1248 lines
40 KiB
Fortran
1248 lines
40 KiB
Fortran
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! ---
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subroutine phi_j_erf_mu_r_xyz_phi(i,j,mu_in, C_center, xyz_ints)
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implicit none
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BEGIN_DOC
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! xyz_ints(1/2/3) = int dr phi_j(r) [erf(mu |r - C|)/|r-C|] x/y/z phi_i(r)
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!
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! where phi_i and phi_j are AOs
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END_DOC
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integer, intent(in) :: i,j
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double precision, intent(in) :: mu_in, C_center(3)
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double precision, intent(out):: xyz_ints(3)
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integer :: num_A,power_A(3), num_b, power_B(3),power_B_tmp(3)
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double precision :: alpha, beta, A_center(3), B_center(3),contrib,NAI_pol_mult_erf
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integer :: n_pt_in,l,m,mm
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xyz_ints = 0.d0
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if(ao_overlap_abs(j,i).lt.1.d-12)then
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return
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endif
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n_pt_in = n_pt_max_integrals
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! j
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num_A = ao_nucl(j)
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power_A(1:3)= ao_power(j,1:3)
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A_center(1:3) = nucl_coord(num_A,1:3)
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! i
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num_B = ao_nucl(i)
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power_B(1:3)= ao_power(i,1:3)
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B_center(1:3) = nucl_coord(num_B,1:3)
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do l=1,ao_prim_num(j)
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alpha = ao_expo_ordered_transp(l,j)
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do m=1,ao_prim_num(i)
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beta = ao_expo_ordered_transp(m,i)
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do mm = 1, 3
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! (x phi_i ) * phi_j
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! x * (x - B_x)^b_x = b_x (x - B_x)^b_x + 1 * (x - B_x)^{b_x+1}
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!
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! first contribution :: B_x (x - B_x)^b_x :: usual integral multiplied by B_x
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power_B_tmp = power_B
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contrib = NAI_pol_mult_erf(A_center,B_center,power_A,power_B_tmp,alpha,beta,C_center,n_pt_in,mu_in)
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xyz_ints(mm) += contrib * B_center(mm) * ao_coef_normalized_ordered_transp(l,j) &
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* ao_coef_normalized_ordered_transp(m,i)
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! second contribution :: 1 * (x - B_x)^(b_x+1) :: integral with b_x=>b_x+1
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power_B_tmp(mm) += 1
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contrib = NAI_pol_mult_erf(A_center,B_center,power_A,power_B_tmp,alpha,beta,C_center,n_pt_in,mu_in)
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xyz_ints(mm) += contrib * 1.d0 * ao_coef_normalized_ordered_transp(l,j) &
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* ao_coef_normalized_ordered_transp(m,i)
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enddo
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enddo
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enddo
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end
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! ---
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double precision function phi_j_erf_mu_r_phi(i, j, mu_in, C_center)
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BEGIN_DOC
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! phi_j_erf_mu_r_phi = int dr phi_j(r) [erf(mu |r - C|)/|r-C|] phi_i(r)
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END_DOC
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implicit none
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integer, intent(in) :: i,j
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double precision, intent(in) :: mu_in, C_center(3)
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integer :: num_A, power_A(3), num_b, power_B(3)
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integer :: n_pt_in, l, m
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double precision :: alpha, beta, A_center(3), B_center(3), contrib
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double precision :: NAI_pol_mult_erf
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phi_j_erf_mu_r_phi = 0.d0
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if(ao_overlap_abs(j,i).lt.1.d-12) then
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return
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endif
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n_pt_in = n_pt_max_integrals
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! j
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num_A = ao_nucl(j)
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power_A(1:3) = ao_power(j,1:3)
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A_center(1:3) = nucl_coord(num_A,1:3)
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! i
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num_B = ao_nucl(i)
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power_B(1:3) = ao_power(i,1:3)
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B_center(1:3) = nucl_coord(num_B,1:3)
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do l = 1, ao_prim_num(j)
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alpha = ao_expo_ordered_transp(l,j)
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do m = 1, ao_prim_num(i)
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beta = ao_expo_ordered_transp(m,i)
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contrib = NAI_pol_mult_erf(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in, mu_in)
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phi_j_erf_mu_r_phi += contrib * ao_coef_normalized_ordered_transp(l,j) * ao_coef_normalized_ordered_transp(m,i)
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enddo
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enddo
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end function phi_j_erf_mu_r_phi
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! ---
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subroutine erfc_mu_gauss_xyz_ij_ao(i, j, mu, C_center, delta, gauss_ints)
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implicit none
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BEGIN_DOC
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! gauss_ints(m) = \int dr exp(-delta (r - C)^2 ) x/y/z * ( 1 - erf(mu |r-r'|))/ |r-r'| * AO_i(r') * AO_j(r')
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!
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! with m = 1 ==> x, m = 2, m = 3 ==> z
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!
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! m = 4 ==> no x/y/z
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END_DOC
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integer, intent(in) :: i,j
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double precision, intent(in) :: mu, C_center(3),delta
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double precision, intent(out):: gauss_ints(4)
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integer :: num_A,power_A(3), num_b, power_B(3)
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double precision :: alpha, beta, A_center(3), B_center(3),contrib,NAI_pol_mult_erf
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double precision :: xyz_ints(4)
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integer :: n_pt_in,l,m,mm
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gauss_ints = 0.d0
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if(ao_overlap_abs(j,i).lt.1.d-12)then
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return
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endif
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n_pt_in = n_pt_max_integrals
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! j
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num_A = ao_nucl(j)
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power_A(1:3)= ao_power(j,1:3)
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A_center(1:3) = nucl_coord(num_A,1:3)
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! i
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num_B = ao_nucl(i)
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power_B(1:3)= ao_power(i,1:3)
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B_center(1:3) = nucl_coord(num_B,1:3)
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gauss_ints = 0.d0
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do l=1,ao_prim_num(j)
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alpha = ao_expo_ordered_transp(l,j)
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do m=1,ao_prim_num(i)
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beta = ao_expo_ordered_transp(m,i)
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call erfc_mu_gauss_xyz(C_center,delta,mu,A_center,B_center,power_A,power_B,alpha,beta,n_pt_in,xyz_ints)
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do mm = 1, 4
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gauss_ints(mm) += xyz_ints(mm) * ao_coef_normalized_ordered_transp(l,j) &
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* ao_coef_normalized_ordered_transp(m,i)
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enddo
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enddo
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enddo
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end
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! ---
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subroutine erf_mu_gauss_ij_ao(i, j, mu, C_center, delta, gauss_ints)
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BEGIN_DOC
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!
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! gauss_ints = \int dr exp(-delta (r - C)^2) * erf(mu |r-C|) / |r-C| * AO_i(r) * AO_j(r)
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!
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END_DOC
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implicit none
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integer, intent(in) :: i, j
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double precision, intent(in) :: mu, C_center(3), delta
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double precision, intent(out) :: gauss_ints
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integer :: n_pt_in, l, m
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integer :: num_A, power_A(3), num_b, power_B(3)
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double precision :: alpha, beta, A_center(3), B_center(3), coef
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double precision :: integral
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double precision :: erf_mu_gauss
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gauss_ints = 0.d0
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if(ao_overlap_abs(j,i).lt.1.d-12) then
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return
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endif
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n_pt_in = n_pt_max_integrals
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! j
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num_A = ao_nucl(j)
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power_A(1:3) = ao_power(j,1:3)
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A_center(1:3) = nucl_coord(num_A,1:3)
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! i
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num_B = ao_nucl(i)
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power_B(1:3) = ao_power(i,1:3)
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B_center(1:3) = nucl_coord(num_B,1:3)
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do l = 1, ao_prim_num(j)
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alpha = ao_expo_ordered_transp(l,j)
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do m = 1, ao_prim_num(i)
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beta = ao_expo_ordered_transp(m,i)
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coef = ao_coef_normalized_ordered_transp(l,j) * ao_coef_normalized_ordered_transp(m,i)
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if(dabs(coef) .lt. 1.d-12) cycle
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integral = erf_mu_gauss(C_center, delta, mu, A_center, B_center, power_A, power_B, alpha, beta, n_pt_in)
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gauss_ints += integral * coef
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enddo
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enddo
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end subroutine erf_mu_gauss_ij_ao
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! ---
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subroutine NAI_pol_x_mult_erf_ao(i_ao, j_ao, mu_in, C_center, ints)
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BEGIN_DOC
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!
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! Computes the following integral :
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!
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! $\int_{-\infty}^{infty} dr x * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
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! $\int_{-\infty}^{infty} dr y * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
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! $\int_{-\infty}^{infty} dr z * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
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!
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END_DOC
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include 'utils/constants.include.F'
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implicit none
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integer, intent(in) :: i_ao, j_ao
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double precision, intent(in) :: mu_in, C_center(3)
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double precision, intent(out) :: ints(3)
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integer :: i, j, num_A, num_B, power_A(3), power_B(3), n_pt_in, power_xA(3), m
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double precision :: A_center(3), B_center(3), integral, alpha, beta, coef
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double precision :: NAI_pol_mult_erf
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ints = 0.d0
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num_A = ao_nucl(i_ao)
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power_A(1:3) = ao_power(i_ao,1:3)
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A_center(1:3) = nucl_coord(num_A,1:3)
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num_B = ao_nucl(j_ao)
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power_B(1:3) = ao_power(j_ao,1:3)
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B_center(1:3) = nucl_coord(num_B,1:3)
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n_pt_in = n_pt_max_integrals
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do i = 1, ao_prim_num(i_ao)
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alpha = ao_expo_ordered_transp(i,i_ao)
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do m = 1, 3
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power_xA = power_A
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! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
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power_xA(m) += 1
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do j = 1, ao_prim_num(j_ao)
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beta = ao_expo_ordered_transp(j,j_ao)
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coef = ao_coef_normalized_ordered_transp(j,j_ao) * ao_coef_normalized_ordered_transp(i,i_ao)
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! First term = (x-Ax)**(ax+1)
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integral = NAI_pol_mult_erf(A_center, B_center, power_xA, power_B, alpha, beta, C_center, n_pt_in, mu_in)
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ints(m) += integral * coef
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! Second term = Ax * (x-Ax)**(ax)
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integral = NAI_pol_mult_erf(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in, mu_in)
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ints(m) += A_center(m) * integral * coef
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enddo
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enddo
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enddo
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end subroutine NAI_pol_x_mult_erf_ao
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! ---
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subroutine NAI_pol_x_mult_erf_ao_v0(i_ao, j_ao, mu_in, C_center, LD_C, ints, LD_ints, n_points)
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BEGIN_DOC
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!
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! Computes the following integral :
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!
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! $\int_{-\infty}^{infty} dr x * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
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! $\int_{-\infty}^{infty} dr y * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
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! $\int_{-\infty}^{infty} dr z * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
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!
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END_DOC
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include 'utils/constants.include.F'
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implicit none
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integer, intent(in) :: i_ao, j_ao, LD_C, LD_ints, n_points
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double precision, intent(in) :: mu_in, C_center(LD_C,3)
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double precision, intent(out) :: ints(LD_ints,3)
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integer :: i, j, num_A, num_B, power_A(3), power_B(3), n_pt_in
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integer :: power_xA(3), m, ipoint
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double precision :: A_center(3), B_center(3), alpha, beta, coef
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double precision, allocatable :: integral(:)
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ints(1:LD_ints,1:3) = 0.d0
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num_A = ao_nucl(i_ao)
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power_A(1:3) = ao_power(i_ao,1:3)
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A_center(1:3) = nucl_coord(num_A,1:3)
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num_B = ao_nucl(j_ao)
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power_B(1:3) = ao_power(j_ao,1:3)
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B_center(1:3) = nucl_coord(num_B,1:3)
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n_pt_in = n_pt_max_integrals
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allocate(integral(n_points))
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integral = 0.d0
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do i = 1, ao_prim_num(i_ao)
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alpha = ao_expo_ordered_transp(i,i_ao)
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do m = 1, 3
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! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
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power_xA = power_A
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power_xA(m) += 1
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do j = 1, ao_prim_num(j_ao)
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beta = ao_expo_ordered_transp(j,j_ao)
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coef = ao_coef_normalized_ordered_transp(j,j_ao) * ao_coef_normalized_ordered_transp(i,i_ao)
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! First term = (x-Ax)**(ax+1)
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call NAI_pol_mult_erf_v(A_center, B_center, power_xA, power_B, alpha, beta, C_center(1:LD_C,1:3), LD_C, n_pt_in, mu_in, integral(1:n_points), n_points, n_points)
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do ipoint = 1, n_points
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ints(ipoint,m) += integral(ipoint) * coef
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enddo
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! Second term = Ax * (x-Ax)**(ax)
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call NAI_pol_mult_erf_v(A_center, B_center, power_A, power_B, alpha, beta, C_center(1:LD_C,1:3), LD_C, n_pt_in, mu_in, integral(1:n_points), n_points, n_points)
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do ipoint = 1, n_points
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ints(ipoint,m) += A_center(m) * integral(ipoint) * coef
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enddo
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enddo
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enddo
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enddo
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deallocate(integral)
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end subroutine NAI_pol_x_mult_erf_ao_v0
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! ---
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subroutine NAI_pol_x_mult_erf_ao_v(i_ao, j_ao, mu_in, C_center, LD_C, ints, LD_ints, n_points)
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BEGIN_DOC
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!
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! Computes the following integral :
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!
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! $\int_{-\infty}^{infty} dr x * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
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!
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! $\int_{-\infty}^{infty} dr y * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
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!
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! $\int_{-\infty}^{infty} dr z * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
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!
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END_DOC
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include 'utils/constants.include.F'
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implicit none
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integer, intent(in) :: i_ao, j_ao, LD_C, LD_ints, n_points(3)
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double precision, intent(in) :: mu_in, C_center(LD_C,3,3)
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double precision, intent(out) :: ints(LD_ints,3)
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integer :: i, j, num_A, num_B, power_A(3), power_B(3), n_pt_in, LD_integral
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integer :: power_xA(3), m, ipoint, n_points_m
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double precision :: A_center(3), B_center(3), alpha, beta, coef
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double precision, allocatable :: integral(:)
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ints(1:LD_ints,1:3) = 0.d0
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num_A = ao_nucl(i_ao)
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power_A(1:3) = ao_power(i_ao,1:3)
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A_center(1:3) = nucl_coord(num_A,1:3)
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num_B = ao_nucl(j_ao)
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power_B(1:3) = ao_power(j_ao,1:3)
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B_center(1:3) = nucl_coord(num_B,1:3)
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n_pt_in = n_pt_max_integrals
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LD_integral = max(max(n_points(1), n_points(2)), n_points(3))
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allocate(integral(LD_integral))
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integral = 0.d0
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do i = 1, ao_prim_num(i_ao)
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alpha = ao_expo_ordered_transp(i,i_ao)
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do m = 1, 3
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n_points_m = n_points(m)
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! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
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power_xA = power_A
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power_xA(m) += 1
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do j = 1, ao_prim_num(j_ao)
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beta = ao_expo_ordered_transp(j,j_ao)
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coef = ao_coef_normalized_ordered_transp(j,j_ao) * ao_coef_normalized_ordered_transp(i,i_ao)
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! First term = (x-Ax)**(ax+1)
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call NAI_pol_mult_erf_v( A_center, B_center, power_xA, power_B, alpha, beta &
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, C_center(1:LD_C,1:3,m), LD_C, n_pt_in, mu_in, integral(1:LD_integral), LD_integral, n_points_m)
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do ipoint = 1, n_points_m
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ints(ipoint,m) += integral(ipoint) * coef
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enddo
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! Second term = Ax * (x-Ax)**(ax)
|
|
call NAI_pol_mult_erf_v( A_center, B_center, power_A, power_B, alpha, beta &
|
|
, C_center(1:LD_C,1:3,m), LD_C, n_pt_in, mu_in, integral(1:LD_integral), LD_integral, n_points_m)
|
|
do ipoint = 1, n_points_m
|
|
ints(ipoint,m) += A_center(m) * integral(ipoint) * coef
|
|
enddo
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
deallocate(integral)
|
|
|
|
end subroutine NAI_pol_x_mult_erf_ao_v
|
|
|
|
! ---
|
|
|
|
double precision function NAI_pol_x_mult_erf_ao_x(i_ao, j_ao, mu_in, C_center)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! $\int_{-\infty}^{infty} dr x * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: i_ao, j_ao
|
|
double precision, intent(in) :: mu_in, C_center(3)
|
|
|
|
integer :: i, j, num_A, num_B, power_A(3), power_B(3), n_pt_in, power_xA(3)
|
|
double precision :: A_center(3), B_center(3), integral, alpha, beta, coef
|
|
|
|
double precision :: NAI_pol_mult_erf
|
|
|
|
NAI_pol_x_mult_erf_ao_x = 0.d0
|
|
if(ao_overlap_abs(j_ao,i_ao) .lt. 1.d-12) return
|
|
|
|
num_A = ao_nucl(i_ao)
|
|
power_A(1:3) = ao_power(i_ao,1:3)
|
|
A_center(1:3) = nucl_coord(num_A,1:3)
|
|
num_B = ao_nucl(j_ao)
|
|
power_B(1:3) = ao_power(j_ao,1:3)
|
|
B_center(1:3) = nucl_coord(num_B,1:3)
|
|
|
|
power_xA = power_A
|
|
power_xA(1) += 1
|
|
|
|
n_pt_in = n_pt_max_integrals
|
|
|
|
do i = 1, ao_prim_num(i_ao)
|
|
alpha = ao_expo_ordered_transp(i,i_ao)
|
|
|
|
do j = 1, ao_prim_num(j_ao)
|
|
beta = ao_expo_ordered_transp(j,j_ao)
|
|
coef = ao_coef_normalized_ordered_transp(j,j_ao) * ao_coef_normalized_ordered_transp(i,i_ao)
|
|
|
|
! First term = (x-Ax)**(ax+1)
|
|
integral = NAI_pol_mult_erf(A_center, B_center, power_xA, power_B, alpha, beta, C_center, n_pt_in, mu_in)
|
|
NAI_pol_x_mult_erf_ao_x += integral * coef
|
|
|
|
! Second term = Ax * (x-Ax)**(ax)
|
|
integral = NAI_pol_mult_erf(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in, mu_in)
|
|
NAI_pol_x_mult_erf_ao_x += A_center(1) * integral * coef
|
|
|
|
enddo
|
|
enddo
|
|
|
|
end function NAI_pol_x_mult_erf_ao_x
|
|
|
|
! ---
|
|
|
|
double precision function NAI_pol_x_mult_erf_ao_y(i_ao, j_ao, mu_in, C_center)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! $\int_{-\infty}^{infty} dr y * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: i_ao, j_ao
|
|
double precision, intent(in) :: mu_in, C_center(3)
|
|
|
|
integer :: i, j, num_A, num_B, power_A(3), power_B(3), n_pt_in, power_xA(3)
|
|
double precision :: A_center(3), B_center(3), integral, alpha, beta, coef
|
|
|
|
double precision :: NAI_pol_mult_erf
|
|
|
|
NAI_pol_x_mult_erf_ao_y = 0.d0
|
|
if(ao_overlap_abs(j_ao,i_ao) .lt. 1.d-12) return
|
|
|
|
num_A = ao_nucl(i_ao)
|
|
power_A(1:3) = ao_power(i_ao,1:3)
|
|
A_center(1:3) = nucl_coord(num_A,1:3)
|
|
num_B = ao_nucl(j_ao)
|
|
power_B(1:3) = ao_power(j_ao,1:3)
|
|
B_center(1:3) = nucl_coord(num_B,1:3)
|
|
|
|
power_xA = power_A
|
|
power_xA(2) += 1
|
|
|
|
n_pt_in = n_pt_max_integrals
|
|
|
|
do i = 1, ao_prim_num(i_ao)
|
|
alpha = ao_expo_ordered_transp(i,i_ao)
|
|
|
|
do j = 1, ao_prim_num(j_ao)
|
|
beta = ao_expo_ordered_transp(j,j_ao)
|
|
coef = ao_coef_normalized_ordered_transp(j,j_ao) * ao_coef_normalized_ordered_transp(i,i_ao)
|
|
|
|
! First term = (x-Ax)**(ax+1)
|
|
integral = NAI_pol_mult_erf(A_center, B_center, power_xA, power_B, alpha, beta, C_center, n_pt_in, mu_in)
|
|
NAI_pol_x_mult_erf_ao_y += integral * coef
|
|
|
|
! Second term = Ax * (x-Ax)**(ax)
|
|
integral = NAI_pol_mult_erf(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in, mu_in)
|
|
NAI_pol_x_mult_erf_ao_y += A_center(2) * integral * coef
|
|
|
|
enddo
|
|
enddo
|
|
|
|
end function NAI_pol_x_mult_erf_ao_y
|
|
|
|
! ---
|
|
|
|
double precision function NAI_pol_x_mult_erf_ao_z(i_ao, j_ao, mu_in, C_center)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! $\int_{-\infty}^{infty} dr z * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: i_ao, j_ao
|
|
double precision, intent(in) :: mu_in, C_center(3)
|
|
|
|
integer :: i, j, num_A, num_B, power_A(3), power_B(3), n_pt_in, power_xA(3)
|
|
double precision :: A_center(3), B_center(3), integral, alpha, beta, coef
|
|
|
|
double precision :: NAI_pol_mult_erf
|
|
|
|
NAI_pol_x_mult_erf_ao_z = 0.d0
|
|
if(ao_overlap_abs(j_ao,i_ao) .lt. 1.d-12) return
|
|
|
|
num_A = ao_nucl(i_ao)
|
|
power_A(1:3) = ao_power(i_ao,1:3)
|
|
A_center(1:3) = nucl_coord(num_A,1:3)
|
|
num_B = ao_nucl(j_ao)
|
|
power_B(1:3) = ao_power(j_ao,1:3)
|
|
B_center(1:3) = nucl_coord(num_B,1:3)
|
|
|
|
power_xA = power_A
|
|
power_xA(3) += 1
|
|
|
|
n_pt_in = n_pt_max_integrals
|
|
|
|
do i = 1, ao_prim_num(i_ao)
|
|
alpha = ao_expo_ordered_transp(i,i_ao)
|
|
|
|
do j = 1, ao_prim_num(j_ao)
|
|
beta = ao_expo_ordered_transp(j,j_ao)
|
|
coef = ao_coef_normalized_ordered_transp(j,j_ao) * ao_coef_normalized_ordered_transp(i,i_ao)
|
|
|
|
! First term = (x-Ax)**(ax+1)
|
|
integral = NAI_pol_mult_erf(A_center, B_center, power_xA, power_B, alpha, beta, C_center, n_pt_in, mu_in)
|
|
NAI_pol_x_mult_erf_ao_z += integral * coef
|
|
|
|
! Second term = Ax * (x-Ax)**(ax)
|
|
integral = NAI_pol_mult_erf(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in, mu_in)
|
|
NAI_pol_x_mult_erf_ao_z += A_center(3) * integral * coef
|
|
|
|
enddo
|
|
enddo
|
|
|
|
end function NAI_pol_x_mult_erf_ao_z
|
|
|
|
! ---
|
|
|
|
double precision function NAI_pol_x_mult_erf_ao_with1s_x(i_ao, j_ao, beta, B_center, mu_in, C_center)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! $\int_{-\infty}^{infty} dr x * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: i_ao, j_ao
|
|
double precision, intent(in) :: beta, B_center(3), mu_in, C_center(3)
|
|
|
|
integer :: i, j, power_Ai(3), power_Aj(3), n_pt_in, power_xA(3)
|
|
double precision :: Ai_center(3), Aj_center(3), integral, alphai, alphaj, coef, coefi
|
|
|
|
double precision, external :: NAI_pol_mult_erf_with1s
|
|
double precision, external :: NAI_pol_x_mult_erf_ao_x
|
|
|
|
ASSERT(beta .ge. 0.d0)
|
|
if(beta .lt. 1d-10) then
|
|
NAI_pol_x_mult_erf_ao_with1s_x = NAI_pol_x_mult_erf_ao_x(i_ao, j_ao, mu_in, C_center)
|
|
return
|
|
endif
|
|
|
|
NAI_pol_x_mult_erf_ao_with1s_x = 0.d0
|
|
if(ao_overlap_abs(j_ao,i_ao) .lt. 1.d-12) then
|
|
return
|
|
endif
|
|
|
|
power_Ai(1:3) = ao_power(i_ao,1:3)
|
|
power_Aj(1:3) = ao_power(j_ao,1:3)
|
|
|
|
Ai_center(1:3) = nucl_coord(ao_nucl(i_ao),1:3)
|
|
Aj_center(1:3) = nucl_coord(ao_nucl(j_ao),1:3)
|
|
|
|
power_xA = power_Ai
|
|
power_xA(1) += 1
|
|
|
|
n_pt_in = n_pt_max_integrals
|
|
|
|
do i = 1, ao_prim_num(i_ao)
|
|
alphai = ao_expo_ordered_transp (i,i_ao)
|
|
coefi = ao_coef_normalized_ordered_transp(i,i_ao)
|
|
|
|
do j = 1, ao_prim_num(j_ao)
|
|
alphaj = ao_expo_ordered_transp (j,j_ao)
|
|
coef = coefi * ao_coef_normalized_ordered_transp(j,j_ao)
|
|
|
|
! First term = (x-Ax)**(ax+1)
|
|
integral = NAI_pol_mult_erf_with1s( Ai_center, Aj_center, power_xA, power_Aj, alphai, alphaj &
|
|
, beta, B_center, C_center, n_pt_in, mu_in )
|
|
NAI_pol_x_mult_erf_ao_with1s_x += integral * coef
|
|
|
|
! Second term = Ax * (x-Ax)**(ax)
|
|
integral = NAI_pol_mult_erf_with1s( Ai_center, Aj_center, power_Ai, power_Aj, alphai, alphaj &
|
|
, beta, B_center, C_center, n_pt_in, mu_in )
|
|
NAI_pol_x_mult_erf_ao_with1s_x += Ai_center(1) * integral * coef
|
|
|
|
enddo
|
|
enddo
|
|
|
|
end function NAI_pol_x_mult_erf_ao_with1s_x
|
|
|
|
! ---
|
|
|
|
double precision function NAI_pol_x_mult_erf_ao_with1s_y(i_ao, j_ao, beta, B_center, mu_in, C_center)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! $\int_{-\infty}^{infty} dr y * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: i_ao, j_ao
|
|
double precision, intent(in) :: beta, B_center(3), mu_in, C_center(3)
|
|
|
|
integer :: i, j, power_Ai(3), power_Aj(3), n_pt_in, power_xA(3)
|
|
double precision :: Ai_center(3), Aj_center(3), integral, alphai, alphaj, coef, coefi
|
|
|
|
double precision, external :: NAI_pol_mult_erf_with1s
|
|
double precision, external :: NAI_pol_x_mult_erf_ao_y
|
|
|
|
ASSERT(beta .ge. 0.d0)
|
|
if(beta .lt. 1d-10) then
|
|
NAI_pol_x_mult_erf_ao_with1s_y = NAI_pol_x_mult_erf_ao_y(i_ao, j_ao, mu_in, C_center)
|
|
return
|
|
endif
|
|
|
|
NAI_pol_x_mult_erf_ao_with1s_y = 0.d0
|
|
if(ao_overlap_abs(j_ao,i_ao) .lt. 1.d-12) then
|
|
return
|
|
endif
|
|
|
|
power_Ai(1:3) = ao_power(i_ao,1:3)
|
|
power_Aj(1:3) = ao_power(j_ao,1:3)
|
|
|
|
Ai_center(1:3) = nucl_coord(ao_nucl(i_ao),1:3)
|
|
Aj_center(1:3) = nucl_coord(ao_nucl(j_ao),1:3)
|
|
|
|
power_xA = power_Ai
|
|
power_xA(2) += 1
|
|
|
|
n_pt_in = n_pt_max_integrals
|
|
|
|
do i = 1, ao_prim_num(i_ao)
|
|
alphai = ao_expo_ordered_transp (i,i_ao)
|
|
coefi = ao_coef_normalized_ordered_transp(i,i_ao)
|
|
|
|
do j = 1, ao_prim_num(j_ao)
|
|
alphaj = ao_expo_ordered_transp (j,j_ao)
|
|
coef = coefi * ao_coef_normalized_ordered_transp(j,j_ao)
|
|
|
|
! First term = (x-Ax)**(ax+1)
|
|
integral = NAI_pol_mult_erf_with1s( Ai_center, Aj_center, power_xA, power_Aj, alphai, alphaj &
|
|
, beta, B_center, C_center, n_pt_in, mu_in )
|
|
NAI_pol_x_mult_erf_ao_with1s_y += integral * coef
|
|
|
|
! Second term = Ax * (x-Ax)**(ax)
|
|
integral = NAI_pol_mult_erf_with1s( Ai_center, Aj_center, power_Ai, power_Aj, alphai, alphaj &
|
|
, beta, B_center, C_center, n_pt_in, mu_in )
|
|
NAI_pol_x_mult_erf_ao_with1s_y += Ai_center(2) * integral * coef
|
|
|
|
enddo
|
|
enddo
|
|
|
|
end function NAI_pol_x_mult_erf_ao_with1s_y
|
|
|
|
! ---
|
|
|
|
double precision function NAI_pol_x_mult_erf_ao_with1s_z(i_ao, j_ao, beta, B_center, mu_in, C_center)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! $\int_{-\infty}^{infty} dr z * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: i_ao, j_ao
|
|
double precision, intent(in) :: beta, B_center(3), mu_in, C_center(3)
|
|
|
|
integer :: i, j, power_Ai(3), power_Aj(3), n_pt_in, power_xA(3)
|
|
double precision :: Ai_center(3), Aj_center(3), integral, alphai, alphaj, coef, coefi
|
|
|
|
double precision, external :: NAI_pol_mult_erf_with1s
|
|
double precision, external :: NAI_pol_x_mult_erf_ao_z
|
|
|
|
ASSERT(beta .ge. 0.d0)
|
|
if(beta .lt. 1d-10) then
|
|
NAI_pol_x_mult_erf_ao_with1s_z = NAI_pol_x_mult_erf_ao_z(i_ao, j_ao, mu_in, C_center)
|
|
return
|
|
endif
|
|
|
|
NAI_pol_x_mult_erf_ao_with1s_z = 0.d0
|
|
if(ao_overlap_abs(j_ao,i_ao) .lt. 1.d-12) then
|
|
return
|
|
endif
|
|
|
|
power_Ai(1:3) = ao_power(i_ao,1:3)
|
|
power_Aj(1:3) = ao_power(j_ao,1:3)
|
|
|
|
Ai_center(1:3) = nucl_coord(ao_nucl(i_ao),1:3)
|
|
Aj_center(1:3) = nucl_coord(ao_nucl(j_ao),1:3)
|
|
|
|
power_xA = power_Ai
|
|
power_xA(3) += 1
|
|
|
|
n_pt_in = n_pt_max_integrals
|
|
|
|
do i = 1, ao_prim_num(i_ao)
|
|
alphai = ao_expo_ordered_transp (i,i_ao)
|
|
coefi = ao_coef_normalized_ordered_transp(i,i_ao)
|
|
|
|
do j = 1, ao_prim_num(j_ao)
|
|
alphaj = ao_expo_ordered_transp (j,j_ao)
|
|
coef = coefi * ao_coef_normalized_ordered_transp(j,j_ao)
|
|
|
|
! First term = (x-Ax)**(ax+1)
|
|
integral = NAI_pol_mult_erf_with1s( Ai_center, Aj_center, power_xA, power_Aj, alphai, alphaj &
|
|
, beta, B_center, C_center, n_pt_in, mu_in )
|
|
NAI_pol_x_mult_erf_ao_with1s_z += integral * coef
|
|
|
|
! Second term = Ax * (x-Ax)**(ax)
|
|
integral = NAI_pol_mult_erf_with1s( Ai_center, Aj_center, power_Ai, power_Aj, alphai, alphaj &
|
|
, beta, B_center, C_center, n_pt_in, mu_in )
|
|
NAI_pol_x_mult_erf_ao_with1s_z += Ai_center(3) * integral * coef
|
|
|
|
enddo
|
|
enddo
|
|
|
|
end function NAI_pol_x_mult_erf_ao_with1s_z
|
|
|
|
! ---
|
|
|
|
subroutine NAI_pol_x_mult_erf_ao_with1s(i_ao, j_ao, beta, B_center, mu_in, C_center, ints)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! $\int_{-\infty}^{infty} dr x * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
! $\int_{-\infty}^{infty} dr y * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
! $\int_{-\infty}^{infty} dr z * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: i_ao, j_ao
|
|
double precision, intent(in) :: beta, B_center(3), mu_in, C_center(3)
|
|
double precision, intent(out) :: ints(3)
|
|
|
|
integer :: i, j, power_Ai(3), power_Aj(3), n_pt_in, power_xA(3), m
|
|
double precision :: Ai_center(3), Aj_center(3), integral, alphai, alphaj, coef, coefi
|
|
|
|
double precision, external :: NAI_pol_mult_erf_with1s
|
|
|
|
ASSERT(beta .ge. 0.d0)
|
|
if(beta .lt. 1d-10) then
|
|
call NAI_pol_x_mult_erf_ao(i_ao, j_ao, mu_in, C_center, ints)
|
|
return
|
|
endif
|
|
|
|
ints = 0.d0
|
|
|
|
power_Ai(1:3) = ao_power(i_ao,1:3)
|
|
power_Aj(1:3) = ao_power(j_ao,1:3)
|
|
|
|
Ai_center(1:3) = nucl_coord(ao_nucl(i_ao),1:3)
|
|
Aj_center(1:3) = nucl_coord(ao_nucl(j_ao),1:3)
|
|
|
|
n_pt_in = n_pt_max_integrals
|
|
|
|
do i = 1, ao_prim_num(i_ao)
|
|
alphai = ao_expo_ordered_transp (i,i_ao)
|
|
coefi = ao_coef_normalized_ordered_transp(i,i_ao)
|
|
|
|
do m = 1, 3
|
|
|
|
! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
|
|
power_xA = power_Ai
|
|
power_xA(m) += 1
|
|
|
|
do j = 1, ao_prim_num(j_ao)
|
|
alphaj = ao_expo_ordered_transp (j,j_ao)
|
|
coef = coefi * ao_coef_normalized_ordered_transp(j,j_ao)
|
|
|
|
! First term = (x-Ax)**(ax+1)
|
|
integral = NAI_pol_mult_erf_with1s(Ai_center, Aj_center, power_xA, power_Aj, alphai, alphaj, beta, B_center, C_center, n_pt_in, mu_in)
|
|
ints(m) += integral * coef
|
|
|
|
! Second term = Ax * (x-Ax)**(ax)
|
|
integral = NAI_pol_mult_erf_with1s(Ai_center, Aj_center, power_Ai, power_Aj, alphai, alphaj, beta, B_center, C_center, n_pt_in, mu_in)
|
|
ints(m) += Ai_center(m) * integral * coef
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine NAI_pol_x_mult_erf_ao_with1s
|
|
|
|
! ---
|
|
|
|
subroutine NAI_pol_x_mult_erf_ao_with1s_v0(i_ao, j_ao, beta, B_center, LD_B, mu_in, C_center, LD_C, ints, LD_ints, n_points)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! $\int_{-\infty}^{infty} dr x * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
! $\int_{-\infty}^{infty} dr y * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
! $\int_{-\infty}^{infty} dr z * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: i_ao, j_ao, LD_B, LD_C, LD_ints, n_points
|
|
double precision, intent(in) :: beta, mu_in
|
|
double precision, intent(in) :: B_center(LD_B,3), C_center(LD_C,3)
|
|
double precision, intent(out) :: ints(LD_ints,3)
|
|
|
|
integer :: i, j, power_Ai(3), power_Aj(3), n_pt_in, power_xA(3), m
|
|
double precision :: Ai_center(3), Aj_center(3), alphai, alphaj, coef, coefi
|
|
|
|
integer :: ipoint
|
|
double precision, allocatable :: integral(:)
|
|
|
|
if(beta .lt. 1d-10) then
|
|
call NAI_pol_x_mult_erf_ao_v0(i_ao, j_ao, mu_in, C_center, LD_C, ints, LD_ints, n_points)
|
|
return
|
|
endif
|
|
|
|
ints(1:LD_ints,1:3) = 0.d0
|
|
|
|
power_Ai(1:3) = ao_power(i_ao,1:3)
|
|
power_Aj(1:3) = ao_power(j_ao,1:3)
|
|
|
|
Ai_center(1:3) = nucl_coord(ao_nucl(i_ao),1:3)
|
|
Aj_center(1:3) = nucl_coord(ao_nucl(j_ao),1:3)
|
|
|
|
n_pt_in = n_pt_max_integrals
|
|
|
|
allocate(integral(n_points))
|
|
integral = 0.d0
|
|
|
|
do i = 1, ao_prim_num(i_ao)
|
|
alphai = ao_expo_ordered_transp (i,i_ao)
|
|
coefi = ao_coef_normalized_ordered_transp(i,i_ao)
|
|
|
|
do m = 1, 3
|
|
|
|
! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
|
|
power_xA = power_Ai
|
|
power_xA(m) += 1
|
|
|
|
do j = 1, ao_prim_num(j_ao)
|
|
alphaj = ao_expo_ordered_transp (j,j_ao)
|
|
coef = coefi * ao_coef_normalized_ordered_transp(j,j_ao)
|
|
|
|
! First term = (x-Ax)**(ax+1)
|
|
|
|
call NAI_pol_mult_erf_with1s_v( Ai_center, Aj_center, power_xA, power_Aj, alphai, alphaj, beta &
|
|
, B_center(1:LD_B,1:3), LD_B, C_center(1:LD_C,1:3), LD_C, n_pt_in, mu_in, integral(1:n_points), n_points, n_points)
|
|
|
|
do ipoint = 1, n_points
|
|
ints(ipoint,m) += integral(ipoint) * coef
|
|
enddo
|
|
|
|
! Second term = Ax * (x-Ax)**(ax)
|
|
call NAI_pol_mult_erf_with1s_v( Ai_center, Aj_center, power_Ai, power_Aj, alphai, alphaj, beta &
|
|
, B_center(1:LD_B,1:3), LD_B, C_center(1:LD_C,1:3), LD_C, n_pt_in, mu_in, integral(1:n_points), n_points, n_points)
|
|
do ipoint = 1, n_points
|
|
ints(ipoint,m) += Ai_center(m) * integral(ipoint) * coef
|
|
enddo
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
deallocate(integral)
|
|
|
|
end subroutine NAI_pol_x_mult_erf_ao_with1s_v0
|
|
|
|
! ---
|
|
|
|
subroutine NAI_pol_x_mult_erf_ao_with1s_v(i_ao, j_ao, beta, B_center, LD_B, mu_in, C_center, LD_C, ints, LD_ints, n_points)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! $\int_{-\infty}^{infty} dr x * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
! $\int_{-\infty}^{infty} dr y * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
! $\int_{-\infty}^{infty} dr z * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: i_ao, j_ao, LD_B, LD_C, LD_ints, n_points(3)
|
|
double precision, intent(in) :: beta, mu_in
|
|
double precision, intent(in) :: B_center(LD_B,3,3), C_center(LD_C,3,3)
|
|
double precision, intent(out) :: ints(LD_ints,3)
|
|
|
|
integer :: i, j, power_Ai(3), power_Aj(3), n_pt_in, power_xA(3), m
|
|
double precision :: Ai_center(3), Aj_center(3), alphai, alphaj, coef, coefi
|
|
|
|
integer :: ipoint, n_points_m, LD_integral
|
|
double precision, allocatable :: integral(:)
|
|
|
|
if(beta .lt. 1d-10) then
|
|
print *, 'small beta', i_ao, j_ao
|
|
call NAI_pol_x_mult_erf_ao_v(i_ao, j_ao, mu_in, C_center, LD_C, ints, LD_ints, n_points)
|
|
return
|
|
endif
|
|
|
|
ints(1:LD_ints,1:3) = 0.d0
|
|
|
|
power_Ai(1:3) = ao_power(i_ao,1:3)
|
|
power_Aj(1:3) = ao_power(j_ao,1:3)
|
|
|
|
Ai_center(1:3) = nucl_coord(ao_nucl(i_ao),1:3)
|
|
Aj_center(1:3) = nucl_coord(ao_nucl(j_ao),1:3)
|
|
|
|
n_pt_in = n_pt_max_integrals
|
|
|
|
LD_integral = max(max(n_points(1), n_points(2)), n_points(3))
|
|
allocate(integral(LD_integral))
|
|
integral = 0.d0
|
|
|
|
do i = 1, ao_prim_num(i_ao)
|
|
alphai = ao_expo_ordered_transp (i,i_ao)
|
|
coefi = ao_coef_normalized_ordered_transp(i,i_ao)
|
|
|
|
do m = 1, 3
|
|
n_points_m = n_points(m)
|
|
|
|
! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
|
|
power_xA = power_Ai
|
|
power_xA(m) += 1
|
|
|
|
do j = 1, ao_prim_num(j_ao)
|
|
alphaj = ao_expo_ordered_transp (j,j_ao)
|
|
coef = coefi * ao_coef_normalized_ordered_transp(j,j_ao)
|
|
|
|
! First term = (x-Ax)**(ax+1)
|
|
|
|
call NAI_pol_mult_erf_with1s_v( Ai_center, Aj_center, power_xA, power_Aj, alphai, alphaj, beta &
|
|
, B_center(1:LD_B,1:3,m), LD_B, C_center(1:LD_C,1:3,m), LD_C, n_pt_in, mu_in, integral(1:LD_integral), LD_integral, n_points_m)
|
|
|
|
do ipoint = 1, n_points_m
|
|
ints(ipoint,m) += integral(ipoint) * coef
|
|
enddo
|
|
|
|
! Second term = Ax * (x-Ax)**(ax)
|
|
call NAI_pol_mult_erf_with1s_v( Ai_center, Aj_center, power_Ai, power_Aj, alphai, alphaj, beta &
|
|
, B_center(1:LD_B,1:3,m), LD_B, C_center(1:LD_C,1:3,m), LD_C, n_pt_in, mu_in, integral(1:LD_integral), LD_integral, n_points_m)
|
|
do ipoint = 1, n_points_m
|
|
ints(ipoint,m) += Ai_center(m) * integral(ipoint) * coef
|
|
enddo
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
deallocate(integral)
|
|
|
|
end subroutine NAI_pol_x_mult_erf_ao_with1s_v
|
|
|
|
! ---
|
|
|
|
subroutine NAI_pol_x_specify_mult_erf_ao(i_ao,j_ao,mu_in,C_center,m,ints)
|
|
implicit none
|
|
BEGIN_DOC
|
|
! Computes the following integral :
|
|
! $\int_{-\infty}^{infty} dr X(m) * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
! if m == 1 X(m) = x, m == 1 X(m) = y, m == 1 X(m) = z
|
|
END_DOC
|
|
include 'utils/constants.include.F'
|
|
integer, intent(in) :: i_ao,j_ao,m
|
|
double precision, intent(in) :: mu_in, C_center(3)
|
|
double precision, intent(out):: ints
|
|
double precision :: A_center(3), B_center(3),integral, alpha,beta
|
|
double precision :: NAI_pol_mult_erf
|
|
integer :: i,j,num_A,num_B, power_A(3), power_B(3), n_pt_in, power_xA(3)
|
|
ints = 0.d0
|
|
if(ao_overlap_abs(j_ao,i_ao).lt.1.d-12)then
|
|
return
|
|
endif
|
|
num_A = ao_nucl(i_ao)
|
|
power_A(1:3)= ao_power(i_ao,1:3)
|
|
A_center(1:3) = nucl_coord(num_A,1:3)
|
|
num_B = ao_nucl(j_ao)
|
|
power_B(1:3)= ao_power(j_ao,1:3)
|
|
B_center(1:3) = nucl_coord(num_B,1:3)
|
|
n_pt_in = n_pt_max_integrals
|
|
|
|
do i = 1, ao_prim_num(i_ao)
|
|
alpha = ao_expo_ordered_transp(i,i_ao)
|
|
power_xA = power_A
|
|
! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
|
|
power_xA(m) += 1
|
|
do j = 1, ao_prim_num(j_ao)
|
|
beta = ao_expo_ordered_transp(j,j_ao)
|
|
! First term = (x-Ax)**(ax+1)
|
|
integral = NAI_pol_mult_erf(A_center,B_center,power_xA,power_B,alpha,beta,C_center,n_pt_in,mu_in)
|
|
ints += integral * ao_coef_normalized_ordered_transp(j,j_ao)*ao_coef_normalized_ordered_transp(i,i_ao)
|
|
! Second term = Ax * (x-Ax)**(ax)
|
|
integral = NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in)
|
|
ints += A_center(m) * integral * ao_coef_normalized_ordered_transp(j,j_ao)*ao_coef_normalized_ordered_transp(i,i_ao)
|
|
enddo
|
|
enddo
|
|
end
|
|
|
|
! ---
|
|
|
|
subroutine NAI_pol_x2_mult_erf_ao_with1s(i_ao, j_ao, beta, B_center, mu_in, C_center, ints)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! $\int_{-\infty}^{infty} dr x^2 * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
! $\int_{-\infty}^{infty} dr y^2 * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
! $\int_{-\infty}^{infty} dr z^2 * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: i_ao, j_ao
|
|
double precision, intent(in) :: beta, B_center(3), mu_in, C_center(3)
|
|
double precision, intent(out) :: ints(3)
|
|
|
|
integer :: i, j, power_Ai(3), power_Aj(3), n_pt_in, m
|
|
integer :: power_A1(3), power_A2(3)
|
|
double precision :: Ai_center(3), Aj_center(3), alphai, alphaj, coef, coefi
|
|
double precision :: integral0, integral1, integral2
|
|
|
|
double precision, external :: NAI_pol_mult_erf_with1s
|
|
|
|
ASSERT(beta .ge. 0.d0)
|
|
if(beta .lt. 1d-10) then
|
|
call NAI_pol_x2_mult_erf_ao(i_ao, j_ao, mu_in, C_center, ints)
|
|
return
|
|
endif
|
|
|
|
ints = 0.d0
|
|
|
|
power_Ai(1:3) = ao_power(i_ao,1:3)
|
|
power_Aj(1:3) = ao_power(j_ao,1:3)
|
|
|
|
Ai_center(1:3) = nucl_coord(ao_nucl(i_ao),1:3)
|
|
Aj_center(1:3) = nucl_coord(ao_nucl(j_ao),1:3)
|
|
|
|
n_pt_in = n_pt_max_integrals
|
|
|
|
do i = 1, ao_prim_num(i_ao)
|
|
alphai = ao_expo_ordered_transp (i,i_ao)
|
|
coefi = ao_coef_normalized_ordered_transp(i,i_ao)
|
|
|
|
do m = 1, 3
|
|
|
|
power_A1 = power_Ai
|
|
power_A1(m) += 1
|
|
|
|
power_A2 = power_Ai
|
|
power_A2(m) += 2
|
|
|
|
do j = 1, ao_prim_num(j_ao)
|
|
alphaj = ao_expo_ordered_transp (j,j_ao)
|
|
coef = coefi * ao_coef_normalized_ordered_transp(j,j_ao)
|
|
|
|
integral0 = NAI_pol_mult_erf_with1s(Ai_center, Aj_center, power_Ai, power_Aj, alphai, alphaj, beta, B_center, C_center, n_pt_in, mu_in)
|
|
integral1 = NAI_pol_mult_erf_with1s(Ai_center, Aj_center, power_A1, power_Aj, alphai, alphaj, beta, B_center, C_center, n_pt_in, mu_in)
|
|
integral2 = NAI_pol_mult_erf_with1s(Ai_center, Aj_center, power_A2, power_Aj, alphai, alphaj, beta, B_center, C_center, n_pt_in, mu_in)
|
|
|
|
ints(m) += coef * (integral2 + Ai_center(m) * (2.d0*integral1 + Ai_center(m)*integral0))
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine NAI_pol_x2_mult_erf_ao_with1s
|
|
|
|
! ---
|
|
|
|
subroutine NAI_pol_x2_mult_erf_ao(i_ao, j_ao, mu_in, C_center, ints)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! $\int_{-\infty}^{infty} dr x^2 * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
! $\int_{-\infty}^{infty} dr y^2 * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
! $\int_{-\infty}^{infty} dr z^2 * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: i_ao, j_ao
|
|
double precision, intent(in) :: mu_in, C_center(3)
|
|
double precision, intent(out) :: ints(3)
|
|
|
|
integer :: i, j, num_A, num_B, power_A(3), power_B(3), n_pt_in, m
|
|
integer :: power_A1(3), power_A2(3)
|
|
double precision :: A_center(3), B_center(3), alpha, beta, coef
|
|
double precision :: integral0, integral1, integral2
|
|
|
|
double precision :: NAI_pol_mult_erf
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ints = 0.d0
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num_A = ao_nucl(i_ao)
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power_A(1:3) = ao_power(i_ao,1:3)
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A_center(1:3) = nucl_coord(num_A,1:3)
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num_B = ao_nucl(j_ao)
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power_B(1:3) = ao_power(j_ao,1:3)
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B_center(1:3) = nucl_coord(num_B,1:3)
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n_pt_in = n_pt_max_integrals
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do i = 1, ao_prim_num(i_ao)
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alpha = ao_expo_ordered_transp(i,i_ao)
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do m = 1, 3
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power_A1 = power_A
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power_A1(m) += 1
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power_A2 = power_A
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power_A2(m) += 2
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do j = 1, ao_prim_num(j_ao)
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beta = ao_expo_ordered_transp(j,j_ao)
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coef = ao_coef_normalized_ordered_transp(j,j_ao) * ao_coef_normalized_ordered_transp(i,i_ao)
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integral0 = NAI_pol_mult_erf(A_center, B_center, power_A , power_B, alpha, beta, C_center, n_pt_in, mu_in)
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integral1 = NAI_pol_mult_erf(A_center, B_center, power_A1, power_B, alpha, beta, C_center, n_pt_in, mu_in)
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integral2 = NAI_pol_mult_erf(A_center, B_center, power_A2, power_B, alpha, beta, C_center, n_pt_in, mu_in)
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ints(m) += coef * (integral2 + A_center(m) * (2.d0*integral1 + A_center(m)*integral0))
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enddo
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enddo
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enddo
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end subroutine NAI_pol_x2_mult_erf_ao
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! ---
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