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https://github.com/QuantumPackage/qp2.git
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137 lines
3.2 KiB
Fortran
137 lines
3.2 KiB
Fortran
BEGIN_PROVIDER [ complex*16, ao_overlap,(ao_num,ao_num) ]
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implicit none
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BEGIN_DOC
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! Overlap between atomic basis functions:
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! :math:`\int \chi_i(r) \chi_j(r) dr)`
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END_DOC
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if (read_ao_integrals_overlap) then
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call read_one_e_integrals_complex('ao_overlap', ao_overlap,&
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size(ao_overlap,1), size(ao_overlap,2))
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print *, 'AO overlap integrals read from disk'
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else
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print *, 'complex AO overlap integrals must be provided'
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endif
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, ao_overlap_abs,(ao_num,ao_num) ]
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implicit none
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BEGIN_DOC
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! Overlap between absolute value of atomic basis functions:
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! :math:`\int |\chi_i(r)| |\chi_j(r)| dr)`
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END_DOC
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integer :: i,j
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!$OMP PARALLEL DO SCHEDULE(GUIDED) &
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!$OMP DEFAULT(NONE) &
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!$OMP PRIVATE(i,j) &
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!$OMP SHARED(ao_overlap_abs,ao_overlap,ao_num)
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do j=1,ao_num
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do i= 1,ao_num
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ao_overlap_abs(i,j)= cdabs(ao_overlap(i,j))
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enddo
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enddo
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!$OMP END PARALLEL DO
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END_PROVIDER
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BEGIN_PROVIDER [ complex*16, S_inv,(ao_num,ao_num) ]
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implicit none
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BEGIN_DOC
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! Inverse of the overlap matrix
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END_DOC
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call get_pseudo_inverse_complex(ao_overlap,size(ao_overlap,1),ao_num,ao_num,S_inv,size(S_inv,1))
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END_PROVIDER
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BEGIN_PROVIDER [ complex*16, S_half_inv, (AO_num,AO_num) ]
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BEGIN_DOC
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! :math:`X = S^{-1/2}` obtained by SVD
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END_DOC
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implicit none
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integer :: num_linear_dependencies
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integer :: LDA, LDC
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double precision, allocatable :: D(:)
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complex*16, allocatable :: U(:,:),Vt(:,:)
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integer :: info, i, j, k
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double precision, parameter :: threshold_overlap_AO_eigenvalues = 1.d-6
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LDA = size(AO_overlap,1)
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LDC = size(S_half_inv,1)
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allocate( &
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U(LDC,AO_num), &
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Vt(LDA,AO_num), &
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D(AO_num))
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call svd_complex( &
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AO_overlap,LDA, &
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U,LDC, &
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D, &
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Vt,LDA, &
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AO_num,AO_num)
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num_linear_dependencies = 0
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do i=1,AO_num
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print*,D(i)
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if(abs(D(i)) <= threshold_overlap_AO_eigenvalues) then
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D(i) = 0.d0
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num_linear_dependencies += 1
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else
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ASSERT (D(i) > 0.d0)
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D(i) = 1.d0/sqrt(D(i))
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endif
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do j=1,AO_num
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S_half_inv(j,i) = (0.d0,0.d0)
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enddo
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enddo
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write(*,*) 'linear dependencies',num_linear_dependencies
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do k=1,AO_num
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if(D(k) /= 0.d0) then
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do j=1,AO_num
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do i=1,AO_num
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S_half_inv(i,j) = S_half_inv(i,j) + U(i,k)*D(k)*Vt(k,j)
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enddo
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enddo
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endif
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enddo
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END_PROVIDER
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BEGIN_PROVIDER [ complex*16, S_half, (ao_num,ao_num) ]
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implicit none
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BEGIN_DOC
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! :math:`S^{1/2}`
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END_DOC
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integer :: i,j,k
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complex*16, allocatable :: U(:,:)
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complex*16, allocatable :: Vt(:,:)
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double precision, allocatable :: D(:)
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allocate(U(ao_num,ao_num),Vt(ao_num,ao_num),D(ao_num))
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call svd_complex(ao_overlap,size(ao_overlap,1),U,size(U,1),D,Vt,size(Vt,1),ao_num,ao_num)
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do i=1,ao_num
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D(i) = dsqrt(D(i))
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do j=1,ao_num
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S_half(j,i) = (0.d0,0.d0)
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enddo
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enddo
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do k=1,ao_num
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do j=1,ao_num
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do i=1,ao_num
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S_half(i,j) = S_half(i,j) + U(i,k)*D(k)*Vt(k,j)
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enddo
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enddo
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enddo
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deallocate(U,Vt,D)
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END_PROVIDER
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