2019-01-25 11:39:31 +01:00
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double precision function overlap_gaussian_x(A_center,B_center,alpha,beta,power_A,power_B,dim)
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implicit none
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BEGIN_DOC
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!.. math::
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!
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! \sum_{-infty}^{+infty} (x-A_x)^ax (x-B_x)^bx exp(-alpha(x-A_x)^2) exp(-beta(x-B_X)^2) dx
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!
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END_DOC
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include 'constants.include.F'
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integer,intent(in) :: dim ! dimension maximum for the arrays representing the polynomials
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double precision,intent(in) :: A_center,B_center ! center of the x1 functions
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integer,intent(in) :: power_A, power_B ! power of the x1 functions
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double precision :: P_new(0:max_dim),P_center,fact_p,p,alpha,beta
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integer :: iorder_p
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call give_explicit_poly_and_gaussian_x(P_new,P_center,p,fact_p,iorder_p,alpha,&
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beta,power_A,power_B,A_center,B_center,dim)
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2020-11-02 17:24:35 +01:00
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if(fact_p.lt.1.d-20)then
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overlap_gaussian_x = 0.d0
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return
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endif
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2019-01-25 11:39:31 +01:00
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overlap_gaussian_x = 0.d0
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integer :: i
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double precision :: F_integral
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do i = 0,iorder_p
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overlap_gaussian_x += P_new(i) * F_integral(i,p)
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enddo
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overlap_gaussian_x*= fact_p
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end
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2023-03-04 17:49:48 +01:00
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subroutine overlap_gaussian_xyz(A_center, B_center, alpha, beta, power_A, power_B, overlap_x, overlap_y, overlap_z, overlap, dim)
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2019-01-25 11:39:31 +01:00
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BEGIN_DOC
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!.. math::
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!
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! S_x = \int (x-A_x)^{a_x} exp(-\alpha(x-A_x)^2) (x-B_x)^{b_x} exp(-beta(x-B_x)^2) dx \\
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! S = S_x S_y S_z
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!
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END_DOC
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2023-03-04 17:49:48 +01:00
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2019-01-25 11:39:31 +01:00
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include 'constants.include.F'
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2023-03-04 17:49:48 +01:00
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implicit none
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2019-01-25 11:39:31 +01:00
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integer,intent(in) :: dim ! dimension maximum for the arrays representing the polynomials
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double precision,intent(in) :: A_center(3),B_center(3) ! center of the x1 functions
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double precision, intent(in) :: alpha,beta
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integer,intent(in) :: power_A(3), power_B(3) ! power of the x1 functions
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double precision, intent(out) :: overlap_x,overlap_y,overlap_z,overlap
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double precision :: P_new(0:max_dim,3),P_center(3),fact_p,p
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double precision :: F_integral_tab(0:max_dim)
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integer :: iorder_p(3)
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integer :: nmax
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double precision :: F_integral
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2023-03-04 17:49:48 +01:00
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call give_explicit_poly_and_gaussian(P_new, P_center, p, fact_p, iorder_p, alpha, beta, power_A, power_B, A_center, B_center, dim)
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if(fact_p.lt.1d-20)then
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overlap_x = 1.d-10
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overlap_y = 1.d-10
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overlap_z = 1.d-10
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overlap = 1.d-10
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return
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endif
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2019-01-25 11:39:31 +01:00
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nmax = maxval(iorder_p)
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do i = 0,nmax
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F_integral_tab(i) = F_integral(i,p)
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enddo
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overlap_x = P_new(0,1) * F_integral_tab(0)
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overlap_y = P_new(0,2) * F_integral_tab(0)
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overlap_z = P_new(0,3) * F_integral_tab(0)
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integer :: i
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do i = 1,iorder_p(1)
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overlap_x = overlap_x + P_new(i,1) * F_integral_tab(i)
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enddo
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call gaussian_product_x(alpha,A_center(1),beta,B_center(1),fact_p,p,P_center(1))
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overlap_x *= fact_p
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do i = 1,iorder_p(2)
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overlap_y = overlap_y + P_new(i,2) * F_integral_tab(i)
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enddo
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call gaussian_product_x(alpha,A_center(2),beta,B_center(2),fact_p,p,P_center(2))
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overlap_y *= fact_p
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do i = 1,iorder_p(3)
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overlap_z = overlap_z + P_new(i,3) * F_integral_tab(i)
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enddo
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call gaussian_product_x(alpha,A_center(3),beta,B_center(3),fact_p,p,P_center(3))
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overlap_z *= fact_p
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overlap = overlap_x * overlap_y * overlap_z
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end
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2023-03-04 17:49:48 +01:00
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! ---
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subroutine overlap_x_abs(A_center, B_center, alpha, beta, power_A, power_B, overlap_x, lower_exp_val, dx, nx)
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2019-01-25 11:39:31 +01:00
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BEGIN_DOC
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! .. math ::
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!
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! \int_{-infty}^{+infty} (x-A_center)^(power_A) * (x-B_center)^power_B * exp(-alpha(x-A_center)^2) * exp(-beta(x-B_center)^2) dx
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!
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END_DOC
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2023-03-04 17:49:48 +01:00
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implicit none
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integer, intent(in) :: power_A, power_B, nx
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double precision, intent(in) :: lower_exp_val, A_center, B_center, alpha, beta
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double precision, intent(out) :: overlap_x, dx
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integer :: i, j, k, l
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double precision :: x_min, x_max, domain, x, factor, dist, p, p_inv, rho
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double precision :: P_center
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double precision :: tmp
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if(power_A.lt.0 .or. power_B.lt.0) then
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2019-01-25 11:39:31 +01:00
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overlap_x = 0.d0
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dx = 0.d0
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return
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endif
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2023-03-04 17:49:48 +01:00
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p = alpha + beta
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p_inv = 1.d0/p
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rho = alpha * beta * p_inv
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dist = (A_center - B_center)*(A_center - B_center)
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2019-01-25 11:39:31 +01:00
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P_center = (alpha * A_center + beta * B_center) * p_inv
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2023-03-04 17:49:48 +01:00
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if(rho*dist.gt.80.d0) then
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2019-01-25 11:39:31 +01:00
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overlap_x= 0.d0
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return
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endif
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2023-03-04 17:49:48 +01:00
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2019-01-25 11:39:31 +01:00
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factor = dexp(-rho * dist)
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tmp = dsqrt(lower_exp_val/p)
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x_min = P_center - tmp
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x_max = P_center + tmp
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domain = x_max-x_min
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dx = domain/dble(nx)
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overlap_x = 0.d0
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x = x_min
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do i = 1, nx
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x += dx
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overlap_x += abs((x-A_center)**power_A * (x-B_center)**power_B) * dexp(-p * (x-P_center)*(x-P_center))
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enddo
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overlap_x = factor * dx * overlap_x
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end
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2023-03-04 17:49:48 +01:00
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! ---
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2019-01-25 11:39:31 +01:00
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2023-02-06 19:00:35 +01:00
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subroutine overlap_gaussian_xyz_v(A_center, B_center, alpha, beta, power_A, power_B, overlap, n_points)
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BEGIN_DOC
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!.. math::
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!
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! S_x = \int (x-A_x)^{a_x} exp(-\alpha(x-A_x)^2) (x-B_x)^{b_x} exp(-beta(x-B_x)^2) dx \\
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! S = S_x S_y S_z
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!
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END_DOC
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include 'constants.include.F'
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implicit none
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integer, intent(in) :: n_points
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integer, intent(in) :: power_A(3), power_B(3) ! power of the x1 functions
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double precision, intent(in) :: A_center(n_points,3), B_center(3) ! center of the x1 functions
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double precision, intent(in) :: alpha, beta
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double precision, intent(out) :: overlap(n_points)
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integer :: i
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integer :: iorder_p(3), ipoint, ldp
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integer :: nmax
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double precision :: F_integral_tab(0:max_dim)
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double precision :: p, overlap_x, overlap_y, overlap_z
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double precision :: F_integral
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double precision, allocatable :: P_new(:,:,:), P_center(:,:), fact_p(:)
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2023-03-04 17:49:48 +01:00
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ldp = maxval( power_A(1:3) + power_B(1:3) )
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2023-02-06 19:00:35 +01:00
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allocate(P_new(n_points,0:ldp,3), P_center(n_points,3), fact_p(n_points))
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call give_explicit_poly_and_gaussian_v(P_new, ldp, P_center, p, fact_p, iorder_p, alpha, beta, power_A, power_B, A_center, n_points, B_center, n_points)
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nmax = maxval(iorder_p)
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do i = 0, nmax
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F_integral_tab(i) = F_integral(i,p)
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enddo
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do ipoint = 1, n_points
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if(fact_p(ipoint) .lt. 1d-20) then
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overlap(ipoint) = 1.d-10
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cycle
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endif
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overlap_x = P_new(ipoint,0,1) * F_integral_tab(0)
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do i = 1, iorder_p(1)
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overlap_x = overlap_x + P_new(ipoint,i,1) * F_integral_tab(i)
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enddo
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overlap_y = P_new(ipoint,0,2) * F_integral_tab(0)
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do i = 1, iorder_p(2)
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overlap_y = overlap_y + P_new(ipoint,i,2) * F_integral_tab(i)
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enddo
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overlap_z = P_new(ipoint,0,3) * F_integral_tab(0)
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do i = 1, iorder_p(3)
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overlap_z = overlap_z + P_new(ipoint,i,3) * F_integral_tab(i)
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enddo
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overlap(ipoint) = overlap_x * overlap_y * overlap_z * fact_p(ipoint)
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enddo
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deallocate(P_new, P_center, fact_p)
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end subroutine overlap_gaussian_xyz_v
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! ---
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