! ---
BEGIN_PROVIDER [ double precision, ao_overlap , (ao_num, ao_num) ]
&BEGIN_PROVIDER [ double precision, ao_overlap_x, (ao_num, ao_num) ]
&BEGIN_PROVIDER [ double precision, ao_overlap_y, (ao_num, ao_num) ]
&BEGIN_PROVIDER [ double precision, ao_overlap_z, (ao_num, ao_num) ]
BEGIN_DOC
! Overlap between atomic basis functions:
!
! :math:`\int \chi_i(r) \chi_j(r) dr`
END_DOC
implicit none
integer :: i, j, n, l, dim1, power_A(3), power_B(3)
double precision :: overlap, overlap_x, overlap_y, overlap_z
double precision :: alpha, beta, c
double precision :: A_center(3), B_center(3)
ao_overlap = 0.d0
ao_overlap_x = 0.d0
ao_overlap_y = 0.d0
ao_overlap_z = 0.d0
if(read_ao_integrals_overlap) then
call ezfio_get_ao_one_e_ints_ao_integrals_overlap(ao_overlap(1:ao_num, 1:ao_num))
print *, 'AO overlap integrals read from disk'
else
if(use_cosgtos) then
!print*, ' use_cosgtos for ao_overlap ?', use_cosgtos
do j = 1, ao_num
do i = 1, ao_num
ao_overlap (i,j) = ao_overlap_cosgtos (i,j)
ao_overlap_x(i,j) = ao_overlap_cosgtos_x(i,j)
ao_overlap_y(i,j) = ao_overlap_cosgtos_y(i,j)
ao_overlap_z(i,j) = ao_overlap_cosgtos_z(i,j)
enddo
enddo
else
dim1=100
!$OMP PARALLEL DO SCHEDULE(GUIDED) &
!$OMP DEFAULT(NONE) &
!$OMP PRIVATE(A_center,B_center,power_A,power_B,&
!$OMP overlap_x,overlap_y, overlap_z, overlap, &
!$OMP alpha, beta,i,j,c) &
!$OMP SHARED(nucl_coord,ao_power,ao_prim_num, &
!$OMP ao_overlap_x,ao_overlap_y,ao_overlap_z,ao_overlap,ao_num,ao_coef_normalized_ordered_transp,ao_nucl, &
!$OMP ao_expo_ordered_transp,dim1)
do j=1,ao_num
A_center(1) = nucl_coord( ao_nucl(j), 1 )
A_center(2) = nucl_coord( ao_nucl(j), 2 )
A_center(3) = nucl_coord( ao_nucl(j), 3 )
power_A(1) = ao_power( j, 1 )
power_A(2) = ao_power( j, 2 )
power_A(3) = ao_power( j, 3 )
do i= 1,ao_num
B_center(1) = nucl_coord( ao_nucl(i), 1 )
B_center(2) = nucl_coord( ao_nucl(i), 2 )
B_center(3) = nucl_coord( ao_nucl(i), 3 )
power_B(1) = ao_power( i, 1 )
power_B(2) = ao_power( i, 2 )
power_B(3) = ao_power( i, 3 )
do n = 1,ao_prim_num(j)
alpha = ao_expo_ordered_transp(n,j)
do l = 1, ao_prim_num(i)
beta = ao_expo_ordered_transp(l,i)
call overlap_gaussian_xyz(A_center,B_center,alpha,beta,power_A,power_B,overlap_x,overlap_y,overlap_z,overlap,dim1)
c = ao_coef_normalized_ordered_transp(n,j) * ao_coef_normalized_ordered_transp(l,i)
ao_overlap(i,j) += c * overlap
if(isnan(ao_overlap(i,j)))then
print*,'i,j',i,j
print*,'l,n',l,n
print*,'c,overlap',c,overlap
print*,overlap_x,overlap_y,overlap_z
stop
endif
ao_overlap_x(i,j) += c * overlap_x
ao_overlap_y(i,j) += c * overlap_y
ao_overlap_z(i,j) += c * overlap_z
enddo
enddo
enddo
enddo
!$OMP END PARALLEL DO
endif
endif
if (write_ao_integrals_overlap) then
call ezfio_set_ao_one_e_ints_ao_integrals_overlap(ao_overlap(1:ao_num, 1:ao_num))
print *, 'AO overlap integrals written to disk'
endif
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, ao_overlap_imag, (ao_num, ao_num) ]
implicit none
BEGIN_DOC
! Imaginary part of the overlap
END_DOC
ao_overlap_imag = 0.d0
END_PROVIDER
! ---
BEGIN_PROVIDER [ complex*16, ao_overlap_complex, (ao_num, ao_num) ]
implicit none
BEGIN_DOC
! Overlap for complex AOs
END_DOC
integer :: i,j
do j=1,ao_num
do i=1,ao_num
ao_overlap_complex(i,j) = dcmplx( ao_overlap(i,j), ao_overlap_imag(i,j) )
enddo
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, ao_overlap_abs, (ao_num, ao_num) ]
BEGIN_DOC
! Overlap between absolute values of atomic basis functions:
!
! :math:`\int |\chi_i(r)| |\chi_j(r)| dr`
END_DOC
implicit none
integer :: i, j, n, l, dim1, power_A(3), power_B(3)
double precision :: overlap_x, overlap_y, overlap_z
double precision :: alpha, beta
double precision :: A_center(3), B_center(3)
double precision :: lower_exp_val, dx
if(is_periodic) then
do j = 1, ao_num
do i = 1, ao_num
ao_overlap_abs(i,j) = cdabs(ao_overlap_complex(i,j))
enddo
enddo
else
dim1=100
lower_exp_val = 40.d0
!$OMP PARALLEL DO SCHEDULE(GUIDED) &
!$OMP DEFAULT(NONE) &
!$OMP PRIVATE(A_center,B_center,power_A,power_B, &
!$OMP overlap_x,overlap_y, overlap_z, &
!$OMP alpha, beta,i,j,dx) &
!$OMP SHARED(nucl_coord,ao_power,ao_prim_num, &
!$OMP ao_overlap_abs,ao_num,ao_coef_normalized_ordered_transp,ao_nucl,&
!$OMP ao_expo_ordered_transp,dim1,lower_exp_val)
do j=1,ao_num
A_center(1) = nucl_coord( ao_nucl(j), 1 )
A_center(2) = nucl_coord( ao_nucl(j), 2 )
A_center(3) = nucl_coord( ao_nucl(j), 3 )
power_A(1) = ao_power( j, 1 )
power_A(2) = ao_power( j, 2 )
power_A(3) = ao_power( j, 3 )
do i= 1,ao_num
ao_overlap_abs(i,j)= 0.d0
B_center(1) = nucl_coord( ao_nucl(i), 1 )
B_center(2) = nucl_coord( ao_nucl(i), 2 )
B_center(3) = nucl_coord( ao_nucl(i), 3 )
power_B(1) = ao_power( i, 1 )
power_B(2) = ao_power( i, 2 )
power_B(3) = ao_power( i, 3 )
do n = 1,ao_prim_num(j)
alpha = ao_expo_ordered_transp(n,j)
do l = 1, ao_prim_num(i)
beta = ao_expo_ordered_transp(l,i)
call overlap_x_abs(A_center(1),B_center(1),alpha,beta,power_A(1),power_B(1),overlap_x,lower_exp_val,dx,dim1)
call overlap_x_abs(A_center(2),B_center(2),alpha,beta,power_A(2),power_B(2),overlap_y,lower_exp_val,dx,dim1)
call overlap_x_abs(A_center(3),B_center(3),alpha,beta,power_A(3),power_B(3),overlap_z,lower_exp_val,dx,dim1)
ao_overlap_abs(i,j) += abs(ao_coef_normalized_ordered_transp(n,j) * ao_coef_normalized_ordered_transp(l,i)) * overlap_x * overlap_y * overlap_z
enddo
enddo
enddo
enddo
!$OMP END PARALLEL DO
endif
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, S_inv,(ao_num,ao_num) ]
implicit none
BEGIN_DOC
! Inverse of the overlap matrix
END_DOC
call get_pseudo_inverse(ao_overlap,size(ao_overlap,1),ao_num,ao_num,S_inv, &
size(S_inv,1),lin_dep_cutoff)
END_PROVIDER
BEGIN_PROVIDER [ complex*16, S_inv_complex,(ao_num,ao_num) ]
implicit none
BEGIN_DOC
! Inverse of the overlap matrix
END_DOC
call get_pseudo_inverse_complex(ao_overlap_complex, size(ao_overlap_complex,1),&
ao_num,ao_num,S_inv_complex,size(S_inv_complex,1),lin_dep_cutoff)
END_PROVIDER
BEGIN_PROVIDER [ double precision, S_half_inv, (AO_num,AO_num) ]
BEGIN_DOC
! :math:`X = S^{-1/2}` obtained by SVD
END_DOC
implicit none
integer :: num_linear_dependencies
integer :: LDA, LDC
double precision, allocatable :: U(:,:),Vt(:,:), D(:)
integer :: info, i, j, k
double precision, parameter :: threshold_overlap_AO_eigenvalues = 1.d-6
LDA = size(AO_overlap,1)
LDC = size(S_half_inv,1)
allocate( &
U(LDC,AO_num), &
Vt(LDA,AO_num), &
D(AO_num))
call svd( &
AO_overlap,LDA, &
U,LDC, &
D, &
Vt,LDA, &
AO_num,AO_num)
num_linear_dependencies = 0
do i=1,AO_num
print*,D(i)
if(abs(D(i)) <= threshold_overlap_AO_eigenvalues) then
D(i) = 0.d0
num_linear_dependencies += 1
else
ASSERT (D(i) > 0.d0)
D(i) = 1.d0/sqrt(D(i))
endif
do j=1,AO_num
S_half_inv(j,i) = 0.d0
enddo
enddo
write(*,*) 'linear dependencies',num_linear_dependencies
do k=1,AO_num
if(D(k) /= 0.d0) then
do j=1,AO_num
do i=1,AO_num
S_half_inv(i,j) = S_half_inv(i,j) + U(i,k)*D(k)*Vt(k,j)
enddo
enddo
endif
enddo
END_PROVIDER
BEGIN_PROVIDER [ double precision, S_half, (ao_num,ao_num) ]
implicit none
BEGIN_DOC
! :math:`S^{1/2}`
END_DOC
integer :: i,j,k
double precision, allocatable :: U(:,:)
double precision, allocatable :: Vt(:,:)
double precision, allocatable :: D(:)
allocate(U(ao_num,ao_num),Vt(ao_num,ao_num),D(ao_num))
call svd(ao_overlap,size(ao_overlap,1),U,size(U,1),D,Vt,size(Vt,1),ao_num,ao_num)
do i=1,ao_num
D(i) = dsqrt(D(i))
do j=1,ao_num
S_half(j,i) = 0.d0
enddo
enddo
do k=1,ao_num
do j=1,ao_num
do i=1,ao_num
S_half(i,j) = S_half(i,j) + U(i,k)*D(k)*Vt(k,j)
enddo
enddo
enddo
deallocate(U,Vt,D)
END_PROVIDER