mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-11-06 22:23:55 +01:00
112 lines
4.0 KiB
Fortran
112 lines
4.0 KiB
Fortran
|
|
! This file is an example of the kind of manipulations that you can do with providers
|
|
!
|
|
|
|
!!!!!!!!!!!!!!!!!!!!!!!!!! Main providers useful for the program !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
|
|
|
|
!!! type name
|
|
BEGIN_PROVIDER [ double precision, trace_mo_one_e_ints]
|
|
implicit none
|
|
BEGIN_DOC
|
|
! trace_mo_one_e_ints = Trace of the one-electron integrals on the MO basis
|
|
!
|
|
! = sum_i mo_one_e_integrals(i,i)
|
|
END_DOC
|
|
integer :: i
|
|
trace_mo_one_e_ints = 0.d0
|
|
do i = 1, mo_num
|
|
trace_mo_one_e_ints += mo_one_e_integrals(i,i)
|
|
enddo
|
|
END_PROVIDER
|
|
|
|
BEGIN_PROVIDER [ double precision, trace_ao_one_e_ints]
|
|
implicit none
|
|
BEGIN_DOC
|
|
! trace_ao_one_e_ints = Trace of the one-electron integrals on the AO basis taking into account the non orthogonality
|
|
!
|
|
! Be aware that the trace of an operator in a non orthonormal basis is Tr(A S^{-1}) = \sum_{m,n}(A_mn S^{-1}_mn)
|
|
!
|
|
! WARNING: it is equal to the trace on the MO basis if and only if the AO basis and MO basis
|
|
! have the same number of functions
|
|
END_DOC
|
|
integer :: i,j
|
|
double precision, allocatable :: inv_overlap_times_integrals(:,:) ! = h S^{-1}
|
|
allocate(inv_overlap_times_integrals(ao_num,ao_num))
|
|
! routine that computes the product of two matrices, you can check it with
|
|
! irpman get_AB_prod
|
|
call get_AB_prod(ao_one_e_integrals,ao_num,ao_num,s_inv,ao_num,inv_overlap_times_integrals)
|
|
! Tr(inv_overlap_times_integrals) = Tr(h S^{-1})
|
|
trace_ao_one_e_ints = 0.d0
|
|
do i = 1, ao_num
|
|
trace_ao_one_e_ints += inv_overlap_times_integrals(i,i)
|
|
enddo
|
|
!
|
|
! testing the formula Tr(A S^{-1}) = \sum_{m,n}(A_mn S^{-1}_mn)
|
|
double precision :: test
|
|
test = 0.d0
|
|
do i = 1, ao_num
|
|
do j = 1, ao_num
|
|
test += ao_one_e_integrals(j,i) * s_inv(i,j)
|
|
enddo
|
|
enddo
|
|
if(dabs(accu - trace_ao_one_e_ints).gt.1.d-12)then
|
|
print*,'Warning ! '
|
|
print*,'Something is wrong because Tr(AB) \ne sum_{mn}A_mn B_nm'
|
|
endif
|
|
END_PROVIDER
|
|
|
|
BEGIN_PROVIDER [ double precision, trace_ao_one_e_ints_from_mo]
|
|
implicit none
|
|
BEGIN_DOC
|
|
! trace_ao_one_e_ints_from_mo = Trace of the one-electron integrals on the AO basis after projection on the MO basis
|
|
!
|
|
! = Tr([SC h {SC}^+] S^{-1})
|
|
!
|
|
! = Be aware that the trace of an operator in a non orthonormal basis is = Tr(A S^{-1}) where S is the metric
|
|
! Must be equal to the trace_mo_one_e_ints
|
|
END_DOC
|
|
integer :: i
|
|
double precision, allocatable :: inv_overlap_times_integrals(:,:)
|
|
allocate(inv_overlap_times_integrals(ao_num,ao_num))
|
|
! Using the provider ao_one_e_integrals_from_mo = [SC h {SC}^+]
|
|
call get_AB_prod(ao_one_e_integrals_from_mo,ao_num,ao_num,s_inv,ao_num,inv_overlap_times_integrals)
|
|
! inv_overlap_times_integrals = [SC h {SC}^+] S^{-1}
|
|
trace_ao_one_e_ints_from_mo = 0.d0
|
|
! Computing the trace
|
|
do i = 1, ao_num
|
|
trace_ao_one_e_ints_from_mo += inv_overlap_times_integrals(i,i)
|
|
enddo
|
|
END_PROVIDER
|
|
|
|
!!!!!!!!!!!!!!!!!!!!!!!!!!! Additional providers to check some stuffs !!!!!!!!!!!!!!!!!!!!!!!!!
|
|
|
|
BEGIN_PROVIDER [ double precision, ao_one_e_int_no_ov_from_mo, (ao_num, ao_num) ]
|
|
BEGIN_DOC
|
|
! ao_one_e_int_no_ov_from_mo = C mo_one_e_integrals C^T
|
|
!
|
|
! WARNING : NON EQUAL TO ao_one_e_integrals due to the non orthogonality
|
|
END_DOC
|
|
call mo_to_ao_no_overlap(mo_one_e_integrals,mo_num,ao_one_e_int_no_ov_from_mo,ao_num)
|
|
END_PROVIDER
|
|
|
|
BEGIN_PROVIDER [ double precision, ao_one_e_int_no_ov_from_mo_ov_ov, (ao_num, ao_num)]
|
|
BEGIN_DOC
|
|
! ao_one_e_int_no_ov_from_mo_ov_ov = S ao_one_e_int_no_ov_from_mo S = SC mo_one_e_integrals (SC)^T
|
|
!
|
|
! EQUAL TO ao_one_e_integrals ONLY IF ao_num = mo_num
|
|
END_DOC
|
|
double precision, allocatable :: tmp(:,:)
|
|
allocate(tmp(ao_num, ao_num))
|
|
call get_AB_prod(ao_overlap,ao_num,ao_num,ao_one_e_int_no_ov_from_mo,ao_num,tmp)
|
|
call get_AB_prod(tmp,ao_num,ao_num,ao_overlap,ao_num,ao_one_e_int_no_ov_from_mo_ov_ov)
|
|
END_PROVIDER
|
|
|
|
BEGIN_PROVIDER [ double precision, c_t_s_c, (mo_num, mo_num)]
|
|
implicit none
|
|
BEGIN_DOC
|
|
! C^T S C = should be the identity
|
|
END_DOC
|
|
call get_AB_prod(mo_coef_transp,mo_num,ao_num,S_mo_coef,mo_num,c_t_s_c)
|
|
END_PROVIDER
|
|
|