
nb = 0
do k=1,n_det_beta_unique
if (det_beta_norm(k) > 0.d0) then
nb += 1
endif
enddo
E = psi_energy(1)
double precision :: cost0, cost
cost0 = elec_alpha_num**3 + elec_beta_num**3
cost = (na-1) * elec_alpha_num**2 + &
(nb-1) * elec_beta_num**2 + &
elec_alpha_num**3 + elec_beta_num**3
cost = cost/cost0
print '(E9.1,2X,I8,2X,F10.2,2X,F10.8,2X,F15.10)', thresh, n_det_prime, &
cost, norm, E
thresh = thresh * dsqrt(10.d0)
enddo
print *, '=========================================================='
end

View File

@ -0,0 +1,13 @@
program abproducts
implicit none
read_wf = .True.
TOUCH read_wf
call run
end
subroutine run
implicit none
call generate_all_alpha_beta_det_products
call diagonalize_ci
call save_wavefunction
end

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@ -0,0 +1,465 @@
program buildpsi_diagSVDit_modif_v2
implicit none
BEGIN_DOC
! perturbative approach to build psi_postsvd
END_DOC
read_wf = .True.
TOUCH read_wf
PROVIDE N_int
call run()
end
subroutine run
USE OMP_LIB
implicit none
integer(bit_kind) :: det1(N_int,2), det2(N_int,2)
integer :: degree, i_state
integer :: i, j, k, l, ii, jj, na, nb
double precision :: norm_psi, inv_sqrt_norm_psi
double precision, allocatable :: Uref(:,:), Dref(:), Vtref(:,:), Aref(:,:), Vref(:,:)
double precision :: err0, err_tmp, e_tmp, E0, overlap, E0_old, tol_energy
double precision :: ctmp, htmp, Ept2
double precision :: E0_postsvd, overlap_postsvd, E_prev
double precision :: norm_coeff_psi, inv_sqrt_norm_coeff_psi
double precision :: overlapU, overlapU_mat, overlapV, overlapV_mat, overlap_psi
double precision, allocatable :: H_diag(:,:), Hkl(:,:), H0(:,:), H(:,:,:,:)
double precision, allocatable :: psi_postsvd(:,:), coeff_psi_perturb(:)
integer :: n_FSVD, n_selected, n_toselect, n_tmp, it_svd, it_svd_max
integer :: n_selected2
integer, allocatable :: numalpha_selected(:), numbeta_selected(:)
integer, allocatable :: numalpha_toselect(:), numbeta_toselect(:)
integer, allocatable :: numalpha_tmp(:), numbeta_tmp(:)
integer(kind=8) :: W_tbeg, W_tend, W_tbeg_it, W_tend_it, W_ir
real(kind=8) :: W_tot_time, W_tot_time_it
real(kind=8) :: CPU_tbeg, CPU_tend, CPU_tbeg_it, CPU_tend_it
real(kind=8) :: CPU_tot_time, CPU_tot_time_it
real(kind=8) :: speedup, speedup_it
integer :: nb_taches
!$OMP PARALLEL
nb_taches = OMP_GET_NUM_THREADS()
!$OMP END PARALLEL
call CPU_TIME(CPU_tbeg)
call SYSTEM_CLOCK(COUNT=W_tbeg, COUNT_RATE=W_ir)
i_state = 1
! ---------------------------------------------------------------------------------------
! construct the initial CISD matrix
print *, ' ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~'
print *, ' CI matrix:', n_det_alpha_unique,'x',n_det_beta_unique
print *, ' N det :', N_det
print *, ' ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~'
norm_psi = 0.d0
do k = 1, N_det
norm_psi = norm_psi + psi_bilinear_matrix_values(k,i_state) &
* psi_bilinear_matrix_values(k,i_state)
enddo
print *, ' initial norm = ', norm_psi
allocate( Aref(n_det_alpha_unique,n_det_beta_unique) )
Aref(:,:) = 0.d0
do k = 1, N_det
i = psi_bilinear_matrix_rows(k)
j = psi_bilinear_matrix_columns(k)
Aref(i,j) = psi_bilinear_matrix_values(k,i_state)
enddo
! ---------------------------------------------------------------------------------------
! ---------------------------------------------------------------------------------------
! perform a Full SVD
allocate( Uref(n_det_alpha_unique,n_det_alpha_unique) )
allocate( Dref(max(n_det_beta_unique,n_det_alpha_unique)) )
allocate( Vref(n_det_beta_unique,n_det_beta_unique) )
allocate( Vtref(n_det_beta_unique,n_det_beta_unique) )
call svd_s(Aref, size(Aref,1), Uref, size(Uref,1), Dref, Vtref, size(Vtref,1) &
, n_det_alpha_unique, n_det_beta_unique)
print *, ' ~~~~~~~~~~~~~~~~~~~~~~~~~~~ '
do l = 1, n_det_beta_unique
do i = 1, n_det_beta_unique
Vref(i,l) = Vtref(l,i)
enddo
enddo
deallocate( Vtref )
! Truncated rank
n_selected = 10 ! n_svd
call write_int(6,n_selected, 'Rank of psi')
!________________________________________________________________________________________________________
!
! loop over SVD iterations
!________________________________________________________________________________________________________
tol_energy = 1.d0
it_svd = 0
it_svd_max = 100
E_prev = 0.d0
allocate(H(n_selected,n_selected,n_det_alpha_unique,n_det_beta_unique))
allocate(H_diag(n_det_alpha_unique,n_det_beta_unique))
allocate(psi_postsvd(n_det_alpha_unique,n_det_beta_unique))
do while( ( it_svd .lt. it_svd_max) .and. ( tol_energy .gt. 1d-6 ) )
call CPU_TIME(CPU_tbeg_it)
call SYSTEM_CLOCK(COUNT=W_tbeg_it, COUNT_RATE=W_ir)
it_svd = it_svd + 1
double precision :: norm
norm = 0.d0
do j = 1, n_selected
norm = norm + Dref(j)*Dref(j)
enddo
Dref = Dref / dsqrt(norm)
! print *, '-- Compute H --'
call const_H_uv(Uref, Vref, H, H_diag, n_selected)
! H0(i,j) = < u_i v_j | H | u_i v_j >
! E0 = < psi_0 | H | psi_0 >
E0 = 0.d0
do j = 1, n_selected
do i = 1, n_selected
E0 = E0 + Dref(i) * H(i,i,j,j) * Dref(j)
enddo
enddo
E0 = E0 + nuclear_repulsion
! print *,' E0 =', E0
double precision, allocatable :: eigval0(:)
double precision, allocatable :: eigvec0(:,:,:)
double precision, allocatable :: H_tmp(:,:,:,:)
allocate( H_tmp(n_selected,n_selected,n_selected,n_selected) )
do l=1,n_selected
do k=1,n_selected
do j=1,n_selected
do i=1,n_selected
H_tmp(i,j,k,l) = H(i,j,k,l)
enddo
enddo
enddo
enddo
allocate( eigval0(n_selected**2),eigvec0(n_selected,n_selected,n_selected**2))
eigvec0 = 0.d0
! print *, ' --- Diag post-SVD --- '
call lapack_diag(eigval0, eigvec0, H_tmp, n_selected**2, n_selected**2)
! print *, 'eig =', eigval0(1) + nuclear_repulsion
deallocate(H_tmp, eigval0)
! print *, ' --- SVD --- '
Dref = 0.d0
call perform_newpostSVD(n_selected, eigvec0(1,1,1), Uref, Vref, Dref)
deallocate(eigvec0)
! print *, ' --- Compute H --- '
call const_H_uv(Uref, Vref, H, H_diag, n_selected)
! H0(i,j) = < u_i v_j | H | u_i v_j >
! E0 = < psi_0 | H | psi_0 >
E0 = 0.d0
norm = 0.d0
do j = 1, n_det_beta_unique
do i = 1, n_selected
E0 = E0 + Dref(i) * H(i,i,j,j) * Dref(j)
enddo
norm = norm + Dref(j)*Dref(j)
enddo
E0 = E0 + nuclear_repulsion
! print *,' E0 =', E0
! print *,' norm =', norm
! print *, ' --- Perturbation --- '
psi_postsvd = 0.d0
do i=1,n_selected
psi_postsvd(i,i) = Dref(i)
enddo
Ept2 = 0.d0
do j=1,n_selected
do i=n_selected+1,n_det_alpha_unique
ctmp = 0.d0
do l=1,n_selected
do k=1,n_selected
ctmp = ctmp + H(k,l,i,j) * psi_postsvd(k,l)
enddo
enddo
psi_postsvd(i,j) = ctmp / (E0 - (H_diag(i,j)+nuclear_repulsion) )
Ept2 += ctmp*ctmp / (E0 - (H_diag(i,j)+nuclear_repulsion) )
enddo
enddo
do j=n_selected+1,n_det_beta_unique
do i=1,n_selected
ctmp = 0.d0
do l=1,n_selected
do k=1,n_selected
ctmp = ctmp + H(k,l,i,j) * psi_postsvd(k,l)
enddo
enddo
psi_postsvd(i,j) = ctmp / (E0 - (H_diag(i,j)+nuclear_repulsion) )
Ept2 += ctmp*ctmp / (E0 - (H_diag(i,j)+nuclear_repulsion) )
enddo
enddo
tol_energy = dabs(E_prev - E0)
print '(I5, 3(3X, F20.10))', it_svd, E0, E0 + Ept2, tol_energy
E_prev = E0
! print *, ' --- SVD --- '
call perform_newpostSVD(n_det_beta_unique, psi_postsvd, Uref, Vref, Dref)
end do
end
subroutine perform_newpostSVD(n_selected, psi_postsvd, Uref, Vref, Dref)
USE OMP_LIB
integer, intent(in) :: n_selected
double precision, intent(in) :: psi_postsvd(n_selected,n_selected)
double precision, intent(inout) :: Uref(n_det_alpha_unique,n_det_alpha_unique)
double precision, intent(inout) :: Vref(n_det_beta_unique ,n_det_beta_unique)
double precision, intent(inout) :: Dref(max(n_det_beta_unique,n_det_alpha_unique))
integer :: mm, nn, i, j, ii0, ii, l, jj, na, nb
double precision :: err0, err_norm, err_tmp, norm_tmp
double precision :: overlapU_mat, overlapV_mat, overlapU, overlapV
double precision, allocatable :: S_mat(:,:), SxVt(:,:)
double precision, allocatable :: U_svd(:,:), V_svd(:,:)
double precision, allocatable :: U_newsvd(:,:), V_newsvd(:,:), Vt_newsvd(:,:), D_newsvd(:), A_newsvd(:,:)
mm = n_det_alpha_unique
nn = n_det_beta_unique
allocate( U_svd(mm,n_selected) , V_svd(nn,n_selected) , S_mat(n_selected,n_selected) )
U_svd(1:mm,1:n_selected) = Uref(1:mm,1:n_selected)
V_svd(1:nn,1:n_selected) = Vref(1:nn,1:n_selected)
S_mat(1:n_selected,1:n_selected) = psi_postsvd(1:n_selected,1:n_selected)
! first compute S_mat x transpose(V_svd)
allocate( SxVt(n_selected,nn) )
call dgemm( 'N', 'T', n_selected, nn, n_selected, 1.d0 &
, S_mat , size(S_mat,1) &
, V_svd , size(V_svd,1) &
, 0.d0, SxVt, size(SxVt ,1) )
deallocate(S_mat)
! then compute U_svd x SxVt
allocate( A_newsvd(mm,nn) )
call dgemm( 'N', 'N', mm, nn, n_selected, 1.d0 &
, U_svd , size(U_svd ,1) &
, SxVt , size(SxVt ,1) &
, 0.d0, A_newsvd, size(A_newsvd,1) )
deallocate( SxVt )
! perform new SVD
allocate( U_newsvd(mm,mm), Vt_newsvd(nn,nn), D_newsvd(max(mm,nn)) )
call svd_s( A_newsvd, size(A_newsvd,1), &
U_newsvd, size(U_newsvd,1), &
D_newsvd, &
Vt_newsvd, size(Vt_newsvd,1), &
mm, nn)
deallocate(A_newsvd)
allocate( V_newsvd(nn,nn) )
do l = 1, nn
do j = 1, nn
V_newsvd(j,l) = Vt_newsvd(l,j)
enddo
enddo
deallocate(Vt_newsvd)
do l = 1, n_selected
Dref(l) = D_newsvd(l)
Uref(1:mm,l) = U_newsvd(1:mm,l)
Vref(1:nn,l) = V_newsvd(1:nn,l)
enddo
deallocate(U_newsvd)
deallocate(V_newsvd)
deallocate(D_newsvd)
end subroutine perform_newpostSVD
subroutine const_H_uv(Uref, Vref, H, H_diag, n_selected)
USE OMP_LIB
implicit none
integer, intent(in) :: n_selected
double precision, intent(in) :: Uref(n_det_alpha_unique,n_det_alpha_unique)
double precision, intent(in) :: Vref(n_det_beta_unique ,n_det_beta_unique)
double precision, intent(out) :: H(n_selected,n_selected, n_det_alpha_unique, n_det_beta_unique)
double precision, intent(out) :: H_diag(n_det_alpha_unique,n_det_beta_unique)
integer(bit_kind) :: det1(N_int,2), det2(N_int,2)
integer :: i, j, k, l, degree
integer :: ii0, jj0, ii, jj, n, m, np, mp
integer :: nn0, mm0, na, nb, mm, ind_gs
integer :: p,q,r,s
double precision :: h12, x
double precision, allocatable :: H0(:,:,:,:)
double precision, allocatable :: H1(:,:,:,:)
double precision, allocatable :: tmp3(:,:,:)
double precision, allocatable :: tmp1(:,:), tmp0(:,:)
double precision :: c_tmp
na = n_det_alpha_unique
nb = n_det_beta_unique
det1(:,1) = psi_det_alpha_unique(:,1)
det2(:,1) = psi_det_alpha_unique(:,1)
det1(:,2) = psi_det_beta_unique(:,1)
det2(:,2) = psi_det_beta_unique(:,1)
call i_H_j(det1, det2, N_int, h12)
call wall_time(t0)
tmp3 = 0.d0
allocate( H0(na,nb,n_selected,n_selected) )
allocate (tmp3(nb,nb,nb))
H0 = 0.d0
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP PRIVATE(i,j,k,l,m,n,det1,det2,degree,h12,c_tmp,tmp1,tmp0)&
!$OMP SHARED(na,nb,psi_det_alpha_unique,psi_det_beta_unique,&
!$OMP N_int,tmp3,Uref,Vref,H_diag,H0,n_selected)
allocate(tmp1(na,na), tmp0(na,na))
do i=1,na
do m=1,na
tmp1(m,i) = Uref(i,m)
enddo
enddo
!$OMP DO
do l = 1, nb
det2(:,2) = psi_det_beta_unique(:,l)
do j = 1, nb
det1(:,2) = psi_det_beta_unique(:,j)
call get_excitation_degree_spin(det1(1,2),det2(1,2),degree,N_int)
if (degree > 2) cycle
do k = 1, na
det2(:,1) = psi_det_alpha_unique(:,k)
do i = 1, na
det1(:,1) = psi_det_alpha_unique(:,i)
call get_excitation_degree(det1,det2,degree,N_int)
if ( degree > 2) cycle
call i_H_j(det1, det2, N_int, h12)
if (h12 == 0.d0) cycle
do m=1,nb
tmp3(m,j,l) = tmp3(m,j,l) + h12 * tmp1(m,i) * tmp1(m,k)
enddo
do n=1,n_selected
c_tmp = h12 * Vref(j,n)
if (c_tmp == 0.d0) cycle
do m=1,n_selected
H0(k,l,m,n) = H0(k,l,m,n) + c_tmp * tmp1(m,i)
enddo
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP DO
do m=1,nb
do l=1,nb
do j=1,nb
tmp1(j,l) = tmp3(m,j,l)
enddo
enddo
call DGEMM('N','N',nb,nb,nb,1.d0, &
tmp1, size(tmp1,1), &
Vref, size(Vref,1), &
0.d0, tmp0, size(tmp0,1))
do n=1,nb
H_diag(m,n) = 0.d0
do j=1,nb
H_diag(m,n) = H_diag(m,n) + tmp0(j,n) * Vref(j,n)
enddo
enddo
enddo
!$OMP END DO
deallocate(tmp1, tmp0)
!$OMP END PARALLEL
call wall_time(t1)
allocate( H1(nb,n_selected,n_selected,na) )
call DGEMM('T','N', nb * n_selected * n_selected, na, na, &
1.d0, H0, size(H0,1), Uref, size(Uref,1), 0.d0, H1, size(H1,1)*size(H1,2)*size(H1,3))
deallocate( H0 )
! (l,p,q,r) -> (p,q,r,s)
call DGEMM('T','N', n_selected * n_selected * na, nb, nb, &
1.d0, H1, size(H1,1), Vref, size(Vref,1), 0.d0, H, size(H,1)*size(H,2)*size(H,3))
! do j=1,n_selected
! do i=1,n_selected
! print *, H_diag(i,j), H(i,j,i,j)
! enddo
! enddo
deallocate(H1)
call wall_time(t2)
! print *, 't=', t1-t0, t2-t1
double precision :: t0, t1, t2
! stop
end

View File

@ -42,6 +42,7 @@ subroutine run
endif
entropy = 0.d0
k=n_det_beta_unique
do i=1,n_det_beta_unique
print *, i, real(D(i)), real(D(i)**2), real(sum(D(1:i)**2))
entropy -= D(i) * dlog(D(i))
@ -53,6 +54,7 @@ subroutine run
print *, 'threshold: ', 2.858 * D(k/2)
print *, 'Entropy : ', entropy
call ezfio_set_spindeterminants_n_svd_coefs(min(n_det_beta_unique,n_det_alpha_unique))
call ezfio_set_spindeterminants_psi_svd_alpha(U)
call ezfio_set_spindeterminants_psi_svd_beta (Vt)
call ezfio_set_spindeterminants_psi_svd_coefs(D)

1
devel/symmetry/NEED Normal file
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@ -0,0 +1 @@
Bitmask Nuclei Determinants

12
devel/symmetry/README.rst Normal file
View File

@ -0,0 +1,12 @@
========
Symmetry
========
Needed Modules
==============
.. Do not edit this section It was auto-generated
.. by the `update_README.py` script.
Documentation
=============
.. Do not edit this section It was auto-generated
.. by the `update_README.py` script.

View File

@ -0,0 +1,28 @@
program Symmetry
implicit none
BEGIN_DOC
! TODO
END_DOC
integer :: i, j, k
character*8 :: sym
do k=1,n_irrep
print *, sym_operation(k)
do i=1,mo_tot_num
print '(1000(F8.4,X))', mo_symm(i,:,k), sum(mo_symm(i,:,k))
enddo
print *, ''
enddo
print *, 'Molecule is linear: ', molecule_is_linear
print *, 'Has center of inversion: ', molecule_has_center_of_inversion
print *, 'Has S2n improper rotation: ', molecule_has_improper_rotation
print *, 'Symmetry rotation axis: ', sym_rotation_axis(:)
print *, 'Group: '//point_group
print *, 'Symmetry irreps : ', sym_irrep(1:n_irrep)
print *, 'Symmetry operations : ', sym_operation(1:n_irrep)
print *, 'Character table'
do i=1,n_irrep
print *, i, real(character_table(i,:))
enddo
end

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@ -0,0 +1,10 @@
Group C1
n 1
Irred Operation
1 A E
Table
1
1 1.00000

View File

@ -0,0 +1,20 @@
Group C10
n 6
Irred Operation
1 A E
2 B C10
3 E1 C5
4 E2 C10^3
5 E3 C5^2
6 E4 C2
Table
1 2 3 4 5 6
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
3 2.00000 1.61800 0.61800 -0.61800 -1.61800 -2.00000
4 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000
5 2.00000 -0.61800 -1.61800 1.61800 0.61800 -2.00000
6 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000

View File

@ -0,0 +1,32 @@
Group C10h
n 12
Irred Operation
1 Ag E
2 Bg C10
3 E1g C5
4 E2g C10^3
5 E3g C5^2
6 E4g C2
7 Au i
8 Bu S10
9 E1u S5
10 E2u S10^3
11 E3u S5^2
12 E4u sh
Table
1 2 3 4 5 6 7 8 9 10 11 12
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000
3 2.00000 1.61800 0.61800 -0.61800 -1.61800 -2.00000 2.00000 -1.61800 -0.61800 0.61800 1.61800 -2.00000
4 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000
5 2.00000 -0.61800 -1.61800 1.61800 0.61800 -2.00000 2.00000 0.61800 1.61800 -1.61800 -0.61800 -2.00000
6 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000
7 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
8 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000
9 2.00000 1.61800 0.61800 -0.61800 -1.61800 -2.00000 -2.00000 1.61800 0.61800 -0.61800 -1.61800 2.00000
10 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 -2.00000 -0.61800 1.61800 1.61800 -0.61800 -2.00000
11 2.00000 -0.61800 -1.61800 1.61800 0.61800 -2.00000 -2.00000 -0.61800 -1.61800 1.61800 0.61800 2.00000
12 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 -2.00000 1.61800 -0.61800 -0.61800 1.61800 -2.00000

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@ -0,0 +1,24 @@
Group C10v
n 8
Irred Operation
1 A1 E
2 A2 C10
3 B1 C5
4 B2 C10^3
5 E1 C5^2
6 E2 C2
7 E3 sv
8 E4 sd
Table
1 2 3 4 5 6 7 8
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000
3 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
4 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000
5 2.00000 1.61800 0.61800 -0.61800 -1.61800 -2.00000 0.00000 0.00000
6 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 0.00000 0.00000
7 2.00000 -0.61800 -1.61800 1.61800 0.61800 -2.00000 0.00000 0.00000
8 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 0.00000 0.00000

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@ -0,0 +1,20 @@
Group C11
n 6
Irred Operation
1 A E
2 E1 C11
3 E2 C11^2
4 E3 C11^3
5 E4 C11^4
6 E5 C11^5
Table
1 2 3 4 5 6
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 2.00000 1.68250 0.83080 -0.28460 -1.30970 -1.91890
3 2.00000 0.83080 -1.30970 -1.91890 -0.28460 1.68250
4 2.00000 -0.28460 -1.91890 0.83080 1.68250 -1.30970
5 2.00000 -1.30970 -0.28460 1.68250 -1.91890 0.83080
6 2.00000 -1.91890 1.68250 -1.30970 0.83080 -0.28460

View File

@ -0,0 +1,32 @@
Group C11h
n 12
Irred Operation
1 A' E
2 A" C11
3 E1' C11^2
4 E1" C11^3
5 E2' C11^4
6 E2" C11^5
7 E3' sh
8 E3" S11
9 E4' S11^3
10 E4" S11^5
11 E5' S11^7
12 E5" S11^9
Table
1 2 3 4 5 6 7 8 9 10 11 12
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
3 2.00000 1.68250 0.83080 -0.28460 -1.30970 -1.91890 2.00000 1.68250 -0.28460 -1.91890 -1.30970 0.83080
4 2.00000 1.68250 0.83080 -0.28460 -1.30970 -1.91890 -2.00000 -1.68250 0.28460 1.91890 1.30970 -0.83080
5 2.00000 0.83080 -1.30970 -1.91890 -0.28460 1.68250 2.00000 0.83080 -1.91890 1.68250 -0.28460 -1.30970
6 2.00000 0.83080 -1.30970 -1.91890 -0.28460 1.68250 -2.00000 -0.83080 1.91890 -1.68250 0.28460 1.30970
7 2.00000 -0.28460 -1.91890 0.83080 1.68250 -1.30970 2.00000 -0.28460 0.83080 -1.30970 1.68250 -1.91890
8 2.00000 -0.28460 -1.91890 0.83080 1.68250 -1.30970 -2.00000 0.28460 -0.83080 1.30970 -1.68250 1.91890
9 2.00000 -1.30970 -0.28460 1.68250 -1.91890 0.83080 2.00000 -1.30970 1.68250 0.83080 -1.91890 -0.28460
10 2.00000 -1.30970 -0.28460 1.68250 -1.91890 0.83080 -2.00000 1.30970 -1.68250 -0.83080 1.91890 0.28460
11 2.00000 -1.91890 1.68250 -1.30970 0.83080 -0.28460 2.00000 -1.91890 -1.30970 -0.28460 0.83080 1.68250
12 2.00000 -1.91890 1.68250 -1.30970 0.83080 -0.28460 -2.00000 1.91890 1.30970 0.28460 -0.83080 -1.68250

View File

@ -0,0 +1,22 @@
Group C11v
n 7
Irred Operation
1 A1 E
2 A2 C11
3 E1 C11^2
4 E2 C11^3
5 E3 C11^4
6 E4 C11^5
7 E5 sv
Table
1 2 3 4 5 6 7
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000
3 2.00000 1.68250 0.83080 -0.28460 -1.30970 -1.91890 0.00000
4 2.00000 0.83080 -1.30970 -1.91890 -0.28460 1.68250 0.00000
5 2.00000 -0.28460 -1.91890 0.83080 1.68250 -1.30970 0.00000
6 2.00000 -1.30970 -0.28460 1.68250 -1.91890 0.83080 0.00000
7 2.00000 -1.91890 1.68250 -1.30970 0.83080 -0.28460 0.00000

View File

@ -0,0 +1,22 @@
Group C12
n 7
Irred Operation
1 A E
2 B C12
3 E1 C6
4 E2 C4
5 E3 C3
6 E4 C12^5
7 E5 C2
Table
1 2 3 4 5 6 7
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
3 2.00000 1.73200 1.00000 0.00000 -1.00000 -1.73200 -2.00000
4 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000
5 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000
6 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000
7 2.00000 -1.73200 1.00000 0.00000 -1.00000 1.73200 -2.00000

View File

@ -0,0 +1,36 @@
Group C12h
n 14
Irred Operation
1 Ag E
2 Bg C12
3 E1g C6
4 E2g C4
5 E3g C3
6 E4g C12^5
7 E5g C2
8 Au i
9 Bu S12
10 E1u S6
11 E2u S4
12 E3u S3
13 E4u S12^5
14 E5u sh
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
3 2.00000 1.73200 1.00000 0.00000 -1.00000 -1.73200 -2.00000 2.00000 -1.73200 -1.00000 0.00000 1.00000 1.73200 -2.00000
4 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000
5 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 -2.00000
6 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000
7 2.00000 -1.73200 1.00000 0.00000 -1.00000 1.73200 -2.00000 2.00000 1.73200 -1.00000 0.00000 1.00000 -1.73200 -2.00000
8 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
9 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
10 2.00000 1.73200 1.00000 0.00000 -1.00000 -1.73200 -2.00000 -2.00000 1.73200 1.00000 0.00000 -1.00000 -1.73200 2.00000
11 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000
12 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 -2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 2.00000
13 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000
14 2.00000 -1.73200 1.00000 0.00000 -1.00000 1.73200 -2.00000 -2.00000 -1.73200 1.00000 0.00000 -1.00000 1.73200 2.00000

View File

@ -0,0 +1,26 @@
Group C12v
n 9
Irred Operation
1 A1 E
2 A2 C12
3 B1 C6
4 B2 C4
5 E1 C3
6 E2 C12^5
7 E3 C2
8 E4 sv
9 E5 sd
Table
1 2 3 4 5 6 7 8 9
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000
3 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000
4 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
5 2.00000 1.73200 1.00000 0.00000 -1.00000 -1.73200 -2.00000 0.00000 0.00000
6 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 0.00000 0.00000
7 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 0.00000
8 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 0.00000 0.00000
9 2.00000 -1.73200 1.00000 0.00000 -1.00000 1.73200 -2.00000 0.00000 0.00000

View File

@ -0,0 +1,22 @@
Group C13
n 7
Irred Operation
1 A E
2 E1 C13
3 E2 C13^2
4 E3 C13^3
5 E4 C13^4
6 E5 C13^5
7 E6 C13^6
Table
1 2 3 4 5 6 7
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 2.00000 1.77090 1.13610 0.24100 -0.70920 -1.49700 -1.94180
3 2.00000 1.13610 -0.70920 -1.94180 -1.49700 0.24100 1.77090
4 2.00000 0.24100 -1.94180 -0.70920 1.77090 1.13610 -1.49700
5 2.00000 -0.70920 -1.49700 1.77090 0.24100 -1.94180 1.13610
6 2.00000 -1.49700 0.24100 1.13610 -1.94180 1.77090 -0.70920
7 2.00000 -1.94180 1.77090 -1.49700 1.13610 -0.70920 0.24100

View File

@ -0,0 +1,36 @@
Group C13h
n 14
Irred Operation
1 A' E
2 A" C13
3 E1' C13^2
4 E1" C13^3
5 E2' C13^4
6 E2" C13^5
7 E3' C13^6
8 E3" sh
9 E4' S13
10 E4" S13^3
11 E5' S13^5
12 E5" S13^7
13 E6' S13^9
14 E6" S13^11
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
3 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 2.00000 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613
4 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -2.00000 -1.77091 -0.24107 1.49702 1.94188 0.70921 -1.13613
5 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 2.00000 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921
6 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 -2.00000 -1.13613 1.94188 -0.24107 -1.77091 1.49702 0.70921
7 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 2.00000 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188
8 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -2.00000 -0.24107 0.70921 -1.13613 1.49702 -1.77091 1.94188
9 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 2.00000 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702
10 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 -2.00000 0.70921 -1.77091 1.94188 -1.13613 -0.24107 1.49702
11 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 2.00000 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107
12 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -2.00000 1.49702 -1.13613 -1.77091 0.70921 1.94188 -0.24107
13 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 2.00000 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091
14 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 -2.00000 1.94188 1.49702 0.70921 -0.24107 -1.13613 -1.77091

View File

@ -0,0 +1,24 @@
Group C13v
n 8
Irred Operation
1 A1 E
2 A2 C13
3 E1 C13^2
4 E2 C13^3
5 E3 C13^4
6 E4 C13^5
7 E5 C13^6
8 E6 sv
Table
1 2 3 4 5 6 7 8
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000
3 2.00000 1.77090 1.13610 0.24100 -0.70920 -1.49700 -1.94180 0.00000
4 2.00000 1.13610 -0.70920 -1.94180 -1.49700 0.24100 1.77090 0.00000
5 2.00000 0.24100 -1.94180 -0.70920 1.77090 1.13610 -1.49700 0.00000
6 2.00000 -0.70920 -1.49700 1.77090 0.24100 -1.94180 1.13610 0.00000
7 2.00000 -1.49700 0.24100 1.13610 -1.94180 1.77090 -0.70920 0.00000
8 2.00000 -1.94180 1.77090 -1.49700 1.13610 -0.70920 0.24100 0.00000

View File

@ -0,0 +1,24 @@
Group C14
n 8
Irred Operation
1 A E
2 B C14
3 E1 C7
4 E2 C14^3
5 E3 C7^2
6 E4 C14^5
7 E5 C7^3
8 E6 C2
Table
1 2 3 4 5 6 7 8
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
3 2.00000 1.80190 1.24690 0.44500 -0.44500 -1.24690 -1.80190 -2.00000
4 2.00000 1.24690 -0.44500 -1.80190 -1.80190 -0.44500 1.24690 2.00000
5 2.00000 0.44500 -1.80190 -1.24690 1.24690 1.80190 -0.44500 -2.00000
6 2.00000 -0.44500 -1.80190 1.24690 1.24690 -1.80190 -0.44500 2.00000
7 2.00000 -1.24690 -0.44500 1.80190 -1.80190 0.44500 1.24690 -2.00000
8 2.00000 -1.80190 1.24690 -0.44500 -0.44500 1.24690 -1.80190 2.00000

View File

@ -0,0 +1,40 @@
Group C14h
n 16
Irred Operation
1 Ag E
2 Bg C14
3 E1g C7
4 E2g C14^3
5 E3g C7^2
6 E4g C14^5
7 E5g C7^3
8 E6g C2
9 Au i
10 Bu S14
11 E1u S7
12 E2u S14^3
13 E3u S7^2
14 E4u S14^5
15 E5u S7^3
16 E6u sh
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000
3 2.00000 1.80190 1.24690 0.44500 -0.44500 -1.24690 -1.80190 -2.00000 2.00000 -1.80190 -1.24690 -0.44500 0.44500 1.24690 1.80190 -2.00000
4 2.00000 1.24690 -0.44500 -1.80190 -1.80190 -0.44500 1.24690 2.00000 2.00000 1.24690 -0.44500 -1.80190 -1.80190 -0.44500 1.24690 2.00000
5 2.00000 0.44500 -1.80190 -1.24690 1.24690 1.80190 -0.44500 -2.00000 2.00000 -0.44500 1.80190 1.24690 -1.24690 -1.80190 0.44500 -2.00000
6 2.00000 -0.44500 -1.80190 1.24690 1.24690 -1.80190 -0.44500 2.00000 2.00000 -0.44500 -1.80190 1.24690 1.24690 -1.80190 -0.44500 2.00000
7 2.00000 -1.24690 -0.44500 1.80190 -1.80190 0.44500 1.24690 -2.00000 2.00000 1.24690 0.44500 -1.80190 1.80190 -0.44500 -1.24690 -2.00000
8 2.00000 -1.80190 1.24690 -0.44500 -0.44500 1.24690 -1.80190 2.00000 2.00000 -1.80190 1.24690 -0.44500 -0.44500 1.24690 -1.80190 2.00000
9 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
10 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000
11 2.00000 1.80190 1.24690 0.44500 -0.44500 -1.24690 -1.80190 -2.00000 -2.00000 1.80190 1.24690 0.44500 -0.44500 -1.24690 -1.80190 2.00000
12 2.00000 1.24690 -0.44500 -1.80190 -1.80190 -0.44500 1.24690 2.00000 -2.00000 -1.24690 0.44500 1.80190 1.80190 0.44500 -1.24690 -2.00000
13 2.00000 0.44500 -1.80190 -1.24690 1.24690 1.80190 -0.44500 -2.00000 -2.00000 0.44500 -1.80190 -1.24690 1.24690 1.80190 -0.44500 2.00000
14 2.00000 -0.44500 -1.80190 1.24690 1.24690 -1.80190 -0.44500 2.00000 -2.00000 0.44500 1.80190 -1.24690 -1.24690 1.80190 0.44500 -2.00000
15 2.00000 -1.24690 -0.44500 1.80190 -1.80190 0.44500 1.24690 -2.00000 -2.00000 -1.24690 -0.44500 1.80190 -1.80190 0.44500 1.24690 2.00000
16 2.00000 -1.80190 1.24690 -0.44500 -0.44500 1.24690 -1.80190 2.00000 -2.00000 1.80190 -1.24690 0.44500 0.44500 -1.24690 1.80190 -2.00000

View File

@ -0,0 +1,28 @@
Group C14v
n 10
Irred Operation
1 A1 E
2 A2 C14
3 B1 C7
4 B2 C14^3
5 E1 C7^2
6 E2 C14^5
7 E3 C7^3
8 E4 C2
9 E5 sv
10 E6 sd
Table
1 2 3 4 5 6 7 8 9 10
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000
3 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
4 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000
5 2.00000 1.80190 1.24690 0.44500 -0.44500 -1.24690 -1.80190 -2.00000 0.00000 0.00000
6 2.00000 1.24690 -0.44500 -1.80190 -1.80190 -0.44500 1.24690 2.00000 0.00000 0.00000
7 2.00000 0.44500 -1.80190 -1.24690 1.24690 1.80190 -0.44500 -2.00000 0.00000 0.00000
8 2.00000 -0.44500 -1.80190 1.24690 1.24690 -1.80190 -0.44500 2.00000 0.00000 0.00000
9 2.00000 -1.24690 -0.44500 1.80190 -1.80190 0.44500 1.24690 -2.00000 0.00000 0.00000
10 2.00000 -1.80190 1.24690 -0.44500 -0.44500 1.24690 -1.80190 2.00000 0.00000 0.00000

View File

@ -0,0 +1,24 @@
Group C15
n 8
Irred Operation
1 A E
2 E1 C15
3 E2 C15^2
4 E3 C5
5 E4 C15^4
6 E5 C3
7 E6 C5^2
8 E7 C15^7
Table
1 2 3 4 5 6 7 8
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 2.00000 1.82700 1.33820 0.61800 -0.20900 -1.00000 -1.61800 -1.95630
3 2.00000 1.33820 -0.20900 -1.61800 -1.95630 -1.00000 0.61800 1.82700
4 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 0.61800 -1.61800
5 2.00000 -0.20900 -1.95630 0.61800 1.82700 -1.00000 -1.61800 1.33820
6 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000
7 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 -1.61800 0.61800
8 2.00000 -1.95630 1.82700 -1.61800 1.33820 -1.00000 0.61800 -0.20900

View File

@ -0,0 +1,40 @@
Group C15h
n 16
Irred Operation
1 A' E
2 A" C15
3 E1' C15^2
4 E1" C5
5 E2' C15^4
6 E2" C3
7 E3' C5^2
8 E3" C15^7
9 E4' sh
10 E4" S15
11 E5' S5
12 E5" S3
13 E6' S15^7
14 E6" S5^3
15 E7' S15^11
16 E7" S15^13
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
3 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 2.00000 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826
4 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -2.00000 -1.82709 -0.61803 1.00000 1.95630 1.61803 0.20906 -1.33826
5 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 2.00000 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906
6 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 -2.00000 -1.33826 1.61803 1.00000 -1.82709 -0.61803 1.95630 0.20906
7 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 2.00000 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803
8 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -2.00000 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803
9 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 2.00000 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630
10 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 -2.00000 0.20906 -0.61803 1.00000 -1.33826 1.61803 -1.82709 1.95630
11 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 2.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000
12 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -2.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000
13 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 2.00000 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803
14 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 -2.00000 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803
15 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 2.00000 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709
16 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -2.00000 1.95630 1.61803 1.00000 0.20906 -0.61803 -1.33826 -1.82709

View File

@ -0,0 +1,26 @@
Group C15v
n 9
Irred Operation
1 A1 E
2 A2 C15
3 E1 C15^2
4 E2 C5
5 E3 C15^4
6 E4 C3
7 E5 C5^2
8 E6 C15^7
9 E7 sv
Table
1 2 3 4 5 6 7 8 9
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000
3 2.00000 1.82700 1.33820 0.61800 -0.20900 -1.00000 -1.61800 -1.95630 0.00000
4 2.00000 1.33820 -0.20900 -1.61800 -1.95630 -1.00000 0.61800 1.82700 0.00000
5 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 0.61800 -1.61800 0.00000
6 2.00000 -0.20900 -1.95630 0.61800 1.82700 -1.00000 -1.61800 1.33820 0.00000
7 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 0.00000
8 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 -1.61800 0.61800 0.00000
9 2.00000 -1.95630 1.82700 -1.61800 1.33820 -1.00000 0.61800 -0.20900 0.00000

View File

@ -0,0 +1,26 @@
Group C16
n 9
Irred Operation
1 A E
2 B C16
3 E1 C8
4 E2 C16^3
5 E3 C4
6 E4 C16^5
7 E5 C8^3
8 E6 C16^7
9 E7 C2
Table
1 2 3 4 5 6 7 8 9
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
3 2.00000 1.84770 1.41420 0.76530 0.00000 -0.76530 -1.41420 -1.84770 -2.00000
4 2.00000 1.41420 0.00000 -1.41420 -2.00000 -1.41420 0.00000 1.41420 2.00000
5 2.00000 0.76530 -1.41420 -1.84770 0.00000 1.84770 1.41420 -0.76530 -2.00000
6 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000
7 2.00000 -0.76530 -1.41420 1.84770 0.00000 -1.84770 1.41420 0.76530 -2.00000
8 2.00000 -1.41420 0.00000 1.41420 -2.00000 1.41420 0.00000 -1.41420 2.00000
9 2.00000 -1.84770 1.41420 -0.76530 0.00000 0.76530 -1.41420 1.84770 -2.00000

View File

@ -0,0 +1,44 @@
Group C16h
n 18
Irred Operation
1 Ag E
2 Bg C16
3 E1g C8
4 E2g C16^3
5 E3g C4
6 E4g C16^5
7 E5g C8^3
8 E6g C16^7
9 E7g C2
10 Au i
11 Bu S16
12 E1u S8
13 E2u S16^3
14 E3u S4
15 E4u S16^5
16 E5u S8^3
17 E6u S16^7
18 E7u sh
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
3 2.00000 1.84770 1.41420 0.76530 0.00000 -0.76530 -1.41420 -1.84770 -2.00000 2.00000 -1.84770 -1.41420 -0.76530 0.00000 0.76530 1.41420 1.84770 -2.00000
4 2.00000 1.41420 0.00000 -1.41420 -2.00000 -1.41420 0.00000 1.41420 2.00000 2.00000 1.41420 0.00000 -1.41420 -2.00000 -1.41420 0.00000 1.41420 2.00000
5 2.00000 0.76530 -1.41420 -1.84770 0.00000 1.84770 1.41420 -0.76530 -2.00000 2.00000 -0.76530 1.41420 1.84770 0.00000 -1.84770 -1.41420 0.76530 -2.00000
6 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000
7 2.00000 -0.76530 -1.41420 1.84770 0.00000 -1.84770 1.41420 0.76530 -2.00000 2.00000 0.76530 1.41420 -1.84770 0.00000 1.84770 -1.41420 -0.76530 -2.00000
8 2.00000 -1.41420 0.00000 1.41420 -2.00000 1.41420 0.00000 -1.41420 2.00000 2.00000 -1.41420 0.00000 1.41420 -2.00000 1.41420 0.00000 -1.41420 2.00000
9 2.00000 -1.84770 1.41420 -0.76530 0.00000 0.76530 -1.41420 1.84770 -2.00000 2.00000 1.84770 -1.41420 0.76530 0.00000 -0.76530 1.41420 -1.84770 -2.00000
10 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
11 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
12 2.00000 1.84770 1.41420 0.76530 0.00000 -0.76530 -1.41420 -1.84770 -2.00000 -2.00000 1.84770 1.41420 0.76530 0.00000 -0.76530 -1.41420 -1.84770 2.00000
13 2.00000 1.41420 0.00000 -1.41420 -2.00000 -1.41420 0.00000 1.41420 2.00000 -2.00000 -1.41420 0.00000 1.41420 2.00000 1.41420 0.00000 -1.41420 -2.00000
14 2.00000 0.76530 -1.41420 -1.84770 0.00000 1.84770 1.41420 -0.76530 -2.00000 -2.00000 0.76530 -1.41420 -1.84770 0.00000 1.84770 1.41420 -0.76530 2.00000
15 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000
16 2.00000 -0.76530 -1.41420 1.84770 0.00000 -1.84770 1.41420 0.76530 -2.00000 -2.00000 -0.76530 -1.41420 1.84770 0.00000 -1.84770 1.41420 0.76530 2.00000
17 2.00000 -1.41420 0.00000 1.41420 -2.00000 1.41420 0.00000 -1.41420 2.00000 -2.00000 1.41420 0.00000 -1.41420 2.00000 -1.41420 0.00000 1.41420 -2.00000
18 2.00000 -1.84770 1.41420 -0.76530 0.00000 0.76530 -1.41420 1.84770 -2.00000 -2.00000 -1.84770 1.41420 -0.76530 0.00000 0.76530 -1.41420 1.84770 2.00000

View File

@ -0,0 +1,30 @@
Group C16v
n 11
Irred Operation
1 A1 E
2 A2 C16
3 B1 C8
4 B2 C16^3
5 E1 C4
6 E2 C16^5
7 E3 C8^3
8 E4 C16^7
9 E5 C2
10 E6 sv
11 E7 sd
Table
1 2 3 4 5 6 7 8 9 10 11
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000
3 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000
4 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
5 2.00000 1.84770 1.41420 0.76530 0.00000 -0.76530 -1.41420 -1.84770 -2.00000 0.00000 0.00000
6 2.00000 1.41420 0.00000 -1.41420 -2.00000 -1.41420 0.00000 1.41420 2.00000 0.00000 0.00000
7 2.00000 0.76530 -1.41420 -1.84770 0.00000 1.84770 1.41420 -0.76530 -2.00000 0.00000 0.00000
8 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 0.00000
9 2.00000 -0.76530 -1.41420 1.84770 0.00000 -1.84770 1.41420 0.76530 -2.00000 0.00000 0.00000
10 2.00000 -1.41420 0.00000 1.41420 -2.00000 1.41420 0.00000 -1.41420 2.00000 0.00000 0.00000
11 2.00000 -1.84770 1.41420 -0.76530 0.00000 0.76530 -1.41420 1.84770 -2.00000 0.00000 0.00000

View File

@ -0,0 +1,26 @@
Group C17
n 9
Irred Operation
1 A E
2 E1 C17
3 E2 C17^2
4 E3 C17^3
5 E4 C17^4
6 E5 C17^5
7 E6 C17^6
8 E7 C17^7
9 E8 C17^8
Table
1 2 3 4 5 6 7 8 9
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 2.00000 1.86490 1.47800 0.89140 0.18450 -0.54730 -1.20520 -1.70040 -1.96590
3 2.00000 1.47800 0.18450 -1.20520 -1.96590 -1.70040 -0.54730 0.89140 1.86490
4 2.00000 0.89140 -1.20520 -1.96590 -0.54730 1.47800 1.86490 0.18450 -1.70040
5 2.00000 0.18450 -1.96590 -0.54730 1.86490 0.89140 -1.70040 -1.20520 1.47800
6 2.00000 -0.54730 -1.70040 1.47800 0.89140 -1.96590 0.18450 1.86490 -1.20520
7 2.00000 -1.20520 -0.54730 1.86490 -1.70040 0.18450 1.47800 -1.96590 0.89140
8 2.00000 -1.70040 0.89140 0.18450 -1.20520 1.86490 -1.96590 1.47800 -0.54730
9 2.00000 -1.96590 1.86490 -1.70040 1.47800 -1.20520 0.89140 -0.54730 0.18450

View File

@ -0,0 +1,44 @@
Group C17h
n 18
Irred Operation
1 A' E
2 A" C17
3 E1' C17^2
4 E1" C17^3
5 E2' C17^4
6 E2" C17^5
7 E3' C17^6
8 E3" C17^7
9 E4' C17^8
10 E4" sh
11 E5' S17
12 E5" S17^3
13 E6' S17^5
14 E6" S17^7
15 E7' S17^9
16 E7" S17^11
17 E8' S17^13
18 E8" S17^15
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
3 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 2.00000 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802
4 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -2.00000 -1.86494 -0.89148 0.54733 1.70043 1.96595 1.20527 -0.18454 -1.47802
5 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 2.00000 1.47802 -1.20527 -1.70043 0.89148 1.86494 -0.54733 -1.96595 0.18454
6 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 -2.00000 -1.47802 1.20527 1.70043 -0.89148 -1.86494 0.54733 1.96595 -0.18454
7 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 2.00000 0.89148 -1.96595 1.47802 0.18454 -1.70043 1.86494 -0.54733 -1.20527
8 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -2.00000 -0.89148 1.96595 -1.47802 -0.18454 1.70043 -1.86494 0.54733 1.20527
9 2.00000 0.18454 -1.96595 -0.54733 1.86494 0.89148 -1.70043 -1.20527 1.47802 2.00000 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595
10 2.00000 0.18454 -1.96595 -0.54733 1.86494 0.89148 -1.70043 -1.20527 1.47802 -2.00000 -0.18454 0.54733 -0.89148 1.20527 -1.47802 1.70043 -1.86494 1.96595
11 2.00000 -0.54733 -1.70043 1.47802 0.89148 -1.96595 0.18454 1.86494 -1.20527 2.00000 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043
12 2.00000 -0.54733 -1.70043 1.47802 0.89148 -1.96595 0.18454 1.86494 -1.20527 -2.00000 0.54733 -1.47802 1.96595 -1.86494 1.20527 -0.18454 -0.89148 1.70043
13 2.00000 -1.20527 -0.54733 1.86494 -1.70043 0.18454 1.47802 -1.96595 0.89148 2.00000 -1.20527 1.86494 0.18454 -1.96595 0.89148 1.47802 -1.70043 -0.54733
14 2.00000 -1.20527 -0.54733 1.86494 -1.70043 0.18454 1.47802 -1.96595 0.89148 -2.00000 1.20527 -1.86494 -0.18454 1.96595 -0.89148 -1.47802 1.70043 0.54733
15 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 2.00000 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148
16 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -2.00000 1.70043 -0.18454 -1.86494 -1.47802 0.54733 1.96595 1.20527 -0.89148
17 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 2.00000 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494
18 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 -2.00000 1.96595 1.70043 1.20527 0.54733 -0.18454 -0.89148 -1.47802 -1.86494

View File

@ -0,0 +1,28 @@
Group C17v
n 10
Irred Operation
1 A1 E
2 A2 C17
3 E1 C17^2
4 E2 C17^3
5 E3 C17^4
6 E4 C17^5
7 E5 C17^6
8 E6 C17^7
9 E7 C17^8
10 E8 sv
Table
1 2 3 4 5 6 7 8 9 10
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000
3 2.00000 1.86490 1.47800 0.89140 0.18450 -0.54730 -1.20520 -1.70040 -1.96590 0.00000
4 2.00000 1.47800 0.18450 -1.20520 -1.96590 -1.70040 -0.54730 0.89140 1.86490 0.00000
5 2.00000 0.89140 -1.20520 -1.96590 -0.54730 1.47800 1.86490 0.18450 -1.70040 0.00000
6 2.00000 0.18450 -1.96590 -0.54730 1.86490 0.89140 -1.70040 -1.20520 1.47800 0.00000
7 2.00000 -0.54730 -1.70040 1.47800 0.89140 -1.96590 0.18450 1.86490 -1.20520 0.00000
8 2.00000 -1.20520 -0.54730 1.86490 -1.70040 0.18450 1.47800 -1.96590 0.89140 0.00000
9 2.00000 -1.70040 0.89140 0.18450 -1.20520 1.86490 -1.96590 1.47800 -0.54730 0.00000
10 2.00000 -1.96590 1.86490 -1.70040 1.47800 -1.20520 0.89140 -0.54730 0.18450 0.00000

View File

@ -0,0 +1,28 @@
Group C18
n 10
Irred Operation
1 A E
2 B C18
3 E1 C9
4 E2 C6
5 E3 C9^2
6 E4 C18^5
7 E5 C3
8 E6 C18^7
9 E7 C9^4
10 E8 C2
Table
1 2 3 4 5 6 7 8 9 10
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
3 2.00000 1.87930 1.53200 1.00000 0.34730 -0.34730 -1.00000 -1.53200 -1.87930 -2.00000
4 2.00000 1.53200 0.34730 -1.00000 -1.87930 -1.87930 -1.00000 0.34730 1.53200 2.00000
5 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000
6 2.00000 0.34730 -1.87930 -1.00000 1.53200 1.53200 -1.00000 -1.87930 0.34730 2.00000
7 2.00000 -0.34730 -1.87930 1.00000 1.53200 -1.53200 -1.00000 1.87930 0.34730 -2.00000
8 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000
9 2.00000 -1.53200 0.34730 1.00000 -1.87930 1.87930 -1.00000 -0.34730 1.53200 -2.00000
10 2.00000 -1.87930 1.53200 -1.00000 0.34730 0.34730 -1.00000 1.53200 -1.87930 2.00000

View File

@ -0,0 +1,48 @@
Group C18h
n 20
Irred Operation
1 Ag E
2 Bg C18
3 E1g C9
4 E2g C6
5 E3g C9^2
6 E4g C18^5
7 E5g C3
8 E6g C18^7
9 E7g C9^4
10 E8g C2
11 Au i
12 Bu S18
13 E1u S9
14 E2u S6
15 E3u S9^2
16 E4u S18^5
17 E5u S3
18 E6u S18^7
19 E7u S9^4
20 E8u sh
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000
3 2.00000 1.87930 1.53200 1.00000 0.34730 -0.34730 -1.00000 -1.53200 -1.87930 -2.00000 2.00000 -1.87930 -1.53200 -1.00000 -0.34730 0.34730 1.00000 1.53200 1.87930 -2.00000
4 2.00000 1.53200 0.34730 -1.00000 -1.87930 -1.87930 -1.00000 0.34730 1.53200 2.00000 2.00000 1.53200 0.34730 -1.00000 -1.87930 -1.87930 -1.00000 0.34730 1.53200 2.00000
5 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 -2.00000
6 2.00000 0.34730 -1.87930 -1.00000 1.53200 1.53200 -1.00000 -1.87930 0.34730 2.00000 2.00000 0.34730 -1.87930 -1.00000 1.53200 1.53200 -1.00000 -1.87930 0.34730 2.00000
7 2.00000 -0.34730 -1.87930 1.00000 1.53200 -1.53200 -1.00000 1.87930 0.34730 -2.00000 2.00000 0.34730 1.87930 -1.00000 -1.53200 1.53200 1.00000 -1.87930 -0.34730 -2.00000
8 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000
9 2.00000 -1.53200 0.34730 1.00000 -1.87930 1.87930 -1.00000 -0.34730 1.53200 -2.00000 2.00000 1.53200 -0.34730 -1.00000 1.87930 -1.87930 1.00000 0.34730 -1.53200 -2.00000
10 2.00000 -1.87930 1.53200 -1.00000 0.34730 0.34730 -1.00000 1.53200 -1.87930 2.00000 2.00000 -1.87930 1.53200 -1.00000 0.34730 0.34730 -1.00000 1.53200 -1.87930 2.00000
11 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
12 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000
13 2.00000 1.87930 1.53200 1.00000 0.34730 -0.34730 -1.00000 -1.53200 -1.87930 -2.00000 -2.00000 1.87930 1.53200 1.00000 0.34730 -0.34730 -1.00000 -1.53200 -1.87930 2.00000
14 2.00000 1.53200 0.34730 -1.00000 -1.87930 -1.87930 -1.00000 0.34730 1.53200 2.00000 -2.00000 -1.53200 -0.34730 1.00000 1.87930 1.87930 1.00000 -0.34730 -1.53200 -2.00000
15 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 2.00000
16 2.00000 0.34730 -1.87930 -1.00000 1.53200 1.53200 -1.00000 -1.87930 0.34730 2.00000 -2.00000 -0.34730 1.87930 1.00000 -1.53200 -1.53200 1.00000 1.87930 -0.34730 -2.00000
17 2.00000 -0.34730 -1.87930 1.00000 1.53200 -1.53200 -1.00000 1.87930 0.34730 -2.00000 -2.00000 -0.34730 -1.87930 1.00000 1.53200 -1.53200 -1.00000 1.87930 0.34730 2.00000
18 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000
19 2.00000 -1.53200 0.34730 1.00000 -1.87930 1.87930 -1.00000 -0.34730 1.53200 -2.00000 -2.00000 -1.53200 0.34730 1.00000 -1.87930 1.87930 -1.00000 -0.34730 1.53200 2.00000
20 2.00000 -1.87930 1.53200 -1.00000 0.34730 0.34730 -1.00000 1.53200 -1.87930 2.00000 -2.00000 1.87930 -1.53200 1.00000 -0.34730 -0.34730 1.00000 -1.53200 1.87930 -2.00000

View File

@ -0,0 +1,32 @@
Group C18v
n 12
Irred Operation
1 A1 E
2 A2 C18
3 B1 C9
4 B2 C6
5 E1 C9^2
6 E2 C18^5
7 E3 C3
8 E4 C18^7
9 E5 C9^4
10 E6 C2
11 E7 sv
12 E8 sd
Table
1 2 3 4 5 6 7 8 9 10 11 12
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000
3 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
4 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000
5 2.00000 1.87930 1.53200 1.00000 0.34730 -0.34730 -1.00000 -1.53200 -1.87930 -2.00000 0.00000 0.00000
6 2.00000 1.53200 0.34730 -1.00000 -1.87930 -1.87930 -1.00000 0.34730 1.53200 2.00000 0.00000 0.00000
7 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 0.00000 0.00000
8 2.00000 0.34730 -1.87930 -1.00000 1.53200 1.53200 -1.00000 -1.87930 0.34730 2.00000 0.00000 0.00000
9 2.00000 -0.34730 -1.87930 1.00000 1.53200 -1.53200 -1.00000 1.87930 0.34730 -2.00000 0.00000 0.00000
10 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 0.00000 0.00000
11 2.00000 -1.53200 0.34730 1.00000 -1.87930 1.87930 -1.00000 -0.34730 1.53200 -2.00000 0.00000 0.00000
12 2.00000 -1.87930 1.53200 -1.00000 0.34730 0.34730 -1.00000 1.53200 -1.87930 2.00000 0.00000 0.00000

View File

@ -0,0 +1,28 @@
Group C19
n 10
Irred Operation
1 A E
2 E1 C19
3 E2 C19^2
4 E3 C19^3
5 E4 C19^4
6 E5 C19^5
7 E6 C19^6
8 E7 C19^7
9 E8 C19^8
10 E9 C19^9
Table
1 2 3 4 5 6 7 8 9 10
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 2.00000 1.89160 1.57820 1.09390 0.49090 -0.16510 -0.80330 -1.35450 -1.75890 -1.97270
3 2.00000 1.57820 0.49090 -0.80330 -1.75890 -1.97270 -1.35450 -0.16510 1.09390 1.89160
4 2.00000 1.09390 -0.80330 -1.97270 -1.35450 0.49090 1.89160 1.57820 -0.16510 -1.75890
5 2.00000 0.49090 -1.75890 -1.35450 1.09390 1.89160 -0.16510 -1.97270 -0.80330 1.57820
6 2.00000 -0.16510 -1.97270 0.49090 1.89160 -0.80330 -1.75890 1.09390 1.57820 -1.35450
7 2.00000 -0.80330 -1.35450 1.89160 -0.16510 -1.75890 1.57820 0.49090 -1.97270 1.09390
8 2.00000 -1.35450 -0.16510 1.57820 -1.97270 1.09390 0.49090 -1.75890 1.89160 -0.80330
9 2.00000 -1.75890 1.09390 -0.16510 -0.80330 1.57820 -1.97270 1.89160 -1.35450 0.49090
10 2.00000 -1.97270 1.89160 -1.75890 1.57820 -1.35450 1.09390 -0.80330 0.49090 -0.16510

View File

@ -0,0 +1,48 @@
Group C19h
n 20
Irred Operation
1 A' E
2 A" C19
3 E1' C19^2
4 E1" C19^3
5 E2' C19^4
6 E2" C19^5
7 E3' C19^6
8 E3" C19^7
9 E4' C19^8
10 E4" C19^9
11 E5' sh
12 E5" S19
13 E6' S19^3
14 E6" S19^5
15 E7' S19^7
16 E7" S19^9
17 E8' S19^11
18 E8" S19^13
19 E9' S19^15
20 E9" S19^17
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
3 2.00000 1.89163 1.57828 1.09390 0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 2.00000 1.89163 1.09390 -0.16516 -1.35456 -1.97272 -1.75895 -0.80339 0.49097 1.57828
4 2.00000 1.89163 1.57828 1.09390 0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 -2.00000 -1.89163 -1.09390 0.16516 1.35456 1.97272 1.75895 0.80339 -0.49097 -1.57828
5 2.00000 1.57828 0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516 1.09390 1.89163 2.00000 1.57828 -0.80339 -1.97272 -0.16516 1.89163 1.09390 -1.35456 -1.75895 0.49097
6 2.00000 1.57828 0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516 1.09390 1.89163 -2.00000 -1.57828 0.80339 1.97272 0.16516 -1.89163 -1.09390 1.35456 1.75895 -0.49097
7 2.00000 1.09390 -0.80339 -1.97272 -1.35456 0.49097 1.89163 1.57828 -0.16516 -1.75895 2.00000 1.09390 -1.97272 0.49097 1.57828 -1.75895 -0.16516 1.89163 -1.35456 -0.80339
8 2.00000 1.09390 -0.80339 -1.97272 -1.35456 0.49097 1.89163 1.57828 -0.16516 -1.75895 -2.00000 -1.09390 1.97272 -0.49097 -1.57828 1.75895 0.16516 -1.89163 1.35456 0.80339
9 2.00000 0.49097 -1.75895 -1.35456 1.09390 1.89163 -0.16516 -1.97272 -0.80339 1.57828 2.00000 0.49097 -1.35456 1.89163 -1.97272 1.57828 -0.80339 -0.16516 1.09390 -1.75895
10 2.00000 0.49097 -1.75895 -1.35456 1.09390 1.89163 -0.16516 -1.97272 -0.80339 1.57828 -2.00000 -0.49097 1.35456 -1.89163 1.97272 -1.57828 0.80339 0.16516 -1.09390 1.75895
11 2.00000 -0.16516 -1.97272 0.49097 1.89163 -0.80339 -1.75895 1.09390 1.57828 -1.35456 2.00000 -0.16516 0.49097 -0.80339 1.09390 -1.35456 1.57828 -1.75895 1.89163 -1.97272
12 2.00000 -0.16516 -1.97272 0.49097 1.89163 -0.80339 -1.75895 1.09390 1.57828 -1.35456 -2.00000 0.16516 -0.49097 0.80339 -1.09390 1.35456 -1.57828 1.75895 -1.89163 1.97272
13 2.00000 -0.80339 -1.35456 1.89163 -0.16516 -1.75895 1.57828 0.49097 -1.97272 1.09390 2.00000 -0.80339 1.89163 -1.75895 0.49097 1.09390 -1.97272 1.57828 -0.16516 -1.35456
14 2.00000 -0.80339 -1.35456 1.89163 -0.16516 -1.75895 1.57828 0.49097 -1.97272 1.09390 -2.00000 0.80339 -1.89163 1.75895 -0.49097 -1.09390 1.97272 -1.57828 0.16516 1.35456
15 2.00000 -1.35456 -0.16516 1.57828 -1.97272 1.09390 0.49097 -1.75895 1.89163 -0.80339 2.00000 -1.35456 1.57828 1.09390 -1.75895 -0.80339 1.89163 0.49097 -1.97272 -0.16516
16 2.00000 -1.35456 -0.16516 1.57828 -1.97272 1.09390 0.49097 -1.75895 1.89163 -0.80339 -2.00000 1.35456 -1.57828 -1.09390 1.75895 0.80339 -1.89163 -0.49097 1.97272 0.16516
17 2.00000 -1.75895 1.09390 -0.16516 -0.80339 1.57828 -1.97272 1.89163 -1.35456 0.49097 2.00000 -1.75895 -0.16516 1.57828 1.89163 0.49097 -1.35456 -1.97272 -0.80339 1.09390
18 2.00000 -1.75895 1.09390 -0.16516 -0.80339 1.57828 -1.97272 1.89163 -1.35456 0.49097 -2.00000 1.75895 0.16516 -1.57828 -1.89163 -0.49097 1.35456 1.97272 0.80339 -1.09390
19 2.00000 -1.97272 1.89163 -1.75895 1.57828 -1.35456 1.09390 -0.80339 0.49097 -0.16516 2.00000 -1.97272 -1.75895 -1.35456 -0.80339 -0.16516 0.49097 1.09390 1.57828 1.89163
20 2.00000 -1.97272 1.89163 -1.75895 1.57828 -1.35456 1.09390 -0.80339 0.49097 -0.16516 -2.00000 1.97272 1.75895 1.35456 0.80339 0.16516 -0.49097 -1.09390 -1.57828 -1.89163

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@ -0,0 +1,30 @@
Group C19v
n 11
Irred Operation
1 A1 E
2 A2 C19
3 E1 C19^2
4 E2 C19^3
5 E3 C19^4
6 E4 C19^5
7 E5 C19^6
8 E6 C19^7
9 E7 C19^8
10 E8 C19^9
11 E9 sv
Table
1 2 3 4 5 6 7 8 9 10 11
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000
3 2.00000 1.89160 1.57820 1.09390 0.49090 -0.16510 -0.80330 -1.35450 -1.75890 -1.97270 0.00000
4 2.00000 1.57820 0.49090 -0.80330 -1.75890 -1.97270 -1.35450 -0.16510 1.09390 1.89160 0.00000
5 2.00000 1.09390 -0.80330 -1.97270 -1.35450 0.49090 1.89160 1.57820 -0.16510 -1.75890 0.00000
6 2.00000 0.49090 -1.75890 -1.35450 1.09390 1.89160 -0.16510 -1.97270 -0.80330 1.57820 0.00000
7 2.00000 -0.16510 -1.97270 0.49090 1.89160 -0.80330 -1.75890 1.09390 1.57820 -1.35450 0.00000
8 2.00000 -0.80330 -1.35450 1.89160 -0.16510 -1.75890 1.57820 0.49090 -1.97270 1.09390 0.00000
9 2.00000 -1.35450 -0.16510 1.57820 -1.97270 1.09390 0.49090 -1.75890 1.89160 -0.80330 0.00000
10 2.00000 -1.75890 1.09390 -0.16510 -0.80330 1.57820 -1.97270 1.89160 -1.35450 0.49090 0.00000
11 2.00000 -1.97270 1.89160 -1.75890 1.57820 -1.35450 1.09390 -0.80330 0.49090 -0.16510 0.00000

View File

@ -0,0 +1,12 @@
Group C1h
n 2
Irred Operation
1 A' E
2 A" sh
Table
1 2
1 1.00000 1.00000
2 1.00000 -1.00000

View File

@ -0,0 +1,12 @@
Group C1v
n 2
Irred Operation
1 A1 E
2 A2 sv
Table
1 2
1 1.00000 1.00000
2 1.00000 -1.00000

View File

@ -0,0 +1,12 @@
Group C2
n 2
Irred Operation
1 A E
2 B C2
Table
1 2
1 1.00000 1.00000
2 1.00000 -1.00000

View File

@ -0,0 +1,30 @@
Group C20
n 11
Irred Operation
1 A E
2 B C20
3 E1 C10
4 E2 C20^3
5 E3 C5
6 E4 C4
7 E5 C10^3
8 E6 C20^7
9 E7 C5^2
10 E8 C20^9
11 E9 C2
Table
1 2 3 4 5 6 7 8 9 10 11
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
3 2.00000 1.90210 1.61800 1.17550 0.61800 0.00000 -0.61800 -1.17550 -1.61800 -1.90210 -2.00000
4 2.00000 1.61800 0.61800 -0.61800 -1.61800 -2.00000 -1.61800 -0.61800 0.61800 1.61800 2.00000
5 2.00000 1.17550 -0.61800 -1.90210 -1.61800 0.00000 1.61800 1.90210 0.61800 -1.17550 -2.00000
6 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000
7 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000
8 2.00000 -0.61800 -1.61800 1.61800 0.61800 -2.00000 0.61800 1.61800 -1.61800 -0.61800 2.00000
9 2.00000 -1.17550 -0.61800 1.90210 -1.61800 0.00000 1.61800 -1.90210 0.61800 1.17550 -2.00000
10 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000
11 2.00000 -1.90210 1.61800 -1.17550 0.61800 0.00000 -0.61800 1.17550 -1.61800 1.90210 -2.00000

View File

@ -0,0 +1,52 @@
Group C20h
n 22
Irred Operation
1 Ag E
2 Bg C20
3 E1g C10
4 E2g C20^3
5 E3g C5
6 E4g C4
7 E5g C10^3
8 E6g C20^7
9 E7g C5^2
10 E8g C20^9
11 E9g C2
12 Au i
13 Bu S20
14 E1u S10
15 E2u S20^3
16 E3u S5
17 E4u S4
18 E5u S10^3
19 E6u S20^7
20 E7u S5^2
21 E8u S20^9
22 E9u sh
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
3 2.00000 1.90210 1.61800 1.17550 0.61800 0.00000 -0.61800 -1.17550 -1.61800 -1.90210 -2.00000 2.00000 -1.90210 -1.61800 -1.17550 -0.61800 0.00000 0.61800 1.17550 1.61800 1.90210 -2.00000
4 2.00000 1.61800 0.61800 -0.61800 -1.61800 -2.00000 -1.61800 -0.61800 0.61800 1.61800 2.00000 2.00000 1.61800 0.61800 -0.61800 -1.61800 -2.00000 -1.61800 -0.61800 0.61800 1.61800 2.00000
5 2.00000 1.17550 -0.61800 -1.90210 -1.61800 0.00000 1.61800 1.90210 0.61800 -1.17550 -2.00000 2.00000 -1.17550 0.61800 1.90210 1.61800 0.00000 -1.61800 -1.90210 -0.61800 1.17550 -2.00000
6 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000
7 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 -2.00000
8 2.00000 -0.61800 -1.61800 1.61800 0.61800 -2.00000 0.61800 1.61800 -1.61800 -0.61800 2.00000 2.00000 -0.61800 -1.61800 1.61800 0.61800 -2.00000 0.61800 1.61800 -1.61800 -0.61800 2.00000
9 2.00000 -1.17550 -0.61800 1.90210 -1.61800 0.00000 1.61800 -1.90210 0.61800 1.17550 -2.00000 2.00000 1.17550 0.61800 -1.90210 1.61800 0.00000 -1.61800 1.90210 -0.61800 -1.17550 -2.00000
10 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000
11 2.00000 -1.90210 1.61800 -1.17550 0.61800 0.00000 -0.61800 1.17550 -1.61800 1.90210 -2.00000 2.00000 1.90210 -1.61800 1.17550 -0.61800 0.00000 0.61800 -1.17550 1.61800 -1.90210 -2.00000
12 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
13 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
14 2.00000 1.90210 1.61800 1.17550 0.61800 0.00000 -0.61800 -1.17550 -1.61800 -1.90210 -2.00000 -2.00000 1.90210 1.61800 1.17550 0.61800 0.00000 -0.61800 -1.17550 -1.61800 -1.90210 2.00000
15 2.00000 1.61800 0.61800 -0.61800 -1.61800 -2.00000 -1.61800 -0.61800 0.61800 1.61800 2.00000 -2.00000 -1.61800 -0.61800 0.61800 1.61800 2.00000 1.61800 0.61800 -0.61800 -1.61800 -2.00000
16 2.00000 1.17550 -0.61800 -1.90210 -1.61800 0.00000 1.61800 1.90210 0.61800 -1.17550 -2.00000 -2.00000 1.17550 -0.61800 -1.90210 -1.61800 0.00000 1.61800 1.90210 0.61800 -1.17550 2.00000
17 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 -2.00000 -0.61800 1.61800 1.61800 -0.61800 -2.00000 -0.61800 1.61800 1.61800 -0.61800 -2.00000
18 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 -2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 2.00000
19 2.00000 -0.61800 -1.61800 1.61800 0.61800 -2.00000 0.61800 1.61800 -1.61800 -0.61800 2.00000 -2.00000 0.61800 1.61800 -1.61800 -0.61800 2.00000 -0.61800 -1.61800 1.61800 0.61800 -2.00000
20 2.00000 -1.17550 -0.61800 1.90210 -1.61800 0.00000 1.61800 -1.90210 0.61800 1.17550 -2.00000 -2.00000 -1.17550 -0.61800 1.90210 -1.61800 0.00000 1.61800 -1.90210 0.61800 1.17550 2.00000
21 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 -2.00000 1.61800 -0.61800 -0.61800 1.61800 -2.00000 1.61800 -0.61800 -0.61800 1.61800 -2.00000
22 2.00000 -1.90210 1.61800 -1.17550 0.61800 0.00000 -0.61800 1.17550 -1.61800 1.90210 -2.00000 -2.00000 -1.90210 1.61800 -1.17550 0.61800 0.00000 -0.61800 1.17550 -1.61800 1.90210 2.00000

View File

@ -0,0 +1,34 @@
Group C20v
n 13
Irred Operation
1 A1 E
2 A2 C20
3 B1 C10
4 B2 C20^3
5 E1 C5
6 E2 C4
7 E3 C10^3
8 E4 C20^7
9 E5 C5^2
10 E6 C20^9
11 E7 C2
12 E8 sv
13 E9 sd
Table
1 2 3 4 5 6 7 8 9 10 11 12 13
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000
3 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000
4 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
5 2.00000 1.90210 1.61800 1.17550 0.61800 0.00000 -0.61800 -1.17550 -1.61800 -1.90210 -2.00000 0.00000 0.00000
6 2.00000 1.61800 0.61800 -0.61800 -1.61800 -2.00000 -1.61800 -0.61800 0.61800 1.61800 2.00000 0.00000 0.00000
7 2.00000 1.17550 -0.61800 -1.90210 -1.61800 0.00000 1.61800 1.90210 0.61800 -1.17550 -2.00000 0.00000 0.00000
8 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 0.61800 -1.61800 -1.61800 0.61800 2.00000 0.00000 0.00000
9 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 0.00000
10 2.00000 -0.61800 -1.61800 1.61800 0.61800 -2.00000 0.61800 1.61800 -1.61800 -0.61800 2.00000 0.00000 0.00000
11 2.00000 -1.17550 -0.61800 1.90210 -1.61800 0.00000 1.61800 -1.90210 0.61800 1.17550 -2.00000 0.00000 0.00000
12 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 -1.61800 0.61800 0.61800 -1.61800 2.00000 0.00000 0.00000
13 2.00000 -1.90210 1.61800 -1.17550 0.61800 0.00000 -0.61800 1.17550 -1.61800 1.90210 -2.00000 0.00000 0.00000

View File

@ -0,0 +1,30 @@
Group C21
n 11
Irred Operation
1 A E
2 E1 C21
3 E2 C21^2
4 E3 C7
5 E4 C21^4
6 E5 C21^5
7 E6 C7^2
8 E7 C3
9 E8 C21^8
10 E9 C7^3
11 E10 C21^10
Table
1 2 3 4 5 6 7 8 9 10 11
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 2.00000 1.91115 1.65248 1.24698 0.73068 0.14946 -0.44504 -1.00000 -1.46610 -1.80194 -1.97766
3 2.00000 1.65248 0.73068 -0.44504 -1.46610 -1.97766 -1.80194 -1.00000 0.14946 1.24698 1.91115
4 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194
5 2.00000 0.73068 -1.46610 -1.80194 0.14946 1.91115 1.24698 -1.00000 -1.97766 -0.44504 1.65248
6 2.00000 0.14946 -1.97766 -0.44504 1.91115 0.73068 -1.80194 -1.00000 1.65248 1.24698 -1.46610
7 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698
8 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000
9 2.00000 -1.46610 0.14946 1.24698 -1.97766 1.65248 -0.44504 -1.00000 1.91115 -1.80194 0.73068
10 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504
11 2.00000 -1.97766 1.91115 -1.80194 1.65248 -1.46610 1.24698 -1.00000 0.73068 -0.44504 0.14946

View File

@ -0,0 +1,52 @@
Group C21h
n 22
Irred Operation
1 A' E
2 A" C21
3 E1' C21^2
4 E1" C7
5 E2' C21^4
6 E2" C21^5
7 E3' C7^2
8 E3" C3
9 E4' C21^8
10 E4" C7^3
11 E5' C21^10
12 E5" sh
13 E6' S21
14 E6" S7
15 E7' S21^5
16 E7" S3
17 E8' S7^3
18 E8" S21^11
19 E9' S21^13
20 E9" S7^5
21 E10' S21^17
22 E10" S21^19
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
3 2.00000 1.91115 1.65248 1.24698 0.73068 0.14946 -0.44504 -1.00000 -1.46610 -1.80194 -1.97766 2.00000 1.91115 1.24698 0.14946 -1.00000 -1.80194 -1.97766 -1.46610 -0.44504 0.73068 1.65248
4 2.00000 1.91115 1.65248 1.24698 0.73068 0.14946 -0.44504 -1.00000 -1.46610 -1.80194 -1.97766 -2.00000 -1.91115 -1.24698 -0.14946 1.00000 1.80194 1.97766 1.46610 0.44504 -0.73068 -1.65248
5 2.00000 1.65248 0.73068 -0.44504 -1.46610 -1.97766 -1.80194 -1.00000 0.14946 1.24698 1.91115 2.00000 1.65248 -0.44504 -1.97766 -1.00000 1.24698 1.91115 0.14946 -1.80194 -1.46610 0.73068
6 2.00000 1.65248 0.73068 -0.44504 -1.46610 -1.97766 -1.80194 -1.00000 0.14946 1.24698 1.91115 -2.00000 -1.65248 0.44504 1.97766 1.00000 -1.24698 -1.91115 -0.14946 1.80194 1.46610 -0.73068
7 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 2.00000 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504
8 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -2.00000 -1.24698 1.80194 0.44504 -2.00000 0.44504 1.80194 -1.24698 -1.24698 1.80194 0.44504
9 2.00000 0.73068 -1.46610 -1.80194 0.14946 1.91115 1.24698 -1.00000 -1.97766 -0.44504 1.65248 2.00000 0.73068 -1.80194 1.91115 -1.00000 -0.44504 1.65248 -1.97766 1.24698 0.14946 -1.46610
10 2.00000 0.73068 -1.46610 -1.80194 0.14946 1.91115 1.24698 -1.00000 -1.97766 -0.44504 1.65248 -2.00000 -0.73068 1.80194 -1.91115 1.00000 0.44504 -1.65248 1.97766 -1.24698 -0.14946 1.46610
11 2.00000 0.14946 -1.97766 -0.44504 1.91115 0.73068 -1.80194 -1.00000 1.65248 1.24698 -1.46610 2.00000 0.14946 -0.44504 0.73068 -1.00000 1.24698 -1.46610 1.65248 -1.80194 1.91115 -1.97766
12 2.00000 0.14946 -1.97766 -0.44504 1.91115 0.73068 -1.80194 -1.00000 1.65248 1.24698 -1.46610 -2.00000 -0.14946 0.44504 -0.73068 1.00000 -1.24698 1.46610 -1.65248 1.80194 -1.91115 1.97766
13 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 2.00000 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194
14 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 -2.00000 0.44504 -1.24698 1.80194 -2.00000 1.80194 -1.24698 0.44504 0.44504 -1.24698 1.80194
15 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 2.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000
16 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -2.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000
17 2.00000 -1.46610 0.14946 1.24698 -1.97766 1.65248 -0.44504 -1.00000 1.91115 -1.80194 0.73068 2.00000 -1.46610 1.24698 1.65248 -1.00000 -1.80194 0.73068 1.91115 -0.44504 -1.97766 0.14946
18 2.00000 -1.46610 0.14946 1.24698 -1.97766 1.65248 -0.44504 -1.00000 1.91115 -1.80194 0.73068 -2.00000 1.46610 -1.24698 -1.65248 1.00000 1.80194 -0.73068 -1.91115 0.44504 1.97766 -0.14946
19 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 2.00000 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698
20 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -2.00000 1.80194 0.44504 -1.24698 -2.00000 -1.24698 0.44504 1.80194 1.80194 0.44504 -1.24698
21 2.00000 -1.97766 1.91115 -1.80194 1.65248 -1.46610 1.24698 -1.00000 0.73068 -0.44504 0.14946 2.00000 -1.97766 -1.80194 -1.46610 -1.00000 -0.44504 0.14946 0.73068 1.24698 1.65248 1.91115
22 2.00000 -1.97766 1.91115 -1.80194 1.65248 -1.46610 1.24698 -1.00000 0.73068 -0.44504 0.14946 -2.00000 1.97766 1.80194 1.46610 1.00000 0.44504 -0.14946 -0.73068 -1.24698 -1.65248 -1.91115

View File

@ -0,0 +1,32 @@
Group C21v
n 12
Irred Operation
1 A1 E
2 A2 C21
3 E1 C21^2
4 E2 C7
5 E3 C21^4
6 E4 C21^5
7 E5 C7^2
8 E6 C3
9 E7 C21^8
10 E8 C7^3
11 E9 C21^10
12 E10 sv
Table
1 2 3 4 5 6 7 8 9 10 11 12
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000
3 2.00000 1.91115 1.65248 1.24698 0.73068 0.14946 -0.44504 -1.00000 -1.46610 -1.80194 -1.97766 0.00000
4 2.00000 1.65248 0.73068 -0.44504 -1.46610 -1.97766 -1.80194 -1.00000 0.14946 1.24698 1.91115 0.00000
5 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 0.00000
6 2.00000 0.73068 -1.46610 -1.80194 0.14946 1.91115 1.24698 -1.00000 -1.97766 -0.44504 1.65248 0.00000
7 2.00000 0.14946 -1.97766 -0.44504 1.91115 0.73068 -1.80194 -1.00000 1.65248 1.24698 -1.46610 0.00000
8 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 0.00000
9 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 0.00000
10 2.00000 -1.46610 0.14946 1.24698 -1.97766 1.65248 -0.44504 -1.00000 1.91115 -1.80194 0.73068 0.00000
11 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 0.00000
12 2.00000 -1.97766 1.91115 -1.80194 1.65248 -1.46610 1.24698 -1.00000 0.73068 -0.44504 0.14946 0.00000

View File

@ -0,0 +1,32 @@
Group C22
n 12
Irred Operation
1 A E
2 B C22
3 E1 C11
4 E2 C22^3
5 E3 C11^2
6 E4 C22^5
7 E5 C11^3
8 E6 C22^7
9 E7 C11^4
10 E8 C22^9
11 E9 C11^5
12 E10 C2
Table
1 2 3 4 5 6 7 8 9 10 11 12
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
3 2.00000 1.91890 1.68250 1.30970 0.83080 0.28460 -0.28460 -0.83080 -1.30970 -1.68250 -1.91890 -2.00000
4 2.00000 1.68250 0.83080 -0.28460 -1.30970 -1.91890 -1.91890 -1.30970 -0.28460 0.83080 1.68250 2.00000
5 2.00000 1.30970 -0.28460 -1.68250 -1.91890 -0.83080 0.83080 1.91890 1.68250 0.28460 -1.30970 -2.00000
6 2.00000 0.83080 -1.30970 -1.91890 -0.28460 1.68250 1.68250 -0.28460 -1.91890 -1.30970 0.83080 2.00000
7 2.00000 0.28460 -1.91890 -0.83080 1.68250 1.30970 -1.30970 -1.68250 0.83080 1.91890 -0.28460 -2.00000
8 2.00000 -0.28460 -1.91890 0.83080 1.68250 -1.30970 -1.30970 1.68250 0.83080 -1.91890 -0.28460 2.00000
9 2.00000 -0.83080 -1.30970 1.91890 -0.28460 -1.68250 1.68250 0.28460 -1.91890 1.30970 0.83080 -2.00000
10 2.00000 -1.30970 -0.28460 1.68250 -1.91890 0.83080 0.83080 -1.91890 1.68250 -0.28460 -1.30970 2.00000
11 2.00000 -1.68250 0.83080 0.28460 -1.30970 1.91890 -1.91890 1.30970 -0.28460 -0.83080 1.68250 -2.00000
12 2.00000 -1.91890 1.68250 -1.30970 0.83080 -0.28460 -0.28460 0.83080 -1.30970 1.68250 -1.91890 2.00000

View File

@ -0,0 +1,56 @@
Group C22h
n 24
Irred Operation
1 Ag E
2 Bg C22
3 E1g C11
4 E2g C22^3
5 E3g C11^2
6 E4g C22^5
7 E5g C11^3
8 E6g C22^7
9 E7g C11^4
10 E8g C22^9
11 E9g C11^5
12 E10g C2
13 Au i
14 Bu S22
15 E1u S11
16 E2u S22^3
17 E3u S11^2
18 E4u S22^5
19 E5u S11^3
20 E6u S22^7
21 E7u S11^4
22 E8u S22^9
23 E9u S11^5
24 E10u sh
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000
3 2.00000 1.91890 1.68250 1.30970 0.83080 0.28460 -0.28460 -0.83080 -1.30970 -1.68250 -1.91890 -2.00000 2.00000 -1.91890 -1.68250 -1.30970 -0.83080 -0.28460 0.28460 0.83080 1.30970 1.68250 1.91890 -2.00000
4 2.00000 1.68250 0.83080 -0.28460 -1.30970 -1.91890 -1.91890 -1.30970 -0.28460 0.83080 1.68250 2.00000 2.00000 1.68250 0.83080 -0.28460 -1.30970 -1.91890 -1.91890 -1.30970 -0.28460 0.83080 1.68250 2.00000
5 2.00000 1.30970 -0.28460 -1.68250 -1.91890 -0.83080 0.83080 1.91890 1.68250 0.28460 -1.30970 -2.00000 2.00000 -1.30970 0.28460 1.68250 1.91890 0.83080 -0.83080 -1.91890 -1.68250 -0.28460 1.30970 -2.00000
6 2.00000 0.83080 -1.30970 -1.91890 -0.28460 1.68250 1.68250 -0.28460 -1.91890 -1.30970 0.83080 2.00000 2.00000 0.83080 -1.30970 -1.91890 -0.28460 1.68250 1.68250 -0.28460 -1.91890 -1.30970 0.83080 2.00000
7 2.00000 0.28460 -1.91890 -0.83080 1.68250 1.30970 -1.30970 -1.68250 0.83080 1.91890 -0.28460 -2.00000 2.00000 -0.28460 1.91890 0.83080 -1.68250 -1.30970 1.30970 1.68250 -0.83080 -1.91890 0.28460 -2.00000
8 2.00000 -0.28460 -1.91890 0.83080 1.68250 -1.30970 -1.30970 1.68250 0.83080 -1.91890 -0.28460 2.00000 2.00000 -0.28460 -1.91890 0.83080 1.68250 -1.30970 -1.30970 1.68250 0.83080 -1.91890 -0.28460 2.00000
9 2.00000 -0.83080 -1.30970 1.91890 -0.28460 -1.68250 1.68250 0.28460 -1.91890 1.30970 0.83080 -2.00000 2.00000 0.83080 1.30970 -1.91890 0.28460 1.68250 -1.68250 -0.28460 1.91890 -1.30970 -0.83080 -2.00000
10 2.00000 -1.30970 -0.28460 1.68250 -1.91890 0.83080 0.83080 -1.91890 1.68250 -0.28460 -1.30970 2.00000 2.00000 -1.30970 -0.28460 1.68250 -1.91890 0.83080 0.83080 -1.91890 1.68250 -0.28460 -1.30970 2.00000
11 2.00000 -1.68250 0.83080 0.28460 -1.30970 1.91890 -1.91890 1.30970 -0.28460 -0.83080 1.68250 -2.00000 2.00000 1.68250 -0.83080 -0.28460 1.30970 -1.91890 1.91890 -1.30970 0.28460 0.83080 -1.68250 -2.00000
12 2.00000 -1.91890 1.68250 -1.30970 0.83080 -0.28460 -0.28460 0.83080 -1.30970 1.68250 -1.91890 2.00000 2.00000 -1.91890 1.68250 -1.30970 0.83080 -0.28460 -0.28460 0.83080 -1.30970 1.68250 -1.91890 2.00000
13 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
14 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000
15 2.00000 1.91890 1.68250 1.30970 0.83080 0.28460 -0.28460 -0.83080 -1.30970 -1.68250 -1.91890 -2.00000 -2.00000 1.91890 1.68250 1.30970 0.83080 0.28460 -0.28460 -0.83080 -1.30970 -1.68250 -1.91890 2.00000
16 2.00000 1.68250 0.83080 -0.28460 -1.30970 -1.91890 -1.91890 -1.30970 -0.28460 0.83080 1.68250 2.00000 -2.00000 -1.68250 -0.83080 0.28460 1.30970 1.91890 1.91890 1.30970 0.28460 -0.83080 -1.68250 -2.00000
17 2.00000 1.30970 -0.28460 -1.68250 -1.91890 -0.83080 0.83080 1.91890 1.68250 0.28460 -1.30970 -2.00000 -2.00000 1.30970 -0.28460 -1.68250 -1.91890 -0.83080 0.83080 1.91890 1.68250 0.28460 -1.30970 2.00000
18 2.00000 0.83080 -1.30970 -1.91890 -0.28460 1.68250 1.68250 -0.28460 -1.91890 -1.30970 0.83080 2.00000 -2.00000 -0.83080 1.30970 1.91890 0.28460 -1.68250 -1.68250 0.28460 1.91890 1.30970 -0.83080 -2.00000
19 2.00000 0.28460 -1.91890 -0.83080 1.68250 1.30970 -1.30970 -1.68250 0.83080 1.91890 -0.28460 -2.00000 -2.00000 0.28460 -1.91890 -0.83080 1.68250 1.30970 -1.30970 -1.68250 0.83080 1.91890 -0.28460 2.00000
20 2.00000 -0.28460 -1.91890 0.83080 1.68250 -1.30970 -1.30970 1.68250 0.83080 -1.91890 -0.28460 2.00000 -2.00000 0.28460 1.91890 -0.83080 -1.68250 1.30970 1.30970 -1.68250 -0.83080 1.91890 0.28460 -2.00000
21 2.00000 -0.83080 -1.30970 1.91890 -0.28460 -1.68250 1.68250 0.28460 -1.91890 1.30970 0.83080 -2.00000 -2.00000 -0.83080 -1.30970 1.91890 -0.28460 -1.68250 1.68250 0.28460 -1.91890 1.30970 0.83080 2.00000
22 2.00000 -1.30970 -0.28460 1.68250 -1.91890 0.83080 0.83080 -1.91890 1.68250 -0.28460 -1.30970 2.00000 -2.00000 1.30970 0.28460 -1.68250 1.91890 -0.83080 -0.83080 1.91890 -1.68250 0.28460 1.30970 -2.00000
23 2.00000 -1.68250 0.83080 0.28460 -1.30970 1.91890 -1.91890 1.30970 -0.28460 -0.83080 1.68250 -2.00000 -2.00000 -1.68250 0.83080 0.28460 -1.30970 1.91890 -1.91890 1.30970 -0.28460 -0.83080 1.68250 2.00000
24 2.00000 -1.91890 1.68250 -1.30970 0.83080 -0.28460 -0.28460 0.83080 -1.30970 1.68250 -1.91890 2.00000 -2.00000 1.91890 -1.68250 1.30970 -0.83080 0.28460 0.28460 -0.83080 1.30970 -1.68250 1.91890 -2.00000

View File

@ -0,0 +1,36 @@
Group C22v
n 14
Irred Operation
1 A1 E
2 A2 C22
3 B1 C11
4 B2 C22^3
5 E1 C11^2
6 E2 C22^5
7 E3 C11^3
8 E4 C22^7
9 E5 C11^4
10 E6 C22^9
11 E7 C11^5
12 E8 C2
13 E9 sv
14 E10 sd
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000
3 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
4 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000
5 2.00000 1.91890 1.68250 1.30970 0.83080 0.28460 -0.28460 -0.83080 -1.30970 -1.68250 -1.91890 -2.00000 0.00000 0.00000
6 2.00000 1.68250 0.83080 -0.28460 -1.30970 -1.91890 -1.91890 -1.30970 -0.28460 0.83080 1.68250 2.00000 0.00000 0.00000
7 2.00000 1.30970 -0.28460 -1.68250 -1.91890 -0.83080 0.83080 1.91890 1.68250 0.28460 -1.30970 -2.00000 0.00000 0.00000
8 2.00000 0.83080 -1.30970 -1.91890 -0.28460 1.68250 1.68250 -0.28460 -1.91890 -1.30970 0.83080 2.00000 0.00000 0.00000
9 2.00000 0.28460 -1.91890 -0.83080 1.68250 1.30970 -1.30970 -1.68250 0.83080 1.91890 -0.28460 -2.00000 0.00000 0.00000
10 2.00000 -0.28460 -1.91890 0.83080 1.68250 -1.30970 -1.30970 1.68250 0.83080 -1.91890 -0.28460 2.00000 0.00000 0.00000
11 2.00000 -0.83080 -1.30970 1.91890 -0.28460 -1.68250 1.68250 0.28460 -1.91890 1.30970 0.83080 -2.00000 0.00000 0.00000
12 2.00000 -1.30970 -0.28460 1.68250 -1.91890 0.83080 0.83080 -1.91890 1.68250 -0.28460 -1.30970 2.00000 0.00000 0.00000
13 2.00000 -1.68250 0.83080 0.28460 -1.30970 1.91890 -1.91890 1.30970 -0.28460 -0.83080 1.68250 -2.00000 0.00000 0.00000
14 2.00000 -1.91890 1.68250 -1.30970 0.83080 -0.28460 -0.28460 0.83080 -1.30970 1.68250 -1.91890 2.00000 0.00000 0.00000

View File

@ -0,0 +1,32 @@
Group C23
n 12
Irred Operation
1 A E
2 E1 C23
3 E2 C23^2
4 E3 C23^3
5 E4 C23^4
6 E5 C23^5
7 E6 C23^6
8 E7 C23^7
9 E8 C23^8
10 E9 C23^9
11 E10 C23^10
12 E11 C23^11
Table
1 2 3 4 5 6 7 8 9 10 11 12
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137
3 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583
4 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442
5 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884
6 2.00000 0.40691 -1.83442 -1.15336 1.36511 1.70884 -0.66976 -1.98137 -0.13648 1.92583 0.92013 -1.55142
7 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511
8 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336
9 2.00000 -1.15336 -0.66976 1.92583 -1.55142 -0.13648 1.70884 -1.83442 0.40691 1.36511 -1.98137 0.92013
10 2.00000 -1.55142 0.40691 0.92013 -1.83442 1.92583 -1.15336 -0.13648 1.36511 -1.98137 1.70884 -0.66976
11 2.00000 -1.83442 1.36511 -0.66976 -0.13648 0.92013 -1.55142 1.92583 -1.98137 1.70884 -1.15336 0.40691
12 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648

View File

@ -0,0 +1,56 @@
Group C23h
n 24
Irred Operation
1 A' E
2 A" C23
3 E1' C23^2
4 E1" C23^3
5 E2' C23^4
6 E2" C23^5
7 E3' C23^6
8 E3" C23^7
9 E4' C23^8
10 E4" C23^9
11 E5' C23^10
12 E5" C23^11
13 E6' sh
14 E6" S23
15 E7' S23^3
16 E7" S23^5
17 E8' S23^7
18 E8" S23^9
19 E9' S23^11
20 E9" S23^13
21 E10' S23^15
22 E10" S23^17
23 E11' S23^19
24 E11" S23^21
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
3 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 2.00000 1.92583 1.36511 0.40691 -0.66976 -1.55142 -1.98137 -1.83442 -1.15336 -0.13648 0.92013 1.70884
4 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 -2.00000 -1.92583 -1.36511 -0.40691 0.66976 1.55142 1.98137 1.83442 1.15336 0.13648 -0.92013 -1.70884
5 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 2.00000 1.70884 -0.13648 -1.83442 -1.55142 0.40691 1.92583 1.36511 -0.66976 -1.98137 -1.15336 0.92013
6 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 -2.00000 -1.70884 0.13648 1.83442 1.55142 -0.40691 -1.92583 -1.36511 0.66976 1.98137 1.15336 -0.92013
7 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 2.00000 1.36511 -1.55142 -1.15336 1.70884 0.92013 -1.83442 -0.66976 1.92583 0.40691 -1.98137 -0.13648
8 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 -2.00000 -1.36511 1.55142 1.15336 -1.70884 -0.92013 1.83442 0.66976 -1.92583 -0.40691 1.98137 0.13648
9 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 2.00000 0.92013 -1.98137 1.36511 0.40691 -1.83442 1.70884 -0.13648 -1.55142 1.92583 -0.66976 -1.15336
10 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 -2.00000 -0.92013 1.98137 -1.36511 -0.40691 1.83442 -1.70884 0.13648 1.55142 -1.92583 0.66976 1.15336
11 2.00000 0.40691 -1.83442 -1.15336 1.36511 1.70884 -0.66976 -1.98137 -0.13648 1.92583 0.92013 -1.55142 2.00000 0.40691 -1.15336 1.70884 -1.98137 1.92583 -1.55142 0.92013 -0.13648 -0.66976 1.36511 -1.83442
12 2.00000 0.40691 -1.83442 -1.15336 1.36511 1.70884 -0.66976 -1.98137 -0.13648 1.92583 0.92013 -1.55142 -2.00000 -0.40691 1.15336 -1.70884 1.98137 -1.92583 1.55142 -0.92013 0.13648 0.66976 -1.36511 1.83442
13 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 2.00000 -0.13648 0.40691 -0.66976 0.92013 -1.15336 1.36511 -1.55142 1.70884 -1.83442 1.92583 -1.98137
14 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 -2.00000 0.13648 -0.40691 0.66976 -0.92013 1.15336 -1.36511 1.55142 -1.70884 1.83442 -1.92583 1.98137
15 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 2.00000 -0.66976 1.70884 -1.98137 1.36511 -0.13648 -1.15336 1.92583 -1.83442 0.92013 0.40691 -1.55142
16 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 -2.00000 0.66976 -1.70884 1.98137 -1.36511 0.13648 1.15336 -1.92583 1.83442 -0.92013 -0.40691 1.55142
17 2.00000 -1.15336 -0.66976 1.92583 -1.55142 -0.13648 1.70884 -1.83442 0.40691 1.36511 -1.98137 0.92013 2.00000 -1.15336 1.92583 -0.13648 -1.83442 1.36511 0.92013 -1.98137 0.40691 1.70884 -1.55142 -0.66976
18 2.00000 -1.15336 -0.66976 1.92583 -1.55142 -0.13648 1.70884 -1.83442 0.40691 1.36511 -1.98137 0.92013 -2.00000 1.15336 -1.92583 0.13648 1.83442 -1.36511 -0.92013 1.98137 -0.40691 -1.70884 1.55142 0.66976
19 2.00000 -1.55142 0.40691 0.92013 -1.83442 1.92583 -1.15336 -0.13648 1.36511 -1.98137 1.70884 -0.66976 2.00000 -1.55142 0.92013 1.92583 -0.13648 -1.98137 -0.66976 1.70884 1.36511 -1.15336 -1.83442 0.40691
20 2.00000 -1.55142 0.40691 0.92013 -1.83442 1.92583 -1.15336 -0.13648 1.36511 -1.98137 1.70884 -0.66976 -2.00000 1.55142 -0.92013 -1.92583 0.13648 1.98137 0.66976 -1.70884 -1.36511 1.15336 1.83442 -0.40691
21 2.00000 -1.83442 1.36511 -0.66976 -0.13648 0.92013 -1.55142 1.92583 -1.98137 1.70884 -1.15336 0.40691 2.00000 -1.83442 -0.66976 0.92013 1.92583 1.70884 0.40691 -1.15336 -1.98137 -1.55142 -0.13648 1.36511
22 2.00000 -1.83442 1.36511 -0.66976 -0.13648 0.92013 -1.55142 1.92583 -1.98137 1.70884 -1.15336 0.40691 -2.00000 1.83442 0.66976 -0.92013 -1.92583 -1.70884 -0.40691 1.15336 1.98137 1.55142 0.13648 -1.36511
23 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 2.00000 -1.98137 -1.83442 -1.55142 -1.15336 -0.66976 -0.13648 0.40691 0.92013 1.36511 1.70884 1.92583
24 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 -2.00000 1.98137 1.83442 1.55142 1.15336 0.66976 0.13648 -0.40691 -0.92013 -1.36511 -1.70884 -1.92583

View File

@ -0,0 +1,34 @@
Group C23v
n 13
Irred Operation
1 A1 E
2 A2 C23
3 E1 C23^2
4 E2 C23^3
5 E3 C23^4
6 E4 C23^5
7 E5 C23^6
8 E6 C23^7
9 E7 C23^8
10 E8 C23^9
11 E9 C23^10
12 E10 C23^11
13 E11 sv
Table
1 2 3 4 5 6 7 8 9 10 11 12 13
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000
3 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 0.00000
4 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 0.00000
5 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 0.00000
6 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 0.00000
7 2.00000 0.40691 -1.83442 -1.15336 1.36511 1.70884 -0.66976 -1.98137 -0.13648 1.92583 0.92013 -1.55142 0.00000
8 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 0.00000
9 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 0.00000
10 2.00000 -1.15336 -0.66976 1.92583 -1.55142 -0.13648 1.70884 -1.83442 0.40691 1.36511 -1.98137 0.92013 0.00000
11 2.00000 -1.55142 0.40691 0.92013 -1.83442 1.92583 -1.15336 -0.13648 1.36511 -1.98137 1.70884 -0.66976 0.00000
12 2.00000 -1.83442 1.36511 -0.66976 -0.13648 0.92013 -1.55142 1.92583 -1.98137 1.70884 -1.15336 0.40691 0.00000
13 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 0.00000

View File

@ -0,0 +1,34 @@
Group C24
n 13
Irred Operation
1 A E
2 B C24
3 E1 C12
4 E2 C8
5 E3 C6
6 E4 C24^5
7 E5 C4
8 E6 C24^7
9 E7 C3
10 E8 C8^3
11 E9 C12^5
12 E10 C24^11
13 E11 C2
Table
1 2 3 4 5 6 7 8 9 10 11 12 13
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
3 2.00000 1.93185 1.73205 1.41421 1.00000 0.51764 0.00000 -0.51764 -1.00000 -1.41421 -1.73205 -1.93185 -2.00000
4 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000
5 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000
6 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000
7 2.00000 0.51764 -1.73205 -1.41421 1.00000 1.93185 0.00000 -1.93185 -1.00000 1.41421 1.73205 -0.51764 -2.00000
8 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000
9 2.00000 -0.51764 -1.73205 1.41421 1.00000 -1.93185 0.00000 1.93185 -1.00000 -1.41421 1.73205 0.51764 -2.00000
10 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000
11 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000
12 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000
13 2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 -2.00000

View File

@ -0,0 +1,60 @@
Group C24h
n 26
Irred Operation
1 Ag E
2 Bg C24
3 E1g C12
4 E2g C8
5 E3g C6
6 E4g C24^5
7 E5g C4
8 E6g C24^7
9 E7g C3
10 E8g C8^3
11 E9g C12^5
12 E10g C24^11
13 E11g C2
14 Au i
15 Bu S24
16 E1u S12
17 E2u S8
18 E3u S6
19 E4u S24^5
20 E5u S4
21 E6u S24^7
22 E7u S3
23 E8u S8^3
24 E9u S12^5
25 E10u S24^11
26 E11u sh
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
3 2.00000 1.93185 1.73205 1.41421 1.00000 0.51764 0.00000 -0.51764 -1.00000 -1.41421 -1.73205 -1.93185 -2.00000 2.00000 -1.93185 -1.73205 -1.41421 -1.00000 -0.51764 0.00000 0.51764 1.00000 1.41421 1.73205 1.93185 -2.00000
4 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000
5 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 -2.00000
6 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000
7 2.00000 0.51764 -1.73205 -1.41421 1.00000 1.93185 0.00000 -1.93185 -1.00000 1.41421 1.73205 -0.51764 -2.00000 2.00000 -0.51764 1.73205 1.41421 -1.00000 -1.93185 0.00000 1.93185 1.00000 -1.41421 -1.73205 0.51764 -2.00000
8 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000
9 2.00000 -0.51764 -1.73205 1.41421 1.00000 -1.93185 0.00000 1.93185 -1.00000 -1.41421 1.73205 0.51764 -2.00000 2.00000 0.51764 1.73205 -1.41421 -1.00000 1.93185 0.00000 -1.93185 1.00000 1.41421 -1.73205 -0.51764 -2.00000
10 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000
11 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 -2.00000
12 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000
13 2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 -2.00000 2.00000 1.93185 -1.73205 1.41421 -1.00000 0.51764 0.00000 -0.51764 1.00000 -1.41421 1.73205 -1.93185 -2.00000
14 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
15 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
16 2.00000 1.93185 1.73205 1.41421 1.00000 0.51764 0.00000 -0.51764 -1.00000 -1.41421 -1.73205 -1.93185 -2.00000 -2.00000 1.93185 1.73205 1.41421 1.00000 0.51764 0.00000 -0.51764 -1.00000 -1.41421 -1.73205 -1.93185 2.00000
17 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000
18 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 2.00000
19 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000
20 2.00000 0.51764 -1.73205 -1.41421 1.00000 1.93185 0.00000 -1.93185 -1.00000 1.41421 1.73205 -0.51764 -2.00000 -2.00000 0.51764 -1.73205 -1.41421 1.00000 1.93185 0.00000 -1.93185 -1.00000 1.41421 1.73205 -0.51764 2.00000
21 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000
22 2.00000 -0.51764 -1.73205 1.41421 1.00000 -1.93185 0.00000 1.93185 -1.00000 -1.41421 1.73205 0.51764 -2.00000 -2.00000 -0.51764 -1.73205 1.41421 1.00000 -1.93185 0.00000 1.93185 -1.00000 -1.41421 1.73205 0.51764 2.00000
23 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000
24 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 -2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 2.00000
25 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000
26 2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 -2.00000 -2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 2.00000

View File

@ -0,0 +1,38 @@
Group C24v
n 15
Irred Operation
1 A1 E
2 A2 C24
3 B1 C12
4 B2 C8
5 E1 C6
6 E2 C24^5
7 E3 C4
8 E4 C24^7
9 E5 C3
10 E6 C8^3
11 E7 C12^5
12 E8 C24^11
13 E9 C2
14 E10 sv
15 E11 sd
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000
3 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000
4 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
5 2.00000 1.93185 1.73205 1.41421 1.00000 0.51764 0.00000 -0.51764 -1.00000 -1.41421 -1.73205 -1.93185 -2.00000 0.00000 0.00000
6 2.00000 1.73205 1.00000 0.00000 -1.00000 -1.73205 -2.00000 -1.73205 -1.00000 0.00000 1.00000 1.73205 2.00000 0.00000 0.00000
7 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 0.00000 0.00000
8 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 0.00000 0.00000
9 2.00000 0.51764 -1.73205 -1.41421 1.00000 1.93185 0.00000 -1.93185 -1.00000 1.41421 1.73205 -0.51764 -2.00000 0.00000 0.00000
10 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 0.00000
11 2.00000 -0.51764 -1.73205 1.41421 1.00000 -1.93185 0.00000 1.93185 -1.00000 -1.41421 1.73205 0.51764 -2.00000 0.00000 0.00000
12 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 0.00000 0.00000
13 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 0.00000 0.00000
14 2.00000 -1.73205 1.00000 0.00000 -1.00000 1.73205 -2.00000 1.73205 -1.00000 0.00000 1.00000 -1.73205 2.00000 0.00000 0.00000
15 2.00000 -1.93185 1.73205 -1.41421 1.00000 -0.51764 0.00000 0.51764 -1.00000 1.41421 -1.73205 1.93185 -2.00000 0.00000 0.00000

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@ -0,0 +1,34 @@
Group C25
n 13
Irred Operation
1 A E
2 E1 C25
3 E2 C25^2
4 E3 C25^3
5 E4 C25^4
6 E5 C5
7 E6 C25^6
8 E7 C25^7
9 E8 C25^8
10 E9 C25^9
11 E10 C5^2
12 E11 C25^11
13 E12 C25^12
Table
1 2 3 4 5 6 7 8 9 10 11 12 13
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423
3 2.00000 1.75261 1.07165 0.12558 -0.85156 -1.61803 -1.98423 -1.85955 -1.27485 -0.37476 0.61803 1.45794 1.93717
4 2.00000 1.45794 0.12558 -1.27485 -1.98423 -1.61803 -0.37476 1.07165 1.93717 1.75261 0.61803 -0.85156 -1.85955
5 2.00000 1.07165 -0.85156 -1.98423 -1.27485 0.61803 1.93717 1.45794 -0.37476 -1.85955 -1.61803 0.12558 1.75261
6 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803
7 2.00000 0.12558 -1.98423 -0.37476 1.93717 0.61803 -1.85955 -0.85156 1.75261 1.07165 -1.61803 -1.27485 1.45794
8 2.00000 -0.37476 -1.85955 1.07165 1.45794 -1.61803 -0.85156 1.93717 0.12558 -1.98423 0.61803 1.75261 -1.27485
9 2.00000 -0.85156 -1.27485 1.93717 -0.37476 -1.61803 1.75261 0.12558 -1.85955 1.45794 0.61803 -1.98423 1.07165
10 2.00000 -1.27485 -0.37476 1.75261 -1.85955 0.61803 1.07165 -1.98423 1.45794 0.12558 -1.61803 1.93717 -0.85156
11 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803
12 2.00000 -1.85955 1.45794 -0.85156 0.12558 0.61803 -1.27485 1.75261 -1.98423 1.93717 -1.61803 1.07165 -0.37476
13 2.00000 -1.98423 1.93717 -1.85955 1.75261 -1.61803 1.45794 -1.27485 1.07165 -0.85156 0.61803 -0.37476 0.12558

View File

@ -0,0 +1,60 @@
Group C25h
n 26
Irred Operation
1 A' E
2 A" C25
3 E1' C25^2
4 E1" C25^3
5 E2' C25^4
6 E2" C5
7 E3' C25^6
8 E3" C25^7
9 E4' C25^8
10 E4" C25^9
11 E5' C5^2
12 E5" C25^11
13 E6' C25^12
14 E6" sh
15 E7' S25
16 E7" S25^3
17 E8' S5
18 E8" S25^7
19 E9' S25^9
20 E9" S25^11
21 E10' S25^13
22 E10" S5^3
23 E11' S25^17
24 E11" S25^19
25 E12' S25^21
26 E12" S25^23
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
3 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 2.00000 1.93717 1.45794 0.61803 -0.37476 -1.27485 -1.85955 -1.98423 -1.61803 -0.85156 0.12558 1.07165 1.75261
4 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 -2.00000 -1.93717 -1.45794 -0.61803 0.37476 1.27485 1.85955 1.98423 1.61803 0.85156 -0.12558 -1.07165 -1.75261
5 2.00000 1.75261 1.07165 0.12558 -0.85156 -1.61803 -1.98423 -1.85955 -1.27485 -0.37476 0.61803 1.45794 1.93717 2.00000 1.75261 0.12558 -1.61803 -1.85955 -0.37476 1.45794 1.93717 0.61803 -1.27485 -1.98423 -0.85156 1.07165
6 2.00000 1.75261 1.07165 0.12558 -0.85156 -1.61803 -1.98423 -1.85955 -1.27485 -0.37476 0.61803 1.45794 1.93717 -2.00000 -1.75261 -0.12558 1.61803 1.85955 0.37476 -1.45794 -1.93717 -0.61803 1.27485 1.98423 0.85156 -1.07165
7 2.00000 1.45794 0.12558 -1.27485 -1.98423 -1.61803 -0.37476 1.07165 1.93717 1.75261 0.61803 -0.85156 -1.85955 2.00000 1.45794 -1.27485 -1.61803 1.07165 1.75261 -0.85156 -1.85955 0.61803 1.93717 -0.37476 -1.98423 0.12558
8 2.00000 1.45794 0.12558 -1.27485 -1.98423 -1.61803 -0.37476 1.07165 1.93717 1.75261 0.61803 -0.85156 -1.85955 -2.00000 -1.45794 1.27485 1.61803 -1.07165 -1.75261 0.85156 1.85955 -0.61803 -1.93717 0.37476 1.98423 -0.12558
9 2.00000 1.07165 -0.85156 -1.98423 -1.27485 0.61803 1.93717 1.45794 -0.37476 -1.85955 -1.61803 0.12558 1.75261 2.00000 1.07165 -1.98423 0.61803 1.45794 -1.85955 0.12558 1.75261 -1.61803 -0.37476 1.93717 -1.27485 -0.85156
10 2.00000 1.07165 -0.85156 -1.98423 -1.27485 0.61803 1.93717 1.45794 -0.37476 -1.85955 -1.61803 0.12558 1.75261 -2.00000 -1.07165 1.98423 -0.61803 -1.45794 1.85955 -0.12558 -1.75261 1.61803 0.37476 -1.93717 1.27485 0.85156
11 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 2.00000 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803
12 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -2.00000 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803
13 2.00000 0.12558 -1.98423 -0.37476 1.93717 0.61803 -1.85955 -0.85156 1.75261 1.07165 -1.61803 -1.27485 1.45794 2.00000 0.12558 -0.37476 0.61803 -0.85156 1.07165 -1.27485 1.45794 -1.61803 1.75261 -1.85955 1.93717 -1.98423
14 2.00000 0.12558 -1.98423 -0.37476 1.93717 0.61803 -1.85955 -0.85156 1.75261 1.07165 -1.61803 -1.27485 1.45794 -2.00000 -0.12558 0.37476 -0.61803 0.85156 -1.07165 1.27485 -1.45794 1.61803 -1.75261 1.85955 -1.93717 1.98423
15 2.00000 -0.37476 -1.85955 1.07165 1.45794 -1.61803 -0.85156 1.93717 0.12558 -1.98423 0.61803 1.75261 -1.27485 2.00000 -0.37476 1.07165 -1.61803 1.93717 -1.98423 1.75261 -1.27485 0.61803 0.12558 -0.85156 1.45794 -1.85955
16 2.00000 -0.37476 -1.85955 1.07165 1.45794 -1.61803 -0.85156 1.93717 0.12558 -1.98423 0.61803 1.75261 -1.27485 -2.00000 0.37476 -1.07165 1.61803 -1.93717 1.98423 -1.75261 1.27485 -0.61803 -0.12558 0.85156 -1.45794 1.85955
17 2.00000 -0.85156 -1.27485 1.93717 -0.37476 -1.61803 1.75261 0.12558 -1.85955 1.45794 0.61803 -1.98423 1.07165 2.00000 -0.85156 1.93717 -1.61803 0.12558 1.45794 -1.98423 1.07165 0.61803 -1.85955 1.75261 -0.37476 -1.27485
18 2.00000 -0.85156 -1.27485 1.93717 -0.37476 -1.61803 1.75261 0.12558 -1.85955 1.45794 0.61803 -1.98423 1.07165 -2.00000 0.85156 -1.93717 1.61803 -0.12558 -1.45794 1.98423 -1.07165 -0.61803 1.85955 -1.75261 0.37476 1.27485
19 2.00000 -1.27485 -0.37476 1.75261 -1.85955 0.61803 1.07165 -1.98423 1.45794 0.12558 -1.61803 1.93717 -0.85156 2.00000 -1.27485 1.75261 0.61803 -1.98423 0.12558 1.93717 -0.85156 -1.61803 1.45794 1.07165 -1.85955 -0.37476
20 2.00000 -1.27485 -0.37476 1.75261 -1.85955 0.61803 1.07165 -1.98423 1.45794 0.12558 -1.61803 1.93717 -0.85156 -2.00000 1.27485 -1.75261 -0.61803 1.98423 -0.12558 -1.93717 0.85156 1.61803 -1.45794 -1.07165 1.85955 0.37476
21 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 2.00000 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803
22 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 -2.00000 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803
23 2.00000 -1.85955 1.45794 -0.85156 0.12558 0.61803 -1.27485 1.75261 -1.98423 1.93717 -1.61803 1.07165 -0.37476 2.00000 -1.85955 -0.85156 0.61803 1.75261 1.93717 1.07165 -0.37476 -1.61803 -1.98423 -1.27485 0.12558 1.45794
24 2.00000 -1.85955 1.45794 -0.85156 0.12558 0.61803 -1.27485 1.75261 -1.98423 1.93717 -1.61803 1.07165 -0.37476 -2.00000 1.85955 0.85156 -0.61803 -1.75261 -1.93717 -1.07165 0.37476 1.61803 1.98423 1.27485 -0.12558 -1.45794
25 2.00000 -1.98423 1.93717 -1.85955 1.75261 -1.61803 1.45794 -1.27485 1.07165 -0.85156 0.61803 -0.37476 0.12558 2.00000 -1.98423 -1.85955 -1.61803 -1.27485 -0.85156 -0.37476 0.12558 0.61803 1.07165 1.45794 1.75261 1.93717
26 2.00000 -1.98423 1.93717 -1.85955 1.75261 -1.61803 1.45794 -1.27485 1.07165 -0.85156 0.61803 -0.37476 0.12558 -2.00000 1.98423 1.85955 1.61803 1.27485 0.85156 0.37476 -0.12558 -0.61803 -1.07165 -1.45794 -1.75261 -1.93717

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@ -0,0 +1,36 @@
Group C25v
n 14
Irred Operation
1 A1 E
2 A2 C25
3 E1 C25^2
4 E2 C25^3
5 E3 C25^4
6 E4 C5
7 E5 C25^6
8 E6 C25^7
9 E7 C25^8
10 E8 C25^9
11 E9 C5^2
12 E10 C25^11
13 E11 C25^12
14 E12 sv
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000
3 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 0.00000
4 2.00000 1.75261 1.07165 0.12558 -0.85156 -1.61803 -1.98423 -1.85955 -1.27485 -0.37476 0.61803 1.45794 1.93717 0.00000
5 2.00000 1.45794 0.12558 -1.27485 -1.98423 -1.61803 -0.37476 1.07165 1.93717 1.75261 0.61803 -0.85156 -1.85955 0.00000
6 2.00000 1.07165 -0.85156 -1.98423 -1.27485 0.61803 1.93717 1.45794 -0.37476 -1.85955 -1.61803 0.12558 1.75261 0.00000
7 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 0.00000
8 2.00000 0.12558 -1.98423 -0.37476 1.93717 0.61803 -1.85955 -0.85156 1.75261 1.07165 -1.61803 -1.27485 1.45794 0.00000
9 2.00000 -0.37476 -1.85955 1.07165 1.45794 -1.61803 -0.85156 1.93717 0.12558 -1.98423 0.61803 1.75261 -1.27485 0.00000
10 2.00000 -0.85156 -1.27485 1.93717 -0.37476 -1.61803 1.75261 0.12558 -1.85955 1.45794 0.61803 -1.98423 1.07165 0.00000
11 2.00000 -1.27485 -0.37476 1.75261 -1.85955 0.61803 1.07165 -1.98423 1.45794 0.12558 -1.61803 1.93717 -0.85156 0.00000
12 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.00000
13 2.00000 -1.85955 1.45794 -0.85156 0.12558 0.61803 -1.27485 1.75261 -1.98423 1.93717 -1.61803 1.07165 -0.37476 0.00000
14 2.00000 -1.98423 1.93717 -1.85955 1.75261 -1.61803 1.45794 -1.27485 1.07165 -0.85156 0.61803 -0.37476 0.12558 0.00000

View File

@ -0,0 +1,36 @@
Group C26
n 14
Irred Operation
1 A E
2 B C26
3 E1 C13
4 E2 C26^3
5 E3 C13^2
6 E4 C26^5
7 E5 C13^3
8 E6 C26^7
9 E7 C13^4
10 E8 C26^9
11 E9 C13^5
12 E10 C26^11
13 E11 C13^6
14 E12 C2
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
3 2.00000 1.94188 1.77091 1.49702 1.13613 0.70921 0.24107 -0.24107 -0.70921 -1.13613 -1.49702 -1.77091 -1.94188 -2.00000
4 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000
5 2.00000 1.49702 0.24107 -1.13613 -1.94188 -1.77091 -0.70921 0.70921 1.77091 1.94188 1.13613 -0.24107 -1.49702 -2.00000
6 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000
7 2.00000 0.70921 -1.49702 -1.77091 0.24107 1.94188 1.13613 -1.13613 -1.94188 -0.24107 1.77091 1.49702 -0.70921 -2.00000
8 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000
9 2.00000 -0.24107 -1.94188 0.70921 1.77091 -1.13613 -1.49702 1.49702 1.13613 -1.77091 -0.70921 1.94188 0.24107 -2.00000
10 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000
11 2.00000 -1.13613 -0.70921 1.94188 -1.49702 -0.24107 1.77091 -1.77091 0.24107 1.49702 -1.94188 0.70921 1.13613 -2.00000
12 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000
13 2.00000 -1.77091 1.13613 -0.24107 -0.70921 1.49702 -1.94188 1.94188 -1.49702 0.70921 0.24107 -1.13613 1.77091 -2.00000
14 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000

View File

@ -0,0 +1,64 @@
Group C26h
n 28
Irred Operation
1 Ag E
2 Bg C26
3 E1g C13
4 E2g C26^3
5 E3g C13^2
6 E4g C26^5
7 E5g C13^3
8 E6g C26^7
9 E7g C13^4
10 E8g C26^9
11 E9g C13^5
12 E10g C26^11
13 E11g C13^6
14 E12g C2
15 Au i
16 Bu S26
17 E1u S13
18 E2u S26^3
19 E3u S13^2
20 E4u S26^5
21 E5u S13^3
22 E6u S26^7
23 E7u S13^4
24 E8u S26^9
25 E9u S13^5
26 E10u S26^11
27 E11u S13^6
28 E12u sh
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000
3 2.00000 1.94188 1.77091 1.49702 1.13613 0.70921 0.24107 -0.24107 -0.70921 -1.13613 -1.49702 -1.77091 -1.94188 -2.00000 2.00000 -1.94188 -1.77091 -1.49702 -1.13613 -0.70921 -0.24107 0.24107 0.70921 1.13613 1.49702 1.77091 1.94188 -2.00000
4 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000
5 2.00000 1.49702 0.24107 -1.13613 -1.94188 -1.77091 -0.70921 0.70921 1.77091 1.94188 1.13613 -0.24107 -1.49702 -2.00000 2.00000 -1.49702 -0.24107 1.13613 1.94188 1.77091 0.70921 -0.70921 -1.77091 -1.94188 -1.13613 0.24107 1.49702 -2.00000
6 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000
7 2.00000 0.70921 -1.49702 -1.77091 0.24107 1.94188 1.13613 -1.13613 -1.94188 -0.24107 1.77091 1.49702 -0.70921 -2.00000 2.00000 -0.70921 1.49702 1.77091 -0.24107 -1.94188 -1.13613 1.13613 1.94188 0.24107 -1.77091 -1.49702 0.70921 -2.00000
8 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000
9 2.00000 -0.24107 -1.94188 0.70921 1.77091 -1.13613 -1.49702 1.49702 1.13613 -1.77091 -0.70921 1.94188 0.24107 -2.00000 2.00000 0.24107 1.94188 -0.70921 -1.77091 1.13613 1.49702 -1.49702 -1.13613 1.77091 0.70921 -1.94188 -0.24107 -2.00000
10 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000
11 2.00000 -1.13613 -0.70921 1.94188 -1.49702 -0.24107 1.77091 -1.77091 0.24107 1.49702 -1.94188 0.70921 1.13613 -2.00000 2.00000 1.13613 0.70921 -1.94188 1.49702 0.24107 -1.77091 1.77091 -0.24107 -1.49702 1.94188 -0.70921 -1.13613 -2.00000
12 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000
13 2.00000 -1.77091 1.13613 -0.24107 -0.70921 1.49702 -1.94188 1.94188 -1.49702 0.70921 0.24107 -1.13613 1.77091 -2.00000 2.00000 1.77091 -1.13613 0.24107 0.70921 -1.49702 1.94188 -1.94188 1.49702 -0.70921 -0.24107 1.13613 -1.77091 -2.00000
14 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000
15 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
16 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000
17 2.00000 1.94188 1.77091 1.49702 1.13613 0.70921 0.24107 -0.24107 -0.70921 -1.13613 -1.49702 -1.77091 -1.94188 -2.00000 -2.00000 1.94188 1.77091 1.49702 1.13613 0.70921 0.24107 -0.24107 -0.70921 -1.13613 -1.49702 -1.77091 -1.94188 2.00000
18 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 -2.00000 -1.77091 -1.13613 -0.24107 0.70921 1.49702 1.94188 1.94188 1.49702 0.70921 -0.24107 -1.13613 -1.77091 -2.00000
19 2.00000 1.49702 0.24107 -1.13613 -1.94188 -1.77091 -0.70921 0.70921 1.77091 1.94188 1.13613 -0.24107 -1.49702 -2.00000 -2.00000 1.49702 0.24107 -1.13613 -1.94188 -1.77091 -0.70921 0.70921 1.77091 1.94188 1.13613 -0.24107 -1.49702 2.00000
20 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 -2.00000 -1.13613 0.70921 1.94188 1.49702 -0.24107 -1.77091 -1.77091 -0.24107 1.49702 1.94188 0.70921 -1.13613 -2.00000
21 2.00000 0.70921 -1.49702 -1.77091 0.24107 1.94188 1.13613 -1.13613 -1.94188 -0.24107 1.77091 1.49702 -0.70921 -2.00000 -2.00000 0.70921 -1.49702 -1.77091 0.24107 1.94188 1.13613 -1.13613 -1.94188 -0.24107 1.77091 1.49702 -0.70921 2.00000
22 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 -2.00000 -0.24107 1.94188 0.70921 -1.77091 -1.13613 1.49702 1.49702 -1.13613 -1.77091 0.70921 1.94188 -0.24107 -2.00000
23 2.00000 -0.24107 -1.94188 0.70921 1.77091 -1.13613 -1.49702 1.49702 1.13613 -1.77091 -0.70921 1.94188 0.24107 -2.00000 -2.00000 -0.24107 -1.94188 0.70921 1.77091 -1.13613 -1.49702 1.49702 1.13613 -1.77091 -0.70921 1.94188 0.24107 2.00000
24 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 -2.00000 0.70921 1.49702 -1.77091 -0.24107 1.94188 -1.13613 -1.13613 1.94188 -0.24107 -1.77091 1.49702 0.70921 -2.00000
25 2.00000 -1.13613 -0.70921 1.94188 -1.49702 -0.24107 1.77091 -1.77091 0.24107 1.49702 -1.94188 0.70921 1.13613 -2.00000 -2.00000 -1.13613 -0.70921 1.94188 -1.49702 -0.24107 1.77091 -1.77091 0.24107 1.49702 -1.94188 0.70921 1.13613 2.00000
26 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 -2.00000 1.49702 -0.24107 -1.13613 1.94188 -1.77091 0.70921 0.70921 -1.77091 1.94188 -1.13613 -0.24107 1.49702 -2.00000
27 2.00000 -1.77091 1.13613 -0.24107 -0.70921 1.49702 -1.94188 1.94188 -1.49702 0.70921 0.24107 -1.13613 1.77091 -2.00000 -2.00000 -1.77091 1.13613 -0.24107 -0.70921 1.49702 -1.94188 1.94188 -1.49702 0.70921 0.24107 -1.13613 1.77091 2.00000
28 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 -2.00000 1.94188 -1.77091 1.49702 -1.13613 0.70921 -0.24107 -0.24107 0.70921 -1.13613 1.49702 -1.77091 1.94188 -2.00000

View File

@ -0,0 +1,40 @@
Group C26v
n 16
Irred Operation
1 A1 E
2 A2 C26
3 B1 C13
4 B2 C26^3
5 E1 C13^2
6 E2 C26^5
7 E3 C13^3
8 E4 C26^7
9 E5 C13^4
10 E6 C26^9
11 E7 C13^5
12 E8 C26^11
13 E9 C13^6
14 E10 C2
15 E11 sv
16 E12 sd
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000
3 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
4 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 1.00000
5 2.00000 1.94188 1.77091 1.49702 1.13613 0.70921 0.24107 -0.24107 -0.70921 -1.13613 -1.49702 -1.77091 -1.94188 -2.00000 0.00000 0.00000
6 2.00000 1.77091 1.13613 0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921 0.24107 1.13613 1.77091 2.00000 0.00000 0.00000
7 2.00000 1.49702 0.24107 -1.13613 -1.94188 -1.77091 -0.70921 0.70921 1.77091 1.94188 1.13613 -0.24107 -1.49702 -2.00000 0.00000 0.00000
8 2.00000 1.13613 -0.70921 -1.94188 -1.49702 0.24107 1.77091 1.77091 0.24107 -1.49702 -1.94188 -0.70921 1.13613 2.00000 0.00000 0.00000
9 2.00000 0.70921 -1.49702 -1.77091 0.24107 1.94188 1.13613 -1.13613 -1.94188 -0.24107 1.77091 1.49702 -0.70921 -2.00000 0.00000 0.00000
10 2.00000 0.24107 -1.94188 -0.70921 1.77091 1.13613 -1.49702 -1.49702 1.13613 1.77091 -0.70921 -1.94188 0.24107 2.00000 0.00000 0.00000
11 2.00000 -0.24107 -1.94188 0.70921 1.77091 -1.13613 -1.49702 1.49702 1.13613 -1.77091 -0.70921 1.94188 0.24107 -2.00000 0.00000 0.00000
12 2.00000 -0.70921 -1.49702 1.77091 0.24107 -1.94188 1.13613 1.13613 -1.94188 0.24107 1.77091 -1.49702 -0.70921 2.00000 0.00000 0.00000
13 2.00000 -1.13613 -0.70921 1.94188 -1.49702 -0.24107 1.77091 -1.77091 0.24107 1.49702 -1.94188 0.70921 1.13613 -2.00000 0.00000 0.00000
14 2.00000 -1.49702 0.24107 1.13613 -1.94188 1.77091 -0.70921 -0.70921 1.77091 -1.94188 1.13613 0.24107 -1.49702 2.00000 0.00000 0.00000
15 2.00000 -1.77091 1.13613 -0.24107 -0.70921 1.49702 -1.94188 1.94188 -1.49702 0.70921 0.24107 -1.13613 1.77091 -2.00000 0.00000 0.00000
16 2.00000 -1.94188 1.77091 -1.49702 1.13613 -0.70921 0.24107 0.24107 -0.70921 1.13613 -1.49702 1.77091 -1.94188 2.00000 0.00000 0.00000

View File

@ -0,0 +1,36 @@
Group C27
n 14
Irred Operation
1 A E
2 E1 C27
3 E2 C27^2
4 E3 C9
5 E4 C27^4
6 E5 C27^5
7 E6 C9^2
8 E7 C27^7
9 E8 C27^8
10 E9 C3
11 E10 C27^10
12 E11 C27^11
13 E12 C9^4
14 E13 C27^13
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 2.00000 1.94609 1.78727 1.53209 1.19432 0.79216 0.34730 -0.11629 -0.57361 -1.00000 -1.37248 -1.67098 -1.87939 -1.98648
3 2.00000 1.78727 1.19432 0.34730 -0.57361 -1.37248 -1.87939 -1.98648 -1.67098 -1.00000 -0.11629 0.79216 1.53209 1.94609
4 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939
5 2.00000 1.19432 -0.57361 -1.87939 -1.67098 -0.11629 1.53209 1.94609 0.79216 -1.00000 -1.98648 -1.37248 0.34730 1.78727
6 2.00000 0.79216 -1.37248 -1.87939 -0.11629 1.78727 1.53209 -0.57361 -1.98648 -1.00000 1.19432 1.94609 0.34730 -1.67098
7 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209
8 2.00000 -0.11629 -1.98648 0.34730 1.94609 -0.57361 -1.87939 0.79216 1.78727 -1.00000 -1.67098 1.19432 1.53209 -1.37248
9 2.00000 -0.57361 -1.67098 1.53209 0.79216 -1.98648 0.34730 1.78727 -1.37248 -1.00000 1.94609 -0.11629 -1.87939 1.19432
10 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000
11 2.00000 -1.37248 -0.11629 1.53209 -1.98648 1.19432 0.34730 -1.67098 1.94609 -1.00000 -0.57361 1.78727 -1.87939 0.79216
12 2.00000 -1.67098 0.79216 0.34730 -1.37248 1.94609 -1.87939 1.19432 -0.11629 -1.00000 1.78727 -1.98648 1.53209 -0.57361
13 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730
14 2.00000 -1.98648 1.94609 -1.87939 1.78727 -1.67098 1.53209 -1.37248 1.19432 -1.00000 0.79216 -0.57361 0.34730 -0.11629

View File

@ -0,0 +1,64 @@
Group C27h
n 28
Irred Operation
1 A' E
2 A" C27
3 E1' C27^2
4 E1" C9
5 E2' C27^4
6 E2" C27^5
7 E3' C9^2
8 E3" C27^7
9 E4' C27^8
10 E4" C3
11 E5' C27^10
12 E5" C27^11
13 E6' C9^4
14 E6" C27^13
15 E7' sh
16 E7" S27
17 E8' S9
18 E8" S27^5
19 E9' S27^7
20 E9" S3
21 E10' S27^11
22 E10" S27^13
23 E11' S9^5
24 E11" S27^17
25 E12' S27^19
26 E12" S9^7
27 E13' S27^23
28 E13" S27^25
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
3 2.00000 1.94609 1.78727 1.53209 1.19432 0.79216 0.34730 -0.11629 -0.57361 -1.00000 -1.37248 -1.67098 -1.87939 -1.98648 2.00000 1.94609 1.53209 0.79216 -0.11629 -1.00000 -1.67098 -1.98648 -1.87939 -1.37248 -0.57361 0.34730 1.19432 1.78727
4 2.00000 1.94609 1.78727 1.53209 1.19432 0.79216 0.34730 -0.11629 -0.57361 -1.00000 -1.37248 -1.67098 -1.87939 -1.98648 -2.00000 -1.94609 -1.53209 -0.79216 0.11629 1.00000 1.67098 1.98648 1.87939 1.37248 0.57361 -0.34730 -1.19432 -1.78727
5 2.00000 1.78727 1.19432 0.34730 -0.57361 -1.37248 -1.87939 -1.98648 -1.67098 -1.00000 -0.11629 0.79216 1.53209 1.94609 2.00000 1.78727 0.34730 -1.37248 -1.98648 -1.00000 0.79216 1.94609 1.53209 -0.11629 -1.67098 -1.87939 -0.57361 1.19432
6 2.00000 1.78727 1.19432 0.34730 -0.57361 -1.37248 -1.87939 -1.98648 -1.67098 -1.00000 -0.11629 0.79216 1.53209 1.94609 -2.00000 -1.78727 -0.34730 1.37248 1.98648 1.00000 -0.79216 -1.94609 -1.53209 0.11629 1.67098 1.87939 0.57361 -1.19432
7 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 2.00000 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730
8 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -2.00000 -1.53209 1.00000 1.87939 -0.34730 -2.00000 -0.34730 1.87939 1.00000 -1.53209 -1.53209 1.00000 1.87939 -0.34730
9 2.00000 1.19432 -0.57361 -1.87939 -1.67098 -0.11629 1.53209 1.94609 0.79216 -1.00000 -1.98648 -1.37248 0.34730 1.78727 2.00000 1.19432 -1.87939 -0.11629 1.94609 -1.00000 -1.37248 1.78727 0.34730 -1.98648 0.79216 1.53209 -1.67098 -0.57361
10 2.00000 1.19432 -0.57361 -1.87939 -1.67098 -0.11629 1.53209 1.94609 0.79216 -1.00000 -1.98648 -1.37248 0.34730 1.78727 -2.00000 -1.19432 1.87939 0.11629 -1.94609 1.00000 1.37248 -1.78727 -0.34730 1.98648 -0.79216 -1.53209 1.67098 0.57361
11 2.00000 0.79216 -1.37248 -1.87939 -0.11629 1.78727 1.53209 -0.57361 -1.98648 -1.00000 1.19432 1.94609 0.34730 -1.67098 2.00000 0.79216 -1.87939 1.78727 -0.57361 -1.00000 1.94609 -1.67098 0.34730 1.19432 -1.98648 1.53209 -0.11629 -1.37248
12 2.00000 0.79216 -1.37248 -1.87939 -0.11629 1.78727 1.53209 -0.57361 -1.98648 -1.00000 1.19432 1.94609 0.34730 -1.67098 -2.00000 -0.79216 1.87939 -1.78727 0.57361 1.00000 -1.94609 1.67098 -0.34730 -1.19432 1.98648 -1.53209 0.11629 1.37248
13 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 2.00000 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939
14 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 -2.00000 -0.34730 1.00000 -1.53209 1.87939 -2.00000 1.87939 -1.53209 1.00000 -0.34730 -0.34730 1.00000 -1.53209 1.87939
15 2.00000 -0.11629 -1.98648 0.34730 1.94609 -0.57361 -1.87939 0.79216 1.78727 -1.00000 -1.67098 1.19432 1.53209 -1.37248 2.00000 -0.11629 0.34730 -0.57361 0.79216 -1.00000 1.19432 -1.37248 1.53209 -1.67098 1.78727 -1.87939 1.94609 -1.98648
16 2.00000 -0.11629 -1.98648 0.34730 1.94609 -0.57361 -1.87939 0.79216 1.78727 -1.00000 -1.67098 1.19432 1.53209 -1.37248 -2.00000 0.11629 -0.34730 0.57361 -0.79216 1.00000 -1.19432 1.37248 -1.53209 1.67098 -1.78727 1.87939 -1.94609 1.98648
17 2.00000 -0.57361 -1.67098 1.53209 0.79216 -1.98648 0.34730 1.78727 -1.37248 -1.00000 1.94609 -0.11629 -1.87939 1.19432 2.00000 -0.57361 1.53209 -1.98648 1.78727 -1.00000 -0.11629 1.19432 -1.87939 1.94609 -1.37248 0.34730 0.79216 -1.67098
18 2.00000 -0.57361 -1.67098 1.53209 0.79216 -1.98648 0.34730 1.78727 -1.37248 -1.00000 1.94609 -0.11629 -1.87939 1.19432 -2.00000 0.57361 -1.53209 1.98648 -1.78727 1.00000 0.11629 -1.19432 1.87939 -1.94609 1.37248 -0.34730 -0.79216 1.67098
19 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 2.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000
20 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -2.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000
21 2.00000 -1.37248 -0.11629 1.53209 -1.98648 1.19432 0.34730 -1.67098 1.94609 -1.00000 -0.57361 1.78727 -1.87939 0.79216 2.00000 -1.37248 1.53209 1.19432 -1.67098 -1.00000 1.78727 0.79216 -1.87939 -0.57361 1.94609 0.34730 -1.98648 -0.11629
22 2.00000 -1.37248 -0.11629 1.53209 -1.98648 1.19432 0.34730 -1.67098 1.94609 -1.00000 -0.57361 1.78727 -1.87939 0.79216 -2.00000 1.37248 -1.53209 -1.19432 1.67098 1.00000 -1.78727 -0.79216 1.87939 0.57361 -1.94609 -0.34730 1.98648 0.11629
23 2.00000 -1.67098 0.79216 0.34730 -1.37248 1.94609 -1.87939 1.19432 -0.11629 -1.00000 1.78727 -1.98648 1.53209 -0.57361 2.00000 -1.67098 0.34730 1.94609 1.19432 -1.00000 -1.98648 -0.57361 1.53209 1.78727 -0.11629 -1.87939 -1.37248 0.79216
24 2.00000 -1.67098 0.79216 0.34730 -1.37248 1.94609 -1.87939 1.19432 -0.11629 -1.00000 1.78727 -1.98648 1.53209 -0.57361 -2.00000 1.67098 -0.34730 -1.94609 -1.19432 1.00000 1.98648 0.57361 -1.53209 -1.78727 0.11629 1.87939 1.37248 -0.79216
25 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 2.00000 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209
26 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 -2.00000 1.87939 1.00000 -0.34730 -1.53209 -2.00000 -1.53209 -0.34730 1.00000 1.87939 1.87939 1.00000 -0.34730 -1.53209
27 2.00000 -1.98648 1.94609 -1.87939 1.78727 -1.67098 1.53209 -1.37248 1.19432 -1.00000 0.79216 -0.57361 0.34730 -0.11629 2.00000 -1.98648 -1.87939 -1.67098 -1.37248 -1.00000 -0.57361 -0.11629 0.34730 0.79216 1.19432 1.53209 1.78727 1.94609
28 2.00000 -1.98648 1.94609 -1.87939 1.78727 -1.67098 1.53209 -1.37248 1.19432 -1.00000 0.79216 -0.57361 0.34730 -0.11629 -2.00000 1.98648 1.87939 1.67098 1.37248 1.00000 0.57361 0.11629 -0.34730 -0.79216 -1.19432 -1.53209 -1.78727 -1.94609

View File

@ -0,0 +1,38 @@
Group C27v
n 15
Irred Operation
1 A1 E
2 A2 C27
3 E1 C27^2
4 E2 C9
5 E3 C27^4
6 E4 C27^5
7 E5 C9^2
8 E6 C27^7
9 E7 C27^8
10 E8 C3
11 E9 C27^10
12 E10 C27^11
13 E11 C9^4
14 E12 C27^13
15 E13 sv
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000
3 2.00000 1.94609 1.78727 1.53209 1.19432 0.79216 0.34730 -0.11629 -0.57361 -1.00000 -1.37248 -1.67098 -1.87939 -1.98648 0.00000
4 2.00000 1.78727 1.19432 0.34730 -0.57361 -1.37248 -1.87939 -1.98648 -1.67098 -1.00000 -0.11629 0.79216 1.53209 1.94609 0.00000
5 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 0.00000
6 2.00000 1.19432 -0.57361 -1.87939 -1.67098 -0.11629 1.53209 1.94609 0.79216 -1.00000 -1.98648 -1.37248 0.34730 1.78727 0.00000
7 2.00000 0.79216 -1.37248 -1.87939 -0.11629 1.78727 1.53209 -0.57361 -1.98648 -1.00000 1.19432 1.94609 0.34730 -1.67098 0.00000
8 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 0.00000
9 2.00000 -0.11629 -1.98648 0.34730 1.94609 -0.57361 -1.87939 0.79216 1.78727 -1.00000 -1.67098 1.19432 1.53209 -1.37248 0.00000
10 2.00000 -0.57361 -1.67098 1.53209 0.79216 -1.98648 0.34730 1.78727 -1.37248 -1.00000 1.94609 -0.11629 -1.87939 1.19432 0.00000
11 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 0.00000
12 2.00000 -1.37248 -0.11629 1.53209 -1.98648 1.19432 0.34730 -1.67098 1.94609 -1.00000 -0.57361 1.78727 -1.87939 0.79216 0.00000
13 2.00000 -1.67098 0.79216 0.34730 -1.37248 1.94609 -1.87939 1.19432 -0.11629 -1.00000 1.78727 -1.98648 1.53209 -0.57361 0.00000
14 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.00000
15 2.00000 -1.98648 1.94609 -1.87939 1.78727 -1.67098 1.53209 -1.37248 1.19432 -1.00000 0.79216 -0.57361 0.34730 -0.11629 0.00000

View File

@ -0,0 +1,38 @@
Group C28
n 15
Irred Operation
1 A E
2 B C28
3 E1 C14
4 E2 C28^3
5 E3 C7
6 E4 C28^5
7 E5 C14^3
8 E6 C4
9 E7 C7^2
10 E8 C28^9
11 E9 C14^5
12 E10 C28^11
13 E11 C7^3
14 E12 C28^13
15 E13 C2
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
3 2.00000 1.94986 1.80194 1.56366 1.24698 0.86777 0.44504 0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000
4 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504 0.44504 1.24698 1.80194 2.00000
5 2.00000 1.56366 0.44504 -0.86777 -1.80194 -1.94986 -1.24698 0.00000 1.24698 1.94986 1.80194 0.86777 -0.44504 -1.56366 -2.00000
6 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000
7 2.00000 0.86777 -1.24698 -1.94986 -0.44504 1.56366 1.80194 0.00000 -1.80194 -1.56366 0.44504 1.94986 1.24698 -0.86777 -2.00000
8 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000 -0.44504 1.80194 1.24698 -1.24698 -1.80194 0.44504 2.00000
9 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000
10 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000
11 2.00000 -0.86777 -1.24698 1.94986 -0.44504 -1.56366 1.80194 0.00000 -1.80194 1.56366 0.44504 -1.94986 1.24698 0.86777 -2.00000
12 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000 1.24698 0.44504 -1.80194 1.80194 -0.44504 -1.24698 2.00000
13 2.00000 -1.56366 0.44504 0.86777 -1.80194 1.94986 -1.24698 0.00000 1.24698 -1.94986 1.80194 -0.86777 -0.44504 1.56366 -2.00000
14 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000
15 2.00000 -1.94986 1.80194 -1.56366 1.24698 -0.86777 0.44504 0.00000 -0.44504 0.86777 -1.24698 1.56366 -1.80194 1.94986 -2.00000

View File

@ -0,0 +1,68 @@
Group C28h
n 30
Irred Operation
1 Ag E
2 Bg C28
3 E1g C14
4 E2g C28^3
5 E3g C7
6 E4g C28^5
7 E5g C14^3
8 E6g C4
9 E7g C7^2
10 E8g C28^9
11 E9g C14^5
12 E10g C28^11
13 E11g C7^3
14 E12g C28^13
15 E13g C2
16 Au i
17 Bu S28
18 E1u S14
19 E2u S28^3
20 E3u S7
21 E4u S28^5
22 E5u S14^3
23 E6u S4
24 E7u S7^2
25 E8u S28^9
26 E9u S14^5
27 E10u S28^11
28 E11u S7^3
29 E12u S28^13
30 E13u sh
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
3 2.00000 1.94986 1.80194 1.56366 1.24698 0.86777 0.44504 0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000 2.00000 -1.94986 -1.80194 -1.56366 -1.24698 -0.86777 -0.44504 0.00000 0.44504 0.86777 1.24698 1.56366 1.80194 1.94986 -2.00000
4 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504 0.44504 1.24698 1.80194 2.00000 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504 0.44504 1.24698 1.80194 2.00000
5 2.00000 1.56366 0.44504 -0.86777 -1.80194 -1.94986 -1.24698 0.00000 1.24698 1.94986 1.80194 0.86777 -0.44504 -1.56366 -2.00000 2.00000 -1.56366 -0.44504 0.86777 1.80194 1.94986 1.24698 0.00000 -1.24698 -1.94986 -1.80194 -0.86777 0.44504 1.56366 -2.00000
6 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000
7 2.00000 0.86777 -1.24698 -1.94986 -0.44504 1.56366 1.80194 0.00000 -1.80194 -1.56366 0.44504 1.94986 1.24698 -0.86777 -2.00000 2.00000 -0.86777 1.24698 1.94986 0.44504 -1.56366 -1.80194 0.00000 1.80194 1.56366 -0.44504 -1.94986 -1.24698 0.86777 -2.00000
8 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000 -0.44504 1.80194 1.24698 -1.24698 -1.80194 0.44504 2.00000 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000 -0.44504 1.80194 1.24698 -1.24698 -1.80194 0.44504 2.00000
9 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 -2.00000
10 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000
11 2.00000 -0.86777 -1.24698 1.94986 -0.44504 -1.56366 1.80194 0.00000 -1.80194 1.56366 0.44504 -1.94986 1.24698 0.86777 -2.00000 2.00000 0.86777 1.24698 -1.94986 0.44504 1.56366 -1.80194 0.00000 1.80194 -1.56366 -0.44504 1.94986 -1.24698 -0.86777 -2.00000
12 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000 1.24698 0.44504 -1.80194 1.80194 -0.44504 -1.24698 2.00000 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000 1.24698 0.44504 -1.80194 1.80194 -0.44504 -1.24698 2.00000
13 2.00000 -1.56366 0.44504 0.86777 -1.80194 1.94986 -1.24698 0.00000 1.24698 -1.94986 1.80194 -0.86777 -0.44504 1.56366 -2.00000 2.00000 1.56366 -0.44504 -0.86777 1.80194 -1.94986 1.24698 0.00000 -1.24698 1.94986 -1.80194 0.86777 0.44504 -1.56366 -2.00000
14 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000
15 2.00000 -1.94986 1.80194 -1.56366 1.24698 -0.86777 0.44504 0.00000 -0.44504 0.86777 -1.24698 1.56366 -1.80194 1.94986 -2.00000 2.00000 1.94986 -1.80194 1.56366 -1.24698 0.86777 -0.44504 0.00000 0.44504 -0.86777 1.24698 -1.56366 1.80194 -1.94986 -2.00000
16 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
17 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
18 2.00000 1.94986 1.80194 1.56366 1.24698 0.86777 0.44504 0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000 -2.00000 1.94986 1.80194 1.56366 1.24698 0.86777 0.44504 0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 2.00000
19 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504 0.44504 1.24698 1.80194 2.00000 -2.00000 -1.80194 -1.24698 -0.44504 0.44504 1.24698 1.80194 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000
20 2.00000 1.56366 0.44504 -0.86777 -1.80194 -1.94986 -1.24698 0.00000 1.24698 1.94986 1.80194 0.86777 -0.44504 -1.56366 -2.00000 -2.00000 1.56366 0.44504 -0.86777 -1.80194 -1.94986 -1.24698 0.00000 1.24698 1.94986 1.80194 0.86777 -0.44504 -1.56366 2.00000
21 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 -2.00000 -1.24698 0.44504 1.80194 1.80194 0.44504 -1.24698 -2.00000 -1.24698 0.44504 1.80194 1.80194 0.44504 -1.24698 -2.00000
22 2.00000 0.86777 -1.24698 -1.94986 -0.44504 1.56366 1.80194 0.00000 -1.80194 -1.56366 0.44504 1.94986 1.24698 -0.86777 -2.00000 -2.00000 0.86777 -1.24698 -1.94986 -0.44504 1.56366 1.80194 0.00000 -1.80194 -1.56366 0.44504 1.94986 1.24698 -0.86777 2.00000
23 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000 -0.44504 1.80194 1.24698 -1.24698 -1.80194 0.44504 2.00000 -2.00000 -0.44504 1.80194 1.24698 -1.24698 -1.80194 0.44504 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000
24 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 -2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 2.00000
25 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -2.00000 0.44504 1.80194 -1.24698 -1.24698 1.80194 0.44504 -2.00000 0.44504 1.80194 -1.24698 -1.24698 1.80194 0.44504 -2.00000
26 2.00000 -0.86777 -1.24698 1.94986 -0.44504 -1.56366 1.80194 0.00000 -1.80194 1.56366 0.44504 -1.94986 1.24698 0.86777 -2.00000 -2.00000 -0.86777 -1.24698 1.94986 -0.44504 -1.56366 1.80194 0.00000 -1.80194 1.56366 0.44504 -1.94986 1.24698 0.86777 2.00000
27 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000 1.24698 0.44504 -1.80194 1.80194 -0.44504 -1.24698 2.00000 -2.00000 1.24698 0.44504 -1.80194 1.80194 -0.44504 -1.24698 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000
28 2.00000 -1.56366 0.44504 0.86777 -1.80194 1.94986 -1.24698 0.00000 1.24698 -1.94986 1.80194 -0.86777 -0.44504 1.56366 -2.00000 -2.00000 -1.56366 0.44504 0.86777 -1.80194 1.94986 -1.24698 0.00000 1.24698 -1.94986 1.80194 -0.86777 -0.44504 1.56366 2.00000
29 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -2.00000 1.80194 -1.24698 0.44504 0.44504 -1.24698 1.80194 -2.00000 1.80194 -1.24698 0.44504 0.44504 -1.24698 1.80194 -2.00000
30 2.00000 -1.94986 1.80194 -1.56366 1.24698 -0.86777 0.44504 0.00000 -0.44504 0.86777 -1.24698 1.56366 -1.80194 1.94986 -2.00000 -2.00000 -1.94986 1.80194 -1.56366 1.24698 -0.86777 0.44504 0.00000 -0.44504 0.86777 -1.24698 1.56366 -1.80194 1.94986 2.00000

View File

@ -0,0 +1,42 @@
Group C28v
n 17
Irred Operation
1 A1 E
2 A2 C28
3 B1 C14
4 B2 C28^3
5 E1 C7
6 E2 C28^5
7 E3 C14^3
8 E4 C4
9 E5 C7^2
10 E6 C28^9
11 E7 C14^5
12 E8 C28^11
13 E9 C7^3
14 E10 C28^13
15 E11 C2
16 E12 sv
17 E13 sd
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000
3 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000
4 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000
5 2.00000 1.94986 1.80194 1.56366 1.24698 0.86777 0.44504 0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000 0.00000 0.00000
6 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504 0.44504 1.24698 1.80194 2.00000 0.00000 0.00000
7 2.00000 1.56366 0.44504 -0.86777 -1.80194 -1.94986 -1.24698 0.00000 1.24698 1.94986 1.80194 0.86777 -0.44504 -1.56366 -2.00000 0.00000 0.00000
8 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 0.00000 0.00000
9 2.00000 0.86777 -1.24698 -1.94986 -0.44504 1.56366 1.80194 0.00000 -1.80194 -1.56366 0.44504 1.94986 1.24698 -0.86777 -2.00000 0.00000 0.00000
10 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000 -0.44504 1.80194 1.24698 -1.24698 -1.80194 0.44504 2.00000 0.00000 0.00000
11 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 0.00000
12 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 0.00000 0.00000
13 2.00000 -0.86777 -1.24698 1.94986 -0.44504 -1.56366 1.80194 0.00000 -1.80194 1.56366 0.44504 -1.94986 1.24698 0.86777 -2.00000 0.00000 0.00000
14 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000 1.24698 0.44504 -1.80194 1.80194 -0.44504 -1.24698 2.00000 0.00000 0.00000
15 2.00000 -1.56366 0.44504 0.86777 -1.80194 1.94986 -1.24698 0.00000 1.24698 -1.94986 1.80194 -0.86777 -0.44504 1.56366 -2.00000 0.00000 0.00000
16 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 0.00000 0.00000
17 2.00000 -1.94986 1.80194 -1.56366 1.24698 -0.86777 0.44504 0.00000 -0.44504 0.86777 -1.24698 1.56366 -1.80194 1.94986 -2.00000 0.00000 0.00000

View File

@ -0,0 +1,38 @@
Group C29
n 15
Irred Operation
1 A E
2 E1 C29
3 E2 C29^2
4 E3 C29^3
5 E4 C29^4
6 E5 C29^5
7 E6 C29^6
8 E7 C29^7
9 E8 C29^8
10 E9 C29^9
11 E10 C29^10
12 E11 C29^11
13 E12 C29^12
14 E13 C29^13
15 E14 C29^14
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 2.00000 1.95324 1.81515 1.59219 1.29477 0.93682 0.53506 0.10828 -0.32356 -0.74028 -1.12237 -1.45199 -1.71371 -1.89531 -1.98828
3 2.00000 1.81515 1.29477 0.53506 -0.32356 -1.12237 -1.71371 -1.98828 -1.89531 -1.45199 -0.74028 0.10828 0.93682 1.59219 1.95324
4 2.00000 1.59219 0.53506 -0.74028 -1.71371 -1.98828 -1.45199 -0.32356 0.93682 1.81515 1.95324 1.29477 0.10828 -1.12237 -1.89531
5 2.00000 1.29477 -0.32356 -1.71371 -1.89531 -0.74028 0.93682 1.95324 1.59219 0.10828 -1.45199 -1.98828 -1.12237 0.53506 1.81515
6 2.00000 0.93682 -1.12237 -1.98828 -0.74028 1.29477 1.95324 0.53506 -1.45199 -1.89531 -0.32356 1.59219 1.81515 0.10828 -1.71371
7 2.00000 0.53506 -1.71371 -1.45199 0.93682 1.95324 0.10828 -1.89531 -1.12237 1.29477 1.81515 -0.32356 -1.98828 -0.74028 1.59219
8 2.00000 0.10828 -1.98828 -0.32356 1.95324 0.53506 -1.89531 -0.74028 1.81515 0.93682 -1.71371 -1.12237 1.59219 1.29477 -1.45199
9 2.00000 -0.32356 -1.89531 0.93682 1.59219 -1.45199 -1.12237 1.81515 0.53506 -1.98828 0.10828 1.95324 -0.74028 -1.71371 1.29477
10 2.00000 -0.74028 -1.45199 1.81515 0.10828 -1.89531 1.29477 0.93682 -1.98828 0.53506 1.59219 -1.71371 -0.32356 1.95324 -1.12237
11 2.00000 -1.12237 -0.74028 1.95324 -1.45199 -0.32356 1.81515 -1.71371 0.10828 1.59219 -1.89531 0.53506 1.29477 -1.98828 0.93682
12 2.00000 -1.45199 0.10828 1.29477 -1.98828 1.59219 -0.32356 -1.12237 1.95324 -1.71371 0.53506 0.93682 -1.89531 1.81515 -0.74028
13 2.00000 -1.71371 0.93682 0.10828 -1.12237 1.81515 -1.98828 1.59219 -0.74028 -0.32356 1.29477 -1.89531 1.95324 -1.45199 0.53506
14 2.00000 -1.89531 1.59219 -1.12237 0.53506 0.10828 -0.74028 1.29477 -1.71371 1.95324 -1.98828 1.81515 -1.45199 0.93682 -0.32356
15 2.00000 -1.98828 1.95324 -1.89531 1.81515 -1.71371 1.59219 -1.45199 1.29477 -1.12237 0.93682 -0.74028 0.53506 -0.32356 0.10828

View File

@ -0,0 +1,68 @@
Group C29h
n 30
Irred Operation
1 A' E
2 A" C29
3 E1' C29^2
4 E1" C29^3
5 E2' C29^4
6 E2" C29^5
7 E3' C29^6
8 E3" C29^7
9 E4' C29^8
10 E4" C29^9
11 E5' C29^10
12 E5" C29^11
13 E6' C29^12
14 E6" C29^13
15 E7' C29^14
16 E7" sh
17 E8' S29
18 E8" S29^3
19 E9' S29^5
20 E9" S29^7
21 E10' S29^9
22 E10" S29^11
23 E11' S29^13
24 E11" S29^15
25 E12' S29^17
26 E12" S29^19
27 E13' S29^21
28 E13" S29^23
29 E14' S29^25
30 E14" S29^27
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
3 2.00000 1.95324 1.81515 1.59219 1.29477 0.93682 0.53506 0.10828 -0.32356 -0.74028 -1.12237 -1.45199 -1.71371 -1.89531 -1.98828 2.00000 1.95324 1.59219 0.93682 0.10828 -0.74028 -1.45199 -1.89531 -1.98828 -1.71371 -1.12237 -0.32356 0.53506 1.29477 1.81515
4 2.00000 1.95324 1.81515 1.59219 1.29477 0.93682 0.53506 0.10828 -0.32356 -0.74028 -1.12237 -1.45199 -1.71371 -1.89531 -1.98828 -2.00000 -1.95324 -1.59219 -0.93682 -0.10828 0.74028 1.45199 1.89531 1.98828 1.71371 1.12237 0.32356 -0.53506 -1.29477 -1.81515
5 2.00000 1.81515 1.29477 0.53506 -0.32356 -1.12237 -1.71371 -1.98828 -1.89531 -1.45199 -0.74028 0.10828 0.93682 1.59219 1.95324 2.00000 1.81515 0.53506 -1.12237 -1.98828 -1.45199 0.10828 1.59219 1.95324 0.93682 -0.74028 -1.89531 -1.71371 -0.32356 1.29477
6 2.00000 1.81515 1.29477 0.53506 -0.32356 -1.12237 -1.71371 -1.98828 -1.89531 -1.45199 -0.74028 0.10828 0.93682 1.59219 1.95324 -2.00000 -1.81515 -0.53506 1.12237 1.98828 1.45199 -0.10828 -1.59219 -1.95324 -0.93682 0.74028 1.89531 1.71371 0.32356 -1.29477
7 2.00000 1.59219 0.53506 -0.74028 -1.71371 -1.98828 -1.45199 -0.32356 0.93682 1.81515 1.95324 1.29477 0.10828 -1.12237 -1.89531 2.00000 1.59219 -0.74028 -1.98828 -0.32356 1.81515 1.29477 -1.12237 -1.89531 0.10828 1.95324 0.93682 -1.45199 -1.71371 0.53506
8 2.00000 1.59219 0.53506 -0.74028 -1.71371 -1.98828 -1.45199 -0.32356 0.93682 1.81515 1.95324 1.29477 0.10828 -1.12237 -1.89531 -2.00000 -1.59219 0.74028 1.98828 0.32356 -1.81515 -1.29477 1.12237 1.89531 -0.10828 -1.95324 -0.93682 1.45199 1.71371 -0.53506
9 2.00000 1.29477 -0.32356 -1.71371 -1.89531 -0.74028 0.93682 1.95324 1.59219 0.10828 -1.45199 -1.98828 -1.12237 0.53506 1.81515 2.00000 1.29477 -1.71371 -0.74028 1.95324 0.10828 -1.98828 0.53506 1.81515 -1.12237 -1.45199 1.59219 0.93682 -1.89531 -0.32356
10 2.00000 1.29477 -0.32356 -1.71371 -1.89531 -0.74028 0.93682 1.95324 1.59219 0.10828 -1.45199 -1.98828 -1.12237 0.53506 1.81515 -2.00000 -1.29477 1.71371 0.74028 -1.95324 -0.10828 1.98828 -0.53506 -1.81515 1.12237 1.45199 -1.59219 -0.93682 1.89531 0.32356
11 2.00000 0.93682 -1.12237 -1.98828 -0.74028 1.29477 1.95324 0.53506 -1.45199 -1.89531 -0.32356 1.59219 1.81515 0.10828 -1.71371 2.00000 0.93682 -1.98828 1.29477 0.53506 -1.89531 1.59219 0.10828 -1.71371 1.81515 -0.32356 -1.45199 1.95324 -0.74028 -1.12237
12 2.00000 0.93682 -1.12237 -1.98828 -0.74028 1.29477 1.95324 0.53506 -1.45199 -1.89531 -0.32356 1.59219 1.81515 0.10828 -1.71371 -2.00000 -0.93682 1.98828 -1.29477 -0.53506 1.89531 -1.59219 -0.10828 1.71371 -1.81515 0.32356 1.45199 -1.95324 0.74028 1.12237
13 2.00000 0.53506 -1.71371 -1.45199 0.93682 1.95324 0.10828 -1.89531 -1.12237 1.29477 1.81515 -0.32356 -1.98828 -0.74028 1.59219 2.00000 0.53506 -1.45199 1.95324 -1.89531 1.29477 -0.32356 -0.74028 1.59219 -1.98828 1.81515 -1.12237 0.10828 0.93682 -1.71371
14 2.00000 0.53506 -1.71371 -1.45199 0.93682 1.95324 0.10828 -1.89531 -1.12237 1.29477 1.81515 -0.32356 -1.98828 -0.74028 1.59219 -2.00000 -0.53506 1.45199 -1.95324 1.89531 -1.29477 0.32356 0.74028 -1.59219 1.98828 -1.81515 1.12237 -0.10828 -0.93682 1.71371
15 2.00000 0.10828 -1.98828 -0.32356 1.95324 0.53506 -1.89531 -0.74028 1.81515 0.93682 -1.71371 -1.12237 1.59219 1.29477 -1.45199 2.00000 0.10828 -0.32356 0.53506 -0.74028 0.93682 -1.12237 1.29477 -1.45199 1.59219 -1.71371 1.81515 -1.89531 1.95324 -1.98828
16 2.00000 0.10828 -1.98828 -0.32356 1.95324 0.53506 -1.89531 -0.74028 1.81515 0.93682 -1.71371 -1.12237 1.59219 1.29477 -1.45199 -2.00000 -0.10828 0.32356 -0.53506 0.74028 -0.93682 1.12237 -1.29477 1.45199 -1.59219 1.71371 -1.81515 1.89531 -1.95324 1.98828
17 2.00000 -0.32356 -1.89531 0.93682 1.59219 -1.45199 -1.12237 1.81515 0.53506 -1.98828 0.10828 1.95324 -0.74028 -1.71371 1.29477 2.00000 -0.32356 0.93682 -1.45199 1.81515 -1.98828 1.95324 -1.71371 1.29477 -0.74028 0.10828 0.53506 -1.12237 1.59219 -1.89531
18 2.00000 -0.32356 -1.89531 0.93682 1.59219 -1.45199 -1.12237 1.81515 0.53506 -1.98828 0.10828 1.95324 -0.74028 -1.71371 1.29477 -2.00000 0.32356 -0.93682 1.45199 -1.81515 1.98828 -1.95324 1.71371 -1.29477 0.74028 -0.10828 -0.53506 1.12237 -1.59219 1.89531
19 2.00000 -0.74028 -1.45199 1.81515 0.10828 -1.89531 1.29477 0.93682 -1.98828 0.53506 1.59219 -1.71371 -0.32356 1.95324 -1.12237 2.00000 -0.74028 1.81515 -1.89531 0.93682 0.53506 -1.71371 1.95324 -1.12237 -0.32356 1.59219 -1.98828 1.29477 0.10828 -1.45199
20 2.00000 -0.74028 -1.45199 1.81515 0.10828 -1.89531 1.29477 0.93682 -1.98828 0.53506 1.59219 -1.71371 -0.32356 1.95324 -1.12237 -2.00000 0.74028 -1.81515 1.89531 -0.93682 -0.53506 1.71371 -1.95324 1.12237 0.32356 -1.59219 1.98828 -1.29477 -0.10828 1.45199
21 2.00000 -1.12237 -0.74028 1.95324 -1.45199 -0.32356 1.81515 -1.71371 0.10828 1.59219 -1.89531 0.53506 1.29477 -1.98828 0.93682 2.00000 -1.12237 1.95324 -0.32356 -1.71371 1.59219 0.53506 -1.98828 0.93682 1.29477 -1.89531 0.10828 1.81515 -1.45199 -0.74028
22 2.00000 -1.12237 -0.74028 1.95324 -1.45199 -0.32356 1.81515 -1.71371 0.10828 1.59219 -1.89531 0.53506 1.29477 -1.98828 0.93682 -2.00000 1.12237 -1.95324 0.32356 1.71371 -1.59219 -0.53506 1.98828 -0.93682 -1.29477 1.89531 -0.10828 -1.81515 1.45199 0.74028
23 2.00000 -1.45199 0.10828 1.29477 -1.98828 1.59219 -0.32356 -1.12237 1.95324 -1.71371 0.53506 0.93682 -1.89531 1.81515 -0.74028 2.00000 -1.45199 1.29477 1.59219 -1.12237 -1.71371 0.93682 1.81515 -0.74028 -1.89531 0.53506 1.95324 -0.32356 -1.98828 0.10828
24 2.00000 -1.45199 0.10828 1.29477 -1.98828 1.59219 -0.32356 -1.12237 1.95324 -1.71371 0.53506 0.93682 -1.89531 1.81515 -0.74028 -2.00000 1.45199 -1.29477 -1.59219 1.12237 1.71371 -0.93682 -1.81515 0.74028 1.89531 -0.53506 -1.95324 0.32356 1.98828 -0.10828
25 2.00000 -1.71371 0.93682 0.10828 -1.12237 1.81515 -1.98828 1.59219 -0.74028 -0.32356 1.29477 -1.89531 1.95324 -1.45199 0.53506 2.00000 -1.71371 0.10828 1.81515 1.59219 -0.32356 -1.89531 -1.45199 0.53506 1.95324 1.29477 -0.74028 -1.98828 -1.12237 0.93682
26 2.00000 -1.71371 0.93682 0.10828 -1.12237 1.81515 -1.98828 1.59219 -0.74028 -0.32356 1.29477 -1.89531 1.95324 -1.45199 0.53506 -2.00000 1.71371 -0.10828 -1.81515 -1.59219 0.32356 1.89531 1.45199 -0.53506 -1.95324 -1.29477 0.74028 1.98828 1.12237 -0.93682
27 2.00000 -1.89531 1.59219 -1.12237 0.53506 0.10828 -0.74028 1.29477 -1.71371 1.95324 -1.98828 1.81515 -1.45199 0.93682 -0.32356 2.00000 -1.89531 -1.12237 0.10828 1.29477 1.95324 1.81515 0.93682 -0.32356 -1.45199 -1.98828 -1.71371 -0.74028 0.53506 1.59219
28 2.00000 -1.89531 1.59219 -1.12237 0.53506 0.10828 -0.74028 1.29477 -1.71371 1.95324 -1.98828 1.81515 -1.45199 0.93682 -0.32356 -2.00000 1.89531 1.12237 -0.10828 -1.29477 -1.95324 -1.81515 -0.93682 0.32356 1.45199 1.98828 1.71371 0.74028 -0.53506 -1.59219
29 2.00000 -1.98828 1.95324 -1.89531 1.81515 -1.71371 1.59219 -1.45199 1.29477 -1.12237 0.93682 -0.74028 0.53506 -0.32356 0.10828 2.00000 -1.98828 -1.89531 -1.71371 -1.45199 -1.12237 -0.74028 -0.32356 0.10828 0.53506 0.93682 1.29477 1.59219 1.81515 1.95324
30 2.00000 -1.98828 1.95324 -1.89531 1.81515 -1.71371 1.59219 -1.45199 1.29477 -1.12237 0.93682 -0.74028 0.53506 -0.32356 0.10828 -2.00000 1.98828 1.89531 1.71371 1.45199 1.12237 0.74028 0.32356 -0.10828 -0.53506 -0.93682 -1.29477 -1.59219 -1.81515 -1.95324

View File

@ -0,0 +1,40 @@
Group C29v
n 16
Irred Operation
1 A1 E
2 A2 C29
3 E1 C29^2
4 E2 C29^3
5 E3 C29^4
6 E4 C29^5
7 E5 C29^6
8 E6 C29^7
9 E7 C29^8
10 E8 C29^9
11 E9 C29^10
12 E10 C29^11
13 E11 C29^12
14 E12 C29^13
15 E13 C29^14
16 E14 sv
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000
3 2.00000 1.95324 1.81515 1.59219 1.29477 0.93682 0.53506 0.10828 -0.32356 -0.74028 -1.12237 -1.45199 -1.71371 -1.89531 -1.98828 0.00000
4 2.00000 1.81515 1.29477 0.53506 -0.32356 -1.12237 -1.71371 -1.98828 -1.89531 -1.45199 -0.74028 0.10828 0.93682 1.59219 1.95324 0.00000
5 2.00000 1.59219 0.53506 -0.74028 -1.71371 -1.98828 -1.45199 -0.32356 0.93682 1.81515 1.95324 1.29477 0.10828 -1.12237 -1.89531 0.00000
6 2.00000 1.29477 -0.32356 -1.71371 -1.89531 -0.74028 0.93682 1.95324 1.59219 0.10828 -1.45199 -1.98828 -1.12237 0.53506 1.81515 0.00000
7 2.00000 0.93682 -1.12237 -1.98828 -0.74028 1.29477 1.95324 0.53506 -1.45199 -1.89531 -0.32356 1.59219 1.81515 0.10828 -1.71371 0.00000
8 2.00000 0.53506 -1.71371 -1.45199 0.93682 1.95324 0.10828 -1.89531 -1.12237 1.29477 1.81515 -0.32356 -1.98828 -0.74028 1.59219 0.00000
9 2.00000 0.10828 -1.98828 -0.32356 1.95324 0.53506 -1.89531 -0.74028 1.81515 0.93682 -1.71371 -1.12237 1.59219 1.29477 -1.45199 0.00000
10 2.00000 -0.32356 -1.89531 0.93682 1.59219 -1.45199 -1.12237 1.81515 0.53506 -1.98828 0.10828 1.95324 -0.74028 -1.71371 1.29477 0.00000
11 2.00000 -0.74028 -1.45199 1.81515 0.10828 -1.89531 1.29477 0.93682 -1.98828 0.53506 1.59219 -1.71371 -0.32356 1.95324 -1.12237 0.00000
12 2.00000 -1.12237 -0.74028 1.95324 -1.45199 -0.32356 1.81515 -1.71371 0.10828 1.59219 -1.89531 0.53506 1.29477 -1.98828 0.93682 0.00000
13 2.00000 -1.45199 0.10828 1.29477 -1.98828 1.59219 -0.32356 -1.12237 1.95324 -1.71371 0.53506 0.93682 -1.89531 1.81515 -0.74028 0.00000
14 2.00000 -1.71371 0.93682 0.10828 -1.12237 1.81515 -1.98828 1.59219 -0.74028 -0.32356 1.29477 -1.89531 1.95324 -1.45199 0.53506 0.00000
15 2.00000 -1.89531 1.59219 -1.12237 0.53506 0.10828 -0.74028 1.29477 -1.71371 1.95324 -1.98828 1.81515 -1.45199 0.93682 -0.32356 0.00000
16 2.00000 -1.98828 1.95324 -1.89531 1.81515 -1.71371 1.59219 -1.45199 1.29477 -1.12237 0.93682 -0.74028 0.53506 -0.32356 0.10828 0.00000

View File

@ -0,0 +1,16 @@
Group C2h
n 4
Irred Operation
1 Ag E
2 Bg C2
3 Au i
4 Bu sh
Table
1 2 3 4
1 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000
3 1.00000 1.00000 -1.00000 -1.00000
4 1.00000 -1.00000 -1.00000 1.00000

View File

@ -0,0 +1,16 @@
Group C2v
n 4
Irred Operation
1 A1 E
2 A2 C2
3 B1 sv
4 B2 sd
Table
1 2 3 4
1 1.00000 1.00000 1.00000 1.00000
2 1.00000 1.00000 -1.00000 -1.00000
3 1.00000 -1.00000 1.00000 -1.00000
4 1.00000 -1.00000 -1.00000 1.00000

View File

@ -0,0 +1,12 @@
Group C3
n 2
Irred Operation
1 A E
2 E C3
Table
1 2
1 1.00000 1.00000
2 2.00000 -1.00000

View File

@ -0,0 +1,40 @@
Group C30
n 16
Irred Operation
1 A E
2 B C30
3 E1 C15
4 E2 C10
5 E3 C15^2
6 E4 C6
7 E5 C5
8 E6 C30^7
9 E7 C15^4
10 E8 C10^3
11 E9 C3
12 E10 C30^11
13 E11 C5^2
14 E12 C30^13
15 E13 C15^7
16 E14 C2
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000
3 2.00000 1.95630 1.82709 1.61803 1.33826 1.00000 0.61803 0.20906 -0.20906 -0.61803 -1.00000 -1.33826 -1.61803 -1.82709 -1.95630 -2.00000
4 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000
5 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000
6 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000
7 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000
8 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000
9 2.00000 0.20906 -1.95630 -0.61803 1.82709 1.00000 -1.61803 -1.33826 1.33826 1.61803 -1.00000 -1.82709 0.61803 1.95630 -0.20906 -2.00000
10 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000
11 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000
12 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000
13 2.00000 -1.33826 -0.20906 1.61803 -1.95630 1.00000 0.61803 -1.82709 1.82709 -0.61803 -1.00000 1.95630 -1.61803 0.20906 1.33826 -2.00000
14 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000
15 2.00000 -1.82709 1.33826 -0.61803 -0.20906 1.00000 -1.61803 1.95630 -1.95630 1.61803 -1.00000 0.20906 0.61803 -1.33826 1.82709 -2.00000
16 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000

View File

@ -0,0 +1,72 @@
Group C30h
n 32
Irred Operation
1 Ag E
2 Bg C30
3 E1g C15
4 E2g C10
5 E3g C15^2
6 E4g C6
7 E5g C5
8 E6g C30^7
9 E7g C15^4
10 E8g C10^3
11 E9g C3
12 E10g C30^11
13 E11g C5^2
14 E12g C30^13
15 E13g C15^7
16 E14g C2
17 Au i
18 Bu S30
19 E1u S15
20 E2u S10
21 E3u S15^2
22 E4u S6
23 E5u S5
24 E6u S30^7
25 E7u S15^4
26 E8u S10^3
27 E9u S3
28 E10u S30^11
29 E11u S5^2
30 E12u S30^13
31 E13u S15^7
32 E14u sh
Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000
3 2.00000 1.95630 1.82709 1.61803 1.33826 1.00000 0.61803 0.20906 -0.20906 -0.61803 -1.00000 -1.33826 -1.61803 -1.82709 -1.95630 -2.00000 2.00000 -1.95630 -1.82709 -1.61803 -1.33826 -1.00000 -0.61803 -0.20906 0.20906 0.61803 1.00000 1.33826 1.61803 1.82709 1.95630 -2.00000
4 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000
5 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 -2.00000
6 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000
7 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 -2.00000
8 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000
9 2.00000 0.20906 -1.95630 -0.61803 1.82709 1.00000 -1.61803 -1.33826 1.33826 1.61803 -1.00000 -1.82709 0.61803 1.95630 -0.20906 -2.00000 2.00000 -0.20906 1.95630 0.61803 -1.82709 -1.00000 1.61803 1.33826 -1.33826 -1.61803 1.00000 1.82709 -0.61803 -1.95630 0.20906 -2.00000
10 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000
11 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 -2.00000
12 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000
13 2.00000 -1.33826 -0.20906 1.61803 -1.95630 1.00000 0.61803 -1.82709 1.82709 -0.61803 -1.00000 1.95630 -1.61803 0.20906 1.33826 -2.00000 2.00000 1.33826 0.20906 -1.61803 1.95630 -1.00000 -0.61803 1.82709 -1.82709 0.61803 1.00000 -1.95630 1.61803 -0.20906 -1.33826 -2.00000
14 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000
15 2.00000 -1.82709 1.33826 -0.61803 -0.20906 1.00000 -1.61803 1.95630 -1.95630 1.61803 -1.00000 0.20906 0.61803 -1.33826 1.82709 -2.00000 2.00000 1.82709 -1.33826 0.61803 0.20906 -1.00000 1.61803 -1.95630 1.95630 -1.61803 1.00000 -0.20906 -0.61803 1.33826 -1.82709 -2.00000
16 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000
17 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
18 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000
19 2.00000 1.95630 1.82709 1.61803 1.33826 1.00000 0.61803 0.20906 -0.20906 -0.61803 -1.00000 -1.33826 -1.61803 -1.82709 -1.95630 -2.00000 -2.00000 1.95630 1.82709 1.61803 1.33826 1.00000 0.61803 0.20906 -0.20906 -0.61803 -1.00000 -1.33826 -1.61803 -1.82709 -1.95630 2.00000
20 2.00000 1.82709 1.33826 0.61803 -0.20906 -1.00000 -1.61803 -1.95630 -1.95630 -1.61803 -1.00000 -0.20906 0.61803 1.33826 1.82709 2.00000 -2.00000 -1.82709 -1.33826 -0.61803 0.20906 1.00000 1.61803 1.95630 1.95630 1.61803 1.00000 0.20906 -0.61803 -1.33826 -1.82709 -2.00000
21 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -2.00000 1.61803 0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803 0.61803 1.61803 2.00000 1.61803 0.61803 -0.61803 -1.61803 2.00000
22 2.00000 1.33826 -0.20906 -1.61803 -1.95630 -1.00000 0.61803 1.82709 1.82709 0.61803 -1.00000 -1.95630 -1.61803 -0.20906 1.33826 2.00000 -2.00000 -1.33826 0.20906 1.61803 1.95630 1.00000 -0.61803 -1.82709 -1.82709 -0.61803 1.00000 1.95630 1.61803 0.20906 -1.33826 -2.00000
23 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 -2.00000 -1.00000 1.00000 2.00000 1.00000 -1.00000 2.00000
24 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000 -0.61803 1.61803 1.61803 -0.61803 -2.00000
25 2.00000 0.20906 -1.95630 -0.61803 1.82709 1.00000 -1.61803 -1.33826 1.33826 1.61803 -1.00000 -1.82709 0.61803 1.95630 -0.20906 -2.00000 -2.00000 0.20906 -1.95630 -0.61803 1.82709 1.00000 -1.61803 -1.33826 1.33826 1.61803 -1.00000 -1.82709 0.61803 1.95630 -0.20906 2.00000
26 2.00000 -0.20906 -1.95630 0.61803 1.82709 -1.00000 -1.61803 1.33826 1.33826 -1.61803 -1.00000 1.82709 0.61803 -1.95630 -0.20906 2.00000 -2.00000 0.20906 1.95630 -0.61803 -1.82709 1.00000 1.61803 -1.33826 -1.33826 1.61803 1.00000 -1.82709 -0.61803 1.95630 0.20906 -2.00000
27 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 -2.00000 -0.61803 -1.61803 1.61803 0.61803 -2.00000 0.61803 1.61803 -1.61803 -0.61803 2.00000 -0.61803 -1.61803 1.61803 0.61803 2.00000
28 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000
29 2.00000 -1.33826 -0.20906 1.61803 -1.95630 1.00000 0.61803 -1.82709 1.82709 -0.61803 -1.00000 1.95630 -1.61803 0.20906 1.33826 -2.00000 -2.00000 -1.33826 -0.20906 1.61803 -1.95630 1.00000 0.61803 -1.82709 1.82709 -0.61803 -1.00000 1.95630 -1.61803 0.20906 1.33826 2.00000
30 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000 1.61803 -0.61803 -0.61803 1.61803 -2.00000
31 2.00000 -1.82709 1.33826 -0.61803 -0.20906 1.00000 -1.61803 1.95630 -1.95630 1.61803 -1.00000 0.20906 0.61803 -1.33826 1.82709 -2.00000 -2.00000 -1.82709 1.33826 -0.61803 -0.20906 1.00000 -1.61803 1.95630 -1.95630 1.61803 -1.00000 0.20906 0.61803 -1.33826 1.82709 2.00000
32 2.00000 -1.95630 1.82709 -1.61803 1.33826 -1.00000 0.61803 -0.20906 -0.20906 0.61803 -1.00000 1.33826 -1.61803 1.82709 -1.95630 2.00000 -2.00000 1.95630 -1.82709 1.61803 -1.33826 1.00000 -0.61803 0.20906 0.20906 -0.61803 1.00000 -1.33826 1.61803 -1.82709 1.95630 -2.00000

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