2019-01-25 11:39:31 +01:00
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BEGIN_PROVIDER [ double precision, ao_overlap,(ao_num,ao_num) ]
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&BEGIN_PROVIDER [ double precision, ao_overlap_x,(ao_num,ao_num) ]
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&BEGIN_PROVIDER [ double precision, ao_overlap_y,(ao_num,ao_num) ]
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&BEGIN_PROVIDER [ double precision, ao_overlap_z,(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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!
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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,n,l
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double precision :: f
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integer :: dim1
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double precision :: overlap, overlap_x, overlap_y, overlap_z
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double precision :: alpha, beta, c
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double precision :: A_center(3), B_center(3)
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integer :: power_A(3), power_B(3)
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ao_overlap = 0.d0
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ao_overlap_x = 0.d0
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ao_overlap_y = 0.d0
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ao_overlap_z = 0.d0
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if (read_ao_integrals_overlap) then
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call ezfio_get_ao_one_e_ints_ao_integrals_overlap(ao_overlap(1:ao_num, 1:ao_num))
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print *, 'AO overlap integrals read from disk'
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else
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dim1=100
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!$OMP PARALLEL DO SCHEDULE(GUIDED) &
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!$OMP DEFAULT(NONE) &
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!$OMP PRIVATE(A_center,B_center,power_A,power_B,&
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!$OMP overlap_x,overlap_y, overlap_z, overlap, &
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!$OMP alpha, beta,i,j,c) &
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!$OMP SHARED(nucl_coord,ao_power,ao_prim_num, &
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!$OMP ao_overlap_x,ao_overlap_y,ao_overlap_z,ao_overlap,ao_num,ao_coef_normalized_ordered_transp,ao_nucl, &
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!$OMP ao_expo_ordered_transp,dim1)
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do j=1,ao_num
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A_center(1) = nucl_coord( ao_nucl(j), 1 )
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A_center(2) = nucl_coord( ao_nucl(j), 2 )
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A_center(3) = nucl_coord( ao_nucl(j), 3 )
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power_A(1) = ao_power( j, 1 )
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power_A(2) = ao_power( j, 2 )
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power_A(3) = ao_power( j, 3 )
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do i= 1,ao_num
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B_center(1) = nucl_coord( ao_nucl(i), 1 )
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B_center(2) = nucl_coord( ao_nucl(i), 2 )
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B_center(3) = nucl_coord( ao_nucl(i), 3 )
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power_B(1) = ao_power( i, 1 )
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power_B(2) = ao_power( i, 2 )
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power_B(3) = ao_power( i, 3 )
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do n = 1,ao_prim_num(j)
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alpha = ao_expo_ordered_transp(n,j)
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do l = 1, ao_prim_num(i)
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beta = ao_expo_ordered_transp(l,i)
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call overlap_gaussian_xyz(A_center,B_center,alpha,beta,power_A,power_B,overlap_x,overlap_y,overlap_z,overlap,dim1)
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c = ao_coef_normalized_ordered_transp(n,j) * ao_coef_normalized_ordered_transp(l,i)
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ao_overlap(i,j) += c * overlap
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ao_overlap_x(i,j) += c * overlap_x
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ao_overlap_y(i,j) += c * overlap_y
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ao_overlap_z(i,j) += c * overlap_z
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enddo
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enddo
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enddo
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enddo
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!$OMP END PARALLEL DO
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endif
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if (write_ao_integrals_overlap) then
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call ezfio_set_ao_one_e_ints_ao_integrals_overlap(ao_overlap(1:ao_num, 1:ao_num))
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print *, 'AO overlap integrals written to disk'
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endif
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END_PROVIDER
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2019-12-02 19:25:35 +01:00
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BEGIN_PROVIDER [ double precision, ao_overlap_imag, (ao_num, ao_num) ]
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implicit none
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BEGIN_DOC
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! Imaginary part of the overlap
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END_DOC
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ao_overlap_imag = 0.d0
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END_PROVIDER
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BEGIN_PROVIDER [ complex*16, ao_overlap_complex, (ao_num, ao_num) ]
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implicit none
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BEGIN_DOC
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! Overlap for complex AOs
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END_DOC
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integer :: i,j
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do j=1,ao_num
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do i=1,ao_num
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ao_overlap_complex(i,j) = dcmplx( ao_overlap(i,j), ao_overlap_imag(i,j) )
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enddo
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enddo
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END_PROVIDER
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2019-01-25 11:39:31 +01:00
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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 values of atomic basis functions:
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!
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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,n,l
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double precision :: f
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integer :: dim1
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double precision :: overlap, overlap_x, overlap_y, overlap_z
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double precision :: alpha, beta
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double precision :: A_center(3), B_center(3)
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integer :: power_A(3), power_B(3)
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double precision :: lower_exp_val, dx
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2019-12-09 19:16:48 +01:00
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if (is_periodic) then
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2019-12-02 19:25:35 +01:00
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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_complex(i,j))
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enddo
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2019-01-25 11:39:31 +01:00
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enddo
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2019-12-02 19:25:35 +01:00
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else
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dim1=100
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lower_exp_val = 40.d0
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!$OMP PARALLEL DO SCHEDULE(GUIDED) &
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!$OMP DEFAULT(NONE) &
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!$OMP PRIVATE(A_center,B_center,power_A,power_B, &
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!$OMP overlap_x,overlap_y, overlap_z, overlap, &
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!$OMP alpha, beta,i,j,dx) &
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!$OMP SHARED(nucl_coord,ao_power,ao_prim_num, &
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!$OMP ao_overlap_abs,ao_num,ao_coef_normalized_ordered_transp,ao_nucl,&
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!$OMP ao_expo_ordered_transp,dim1,lower_exp_val)
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do j=1,ao_num
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A_center(1) = nucl_coord( ao_nucl(j), 1 )
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A_center(2) = nucl_coord( ao_nucl(j), 2 )
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A_center(3) = nucl_coord( ao_nucl(j), 3 )
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power_A(1) = ao_power( j, 1 )
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power_A(2) = ao_power( j, 2 )
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power_A(3) = ao_power( j, 3 )
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do i= 1,ao_num
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ao_overlap_abs(i,j)= 0.d0
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B_center(1) = nucl_coord( ao_nucl(i), 1 )
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B_center(2) = nucl_coord( ao_nucl(i), 2 )
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B_center(3) = nucl_coord( ao_nucl(i), 3 )
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power_B(1) = ao_power( i, 1 )
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power_B(2) = ao_power( i, 2 )
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power_B(3) = ao_power( i, 3 )
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do n = 1,ao_prim_num(j)
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alpha = ao_expo_ordered_transp(n,j)
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do l = 1, ao_prim_num(i)
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beta = ao_expo_ordered_transp(l,i)
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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)
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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)
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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)
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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
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enddo
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enddo
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enddo
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enddo
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!$OMP END PARALLEL DO
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endif
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2019-01-25 11:39:31 +01:00
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, 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(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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2019-12-02 19:25:35 +01:00
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BEGIN_PROVIDER [ complex*16, S_inv_complex,(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_complex, &
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size(ao_overlap_complex,1),ao_num,ao_num,S_inv_complex,size(S_inv_complex,1))
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END_PROVIDER
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2019-01-25 11:39:31 +01:00
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BEGIN_PROVIDER [ double precision, 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 :: U(:,:),Vt(:,:), D(:)
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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( &
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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
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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 [ double precision, 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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double precision, allocatable :: U(:,:)
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double precision, 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(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
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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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