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QuantumPackage/src/casscf/hessian.irp.f

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Fortran
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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
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
indx=1
do i=1,n_core_inact_orb
do t=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(indx,jndx)=hessmat_itju(i,t,j,u)
hessmat2(jndx,indx)=hessmat2(indx,jndx)
jndx+=1
end do
end do
do j=1,n_core_inact_orb
do a=1,n_virt_orb
hessmat2(indx,jndx)=hessmat_itja(i,t,j,a)
hessmat2(jndx,indx)=hessmat2(indx,jndx)
jndx+=1
end do
end do
do u=1,n_act_orb
do a=1,n_virt_orb
hessmat2(indx,jndx)=hessmat_itua(i,t,u,a)
hessmat2(jndx,indx)=hessmat2(indx,jndx)
jndx+=1
end do
end do
indx+=1
end do
end do
do i=1,n_core_inact_orb
do a=1,n_virt_orb
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(indx,jndx)=hessmat_iajb(i,a,j,b)
hessmat2(jndx,indx)=hessmat2(indx,jndx)
jndx+=1
end do
end do
do t=1,n_act_orb
do b=1,n_virt_orb
hessmat2(indx,jndx)=hessmat_iatb(i,a,t,b)
hessmat2(jndx,indx)=hessmat2(indx,jndx)
jndx+=1
end do
end do
indx+=1
end do
end do
do t=1,n_act_orb
do a=1,n_virt_orb
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(indx,jndx)=hessmat_taub(t,a,u,b)
hessmat2(jndx,indx)=hessmat2(indx,jndx)
jndx+=1
end do
end do
indx+=1
end do
end do
END_PROVIDER
real*8 function hessmat_itju(i,t,j,u)
BEGIN_DOC
! the orbital hessian for core/inactive -> active, core/inactive -> active
! i, t, j, u are list indices, the corresponding orbitals are ii,tt,jj,uu
!
! we assume natural orbitals
END_DOC
implicit none
integer :: i,t,j,u,ii,tt,uu,v,vv,x,xx,y,jj
real*8 :: term,t2
ii=list_core_inact(i)
tt=list_act(t)
if (i.eq.j) then
if (t.eq.u) then
! diagonal element
term=occnum(tt)*Fipq(ii,ii)+2.D0*(Fipq(tt,tt)+Fapq(tt,tt)) &
-2.D0*(Fipq(ii,ii)+Fapq(ii,ii))
term+=2.D0*(3.D0*bielec_pxxq_no(tt,i,i,tt)-bielec_pqxx_no(tt,tt,i,i))
term-=2.D0*occnum(tt)*(3.D0*bielec_pxxq_no(tt,i,i,tt) &
-bielec_pqxx_no(tt,tt,i,i))
term-=occnum(tt)*Fipq(tt,tt)
do v=1,n_act_orb
vv=list_act(v)
do x=1,n_act_orb
xx=list_act(x)
term+=2.D0*(P0tuvx_no(t,t,v,x)*bielec_pqxx_no(vv,xx,i,i) &
+(P0tuvx_no(t,x,v,t)+P0tuvx_no(t,x,t,v))* &
bielec_pxxq_no(vv,i,i,xx))
do y=1,n_act_orb
term-=2.D0*P0tuvx_no(t,v,x,y)*bielecCI_no(t,v,y,xx)
end do
end do
end do
else
! it/iu, t != u
uu=list_act(u)
term=2.D0*(Fipq(tt,uu)+Fapq(tt,uu))
term+=2.D0*(4.D0*bielec_PxxQ_no(tt,i,j,uu)-bielec_PxxQ_no(uu,i,j,tt) &
-bielec_PQxx_no(tt,uu,i,j))
term-=occnum(tt)*Fipq(uu,tt)
term-=(occnum(tt)+occnum(uu)) &
*(3.D0*bielec_PxxQ_no(tt,i,i,uu)-bielec_PQxx_no(uu,tt,i,i))
do v=1,n_act_orb
vv=list_act(v)
! term-=D0tu(u,v)*Fipq(tt,vv) ! published, but inverting t and u seems more correct
do x=1,n_act_orb
xx=list_act(x)
term+=2.D0*(P0tuvx_no(u,t,v,x)*bielec_pqxx_no(vv,xx,i,i) &
+(P0tuvx_no(u,x,v,t)+P0tuvx_no(u,x,t,v)) &
*bielec_pxxq_no(vv,i,i,xx))
do y=1,n_act_orb
term-=2.D0*P0tuvx_no(t,v,x,y)*bielecCI_no(u,v,y,xx)
end do
end do
end do
end if
else
! it/ju
jj=list_core_inact(j)
uu=list_act(u)
if (t.eq.u) then
term=occnum(tt)*Fipq(ii,jj)
term-=2.D0*(Fipq(ii,jj)+Fapq(ii,jj))
else
term=0.D0
end if
term+=2.D0*(4.D0*bielec_PxxQ_no(tt,i,j,uu)-bielec_PxxQ_no(uu,i,j,tt) &
-bielec_PQxx_no(tt,uu,i,j))
term-=(occnum(tt)+occnum(uu))* &
(4.D0*bielec_PxxQ_no(tt,i,j,uu)-bielec_PxxQ_no(uu,i,j,tt) &
-bielec_PQxx_no(uu,tt,i,j))
do v=1,n_act_orb
vv=list_act(v)
do x=1,n_act_orb
xx=list_act(x)
term+=2.D0*(P0tuvx_no(u,t,v,x)*bielec_pqxx_no(vv,xx,i,j) &
+(P0tuvx_no(u,x,v,t)+P0tuvx_no(u,x,t,v)) &
*bielec_pxxq_no(vv,i,j,xx))
end do
end do
end if
term*=2.D0
hessmat_itju=term
end function hessmat_itju
real*8 function hessmat_itja(i,t,j,a)
BEGIN_DOC
! the orbital hessian for core/inactive -> active, core/inactive -> virtual
END_DOC
implicit none
integer :: i,t,j,a,ii,tt,jj,aa,v,vv,x,y
real*8 :: term
! it/ja
ii=list_core_inact(i)
tt=list_act(t)
jj=list_core_inact(j)
aa=list_virt(a)
term=2.D0*(4.D0*bielec_pxxq_no(aa,j,i,tt) &
-bielec_pqxx_no(aa,tt,i,j) -bielec_pxxq_no(aa,i,j,tt))
term-=occnum(tt)*(4.D0*bielec_pxxq_no(aa,j,i,tt) &
-bielec_pqxx_no(aa,tt,i,j) -bielec_pxxq_no(aa,i,j,tt))
if (i.eq.j) then
term+=2.D0*(Fipq(aa,tt)+Fapq(aa,tt))
term-=0.5D0*occnum(tt)*Fipq(aa,tt)
do v=1,n_act_orb
do x=1,n_act_orb
do y=1,n_act_orb
term-=P0tuvx_no(t,v,x,y)*bielecCI_no(x,y,v,aa)
end do
end do
end do
end if
term*=2.D0
hessmat_itja=term
end function hessmat_itja
real*8 function hessmat_itua(i,t,u,a)
BEGIN_DOC
! the orbital hessian for core/inactive -> active, active -> virtual
END_DOC
implicit none
integer :: i,t,u,a,ii,tt,uu,aa,v,vv,x,xx,u3,t3,v3
real*8 :: term
ii=list_core_inact(i)
tt=list_act(t)
t3=t+n_core_inact_orb
uu=list_act(u)
u3=u+n_core_inact_orb
aa=list_virt(a)
if (t.eq.u) then
term=-occnum(tt)*Fipq(aa,ii)
else
term=0.D0
end if
term-=occnum(uu)*(bielec_pqxx_no(aa,ii,t3,u3)-4.D0*bielec_pqxx_no(aa,uu,t3,i)&
+bielec_pxxq_no(aa,t3,u3,ii))
do v=1,n_act_orb
vv=list_act(v)
v3=v+n_core_inact_orb
do x=1,n_act_orb
integer :: x3
xx=list_act(x)
x3=x+n_core_inact_orb
term-=2.D0*(P0tuvx_no(t,u,v,x)*bielec_pqxx_no(aa,ii,v3,x3) &
+(P0tuvx_no(t,v,u,x)+P0tuvx_no(t,v,x,u)) &
*bielec_pqxx_no(aa,xx,v3,i))
end do
end do
if (t.eq.u) then
term+=Fipq(aa,ii)+Fapq(aa,ii)
end if
term*=2.D0
hessmat_itua=term
end function hessmat_itua
real*8 function hessmat_iajb(i,a,j,b)
BEGIN_DOC
! the orbital hessian for core/inactive -> virtual, core/inactive -> virtual
END_DOC
implicit none
integer :: i,a,j,b,ii,aa,jj,bb
real*8 :: term
ii=list_core_inact(i)
aa=list_virt(a)
if (i.eq.j) then
if (a.eq.b) then
! ia/ia
term=2.D0*(Fipq(aa,aa)+Fapq(aa,aa)-Fipq(ii,ii)-Fapq(ii,ii))
term+=2.D0*(3.D0*bielec_pxxq_no(aa,i,i,aa)-bielec_pqxx_no(aa,aa,i,i))
else
bb=list_virt(b)
! ia/ib
term=2.D0*(Fipq(aa,bb)+Fapq(aa,bb))
term+=2.D0*(3.D0*bielec_pxxq_no(aa,i,i,bb)-bielec_pqxx_no(aa,bb,i,i))
end if
else
! ia/jb
jj=list_core_inact(j)
bb=list_virt(b)
term=2.D0*(4.D0*bielec_pxxq_no(aa,i,j,bb)-bielec_pqxx_no(aa,bb,i,j) &
-bielec_pxxq_no(aa,j,i,bb))
if (a.eq.b) then
term-=2.D0*(Fipq(ii,jj)+Fapq(ii,jj))
end if
end if
term*=2.D0
hessmat_iajb=term
end function hessmat_iajb
real*8 function hessmat_iatb(i,a,t,b)
BEGIN_DOC
! the orbital hessian for core/inactive -> virtual, active -> virtual
END_DOC
implicit none
integer :: i,a,t,b,ii,aa,tt,bb,v,vv,x,y,v3,t3
real*8 :: term
ii=list_core_inact(i)
aa=list_virt(a)
tt=list_act(t)
bb=list_virt(b)
t3=t+n_core_inact_orb
term=occnum(tt)*(4.D0*bielec_pxxq_no(aa,i,t3,bb)-bielec_pxxq_no(aa,t3,i,bb)&
-bielec_pqxx_no(aa,bb,i,t3))
if (a.eq.b) then
term-=Fipq(tt,ii)+Fapq(tt,ii)
term-=0.5D0*occnum(tt)*Fipq(tt,ii)
do v=1,n_act_orb
do x=1,n_act_orb
do y=1,n_act_orb
term-=P0tuvx_no(t,v,x,y)*bielecCI_no(x,y,v,ii)
end do
end do
end do
end if
term*=2.D0
hessmat_iatb=term
end function hessmat_iatb
real*8 function hessmat_taub(t,a,u,b)
BEGIN_DOC
! the orbital hessian for act->virt,act->virt
END_DOC
implicit none
integer :: t,a,u,b,tt,aa,uu,bb,v,vv,x,xx,y
integer :: v3,x3
real*8 :: term,t1,t2,t3
tt=list_act(t)
aa=list_virt(a)
if (t.eq.u) then
if (a.eq.b) then
! ta/ta
t1=occnum(tt)*Fipq(aa,aa)
t2=0.D0
t3=0.D0
t1-=occnum(tt)*Fipq(tt,tt)
do v=1,n_act_orb
vv=list_act(v)
v3=v+n_core_inact_orb
do x=1,n_act_orb
xx=list_act(x)
x3=x+n_core_inact_orb
t2+=2.D0*(P0tuvx_no(t,t,v,x)*bielec_pqxx_no(aa,aa,v3,x3) &
+(P0tuvx_no(t,x,v,t)+P0tuvx_no(t,x,t,v))* &
bielec_pxxq_no(aa,x3,v3,aa))
do y=1,n_act_orb
t3-=2.D0*P0tuvx_no(t,v,x,y)*bielecCI_no(t,v,y,xx)
end do
end do
end do
term=t1+t2+t3
else
bb=list_virt(b)
! ta/tb b/=a
term=occnum(tt)*Fipq(aa,bb)
do v=1,n_act_orb
vv=list_act(v)
v3=v+n_core_inact_orb
do x=1,n_act_orb
xx=list_act(x)
x3=x+n_core_inact_orb
term+=2.D0*(P0tuvx_no(t,t,v,x)*bielec_pqxx_no(aa,bb,v3,x3) &
+(P0tuvx_no(t,x,v,t)+P0tuvx_no(t,x,t,v)) &
*bielec_pxxq_no(aa,x3,v3,bb))
end do
end do
end if
else
! ta/ub t/=u
uu=list_act(u)
bb=list_virt(b)
term=0.D0
do v=1,n_act_orb
vv=list_act(v)
v3=v+n_core_inact_orb
do x=1,n_act_orb
xx=list_act(x)
x3=x+n_core_inact_orb
term+=2.D0*(P0tuvx_no(t,u,v,x)*bielec_pqxx_no(aa,bb,v3,x3) &
+(P0tuvx_no(t,x,v,u)+P0tuvx_no(t,x,u,v)) &
*bielec_pxxq_no(aa,x3,v3,bb))
end do
end do
if (a.eq.b) then
term-=0.5D0*(occnum(tt)*Fipq(uu,tt)+occnum(uu)*Fipq(tt,uu))
do v=1,n_act_orb
do x=1,n_act_orb
do y=1,n_act_orb
term-=P0tuvx_no(t,v,x,y)*bielecCI_no(x,y,v,uu)
term-=P0tuvx_no(u,v,x,y)*bielecCI_no(x,y,v,tt)
end do
end do
end do
end if
end if
term*=2.D0
hessmat_taub=term
end function hessmat_taub
BEGIN_PROVIDER [real*8, hessdiag, (nMonoEx)]
BEGIN_DOC
! the diagonal of the Hessian, needed for the Davidson procedure
END_DOC
implicit none
integer :: i,t,a,indx
real*8 :: hessmat_itju,hessmat_iajb,hessmat_taub
indx=0
do i=1,n_core_inact_orb
do t=1,n_act_orb
indx+=1
hessdiag(indx)=hessmat_itju(i,t,i,t)
end do
end do
do i=1,n_core_inact_orb
do a=1,n_virt_orb
indx+=1
hessdiag(indx)=hessmat_iajb(i,a,i,a)
end do
end do
do t=1,n_act_orb
do a=1,n_virt_orb
indx+=1
hessdiag(indx)=hessmat_taub(t,a,t,a)
end do
end do
END_PROVIDER
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