/
focas_hessian.F90
1236 lines (804 loc) · 37.4 KB
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focas_hessian.F90
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!!
!@BEGIN LICENSE
!
! v2RDM-CASSCF, a plugin to:
!
! Psi4: an open-source quantum chemistry software package
!
! This program is free software; you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation; either version 2 of the License, or
! (at your option) any later version.
!
! This program is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License along
! with this program; if not, write to the Free Software Foundation, Inc.,
! 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
!
!@END LICENSE
!
!!
module focas_hessian
use focas_data
implicit none
contains
subroutine diagonal_hessian(q,z,int2,den1,den2)
implicit none
real(wp), intent(in) :: int2(:),den1(:),den2(:)
real(wp), intent(in) :: q(:,:),z(:,:)
integer :: error
min_diag_hessian_ = 1.0e-2_wp
num_negative_diagonal_hessian_ = 0
! active-doubly occupied pairs
if ( rot_pair_%n_ad > 0 ) error=diagonal_hessian_ad(fock_i_%occ,fock_a_%occ,q,z,int2,den1,den2)
! active-active pairs
if ( rot_pair_%n_aa > 0 ) error=diagonal_hessian_aa(fock_i_%occ,fock_a_%occ,q,z,int2,den1,den2)
! external-doubly occupied pairs
if ( rot_pair_%n_ed > 0 ) error=diagonal_hessian_ed(fock_i_%occ,fock_i_%ext,fock_a_%occ,fock_a_%ext,int2)
! external-active pairs
if ( rot_pair_%n_ea > 0 ) error=diagonal_hessian_ea(fock_i_%ext,fock_a_%ext,q,z,int2,den1,den2)
! ! print the orbital hessian
! call print_orbital_hessian()
return
end subroutine diagonal_hessian
integer function diagonal_hessian_ad(f_i,f_a,q,z,int2,den1,den2)
implicit none
! subroutine to compute the diagonal Hessian matrix element H(ti|ti) according to Eq. 4.7c of
! Chaban, Schmidt, Gordon, Theor. Chem. Acc., 97, 88-95 (1997)
! H(ti|ti) = 2 * [ 2 * { ( f_i(t,t) + f_a(t,t) ) - ( f_i(i,i) + f_a(i,i) ) } + d(t,t) * ( f_i(i,i) + f_a(i,i) ) - q(t,t) -z(t) ]
! where z(t,t) = sum_{u} [ d(t,u) * f_i(t,u) ] ] && a \in ext & t,u \in act
real(wp), intent(in) :: q(:,:),z(:,:),den1(:),den2(:),int2(:)
type(matrix_block), intent(in) :: f_i(:),f_a(:)
integer :: grad_ind,t,i,tt_den,t_sym,t_i,i_i
real(wp) :: h_val
! loop over all active - doubly-occupied pairs
do t_sym = 1 , nirrep_
grad_ind = rot_pair_%pair_offset(t_sym,rot_pair_%act_doc_type)
do i = first_index_(t_sym,1) , last_index_(t_sym,1)
do t = first_index_(t_sym,2) , last_index_(t_sym,2)
! look up integral/density indeces
tt_den = dens_%gemind(t,t)
i_i = trans_%class_to_irrep_map(i)
t_i = trans_%class_to_irrep_map(t)
! update gradient index
grad_ind = grad_ind + 1
! compute Hessian value
h_val = 2.0_wp * ( &
2.0_wp * ( ( f_i(t_sym)%val(t_i,t_i) + f_a(t_sym)%val(t_i,t_i) ) &
- ( f_i(t_sym)%val(i_i,i_i) + f_a(t_sym)%val(i_i,i_i) ) ) &
+ den1(tt_den) * f_i(t_sym)%val(i_i,i_i) - q(t-ndoc_tot_,t) - z(t-ndoc_tot_,t) )
if ( use_exact_hessian_diagonal_ == 0 ) then
h_val = h_val + 2.0_wp * den1(tt_den) * f_a(t_sym)%val(i_i,i_i)
else
if ( df_vars_%use_df_teints == 1 ) then
h_val = h_val + te_terms_ad_df(i,t,t_sym,int2,den1,den2)
else
h_val = h_val + te_terms_ad(i,t,t_sym,int2,den1,den2)
endif
endif
if ( h_val < 0.0_wp ) h_val = - h_val
if ( h_val < min_diag_hessian_ ) h_val = min_diag_hessian_
orbital_hessian_(grad_ind) = h_val
end do
end do
end do
diagonal_hessian_ad = 0
return
end function diagonal_hessian_ad
function te_terms_ad(i,t,t_sym,int2,den1,den2)
! function to compute exact 2-e contribution for active-doubly occupied diagonal Hessian
! using 4-index integrals
! H(it|it) = 2 * sum{u,v} [ d(tt|uv) * g(ii|uv) + 2 * d(tv|tu) * g(ui|vi) ]
! + 4 * sum{u} [ ( delta(t,u) - d(t,u) ) * ( 3 * g(ui|ti) - g(ii|tu) ) ]
integer, intent(in) :: i,t,t_sym
real(wp), intent(in) :: int2(:),den1(:),den2(:)
integer :: tt_den,uv_den,tv_den,tu_den,uu_den
integer :: ii_int,uv_int,ui_int,vi_int,ti_int,tu_int,uu_int
integer :: u,v,u_sym,tu_sym,int_ind,den_ind,den_offset,int_offset
real(wp) :: te_terms_ad,dfac,val,int_val
val = 0.0_wp
tt_den = dens_%gemind(t,t)
ii_int = ints_%gemind(i,i)
ti_int = ints_%gemind(i,t)
do u_sym = 1 , nirrep_
tu_sym = group_mult_tab_(t_sym,u_sym)
den_offset = dens_%offset(tu_sym)
int_offset = ints_%offset(tu_sym)
do u = first_index_(u_sym,2) , last_index_(u_sym,2)
tu_den = dens_%gemind(t,u)
uu_den = dens_%gemind(u,u)
ui_int = ints_%gemind(u,i)
uu_int = ints_%gemind(u,u)
! u > v --> factor of 2
do v = first_index_(u_sym,2) , u - 1
uv_den = dens_%gemind(u,v)
tv_den = dens_%gemind(t,v)
uv_int = ints_%gemind(u,v)
vi_int = ints_%gemind(i,v)
! 2 * d(tt|uv) * g(ii|uv)
den_ind = pq_index(tt_den,uv_den)
int_ind = pq_index(ii_int,uv_int)
val = val + 2.0_wp * den2(den_ind) * int2(int_ind)
! 4 * d(tv|tu) * g(ui|vi)
den_ind = pq_index(tv_den,tu_den) + den_offset
int_ind = pq_index(ui_int,vi_int) + int_offset
val = val + 4.0_wp * den2(den_ind) * int2(int_ind)
end do
! u = v --> factor of 1
! d(tt|uu) * g(ii|uu)
den_ind = pq_index(tt_den,uu_den)
int_ind = pq_index(ii_int,uu_int)
val = val + den2(den_ind) * int2(int_ind)
! 2 * d(tu|tu) * g(ui|ui)
den_ind = pq_index(tu_den,tu_den) + den_offset
int_ind = pq_index(ui_int,ui_int) + int_offset
val = val + 2.0_wp * den2(den_ind) * int2(int_ind)
end do
end do
! 4 * sum{u} [ ( delta(t,u) - d(t,u) ) * ( 3 * g(ui|ti) - g(ii|tu) ) ]
do u = first_index_(t_sym,2) , last_index_(t_sym,2)
tu_den = dens_%gemind(t,u)
ui_int = ints_%gemind(u,i)
tu_int = ints_%gemind(t,u)
if ( t == u ) then
dfac = 1.0_wp - den1(tu_den)
else
dfac = - den1(tu_den)
endif
! 3 * g(ui|ti)
int_ind = pq_index(ui_int,ti_int)
int_val = 3.0_wp * int2(int_ind)
! - g(ii|tu)
int_ind = pq_index(ii_int,tu_int)
int_val = int_val - int2(int_ind)
! only factor of 2 because of multiplication below
val = val + 2.0_wp * dfac * int_val
end do
! factor of 2 because only LT elements are accessed
te_terms_ad = 2.0_wp * val
return
end function te_terms_ad
function te_terms_ad_df(i,t,t_sym,int2,den1,den2)
! function to compute exact 2-e contribution for active-doubly occupied diagonal Hessian
! using 3-index integrals
! H(it|it) = 2 * sum{u,v} [ d(tt|uv) * g(ii|uv) + 2 * d(tv|tu) * g(ui|vi) ]
! + 4 * sum{u} [ ( delta(t,u) - d(t,u) ) * ( 3 * g(ui|ti) - g(ii|tu) ) ]
integer, intent(in) :: i,t,t_sym
real(wp), intent(in) :: int2(:),den1(:),den2(:)
integer :: tt_den,uv_den,tv_den,tu_den,uu_den
integer(ip) :: ii,uv,ui,vi,ti,tu,uu,nQ
integer :: idf,adf,udf,vdf,tdf
integer :: u,v,u_sym,tu_sym,den_ind,den_offset
real(wp) :: te_terms_ad_df,dfac,val,int_val
real(wp) :: v_ui(df_vars_%nQ),v_ii(df_vars_%nQ),v_ti(df_vars_%nQ)
val = 0.0_wp
nQ = int(df_vars_%nQ,kind=ip)
idf = df_vars_%class_to_df_map(i)
tdf = df_vars_%class_to_df_map(t)
tt_den = dens_%gemind(t,t)
ii = df_pq_index(idf,idf)
ti = df_pq_index(idf,tdf)
call my_dcopy(df_vars_%nQ,int2(ii+1:),df_vars_%Qstride,v_ii,1)
call my_dcopy(df_vars_%nQ,int2(ti+1:),df_vars_%Qstride,v_ti,1)
do u_sym = 1 , nirrep_
tu_sym = group_mult_tab_(t_sym,u_sym)
den_offset = dens_%offset(tu_sym)
do u = first_index_(u_sym,2) , last_index_(u_sym,2)
tu_den = dens_%gemind(t,u)
uu_den = dens_%gemind(u,u)
udf = df_vars_%class_to_df_map(u)
ui = df_pq_index(udf,idf)
uu = df_pq_index(udf,udf)
call my_dcopy(df_vars_%nQ,int2(ui+1:),df_vars_%Qstride,v_ui,1)
! u > v --> factor of 2
do v = first_index_(u_sym,2) , u - 1
uv_den = dens_%gemind(u,v)
tv_den = dens_%gemind(t,v)
vdf = df_vars_%class_to_df_map(v)
uv = df_pq_index(udf,vdf)
vi = df_pq_index(idf,vdf)
! 2 * d(tt|uv) * g(ii|uv)
den_ind = pq_index(tt_den,uv_den)
val = val + 2.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_ii,1,int2(uv+1:),df_vars_%Qstride)
! 4 * d(tv|tu) * g(ui|vi)
den_ind = pq_index(tv_den,tu_den) + den_offset
val = val + 4.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_ui,1,int2(vi+1:),df_vars_%Qstride)
end do
! u = v --> factor of 1
! d(tt|uu) * g(ii|uu)
den_ind = pq_index(tt_den,uu_den)
val = val + den2(den_ind) * my_ddot(df_vars_%nQ,v_ii,1,int2(uu+1:),df_vars_%Qstride)
! 2 * d(tu|tu) * g(ui|ui)
den_ind = pq_index(tu_den,tu_den) + den_offset
val = val + 2.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_ui,1,v_ui,1)
end do
end do
! 4 * sum{u} [ ( delta(t,u) - d(t,u) ) * ( 3 * g(ui|ti) - g(ii|tu) ) ]
do u = first_index_(t_sym,2) , last_index_(t_sym,2)
tu_den = dens_%gemind(t,u)
udf = df_vars_%class_to_df_map(u)
ui = df_pq_index(udf,idf)
tu = df_pq_index(tdf,udf)
if ( t == u ) then
dfac = 1.0_wp - den1(tu_den)
else
dfac = - den1(tu_den)
endif
! 3 * g(ui|ti)
int_val = 3.0_wp * my_ddot(df_vars_%nQ,v_ti,1,int2(ui+1:),df_vars_%Qstride)
! - g(ii|tu)
int_val = int_val - my_ddot(df_vars_%nQ,v_ii,1,int2(tu+1:),df_vars_%Qstride)
! only factor of 2 because of multiplication below
val = val + 2.0_wp * dfac * int_val
end do
! factor of 2 because only LT elements are accessed
te_terms_ad_df = 2.0_wp * val
return
end function te_terms_ad_df
integer function diagonal_hessian_aa(f_i,f_a,q,z,int2,den1,den2)
implicit none
! subroutine to compute the exact diagonal Hessian matrix element H(tu|tu)
! according to Eq. A.3 in Jensen, Chem. Phys. 104, 229, (1982)
! H(tu|tu) = 2 * ( d(t,t) * f_i(u,u) + d(u,u) * f_i(t,t) - 2 * d(u,t) * f_i(u,t)
! - ( q(u,u) + q(t,t) + z(t,t) +z(u,u) ) )
! some 2-e contributions are neglected
real(wp), intent(in) :: den1(:),int2(:),den2(:)
real(wp), intent(in) :: z(:,:),q(:,:)
type(matrix_block), intent(in) :: f_i(:),f_a(:)
integer :: t_sym,t,u,grad_ind
integer :: t_i,u_i
integer :: tt_den,uu_den,ut_den
integer :: tt_int,uu_int,ut_int
real(wp) :: h_val
! loop over all active - active pairs
do t_sym = 1 , nirrep_
grad_ind = rot_pair_%pair_offset(t_sym,rot_pair_%act_act_type)
do u = first_index_(t_sym,2) , last_index_(t_sym,2)
do t = u + 1 , last_index_(t_sym,2)
grad_ind = grad_ind + 1
! compute Hessian value
! Fock matrix addressing
u_i = trans_%class_to_irrep_map(u)
t_i = trans_%class_to_irrep_map(t)
! Density addressing
tt_den = dens_%gemind(t,t)
uu_den = dens_%gemind(u,u)
ut_den = dens_%gemind(u,t)
if ( use_exact_hessian_diagonal_ == 1 ) then
h_val = 2.0_wp * ( den1(tt_den) * f_i(t_sym)%val(u_i,u_i) + &
& den1(uu_den) * f_i(t_sym)%val(t_i,t_i) &
& - ( 2.0_wp * den1(ut_den) * f_i(t_sym)%val(t_i,u_i) &
& + q(t-ndoc_tot_,t) + q(u-ndoc_tot_,u) &
& + z(t-ndoc_tot_,t) + z(u-ndoc_tot_,u) ) )
if ( df_vars_%use_df_teints == 1 ) then
h_val = h_val + te_terms_aa_df(t,u,t_sym,int2,den2)
else
h_val = h_val + te_terms_aa(t,u,t_sym,int2,den2)
endif
else
h_val = 2.0_wp * ( &
& den1(tt_den) * ( f_i(t_sym)%val(u_i,u_i) + f_i(t_sym)%val(u_i,u_i) ) &
& + den1(uu_den) * ( f_i(t_sym)%val(t_i,t_i) + f_i(t_sym)%val(t_i,t_i) ) &
& - ( q(t-ndoc_tot_,t) + z(t-ndoc_tot_,t) ) &
& - ( q(u-ndoc_tot_,u) + z(u-ndoc_tot_,u) ) &
& - 2.0_wp * den1(ut_den) * f_i(t_sym)%val(u_i,t_i) &
& )
end if
if ( h_val < 0.0_wp ) h_val = - h_val
if ( h_val < min_diag_hessian_ ) h_val = min_diag_hessian_
orbital_hessian_(grad_ind) = h_val
end do
end do
end do
diagonal_hessian_aa = 0
return
end function diagonal_hessian_aa
function te_terms_aa_df(t,u,t_sym,int2,den2)
! function to accumulate 2-e contributions to exact Hessian active-active diagonal element
! using 4-index integrals according to Eq. A3 in Jensen Chem. Phys. 104, 229 (1982)
! val = sum(x,y) [ 4 * d(tx|ty) * g(ux|uy) + 4 * d(ux|uy) * g(tx|ty)
! + 2 * d(tt|xy) * g(uu|xy) + 2 * d(uu|xy) * g(tt|xy)
! - 8 * d(ux|ty) * g(ux|ty) - 4 * d(ut|xy) * g(ut|xy) ]
! the operations are performed in two steps
! i) x>y --> factor of 2 (use coefficients above)
! ii) x=y --> factor of 1 (use 1/2 the coefficients above)
! and then multiplying the result by 2 at the end
real(wp) :: te_terms_aa
real(wp), intent(in) :: int2(:),den2(:)
integer, intent(in) :: t,u,t_sym
integer :: x,y
integer :: ux_den,uy_den,tx_den,ty_den,tt_den,uu_den,ut_den,xy_den,xx_den
integer :: udf,tdf,xdf,ydf
integer(ip) :: ux,uy,tx,ty,uu,tt,ut,xy,xx,nQ
integer :: den_offset,den_ind
integer :: x_sym,xt_sym
real(wp) :: te_terms_aa_df,val
real(wp) :: v_uu(df_vars_%nQ),v_tt(df_vars_%nQ),v_ut(df_vars_%nQ)
real(wp) :: v_ux(df_vars_%nQ),v_tx(df_vars_%nQ),v_xy(df_varS_%nQ)
real(wp) :: v_ty(df_vars_%nQ)
nQ = int(df_vars_%nQ,kind=ip)
val = 0.0_wp
! integral/density indeces
tt_den = dens_%gemind(t,t)
uu_den = dens_%gemind(u,u)
ut_den = dens_%gemind(u,t)
tdf = df_vars_%class_to_df_map(t)
udf = df_vars_%class_to_df_map(u)
tt = df_pq_index(tdf,tdf)
uu = df_pq_index(udf,udf)
ut = df_pq_index(udf,tdf)
call my_dcopy(df_vars_%nQ,int2(tt+1:),df_vars_%Qstride,v_tt,1)
call my_dcopy(df_vars_%nQ,int2(uu+1:),df_vars_%Qstride,v_uu,1)
call my_dcopy(df_vars_%nQ,int2(ut+1:),df_vars_%Qstride,v_ut,1)
! loop over symmetries for x
do x_sym = 1 , nirrep_
! loop over active x indeces
do x = first_index_(x_sym,2) , last_index_(x_sym,2)
xdf = df_vars_%clasS_to_df_map(x)
xt_sym = group_mult_tab_(x_sym,t_sym)
! integral/density indeces
ux_den = dens_%gemind(u,x)
tx_den = dens_%gemind(t,x)
xx_den = dens_%gemind(x,x)
ux = df_pq_index(udf,xdf)
tx = df_pq_index(tdf,xdf)
xx = df_pq_index(xdf,xdf)
call my_dcopy(df_vars_%nQ,int2(ux+1:),df_vars_%Qstride,v_ux,1)
call my_dcopy(df_vars_%nQ,int2(tx+1:),df_vars_%Qstride,v_tx,1)
den_offset = dens_%offset(xt_sym)
! x > y --> factor of 2
do y = first_index_(x_sym,2) , x - 1
ydf = df_vars_%class_to_df_map(y)
! integral/density indeces
uy_den = dens_%gemind(u,y)
ty_den = dens_%gemind(t,y)
xy_den = dens_%gemind(x,y)
uy = df_pq_index(udf,ydf)
ty = df_pq_index(tdf,ydf)
xy = df_pq_index(xdf,ydf)
call my_dcopy(df_vars_%nQ,int2(xy+1:),df_vars_%Qstride,v_xy,1)
call my_dcopy(df_vars_%nQ,int2(ty+1:),df_vars_%Qstride,v_ty,1)
! 4 * d(tx|ty) * g(ux|uy)
den_ind = pq_index(tx_den,ty_den) + den_offset
val = val + 4.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_ux,1,int2(uy+1:),df_vars_%Qstride)
! 4 * d(ux|uy) * g(tx|ty)
den_ind = pq_index(ux_den,uy_den) + den_offset
val = val + 4.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_tx,1,v_ty,1)
! 2 * d(tt,xy) * g(uu|xy)
den_ind = pq_index(tt_den,xy_den)
val = val + 2.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_uu,1,v_xy,1)
! 2 * d(uu,xy) * g(tt|xy)
den_ind = pq_index(uu_den,xy_den)
val = val + 2.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_tt,1,v_xy,1)
! - 8 * d(ux|ty) * g(ux|ty)
den_ind = pq_index(ux_den,ty_den) + den_offset
val = val - 8.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_ux,1,v_ty,1)
! - 4 * d(tu|xy) * g(ut|xy)
den_ind = pq_index(ut_den,xy_den)
val = val - 4.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_ut,1,v_xy,1)
end do
! x == y
call my_dcopy(df_vars_%nQ,int2(xx+1:),df_vars_%Qstride,v_xy,1)
! 2 * d(tx|tx) * g(ux|ux)
den_ind = pq_index(tx_den,tx_den) + den_offset
val = val + 2.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_ux,1,v_ux,1)
! 2 * d(ux|ux) * g(tx|tx)
den_ind = pq_index(ux_den,ux_den) + den_offset
val = val + 2.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_tx,1,v_tx,1)
! d(tt,xx) * g(uu|xx)
den_ind = pq_index(tt_den,xx_den)
val = val + den2(den_ind) * my_ddot(df_vars_%nQ,v_uu,1,v_xy,1)
! d(uu,xx) * g(tt|xx)
den_ind = pq_index(uu_den,xx_den)
val = val + den2(den_ind) * my_ddot(df_vars_%nQ,v_tt,1,v_xy,1)
! - 4 * d(ux|tx) * g(ux|tx)
den_ind = pq_index(ux_den,tx_den) + den_offset
val = val - 4.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_ux,1,v_tx,1)
! - 2 * d(tu|xx) * g(ut|xx)
den_ind = pq_index(ut_den,xx_den)
val = val - 2.0_wp * den2(den_ind) * my_ddot(df_vars_%nQ,v_ut,1,v_xy,1)
end do
end do
! factor of 2 because only LT elements are accessed
te_terms_aa_df = 2.0_wp * val
return
end function te_terms_aa_df
function te_terms_aa(t,u,t_sym,int2,den2)
! function to accumulate 2-e contributions to exact Hessian active-active diagonal element
! using 4-index integrals according to Eq. A3 in Jensen Chem. Phys. 104, 229 (1982)
! val = sum(x,y) [ 4 * d(tx|ty) * g(ux|uy) + 4 * d(ux|uy) * g(tx|ty)
! + 2 * d(tt|xy) * g(uu|xy) + 2 * d(uu|xy) * g(tt|xy)
! - 8 * d(ux|ty) * g(ux|ty) - 4 * d(ut|xy) * g(ut|xy) ]
! the operations are performed in two steps
! i) x>y --> factor of 2 (use coefficients above)
! ii) x=y --> factor of 1 (use 1/2 the coefficients above)
! and then multiplying the result by 2 at the end
real(wp) :: te_terms_aa
real(wp), intent(in) :: int2(:),den2(:)
integer, intent(in) :: t,u,t_sym
integer :: x,y
integer :: ux_den,uy_den,tx_den,ty_den,tt_den,uu_den,ut_den,xy_den,xx_den
integer :: ux_int,uy_int,tx_int,ty_int,uu_int,tt_int,ut_int,xy_int,xx_int
integer :: den_offset,int_offset,den_ind,int_ind
integer :: x_sym,xt_sym
real(wp) :: val
! initialize 2-e contribution
val = 0.0_wp
! integral/density indeces
tt_den = dens_%gemind(t,t)
uu_den = dens_%gemind(u,u)
ut_den = dens_%gemind(u,t)
tt_int = ints_%gemind(t,t)
uu_int = ints_%gemind(u,u)
ut_int = ints_%gemind(u,t)
! loop over symmetries for x
do x_sym = 1 , nirrep_
! loop over active x indeces
do x = first_index_(x_sym,2) , last_index_(x_sym,2)
xt_sym = group_mult_tab_(x_sym,t_sym)
! integral/density indeces
ux_den = dens_%gemind(u,x)
tx_den = dens_%gemind(t,x)
xx_den = dens_%gemind(x,x)
ux_int = ints_%gemind(u,x)
tx_int = ints_%gemind(t,x)
xx_int = ints_%gemind(x,x)
den_offset = dens_%offset(xt_sym)
int_offset = ints_%offset(xt_sym)
! x > y --> factor of 2
do y = first_index_(x_sym,2) , x - 1
! integral/density indeces
uy_den = dens_%gemind(u,y)
ty_den = dens_%gemind(t,y)
xy_den = dens_%gemind(x,y)
uy_int = ints_%gemind(u,y)
ty_int = ints_%gemind(t,y)
xy_int = ints_%gemind(x,y)
! 4 * d(tx|ty) * g(ux|uy)
den_ind = pq_index(tx_den,ty_den) + den_offset
int_ind = pq_index(ux_int,uy_int) + int_offset
val = val + 4.0_wp * den2(den_ind) * int2(int_ind)
! 4 * d(ux|uy) * g(tx|ty)
den_ind = pq_index(ux_den,uy_den) + den_offset
int_ind = pq_index(tx_int,ty_int) + int_offset
val = val + 4.0_wp * den2(den_ind) * int2(int_ind)
! 2 * d(tt,xy) * g(uu|xy)
den_ind = pq_index(tt_den,xy_den)
int_ind = pq_index(uu_int,xy_int)
val = val + 2.0_wp * den2(den_ind) * int2(int_ind)
! 2 * d(uu,xy) * g(tt|xy)
den_ind = pq_index(uu_den,xy_den)
int_ind = pq_index(tt_int,xy_int)
val = val + 2.0_wp * den2(den_ind) * int2(int_ind)
! - 8 * d(ux|ty) * g(ux|ty)
den_ind = pq_index(ux_den,ty_den) + den_offset
int_ind = pq_index(ux_int,ty_int) + int_offset
val = val - 8.0_wp * den2(den_ind) * int2(int_ind)
! - 4 * d(tu|xy) * g(ut|xy)
den_ind = pq_index(ut_den,xy_den)
int_ind = pq_index(ut_int,xy_int)
val = val - 4.0_wp * den2(den_ind) * int2(int_ind)
end do
! x == y
! 2 * d(tx|tx) * g(ux|ux)
den_ind = pq_index(tx_den,tx_den) + den_offset
int_ind = pq_index(ux_int,ux_int) + int_offset
val = val + 2.0_wp * den2(den_ind) * int2(int_ind)
! 2 * d(ux|ux) * g(tx|tx)
den_ind = pq_index(ux_den,ux_den) + den_offset
int_ind = pq_index(tx_int,tx_int) + int_offset
val = val + 2.0_wp * den2(den_ind) * int2(int_ind)
! d(tt,xx) * g(uu|xx)
den_ind = pq_index(tt_den,xx_den)
int_ind = pq_index(uu_int,xx_int)
val = val + den2(den_ind) * int2(int_ind)
! d(uu,xx) * g(tt|xx)
den_ind = pq_index(uu_den,xx_den)
int_ind = pq_index(tt_int,xx_int)
val = val + den2(den_ind) * int2(int_ind)
! - 4 * d(ux|tx) * g(ux|tx)
den_ind = pq_index(ux_den,tx_den) + den_offset
int_ind = pq_index(ux_int,tx_int) + int_offset
val = val - 4.0_wp * den2(den_ind) * int2(int_ind)
! - 2 * d(tu|xx) * g(ut|xx)
den_ind = pq_index(ut_den,xx_den)
int_ind = pq_index(ut_int,xx_int)
val = val - 2.0_wp * den2(den_ind) * int2(int_ind)
end do
end do
! factor of 2 because only LT elements are accessed
te_terms_aa = 2.0_wp * val
return
end function te_terms_aa
integer function diagonal_hessian_ed(f_i,f_i_ext,f_a,f_a_ext,int2)
implicit none
! subroutine to compute the diagonal Hessian matrix element H(ia|ia)according to Eq. 4.7a of
! Chaban, Schmidt, Gordon, Theor. Chem. Acc., 97, 88-95 (1997)
! H(ai|ai) = 4 * (f_i(a,a) + f_a(a,a) ) - 4 * ( f_i(i,i) + f_a(i,i))
! a \in ext & i \in act
real(wp), intent(in) :: int2(:)
type(vector_block), intent(in) :: f_i_ext(:),f_a_ext(:)
type(matrix_block), intent(in) :: f_i(:),f_a(:)
integer :: a,i,grad_ind,a_sym,i_i,a_i
real(wp) :: h_val
! loop over all external - doubly-occupied pairs
do a_sym = 1 , nirrep_
grad_ind = rot_pair_%pair_offset(a_sym,rot_pair_%ext_doc_type)
do i = first_index_(a_sym,1) , last_index_(a_sym,1)
do a = first_index_(a_sym,3) , last_index_(a_sym,3)
! update Hessian index
grad_ind = grad_ind + 1
! inactive/active fock matrix indeces
i_i = trans_%class_to_irrep_map(i)
a_i = trans_%class_to_irrep_map(a)-ndocpi_(a_sym)-nactpi_(a_sym)
! calculate diagonal Hessian element
h_val = 4.0 * ( f_i_ext(a_sym)%val(a_i) + f_a_ext(a_sym)%val(a_i) - &
& f_i(a_sym)%val(i_i,i_i) - f_a(a_sym)%val(i_i,i_i) )
if ( use_exact_hessian_diagonal_ == 1 ) then
if ( df_vars_%use_df_teints == 1 ) then
h_val = h_val + te_terms_ed_df(i,a,int2)
else
h_val = h_val + te_terms_ed(i,a,int2)
endif
endif
if ( h_val < 0.0_wp ) h_val = - h_val
if ( h_val < min_diag_hessian_ ) h_val = min_diag_hessian_
orbital_hessian_(grad_ind) = h_val
end do
end do
end do
diagonal_hessian_ed = 0
return
end function diagonal_hessian_ed
function te_terms_ed(i,a,int2)
! function to compute the 2-e contributions to the external-doubly occupied diagonal Hessian
! using 4-index integrals element according to
! te_(i,a) = 4 (3 g(ai|ai) - (aa|ii) )
integer, intent(in) :: i,a
real(wp), intent(in) :: int2(:)
integer :: aa_int,ii_int,ai_int,int_ind
real(wp) :: te_terms_ed,val
aa_int = ints_%gemind(a,a)
ii_int = ints_%gemind(i,i)
ai_int = ints_%gemind(a,i)
! 3 * g(ai|ai)
int_ind = pq_index(ai_int,ai_int)
val = 2.0_wp * int2(int_ind)
! - g(aa|ii)
int_ind = pq_index(aa_int,ii_int)
val = val - int2(int_ind)
! factor of 4 from overall formula
te_terms_ed = 4.0_wp * val
return
end function te_terms_ed
function te_terms_ed_df(i,a,int2)
! function to compute the 2-e contributions to the external-doubly occupied diagonal Hessian
! using 3-index integrals element according to
! te_(i,a) = 4 (3 g(ai|ai) - (aa|ii) )
integer, intent(in) :: i,a
real(wp), intent(in) :: int2(:)
integer(ip) :: ii,ai,aa,nQ
integer :: adf,idf
real(wp) :: te_terms_ed_df,val
nQ = int(df_vars_%nQ,kind=ip)
adf = df_vars_%class_to_df_map(a)
idf = df_vars_%class_to_df_map(i)
aa = df_pq_index(adf,adf)
ii = df_pq_index(idf,idf)
ai = df_pq_index(adf,idf)
! 3 * g(ai|ai)
val = 3.0_wp * my_ddot(df_vars_%nQ,int2(ai+1:),df_vars_%Qstride,int2(ai+1:),df_vars_%Qstride)
! - g(aa|ii)
val = val - my_ddot(df_vars_%nQ,int2(aa+1:),df_vars_%Qstride,int2(ii+1:),df_vars_%Qstride)
! factor of 4 from overall formula
te_terms_ed_df = 4.0_wp * val
return
end function te_terms_ed_df
integer function diagonal_hessian_ea(f_i_ext,f_a_ext,q,z,int2,den1,den2)
implicit none
! subroutine to compute the diagonal Hessian matrix element H(ai|ai) according to Eq. 4.7b of
! Chaban, Schmidt, Gordon, Theor. Chem. Acc., 97, 88-95 (1997)
! H(at|at) = 2 * [ d(t,t) * ( f_i(a,a) + f_a(a,a) ) - q(t,t) - z(t,t) ]
! where z(t,t) = sum_{u} [ d(t,u) * f_i(t,u) ] && a \in ext & t,u \in act
real(wp), intent(in) :: z(:,:),q(:,:),int2(:),den1(:),den2(:)
type(vector_block), intent(in) :: f_i_ext(:),f_a_ext(:)
integer :: a,t,grad_ind,tt_den,a_sym,a_i
real(wp) :: h_val
! loop over all external - doubly-occupied pairs
do a_sym = 1 , nirrep_
grad_ind = rot_pair_%pair_offset(a_sym,rot_pair_%ext_act_type)
do t = first_index_(a_sym,2) , last_index_(a_sym,2)
do a = first_index_(a_sym,3) , last_index_(a_sym,3)
! integral/density indeces
tt_den = dens_%gemind(t,t)
a_i = trans_%class_to_irrep_map(a)-ndocpi_(a_sym)-nactpi_(a_sym)
! update diagonal Hessian index
grad_ind = grad_ind + 1
! calculate diagonal Hessian element
h_val = 2.0_wp * ( den1(tt_den) * f_i_ext(a_sym)%val(a_i) - q(t-ndoc_tot_,t) - z(t-ndoc_tot_,t) )
if ( use_exact_hessian_diagonal_ == 0 ) then
h_val = h_val + 2.0_wp * den1(tt_den) * f_a_ext(a_sym)%val(a_i)
else
if ( df_vars_%use_df_teints == 1 ) then
h_val = h_val + 2.0_wp * den1(tt_den) * f_a_ext(a_sym)%val(a_i)
else
h_val = h_val + te_terms_ea(t,a,a_sym,int2,den2)
endif
endif
if ( h_val < 0.0_wp ) h_val = - h_val
if ( h_val < min_diag_hessian_ ) h_val = min_diag_hessian_
orbital_hessian_(grad_ind) = h_val
end do
end do
end do
diagonal_hessian_ea = 0
return
end function diagonal_hessian_ea
function te_terms_ea(t,a,a_sym,int2,den2)
! function to compute 2-e approximation to the active-external digaonal Hessian
! using 4-index integrals according to
! te = 2* sum{u,v} [ d(tt|uv) * g(aa|uv) + 2 * d(tv|tu) * g(av|au) ]
integer, intent(in) :: t,a,a_sym
real(wp), intent(in) :: int2(:),den2(:)
integer :: u,v,u_sym,au_sym
integer :: tt_den,uv_den,tv_den,tu_den,uu_den
integer :: aa_int,uv_int,av_int,au_int,uu_int
integer :: den_offset,int_offset,int_ind,den_ind
real(wp) :: te_terms_ea,val
val = 0.0_wp
tt_den = dens_%gemind(t,t)
aa_int = ints_%gemind(a,a)
do u_sym = 1 , nirrep_
au_sym = group_mult_tab_(a_sym,u_sym)
den_offset = dens_%offset(au_sym)
int_offset = ints_%offset(au_sym)
do u = first_index_(u_sym,2) , last_index_(u_sym,2)