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qp2/plugins/local/ao_many_one_e_ints/taylor_exp.irp.f

102 lines
4.0 KiB
Fortran

double precision function exp_dl(x,n)
implicit none
double precision, intent(in) :: x
integer , intent(in) :: n
integer :: i
exp_dl = 1.d0
do i = 1, n
exp_dl += fact_inv(i) * x**dble(i)
enddo
end
subroutine exp_dl_rout(x,n, array)
implicit none
double precision, intent(in) :: x
integer , intent(in) :: n
double precision, intent(out):: array(0:n)
integer :: i
double precision :: accu
accu = 1.d0
array(0) = 1.d0
do i = 1, n
accu += fact_inv(i) * x**dble(i)
array(i) = accu
enddo
end
subroutine exp_dl_ovlp_stg_phi_ij(zeta,D_center,gam,delta,A_center,B_center,power_A,power_B,alpha,beta,n_taylor,array_ints,integral_taylor,exponent_exp)
BEGIN_DOC
! Computes the following integrals :
!
! .. math::
!
! array(i) = \int dr EXP{exponent_exp * [exp(-gam*i (r - D)) exp(-delta*i * (r -D)^2)] (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
!
!
! and gives back the Taylor expansion of the exponential in integral_taylor
END_DOC
implicit none
double precision, intent(in) :: zeta ! prefactor of the argument of the exp(-zeta*x)
integer, intent(in) :: n_taylor ! order of the Taylor expansion of the exponential
double precision, intent(in) :: D_center(3), gam ! pure Slater "D" in r-r_D
double precision, intent(in) :: delta ! gaussian in r-r_D
double precision, intent(in) :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
double precision, intent(in) :: exponent_exp
integer, intent(in) :: power_A(3),power_B(3)
double precision, intent(out) :: array_ints(0:n_taylor),integral_taylor
integer :: i,dim1
double precision :: delta_exp,gam_exp,ovlp_stg_gauss_int_phi_ij
double precision :: overlap_x,overlap_y,overlap_z,overlap
dim1=100
call overlap_gaussian_xyz(A_center,B_center,alpha,beta,power_A,power_B,overlap_x,overlap_y,overlap_z,overlap,dim1)
array_ints(0) = overlap
integral_taylor = array_ints(0)
do i = 1, n_taylor
delta_exp = dble(i) * delta
gam_exp = dble(i) * gam
array_ints(i) = ovlp_stg_gauss_int_phi_ij(D_center,gam_exp,delta_exp,A_center,B_center,power_A,power_B,alpha,beta)
integral_taylor += (-zeta*exponent_exp)**dble(i) * fact_inv(i) * array_ints(i)
enddo
end
subroutine exp_dl_erf_stg_phi_ij(zeta,D_center,gam,delta,A_center,B_center,power_A,power_B,alpha,beta,C_center,mu,n_taylor,array_ints,integral_taylor)
BEGIN_DOC
! Computes the following integrals :
!
! .. math::
!
! array(i) = \int dr exp(-gam*i (r - D)) exp(-delta*i * (r -D)^2) (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
! \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
!
!
! and gives back the Taylor expansion of the exponential in integral_taylor
END_DOC
implicit none
integer, intent(in) :: n_taylor ! order of the Taylor expansion of the exponential
double precision, intent(in) :: zeta ! prefactor of the argument of the exp(-zeta*x)
double precision, intent(in) :: D_center(3), gam ! pure Slater "D" in r-r_D
double precision, intent(in) :: delta ! gaussian in r-r_D
double precision, intent(in) :: C_center(3),mu ! coulomb center "C" and "mu" in the erf(mu*x)/x function
double precision, intent(in) :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
integer, intent(in) :: power_A(3),power_B(3)
double precision, intent(out) :: array_ints(0:n_taylor),integral_taylor
integer :: i,dim1
double precision :: delta_exp,gam_exp,NAI_pol_mult_erf,erf_mu_stg_gauss_int_phi_ij
dim1=100
array_ints(0) = NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_max_integrals,mu)
integral_taylor = array_ints(0)
do i = 1, n_taylor
delta_exp = dble(i) * delta
gam_exp = dble(i) * gam
array_ints(i) = erf_mu_stg_gauss_int_phi_ij(D_center,gam_exp,delta_exp,A_center,B_center,power_A,power_B,alpha,beta,C_center,mu)
integral_taylor += (-zeta)**dble(i) * fact_inv(i) * array_ints(i)
enddo
end