730 lines
36 KiB
Fortran
730 lines
36 KiB
Fortran
! ---
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double precision function j1b_gauss_2e_j2(i, j, k, l)
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BEGIN_DOC
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!
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! integral in the AO basis:
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! i(r1) j(r1) f(r12) k(r2) l(r2)
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!
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! with:
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! f(r12) = - [ (0.5 - 0.5 erf(mu r12)) / r12 ] (r1-r2) \cdot \sum_A (-2 a_A c_A) [ r1A exp(-aA r1A^2) - r2A exp(-aA r2A^2) ]
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! = [ (1 - erf(mu r12) / r12 ] \sum_A a_A c_A [ (r1-RA)^2 exp(-aA r1A^2)
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! + (r2-RA)^2 exp(-aA r2A^2)
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! - (r1-RA) \cdot (r2-RA) exp(-aA r1A^2)
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! - (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
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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, j, k, l
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integer :: p, q, r, s
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integer :: num_i, num_j, num_k, num_l, num_ii
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integer :: I_power(3), J_power(3), K_power(3), L_power(3)
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integer :: iorder_p(3), iorder_q(3)
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integer :: shift_P(3), shift_Q(3)
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integer :: dim1
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double precision :: coef1, coef2, coef3, coef4
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double precision :: expo1, expo2, expo3, expo4
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double precision :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1, p1_inv
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double precision :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1, q1_inv
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double precision :: I_center(3), J_center(3), K_center(3), L_center(3)
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double precision :: ff, gg, cx, cy, cz
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double precision :: j1b_gauss_2e_j2_schwartz
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dim1 = n_pt_max_integrals
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if( ao_prim_num(i) * ao_prim_num(j) * ao_prim_num(k) * ao_prim_num(l) > 1024 ) then
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j1b_gauss_2e_j2 = j1b_gauss_2e_j2_schwartz(i, j, k, l)
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return
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endif
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num_i = ao_nucl(i)
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num_j = ao_nucl(j)
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num_k = ao_nucl(k)
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num_l = ao_nucl(l)
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do p = 1, 3
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I_power(p) = ao_power(i,p)
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J_power(p) = ao_power(j,p)
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K_power(p) = ao_power(k,p)
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L_power(p) = ao_power(l,p)
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I_center(p) = nucl_coord(num_i,p)
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J_center(p) = nucl_coord(num_j,p)
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K_center(p) = nucl_coord(num_k,p)
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L_center(p) = nucl_coord(num_l,p)
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enddo
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j1b_gauss_2e_j2 = 0.d0
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do p = 1, ao_prim_num(i)
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coef1 = ao_coef_normalized_ordered_transp(p, i)
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expo1 = ao_expo_ordered_transp(p, i)
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do q = 1, ao_prim_num(j)
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coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
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expo2 = ao_expo_ordered_transp(q, j)
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call give_explicit_poly_and_gaussian( P1_new, P1_center, pp1, fact_p1, iorder_p, expo1, expo2 &
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, I_power, J_power, I_center, J_center, dim1 )
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p1_inv = 1.d0 / pp1
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do r = 1, ao_prim_num(k)
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coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
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expo3 = ao_expo_ordered_transp(r, k)
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do s = 1, ao_prim_num(l)
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coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
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expo4 = ao_expo_ordered_transp(s, l)
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call give_explicit_poly_and_gaussian( Q1_new, Q1_center, qq1, fact_q1, iorder_q, expo3, expo4 &
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, K_power, L_power, K_center, L_center, dim1 )
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q1_inv = 1.d0 / qq1
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call get_cxcycz_j2( dim1, cx, cy, cz &
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, P1_center, P1_new, pp1, fact_p1, p1_inv, iorder_p &
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, Q1_center, Q1_new, qq1, fact_q1, q1_inv, iorder_q )
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j1b_gauss_2e_j2 = j1b_gauss_2e_j2 + coef4 * ( cx + cy + cz )
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enddo ! s
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enddo ! r
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enddo ! q
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enddo ! p
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return
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end function j1b_gauss_2e_j2
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! ---
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double precision function j1b_gauss_2e_j2_schwartz(i, j, k, l)
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BEGIN_DOC
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!
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! integral in the AO basis:
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! i(r1) j(r1) f(r12) k(r2) l(r2)
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!
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! with:
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! f(r12) = - [ (0.5 - 0.5 erf(mu r12)) / r12 ] (r1-r2) \cdot \sum_A (-2 a_A c_A) [ r1A exp(-aA r1A^2) - r2A exp(-aA r2A^2) ]
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! = [ (1 - erf(mu r12) / r12 ] \sum_A a_A c_A [ (r1-RA)^2 exp(-aA r1A^2)
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! + (r2-RA)^2 exp(-aA r2A^2)
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! - (r1-RA) \cdot (r2-RA) exp(-aA r1A^2)
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! - (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
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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, j, k, l
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integer :: p, q, r, s
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integer :: num_i, num_j, num_k, num_l, num_ii
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integer :: I_power(3), J_power(3), K_power(3), L_power(3)
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integer :: iorder_p(3), iorder_q(3)
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integer :: dim1
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double precision :: coef1, coef2, coef3, coef4
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double precision :: expo1, expo2, expo3, expo4
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double precision :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1, p1_inv
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double precision :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1, q1_inv
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double precision :: I_center(3), J_center(3), K_center(3), L_center(3)
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double precision :: cx, cy, cz
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double precision :: schwartz_ij, thr
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double precision, allocatable :: schwartz_kl(:,:)
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dim1 = n_pt_max_integrals
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thr = ao_integrals_threshold * ao_integrals_threshold
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num_i = ao_nucl(i)
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num_j = ao_nucl(j)
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num_k = ao_nucl(k)
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num_l = ao_nucl(l)
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do p = 1, 3
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I_power(p) = ao_power(i,p)
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J_power(p) = ao_power(j,p)
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K_power(p) = ao_power(k,p)
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L_power(p) = ao_power(l,p)
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I_center(p) = nucl_coord(num_i,p)
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J_center(p) = nucl_coord(num_j,p)
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K_center(p) = nucl_coord(num_k,p)
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L_center(p) = nucl_coord(num_l,p)
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enddo
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allocate( schwartz_kl(0:ao_prim_num(l) , 0:ao_prim_num(k)) )
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schwartz_kl(0,0) = 0.d0
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do r = 1, ao_prim_num(k)
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expo3 = ao_expo_ordered_transp(r,k)
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coef3 = ao_coef_normalized_ordered_transp(r,k) * ao_coef_normalized_ordered_transp(r,k)
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schwartz_kl(0,r) = 0.d0
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do s = 1, ao_prim_num(l)
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expo4 = ao_expo_ordered_transp(s,l)
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coef4 = coef3 * ao_coef_normalized_ordered_transp(s,l) * ao_coef_normalized_ordered_transp(s,l)
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call give_explicit_poly_and_gaussian( Q1_new, Q1_center, qq1, fact_q1, iorder_q, expo3, expo4 &
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, K_power, L_power, K_center, L_center, dim1 )
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q1_inv = 1.d0 / qq1
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call get_cxcycz_j2( dim1, cx, cy, cz &
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, Q1_center, Q1_new, qq1, fact_q1, q1_inv, iorder_q &
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, Q1_center, Q1_new, qq1, fact_q1, q1_inv, iorder_q )
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schwartz_kl(s,r) = coef4 * dabs( cx + cy + cz )
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schwartz_kl(0,r) = max( schwartz_kl(0,r) , schwartz_kl(s,r) )
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enddo
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schwartz_kl(0,0) = max( schwartz_kl(0,r) , schwartz_kl(0,0) )
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enddo
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j1b_gauss_2e_j2_schwartz = 0.d0
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do p = 1, ao_prim_num(i)
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expo1 = ao_expo_ordered_transp(p, i)
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coef1 = ao_coef_normalized_ordered_transp(p, i)
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do q = 1, ao_prim_num(j)
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expo2 = ao_expo_ordered_transp(q, j)
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coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
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call give_explicit_poly_and_gaussian( P1_new, P1_center, pp1, fact_p1, iorder_p, expo1, expo2 &
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, I_power, J_power, I_center, J_center, dim1 )
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p1_inv = 1.d0 / pp1
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call get_cxcycz_j2( dim1, cx, cy, cz &
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, P1_center, P1_new, pp1, fact_p1, p1_inv, iorder_p &
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, P1_center, P1_new, pp1, fact_p1, p1_inv, iorder_p )
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schwartz_ij = coef2 * coef2 * dabs( cx + cy + cz )
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if( schwartz_kl(0,0) * schwartz_ij < thr ) cycle
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do r = 1, ao_prim_num(k)
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if( schwartz_kl(0,r) * schwartz_ij < thr ) cycle
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coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
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expo3 = ao_expo_ordered_transp(r, k)
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do s = 1, ao_prim_num(l)
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if( schwartz_kl(s,r) * schwartz_ij < thr ) cycle
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coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
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expo4 = ao_expo_ordered_transp(s, l)
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call give_explicit_poly_and_gaussian( Q1_new, Q1_center, qq1, fact_q1, iorder_q, expo3, expo4 &
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, K_power, L_power, K_center, L_center, dim1 )
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q1_inv = 1.d0 / qq1
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call get_cxcycz_j2( dim1, cx, cy, cz &
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, P1_center, P1_new, pp1, fact_p1, p1_inv, iorder_p &
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, Q1_center, Q1_new, qq1, fact_q1, q1_inv, iorder_q )
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j1b_gauss_2e_j2_schwartz = j1b_gauss_2e_j2_schwartz + coef4 * ( cx + cy + cz )
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enddo ! s
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enddo ! r
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enddo ! q
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enddo ! p
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deallocate( schwartz_kl )
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return
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end function j1b_gauss_2e_j2_schwartz
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! ---
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subroutine get_cxcycz_j2( dim1, cx, cy, cz &
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, P1_center, P1_new, pp1, fact_p1, p1_inv, iorder_p &
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, Q1_center, Q1_new, qq1, fact_q1, q1_inv, iorder_q )
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include 'utils/constants.include.F'
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implicit none
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integer, intent(in) :: dim1
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integer, intent(in) :: iorder_p(3), iorder_q(3)
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double precision, intent(in) :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1, p1_inv
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double precision, intent(in) :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1, q1_inv
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double precision, intent(out) :: cx, cy, cz
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integer :: ii
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integer :: shift_P(3), shift_Q(3)
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double precision :: coefii, expoii, factii, Centerii(3)
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double precision :: P2_new(0:max_dim,3), P2_center(3), fact_p2, pp2, p2_inv
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double precision :: Q2_new(0:max_dim,3), Q2_center(3), fact_q2, qq2, q2_inv
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double precision :: ff, gg
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double precision :: general_primitive_integral_erf_shifted
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double precision :: general_primitive_integral_coul_shifted
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PROVIDE j1b_pen j1b_coeff
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cx = 0.d0
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cy = 0.d0
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cz = 0.d0
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do ii = 1, nucl_num
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expoii = j1b_pen (ii)
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coefii = j1b_coeff(ii)
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Centerii(1:3) = nucl_coord(ii, 1:3)
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call gaussian_product(pp1, P1_center, expoii, Centerii, factii, pp2, P2_center)
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fact_p2 = fact_p1 * factii
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p2_inv = 1.d0 / pp2
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call pol_modif_center( P1_center, P2_center, iorder_p, P1_new, P2_new )
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call gaussian_product(qq1, Q1_center, expoii, Centerii, factii, qq2, Q2_center)
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fact_q2 = fact_q1 * factii
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q2_inv = 1.d0 / qq2
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call pol_modif_center( Q1_center, Q2_center, iorder_q, Q1_new, Q2_new )
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! ----------------------------------------------------------------------------------------------------
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! [ (1-erf(mu r12)) / r12 ] \sum_A a_A c_A [ (r1-RA)^2 exp(-aA r1A^2)
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! ----------------------------------------------------------------------------------------------------
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shift_Q = (/ 0, 0, 0 /)
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! x term:
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ff = P2_center(1) - Centerii(1)
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shift_P = (/ 2, 0, 0 /)
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cx = cx + expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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cx = cx - expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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shift_P = (/ 1, 0, 0 /)
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cx = cx + expoii * coefii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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cx = cx - expoii * coefii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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shift_P = (/ 0, 0, 0 /)
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cx = cx + expoii * coefii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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cx = cx - expoii * coefii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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! y term:
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ff = P2_center(2) - Centerii(2)
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shift_P = (/ 0, 2, 0 /)
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cy = cy + expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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cy = cy - expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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shift_P = (/ 0, 1, 0 /)
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cy = cy + expoii * coefii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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cy = cy - expoii * coefii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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shift_P = (/ 0, 0, 0 /)
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cy = cy + expoii * coefii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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cy = cy - expoii * coefii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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! z term:
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ff = P2_center(3) - Centerii(3)
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shift_P = (/ 0, 0, 2 /)
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cz = cz + expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
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cz = cz - expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
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, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
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, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
shift_P = (/ 0, 0, 1 /)
|
|
cz = cz + expoii * coefii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cz = cz - expoii * coefii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
shift_P = (/ 0, 0, 0 /)
|
|
cz = cz + expoii * coefii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cz = cz - expoii * coefii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
! ----------------------------------------------------------------------------------------------------
|
|
|
|
|
|
|
|
! ----------------------------------------------------------------------------------------------------
|
|
! [ (1-erf(mu r12)) / r12 ] \sum_A a_A c_A [ (r2-RA)^2 exp(-aA r2A^2)
|
|
! ----------------------------------------------------------------------------------------------------
|
|
|
|
shift_P = (/ 0, 0, 0 /)
|
|
|
|
! x term:
|
|
ff = Q2_center(1) - Centerii(1)
|
|
|
|
shift_Q = (/ 2, 0, 0 /)
|
|
cx = cx + expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cx = cx - expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_Q = (/ 1, 0, 0 /)
|
|
cx = cx + expoii * coefii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cx = cx - expoii * coefii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cx = cx + expoii * coefii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cx = cx - expoii * coefii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
! y term:
|
|
ff = Q2_center(2) - Centerii(2)
|
|
|
|
shift_Q = (/ 0, 2, 0 /)
|
|
cy = cy + expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cy = cy - expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_Q = (/ 0, 1, 0 /)
|
|
cy = cy + expoii * coefii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cy = cy - expoii * coefii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cy = cy + expoii * coefii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cy = cy - expoii * coefii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
! z term:
|
|
ff = Q2_center(3) - Centerii(3)
|
|
|
|
shift_Q = (/ 0, 0, 2 /)
|
|
cz = cz + expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cz = cz - expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_Q = (/ 0, 0, 1 /)
|
|
cz = cz + expoii * coefii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cz = cz - expoii * coefii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cz = cz + expoii * coefii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cz = cz - expoii * coefii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
! ----------------------------------------------------------------------------------------------------
|
|
|
|
|
|
|
|
! ----------------------------------------------------------------------------------------------------
|
|
! - [ (1-erf(mu r12)) / r12 ] \sum_A a_A c_A [ (r1-RA) \cdot (r2-RA) exp(-aA r1A^2) ]
|
|
! ----------------------------------------------------------------------------------------------------
|
|
|
|
! x term:
|
|
ff = P2_center(1) - Centerii(1)
|
|
gg = Q1_center(1) - Centerii(1)
|
|
|
|
shift_p = (/ 1, 0, 0 /)
|
|
shift_Q = (/ 1, 0, 0 /)
|
|
cx = cx - expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cx = cx + expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 1, 0, 0 /)
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cx = cx - expoii * coefii * gg * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cx = cx + expoii * coefii * gg * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 1, 0, 0 /)
|
|
cx = cx - expoii * coefii * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cx = cx + expoii * coefii * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cx = cx - expoii * coefii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cx = cx + expoii * coefii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
! y term:
|
|
ff = P2_center(2) - Centerii(2)
|
|
gg = Q1_center(2) - Centerii(2)
|
|
|
|
shift_p = (/ 0, 1, 0 /)
|
|
shift_Q = (/ 0, 1, 0 /)
|
|
cy = cy - expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cy = cy + expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 1, 0 /)
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cy = cy - expoii * coefii * gg * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cy = cy + expoii * coefii * gg * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 0, 1, 0 /)
|
|
cy = cy - expoii * coefii * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cy = cy + expoii * coefii * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cy = cy - expoii * coefii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cy = cy + expoii * coefii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
! z term:
|
|
ff = P2_center(3) - Centerii(3)
|
|
gg = Q1_center(3) - Centerii(3)
|
|
|
|
shift_p = (/ 0, 0, 1 /)
|
|
shift_Q = (/ 0, 0, 1 /)
|
|
cz = cz - expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cz = cz + expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 1 /)
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cz = cz - expoii * coefii * gg * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cz = cz + expoii * coefii * gg * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 0, 0, 1 /)
|
|
cz = cz - expoii * coefii * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cz = cz + expoii * coefii * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cz = cz - expoii * coefii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
cz = cz + expoii * coefii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
|
|
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
|
|
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
|
|
|
|
! ----------------------------------------------------------------------------------------------------
|
|
|
|
|
|
|
|
! ----------------------------------------------------------------------------------------------------
|
|
! - [ (1-erf(mu r12)) / r12 ] \sum_A a_A c_A [ (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
|
|
! ----------------------------------------------------------------------------------------------------
|
|
|
|
! x term:
|
|
ff = P1_center(1) - Centerii(1)
|
|
gg = Q2_center(1) - Centerii(1)
|
|
|
|
shift_p = (/ 1, 0, 0 /)
|
|
shift_Q = (/ 1, 0, 0 /)
|
|
cx = cx - expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cx = cx + expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 1, 0, 0 /)
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cx = cx - expoii * coefii * gg * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cx = cx + expoii * coefii * gg * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 1, 0, 0 /)
|
|
cx = cx - expoii * coefii * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cx = cx + expoii * coefii * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cx = cx - expoii * coefii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
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, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
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, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
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cx = cx + expoii * coefii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
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, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
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, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
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! y term:
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ff = P1_center(2) - Centerii(2)
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gg = Q2_center(2) - Centerii(2)
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shift_p = (/ 0, 1, 0 /)
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shift_Q = (/ 0, 1, 0 /)
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cy = cy - expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
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, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
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, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
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cy = cy + expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
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, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
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, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
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|
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shift_p = (/ 0, 1, 0 /)
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|
shift_Q = (/ 0, 0, 0 /)
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cy = cy - expoii * coefii * gg * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cy = cy + expoii * coefii * gg * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 0, 1, 0 /)
|
|
cy = cy - expoii * coefii * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cy = cy + expoii * coefii * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cy = cy - expoii * coefii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cy = cy + expoii * coefii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
! z term:
|
|
ff = P1_center(3) - Centerii(3)
|
|
gg = Q2_center(3) - Centerii(3)
|
|
|
|
shift_p = (/ 0, 0, 1 /)
|
|
shift_Q = (/ 0, 0, 1 /)
|
|
cz = cz - expoii * coefii * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cz = cz + expoii * coefii * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 1 /)
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cz = cz - expoii * coefii * gg * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cz = cz + expoii * coefii * gg * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 0, 0, 1 /)
|
|
cz = cz - expoii * coefii * ff * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cz = cz + expoii * coefii * ff * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
shift_p = (/ 0, 0, 0 /)
|
|
shift_Q = (/ 0, 0, 0 /)
|
|
cz = cz - expoii * coefii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
cz = cz + expoii * coefii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
|
|
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
|
|
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
|
|
|
|
! ----------------------------------------------------------------------------------------------------
|
|
|
|
enddo
|
|
|
|
return
|
|
end subroutine get_cxcycz_j2
|
|
|
|
! ---
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