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