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