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mirror of https://gitlab.com/scemama/qp_plugins_scemama.git synced 2024-06-02 03:15:25 +02:00

Merge branch 'master' into 'master'

Dressing works

See merge request AbdAmmar/qp_plugins_scemama!1
This commit is contained in:
Abdallah Ammar 2021-07-31 09:10:27 +00:00
commit 232b8bdb70
256 changed files with 13942 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 +1,36 @@
program dmc_dress
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 pre
call routine
call save_wavefunction_general(N_det,N_states,psi_det_sorted,size(psi_coef_sorted,1),psi_coef_sorted)
end
subroutine pre
implicit none
double precision, allocatable :: left(:,:), right(:,:), tmp(:,:), res(:,:)
integer :: i
allocate (left(1,1:N_det), right(1:N_det,1), tmp(1:N_det,1), res(1,1))
left(1,1:N_det) = psi_coef(1:N_det,1)
right(1:N_det,1) = psi_coef(1:N_det,1)
tmp(1:N_det,1:1) = matmul(h_matrix_dressed(1:N_det,1:N_det), right(1:N_det,1:1))
res(1:1,1:1) = matmul(left(1:1,1:N_det), tmp(1:N_det,1:1))
print *, 'E_in = ', res(1,1)
do i=1,N_det
print *, 'HPsi/c0 = ', tmp(i,1)/psi_coef(i,1)
enddo
end
subroutine routine
implicit none
psi_coef(1:N_det,1) = ci_eigenvectors_dressed(1:N_det,1)
print*,'N_det = ',N_det
print *, 'E = ', ci_energy_dressed(1) + nuclear_repulsion
SOFT_TOUCH psi_coef
end

40
devel/dmc_dress/dress.py Executable file
View File

@ -0,0 +1,40 @@
#!/usr/bin/env python
import numpy as np
import subprocess
import sys
import os
QP_PATH=os.environ["QP_ROOT"]+"/external/ezfio/Python/"
sys.path.insert(0,QP_PATH)
from ezfio import ezfio
def read_hamiltonian(inp):
text = subprocess.run(["qmcchem", "result", inp], capture_output=True).stdout
inside = None
h = []
s = []
norm = None
for line in text.splitlines():
line = str(line)
print (line)
if "Psi_norm :" in line:
norm = float(line.split()[3])
if "]" in line:
inside = None
if inside == "H":
data = line.split()
h.append(float(data[3]))
elif "Ci_dress" in line:
inside = "H"
h = np.array(h)/norm
return h
h = read_hamiltonian(sys.argv[1])
ezfio.set_file(sys.argv[1])
ezfio.set_dmc_dress_dmc_delta_h(h)
print(h)

View File

@ -0,0 +1,33 @@
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
! Diagonal element is divided by 2 because Delta = D + D^t
END_DOC
integer :: i,ii,k,j, l
double precision :: f, tmp
double precision, allocatable :: delta(:)
allocate(delta(N_det))
delta(1:N_det) = dmc_delta_h(1:N_det)
call dset_order(delta,psi_bilinear_matrix_order_reverse,N_det)
dressing_column_h(:,:) = 0.d0
dressing_column_s(:,:) = 0.d0
l = dressed_column_idx(1)
do j = 1, n_det
if (j == l) cycle
dressing_column_h(j,1) = delta(j)
dressing_column_h(l,1) -= psi_coef(j,1) * delta(j) / psi_coef(l,1)
enddo
dressing_column_h(l,1) += delta(l)
dressing_column_h(l,1) *= 0.5d0
END_PROVIDER

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@ -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

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@ -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

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@ -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
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@ -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.

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@ -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

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@ -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

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@ -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

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@ -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

View File

@ -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

View File

@ -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

View File

@ -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

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