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qp2/plugins/local/ao_many_one_e_ints/prim_int_gauss_gauss.irp.f
2024-01-15 12:02:38 +01:00

341 lines
13 KiB
Fortran

! ---
double precision function overlap_gauss_r12(D_center, delta, A_center, B_center, power_A, power_B, alpha, beta)
BEGIN_DOC
!
! Computes the following integral :
!
! .. math ::
!
! \int dr exp(-delta (r - D)^2 ) (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
!
END_DOC
include 'constants.include.F'
implicit none
double precision, intent(in) :: D_center(3), delta ! pure gaussian "D"
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 :: overlap_x,overlap_y,overlap_z,overlap
! 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), dim1
dim1 = 100
thr = 1.d-10
d(:) = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
overlap_gauss_r12 = 0.d0
! 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)
if(fact_a_new.lt.thr)return
! 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)*fact_a_new
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
call overlap_gaussian_xyz( A_center_new, B_center, alpha_new, beta, iorder_tmp, power_B &
, overlap_x, overlap_y, overlap_z, overlap, dim1)
accu += coefxyz * overlap
enddo
enddo
enddo
overlap_gauss_r12 = accu
end
!---
double precision function overlap_abs_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta)
BEGIN_DOC
! Computes the following integral :
!
! .. math ::
!
! \int dr exp(-delta (r - D)^2 ) |(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 ! pure gaussian "D"
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 :: overlap_x,overlap_y,overlap_z,overlap
! 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,dx,lower_exp_val
integer :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1
dim1=50
lower_exp_val = 40.d0
thr = 1.d-12
d(:) = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
overlap_abs_gauss_r12 = 0.d0
! 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)
if(fact_a_new.lt.thr)return
! 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)*fact_a_new
! 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
call overlap_x_abs(A_center_new(1),B_center(1),alpha_new,beta,iorder_tmp(1),power_B(1),overlap_x,lower_exp_val,dx,dim1)
call overlap_x_abs(A_center_new(2),B_center(2),alpha_new,beta,iorder_tmp(2),power_B(2),overlap_y,lower_exp_val,dx,dim1)
call overlap_x_abs(A_center_new(3),B_center(3),alpha_new,beta,iorder_tmp(3),power_B(3),overlap_z,lower_exp_val,dx,dim1)
accu += dabs(coefxyz * overlap_x * overlap_y * overlap_z)
enddo
enddo
enddo
overlap_abs_gauss_r12= accu
end
!---
! TODO apply Gaussian product three times first
subroutine overlap_gauss_r12_v(D_center, LD_D, delta, A_center, B_center, power_A, power_B, alpha, beta, rvec, LD_rvec, n_points)
BEGIN_DOC
!
! Computes the following integral :
!
! \int dr exp(-delta (r - D)^2) (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2)
! using an array of D_centers
!
! n_points: nb of integrals
!
END_DOC
implicit none
include 'constants.include.F'
integer, intent(in) :: LD_D, LD_rvec, n_points
integer, intent(in) :: power_A(3), power_B(3)
double precision, intent(in) :: D_center(LD_D,3), delta
double precision, intent(in) :: A_center(3), B_center(3), alpha, beta
double precision, intent(out) :: rvec(LD_rvec)
integer :: maxab
integer :: d(3), i, lx, ly, lz, iorder_tmp(3), ipoint
double precision :: overlap_x, overlap_y, overlap_z
double precision :: alpha_new
double precision :: accu, thr, coefxy
integer, allocatable :: iorder_a_new(:)
double precision, allocatable :: overlap(:)
double precision, allocatable :: A_new(:,:,:), A_center_new(:,:)
double precision, allocatable :: fact_a_new(:)
thr = 1.d-10
d(:) = 0
maxab = maxval(power_A(1:3))
allocate(A_new(n_points,0:maxab,3), A_center_new(n_points,3), fact_a_new(n_points), iorder_a_new(3), overlap(n_points))
call give_explicit_poly_and_gaussian_v(A_new, maxab, A_center_new, alpha_new, fact_a_new, iorder_a_new, delta, alpha, d, power_A, D_center, LD_D, A_center, n_points)
rvec(:) = 0.d0
do lx = 0, iorder_a_new(1)
iorder_tmp(1) = lx
do ly = 0, iorder_a_new(2)
iorder_tmp(2) = ly
do lz = 0, iorder_a_new(3)
iorder_tmp(3) = lz
call overlap_gaussian_xyz_v(A_center_new, B_center, alpha_new, beta, iorder_tmp, power_B, overlap, n_points)
do ipoint = 1, n_points
rvec(ipoint) = rvec(ipoint) + A_new(ipoint,lx,1) * A_new(ipoint,ly,2) * A_new(ipoint,lz,3) * overlap(ipoint)
enddo
enddo
enddo
enddo
do ipoint = 1, n_points
rvec(ipoint) = rvec(ipoint) * fact_a_new(ipoint)
enddo
deallocate(A_new, A_center_new, fact_a_new, iorder_a_new, overlap)
end
!---
subroutine overlap_gauss_xyz_r12(D_center, delta, A_center, B_center, power_A, power_B, alpha, beta, gauss_ints)
BEGIN_DOC
! Computes the following integral :
!
! .. math::
!
! gauss_ints(m) = \int dr exp(-delta (r - D)^2 ) * x/y/z (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
!
! with m == 1 ==> x, m == 2 ==> y, m == 3 ==> z
END_DOC
implicit none
include 'constants.include.F'
double precision, intent(in) :: D_center(3), delta ! pure gaussian "D"
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) :: gauss_ints(3)
double precision :: overlap_x,overlap_y,overlap_z,overlap
! 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
integer :: power_B_new(3)
double precision :: alpha_new ! new exponent
double precision :: fact_a_new ! constant factor
double precision :: coefx,coefy,coefz,coefxy,coefxyz,thr
integer :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1,m
dim1=100
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
gauss_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
do m = 1, 3
! change (x-Bx)^bx --> (x-Bx)^(bx+1) + Bx(x-Bx)^bx
power_B_new = power_B
power_B_new(m) += 1 ! (x-Bx)^(bx+1)
call overlap_gaussian_xyz(A_center_new,B_center,alpha_new,beta,iorder_tmp,power_B_new,overlap_x,overlap_y,overlap_z,overlap,dim1)
gauss_ints(m) += coefxyz * overlap
power_B_new = power_B
call overlap_gaussian_xyz(A_center_new,B_center,alpha_new,beta,iorder_tmp,power_B_new,overlap_x,overlap_y,overlap_z,overlap,dim1)
gauss_ints(m) += coefxyz * overlap * B_center(m) ! Bx (x-Bx)^(bx)
enddo
enddo
enddo
enddo
gauss_ints *= fact_a_new
end
double precision function overlap_gauss_xyz_r12_specific(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,mx)
BEGIN_DOC
! Computes the following integral :
!
! .. math::
!
! \int dr exp(-delta (r - D)^2 ) * x/y/z (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
!
! with mx == 1 ==> x, mx == 2 ==> y, mx == 3 ==> z
END_DOC
implicit none
include 'constants.include.F'
double precision, intent(in) :: D_center(3), delta ! pure gaussian "D"
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),mx
double precision :: overlap_x,overlap_y,overlap_z,overlap
! 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
integer :: power_B_new(3)
double precision :: alpha_new ! new exponent
double precision :: fact_a_new ! constant factor
double precision :: coefx,coefy,coefz,coefxy,coefxyz,thr
integer :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1,m
dim1=100
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
overlap_gauss_xyz_r12_specific = 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
m = mx
! change (x-Bx)^bx --> (x-Bx)^(bx+1) + Bx(x-Bx)^bx
power_B_new = power_B
power_B_new(m) += 1 ! (x-Bx)^(bx+1)
call overlap_gaussian_xyz(A_center_new,B_center,alpha_new,beta,iorder_tmp,power_B_new,overlap_x,overlap_y,overlap_z,overlap,dim1)
overlap_gauss_xyz_r12_specific += coefxyz * overlap
power_B_new = power_B
call overlap_gaussian_xyz(A_center_new,B_center,alpha_new,beta,iorder_tmp,power_B_new,overlap_x,overlap_y,overlap_z,overlap,dim1)
overlap_gauss_xyz_r12_specific += coefxyz * overlap * B_center(m) ! Bx (x-Bx)^(bx)
enddo
enddo
enddo
overlap_gauss_xyz_r12_specific *= fact_a_new
end