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qp2/src/utils/one_e_integration.irp.f

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4.7 KiB
Fortran
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2019-01-25 11:39:31 +01:00
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.0.000001d0)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)
implicit none
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'
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)
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 = 0.d0
! overlap_y = 0.d0
! overlap_z = 0.d0
! overlap = 0.d0
! return
! endif
integer :: nmax
double precision :: F_integral
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)
implicit none
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
integer :: i,j,k,l
integer,intent(in) :: power_A,power_B
double precision, intent(in) :: lower_exp_val
double precision,intent(in) :: A_center, B_center,alpha,beta
double precision, intent(out) :: overlap_x,dx
integer, intent(in) :: nx
double precision :: x_min,x_max,domain,x,factor,dist,p,p_inv,rho
double precision :: P_center
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)
double precision :: tmp
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