mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-11-07 22:53:52 +01:00
361 lines
8.0 KiB
Fortran
361 lines
8.0 KiB
Fortran
subroutine first_hessian_opt(n,H,h_tmpr)
|
|
|
|
include 'constants.h'
|
|
|
|
implicit none
|
|
|
|
!==================================================================
|
|
! Compute the hessian of energy with respects to orbital rotations
|
|
!==================================================================
|
|
|
|
!===========
|
|
! Variables
|
|
!===========
|
|
|
|
! in
|
|
integer, intent(in) :: n
|
|
!n : integer, n = mo_num*(mo_num-1)/2
|
|
|
|
! out
|
|
double precision, intent(out) :: H(n,n),h_tmpr(mo_num,mo_num,mo_num,mo_num)
|
|
! H : n by n double precision matrix containing the 2D hessian
|
|
|
|
! internal
|
|
double precision, allocatable :: hessian(:,:,:,:)
|
|
integer :: p,q
|
|
integer :: r,s,t,u,v
|
|
integer :: pq,rs
|
|
double precision :: t1,t2,t3,t4,t5,t6
|
|
! hessian : mo_num 4D double precision matrix containing the hessian before the permutations
|
|
! h_tmpr : mo_num 4D double precision matrix containing the hessian after the permutations
|
|
! p,q,r,s : integer, indexes of the 4D hessian matrix
|
|
! t,u,v : integer, indexes to compute hessian elements
|
|
! pq,rs : integer, indexes for the conversion from 4D to 2D hessian matrix
|
|
! t1,t2,t3 : double precision, t3 = t2 - t1, time to compute the hessian
|
|
|
|
! Funtion
|
|
double precision :: get_two_e_integral
|
|
! get_two_e_integral : double precision function, two e integrals
|
|
|
|
! Provided :
|
|
! mo_one_e_integrals : mono e- integrals
|
|
! get_two_e_integral : two e- integrals
|
|
! one_e_dm_mo_alpha, one_e_dm_mo_beta : one body density matrix
|
|
! two_e_dm_mo : two body density matrix
|
|
|
|
!============
|
|
! Allocation
|
|
!============
|
|
|
|
allocate(hessian(mo_num,mo_num,mo_num,mo_num))
|
|
|
|
!=============
|
|
! Calculation
|
|
!=============
|
|
|
|
if (debug) then
|
|
print*,'Enter in first_hess'
|
|
endif
|
|
|
|
! From Anderson et. al. (2014)
|
|
! The Journal of Chemical Physics 141, 244104 (2014); doi: 10.1063/1.4904384
|
|
|
|
CALL wall_time(t1)
|
|
|
|
! Initialization
|
|
hessian = 0d0
|
|
|
|
!========================
|
|
! First line, first term
|
|
!========================
|
|
|
|
CALL wall_time(t4)
|
|
|
|
do p = 1, mo_num
|
|
do q = 1, mo_num
|
|
do r = 1, mo_num
|
|
do s = 1, mo_num
|
|
|
|
if (q==r) then
|
|
do u = 1, mo_num
|
|
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
|
mo_one_e_integrals(u,p) * one_e_dm_mo(u,s) &
|
|
+ mo_one_e_integrals(s,u) * one_e_dm_mo(p,u))
|
|
|
|
enddo
|
|
endif
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
CALL wall_time(t5)
|
|
t6 = t5-t4
|
|
print*,'l1 1 :', t6
|
|
|
|
!=========================
|
|
! First line, second term
|
|
!=========================
|
|
|
|
CALL wall_time(t4)
|
|
|
|
do p = 1, mo_num
|
|
do q = 1, mo_num
|
|
do r = 1, mo_num
|
|
do s = 1, mo_num
|
|
|
|
if (p==s) then
|
|
do u = 1, mo_num
|
|
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
|
mo_one_e_integrals(u,r) * one_e_dm_mo(u,q) &
|
|
+ mo_one_e_integrals(q,u) * one_e_dm_mo(r,u))
|
|
enddo
|
|
endif
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
CALL wall_time(t5)
|
|
t6 = t5-t4
|
|
print*,'l1 2 :', t6
|
|
|
|
!========================
|
|
! First line, third term
|
|
!========================
|
|
|
|
CALL wall_time(t4)
|
|
|
|
do p = 1, mo_num
|
|
do q = 1, mo_num
|
|
do r = 1, mo_num
|
|
do s = 1, mo_num
|
|
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) &
|
|
- mo_one_e_integrals(s,p) * one_e_dm_mo(r,q)&
|
|
- mo_one_e_integrals(q,r) * one_e_dm_mo(p,s)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
CALL wall_time(t5)
|
|
t6 = t5-t4
|
|
print*,'l1 3 :', t6
|
|
|
|
|
|
!=========================
|
|
! Second line, first term
|
|
!=========================
|
|
|
|
CALL wall_time(t4)
|
|
|
|
do s = 1, mo_num
|
|
do r = 1, mo_num
|
|
do q = 1, mo_num
|
|
do p = 1, mo_num
|
|
|
|
! do p = 1, mo_num
|
|
! do q = 1, mo_num
|
|
! do r = 1, mo_num
|
|
! do s = 1, mo_num
|
|
|
|
if (q==r) then
|
|
do t = 1, mo_num
|
|
do u = 1, mo_num
|
|
do v = 1, mo_num
|
|
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
|
get_two_e_integral(u,v,p,t,mo_integrals_map) * two_e_dm_mo(u,v,s,t) &
|
|
+ get_two_e_integral(s,t,u,v,mo_integrals_map) * two_e_dm_mo(p,t,u,v))
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
endif
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
CALL wall_time(t5)
|
|
t6 = t5-t4
|
|
print*,'l2 1 :', t6
|
|
|
|
!==========================
|
|
! Second line, second term
|
|
!==========================
|
|
|
|
CALL wall_time(t4)
|
|
|
|
do s = 1, mo_num
|
|
do r = 1, mo_num
|
|
do q = 1, mo_num
|
|
do p = 1, mo_num
|
|
|
|
! do p = 1, mo_num
|
|
! do q = 1, mo_num
|
|
! do r = 1, mo_num
|
|
! do s = 1, mo_num
|
|
|
|
if (p==s) then
|
|
do t = 1, mo_num
|
|
do u = 1, mo_num
|
|
do v = 1, mo_num
|
|
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
|
get_two_e_integral(q,t,u,v,mo_integrals_map) * two_e_dm_mo(r,t,u,v) &
|
|
+ get_two_e_integral(u,v,r,t,mo_integrals_map) * two_e_dm_mo(u,v,q,t))
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
endif
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
CALL wall_time(t5)
|
|
t6 = t5-t4
|
|
print*,'l2 2 :', t6
|
|
|
|
!========================
|
|
! Third line, first term
|
|
!========================
|
|
|
|
CALL wall_time(t4)
|
|
|
|
do s = 1, mo_num
|
|
do r = 1, mo_num
|
|
do q = 1, mo_num
|
|
do p = 1, mo_num
|
|
|
|
! do p = 1, mo_num
|
|
! do q = 1, mo_num
|
|
! do r = 1, mo_num
|
|
! do s = 1, mo_num
|
|
|
|
do u = 1, mo_num
|
|
do v = 1, mo_num
|
|
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) &
|
|
+ get_two_e_integral(u,v,p,r,mo_integrals_map) * two_e_dm_mo(u,v,q,s) &
|
|
+ get_two_e_integral(q,s,u,v,mo_integrals_map) * two_e_dm_mo(p,r,u,v)
|
|
|
|
enddo
|
|
enddo
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
CALL wall_time(t5)
|
|
t6 = t5-t4
|
|
print*,'l3 1 :', t6
|
|
|
|
!=========================
|
|
! Third line, second term
|
|
!=========================
|
|
|
|
CALL wall_time(t4)
|
|
|
|
do s = 1, mo_num
|
|
do r = 1, mo_num
|
|
do q = 1, mo_num
|
|
do p = 1, mo_num
|
|
|
|
! do p = 1, mo_num
|
|
! do q = 1, mo_num
|
|
! do r = 1, mo_num
|
|
! do s = 1, mo_num
|
|
|
|
do t = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) &
|
|
- get_two_e_integral(s,t,p,u,mo_integrals_map) * two_e_dm_mo(r,t,q,u) &
|
|
- get_two_e_integral(t,s,p,u,mo_integrals_map) * two_e_dm_mo(t,r,q,u) &
|
|
- get_two_e_integral(q,u,r,t,mo_integrals_map) * two_e_dm_mo(p,u,s,t) &
|
|
- get_two_e_integral(q,u,t,r,mo_integrals_map) * two_e_dm_mo(p,u,t,s)
|
|
|
|
enddo
|
|
enddo
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
CALL wall_time(t5)
|
|
t6 = t5-t4
|
|
print*,'l3 2 :', t6
|
|
|
|
CALL wall_time(t2)
|
|
t3 = t2 -t1
|
|
print*,'Time to compute the hessian : ', t3
|
|
|
|
!==============
|
|
! Permutations
|
|
!==============
|
|
|
|
! Hessian(p,q,r,s) = P_pq P_rs [ ...]
|
|
! => Hessian(p,q,r,s) = (p,q,r,s) - (q,p,r,s) - (p,q,s,r) + (q,p,s,r)
|
|
|
|
do s = 1, mo_num
|
|
do r = 1, mo_num
|
|
do q = 1, mo_num
|
|
do p = 1, mo_num
|
|
|
|
h_tmpr(p,q,r,s) = (hessian(p,q,r,s) - hessian(q,p,r,s) - hessian(p,q,s,r) + hessian(q,p,s,r))
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
!========================
|
|
! 4D matrix to 2D matrix
|
|
!========================
|
|
|
|
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
|
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
|
! H(pq,rs) : p<q and r<s
|
|
|
|
! 4D mo_num matrix to 2D n matrix
|
|
do pq = 1, n
|
|
call vec_to_mat_index(pq,p,q)
|
|
do rs = 1, n
|
|
call vec_to_mat_index(rs,r,s)
|
|
H(pq,rs) = h_tmpr(p,q,r,s)
|
|
enddo
|
|
enddo
|
|
|
|
! Display
|
|
if (debug) then
|
|
print*,'2D Hessian matrix'
|
|
do pq = 1, n
|
|
write(*,'(100(F10.5))') H(pq,:)
|
|
enddo
|
|
endif
|
|
|
|
!==============
|
|
! Deallocation
|
|
!==============
|
|
|
|
deallocate(hessian)
|
|
|
|
if (debug) then
|
|
print*,'Leave first_hess'
|
|
endif
|
|
|
|
end subroutine
|