mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-11-08 14:33:38 +01:00
196 lines
8.4 KiB
Fortran
196 lines
8.4 KiB
Fortran
double precision function NAI_pol_mult_erf_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,C_center,mu)
|
|
BEGIN_DOC
|
|
! Computes the following integral R^3 :
|
|
!
|
|
! .. math::
|
|
!
|
|
! \int dr (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 | }$ exp(-delta (r - D)^2 ).
|
|
!
|
|
END_DOC
|
|
|
|
implicit none
|
|
include 'constants.include.F'
|
|
double precision, intent(in) :: D_center(3), delta ! pure gaussian "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 :: NAI_pol_mult_erf
|
|
! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
|
|
double precision :: A_new(0:max_dim,3)! new polynom
|
|
double precision :: A_center_new(3) ! new center
|
|
integer :: iorder_a_new(3) ! i_order(i) = order of the new polynom ==> should be equal to power_A
|
|
double precision :: alpha_new ! new exponent
|
|
double precision :: fact_a_new ! constant factor
|
|
double precision :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr
|
|
integer :: d(3),i,lx,ly,lz,iorder_tmp(3)
|
|
thr = 1.d-10
|
|
d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
|
|
|
|
! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
|
|
call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , &
|
|
delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
|
|
! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
|
|
accu = 0.d0
|
|
do lx = 0, iorder_a_new(1)
|
|
coefx = A_new(lx,1)
|
|
if(dabs(coefx).lt.thr)cycle
|
|
iorder_tmp(1) = lx
|
|
do ly = 0, iorder_a_new(2)
|
|
coefy = A_new(ly,2)
|
|
coefxy = coefx * coefy
|
|
if(dabs(coefxy).lt.thr)cycle
|
|
iorder_tmp(2) = ly
|
|
do lz = 0, iorder_a_new(3)
|
|
coefz = A_new(lz,3)
|
|
coefxyz = coefxy * coefz
|
|
if(dabs(coefxyz).lt.thr)cycle
|
|
iorder_tmp(3) = lz
|
|
accu += coefxyz * NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B,alpha_new,beta,C_center,n_pt_max_integrals,mu)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
NAI_pol_mult_erf_gauss_r12 = fact_a_new * accu
|
|
end
|
|
|
|
subroutine erfc_mu_gauss_xyz(D_center,delta,mu,A_center,B_center,power_A,power_B,alpha,beta,n_pt_in,xyz_ints)
|
|
BEGIN_DOC
|
|
! Computes the following integral :
|
|
!
|
|
! .. math::
|
|
!
|
|
! \int dr exp(-delta (r - D)^2 ) x/y/z * (1 - erf(mu |r-r'|))/ |r-r'| * (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
|
|
!
|
|
! xyz_ints(1) = x , xyz_ints(2) = y, xyz_ints(3) = z, xyz_ints(4) = x^0
|
|
END_DOC
|
|
|
|
implicit none
|
|
include 'constants.include.F'
|
|
double precision, intent(in) :: D_center(3), delta,mu ! pure gaussian "D" and mu parameter
|
|
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),n_pt_in
|
|
double precision, intent(out) :: xyz_ints(4)
|
|
|
|
double precision :: NAI_pol_mult_erf
|
|
! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
|
|
double precision :: A_new(0:max_dim,3)! new polynom
|
|
double precision :: A_center_new(3) ! new center
|
|
integer :: iorder_a_new(3) ! i_order(i) = order of the new polynom ==> should be equal to power_A
|
|
double precision :: alpha_new ! new exponent
|
|
double precision :: fact_a_new ! constant factor
|
|
double precision :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr,contrib,contrib_inf,mu_inf
|
|
integer :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1,mm
|
|
integer :: power_B_tmp(3)
|
|
dim1=100
|
|
mu_inf = 1.d+10
|
|
thr = 1.d-10
|
|
d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
|
|
|
|
! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
|
|
call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , &
|
|
delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
|
|
! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
|
|
xyz_ints = 0.d0
|
|
do lx = 0, iorder_a_new(1)
|
|
coefx = A_new(lx,1)
|
|
if(dabs(coefx).lt.thr)cycle
|
|
iorder_tmp(1) = lx
|
|
do ly = 0, iorder_a_new(2)
|
|
coefy = A_new(ly,2)
|
|
coefxy = coefx * coefy
|
|
if(dabs(coefxy).lt.thr)cycle
|
|
iorder_tmp(2) = ly
|
|
do lz = 0, iorder_a_new(3)
|
|
coefz = A_new(lz,3)
|
|
coefxyz = coefxy * coefz
|
|
if(dabs(coefxyz).lt.thr)cycle
|
|
iorder_tmp(3) = lz
|
|
power_B_tmp = power_B
|
|
contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu)
|
|
contrib_inf = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu_inf)
|
|
xyz_ints(4) += (contrib_inf - contrib) * coefxyz ! usual term with no x/y/z
|
|
|
|
do mm = 1, 3
|
|
! (x phi_i ) * phi_j
|
|
! x * (x - B_x)^b_x = B_x (x - B_x)^b_x + 1 * (x - B_x)^{b_x+1}
|
|
|
|
!
|
|
! first contribution :: B_x (x - B_x)^b_x :: usual integral multiplied by B_x
|
|
power_B_tmp = power_B
|
|
contrib_inf = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu_inf)
|
|
contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu)
|
|
xyz_ints(mm) += (contrib_inf - contrib) * B_center(mm) * coefxyz
|
|
|
|
!
|
|
! second contribution :: (x - B_x)^(b_x+1) :: integral with b_x=>b_x+1
|
|
power_B_tmp(mm) += 1
|
|
contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu)
|
|
contrib_inf = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu_inf)
|
|
xyz_ints(mm) += (contrib_inf - contrib) * coefxyz
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
xyz_ints *= fact_a_new
|
|
end
|
|
|
|
|
|
double precision function erf_mu_gauss(D_center,delta,mu,A_center,B_center,power_A,power_B,alpha,beta,n_pt_in)
|
|
BEGIN_DOC
|
|
! Computes the following integral :
|
|
!
|
|
! .. math::
|
|
!
|
|
! \int dr exp(-delta (r - D)^2 ) erf(mu*|r-r'|)/ |r-r'| * (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
|
|
!
|
|
END_DOC
|
|
|
|
implicit none
|
|
include 'constants.include.F'
|
|
double precision, intent(in) :: D_center(3), delta,mu ! pure gaussian "D" and mu parameter
|
|
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),n_pt_in
|
|
|
|
double precision :: NAI_pol_mult_erf
|
|
! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
|
|
double precision :: A_new(0:max_dim,3)! new polynom
|
|
double precision :: A_center_new(3) ! new center
|
|
integer :: iorder_a_new(3) ! i_order(i) = order of the new polynom ==> should be equal to power_A
|
|
double precision :: alpha_new ! new exponent
|
|
double precision :: fact_a_new ! constant factor
|
|
double precision :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr,contrib,contrib_inf,mu_inf
|
|
integer :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1,mm
|
|
dim1=100
|
|
mu_inf = 1.d+10
|
|
thr = 1.d-10
|
|
d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
|
|
|
|
! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
|
|
call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , &
|
|
delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
|
|
! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
|
|
erf_mu_gauss = 0.d0
|
|
do lx = 0, iorder_a_new(1)
|
|
coefx = A_new(lx,1)
|
|
if(dabs(coefx).lt.thr)cycle
|
|
iorder_tmp(1) = lx
|
|
do ly = 0, iorder_a_new(2)
|
|
coefy = A_new(ly,2)
|
|
coefxy = coefx * coefy
|
|
if(dabs(coefxy).lt.thr)cycle
|
|
iorder_tmp(2) = ly
|
|
do lz = 0, iorder_a_new(3)
|
|
coefz = A_new(lz,3)
|
|
coefxyz = coefxy * coefz
|
|
if(dabs(coefxyz).lt.thr)cycle
|
|
iorder_tmp(3) = lz
|
|
contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B,alpha_new,beta,D_center,n_pt_in,mu)
|
|
erf_mu_gauss += contrib * coefxyz
|
|
enddo
|
|
enddo
|
|
enddo
|
|
erf_mu_gauss *= fact_a_new
|
|
end
|
|
|