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QuantumPackage/src/ao_one_e_ints/pot_ao_ints.irp.f

636 lines
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Fortran
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BEGIN_PROVIDER [ double precision, ao_integrals_n_e, (ao_num,ao_num)]
BEGIN_DOC
! Nucleus-electron interaction, in the |AO| basis set.
!
! :math:`\langle \chi_i | -\sum_A \frac{1}{|r-R_A|} | \chi_j \rangle`
!
! These integrals also contain the pseudopotential integrals.
END_DOC
implicit none
double precision :: alpha, beta, gama, delta
integer :: num_A,num_B
double precision :: A_center(3),B_center(3),C_center(3)
integer :: power_A(3),power_B(3)
integer :: i,j,k,l,n_pt_in,m
double precision :: overlap_x,overlap_y,overlap_z,overlap,dx,NAI_pol_mult
if (read_ao_integrals_n_e) then
call ezfio_get_ao_one_e_ints_ao_integrals_n_e(ao_integrals_n_e)
print *, 'AO N-e integrals read from disk'
else
ao_integrals_n_e = 0.d0
! _
! /| / |_)
! | / | \
!
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,l,m,alpha,beta,A_center,B_center,C_center,power_A,power_B,&
!$OMP num_A,num_B,Z,c,n_pt_in) &
!$OMP SHARED (ao_num,ao_prim_num,ao_expo_ordered_transp,ao_power,ao_nucl,nucl_coord,ao_coef_normalized_ordered_transp,&
!$OMP n_pt_max_integrals,ao_integrals_n_e,nucl_num,nucl_charge)
n_pt_in = n_pt_max_integrals
!$OMP DO SCHEDULE (dynamic)
do j = 1, ao_num
num_A = ao_nucl(j)
power_A(1:3)= ao_power(j,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
do i = 1, ao_num
num_B = ao_nucl(i)
power_B(1:3)= ao_power(i,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
do l=1,ao_prim_num(j)
alpha = ao_expo_ordered_transp(l,j)
do m=1,ao_prim_num(i)
beta = ao_expo_ordered_transp(m,i)
double precision :: c
c = 0.d0
do k = 1, nucl_num
double precision :: Z
Z = nucl_charge(k)
C_center(1:3) = nucl_coord(k,1:3)
c = c - Z * NAI_pol_mult(A_center,B_center, &
power_A,power_B,alpha,beta,C_center,n_pt_in)
enddo
ao_integrals_n_e(i,j) = ao_integrals_n_e(i,j) &
+ ao_coef_normalized_ordered_transp(l,j) &
* ao_coef_normalized_ordered_transp(m,i) * c
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
IF (DO_PSEUDO) THEN
ao_integrals_n_e += ao_pseudo_integrals
ENDIF
endif
if (write_ao_integrals_n_e) then
call ezfio_set_ao_one_e_ints_ao_integrals_n_e(ao_integrals_n_e)
print *, 'AO N-e integrals written to disk'
endif
END_PROVIDER
BEGIN_PROVIDER [ double precision, ao_integrals_n_e_imag, (ao_num,ao_num)]
BEGIN_DOC
! Nucleus-electron interaction, in the |AO| basis set.
!
! :math:`\langle \chi_i | -\sum_A \frac{1}{|r-R_A|} | \chi_j \rangle`
END_DOC
implicit none
double precision :: alpha, beta, gama, delta
integer :: num_A,num_B
double precision :: A_center(3),B_center(3),C_center(3)
integer :: power_A(3),power_B(3)
integer :: i,j,k,l,n_pt_in,m
double precision :: overlap_x,overlap_y,overlap_z,overlap,dx,NAI_pol_mult
if (read_ao_integrals_n_e) then
call ezfio_get_ao_one_e_ints_ao_integrals_n_e_imag(ao_integrals_n_e_imag)
print *, 'AO N-e integrals read from disk'
else
print *, irp_here, ': Not yet implemented'
endif
END_PROVIDER
BEGIN_PROVIDER [ double precision, ao_integrals_n_e_per_atom, (ao_num,ao_num,nucl_num)]
BEGIN_DOC
! Nucleus-electron interaction in the |AO| basis set, per atom A.
!
! :math:`\langle \chi_i | -\frac{1}{|r-R_A|} | \chi_j \rangle`
END_DOC
implicit none
double precision :: alpha, beta, gama, delta
integer :: i_c,num_A,num_B
double precision :: A_center(3),B_center(3),C_center(3)
integer :: power_A(3),power_B(3)
integer :: i,j,k,l,n_pt_in,m
double precision :: overlap_x,overlap_y,overlap_z,overlap,dx,NAI_pol_mult
ao_integrals_n_e_per_atom = 0.d0
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,l,m,alpha,beta,A_center,B_center,power_A,power_B,&
!$OMP num_A,num_B,c,n_pt_in,C_center) &
!$OMP SHARED (ao_num,ao_prim_num,ao_expo_ordered_transp,ao_power,ao_nucl,nucl_coord,ao_coef_normalized_ordered_transp,&
!$OMP n_pt_max_integrals,ao_integrals_n_e_per_atom,nucl_num)
n_pt_in = n_pt_max_integrals
!$OMP DO SCHEDULE (dynamic)
double precision :: c
do j = 1, ao_num
power_A(1)= ao_power(j,1)
power_A(2)= ao_power(j,2)
power_A(3)= ao_power(j,3)
num_A = ao_nucl(j)
A_center(1) = nucl_coord(num_A,1)
A_center(2) = nucl_coord(num_A,2)
A_center(3) = nucl_coord(num_A,3)
do k = 1, nucl_num
C_center(1) = nucl_coord(k,1)
C_center(2) = nucl_coord(k,2)
C_center(3) = nucl_coord(k,3)
do i = 1, ao_num
power_B(1)= ao_power(i,1)
power_B(2)= ao_power(i,2)
power_B(3)= ao_power(i,3)
num_B = ao_nucl(i)
B_center(1) = nucl_coord(num_B,1)
B_center(2) = nucl_coord(num_B,2)
B_center(3) = nucl_coord(num_B,3)
c = 0.d0
do l=1,ao_prim_num(j)
alpha = ao_expo_ordered_transp(l,j)
do m=1,ao_prim_num(i)
beta = ao_expo_ordered_transp(m,i)
c = c + NAI_pol_mult(A_center,B_center,power_A,power_B, &
alpha,beta,C_center,n_pt_in) &
* ao_coef_normalized_ordered_transp(l,j) &
* ao_coef_normalized_ordered_transp(m,i)
enddo
enddo
ao_integrals_n_e_per_atom(i,j,k) = -c
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
END_PROVIDER
double precision function NAI_pol_mult(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in)
BEGIN_DOC
! Computes the electron-nucleus attraction with two primitves.
!
! :math:`\langle g_i | \frac{1}{|r-R_c|} | g_j \rangle`
END_DOC
implicit none
integer, intent(in) :: n_pt_in
double precision,intent(in) :: C_center(3),A_center(3),B_center(3),alpha,beta
integer :: power_A(3),power_B(3)
integer :: i,j,k,l,n_pt
double precision :: P_center(3)
double precision :: d(0:n_pt_in),pouet,coeff,rho,dist,const,pouet_2,p,p_inv,factor
double precision :: I_n_special_exact,integrate_bourrin,I_n_bibi
double precision :: V_n_e,const_factor,dist_integral,tmp
double precision :: accu,epsilo,rint
integer :: n_pt_out,lmax
include 'utils/constants.include.F'
if ( (A_center(1)/=B_center(1)).or. &
(A_center(2)/=B_center(2)).or. &
(A_center(3)/=B_center(3)).or. &
(A_center(1)/=C_center(1)).or. &
(A_center(2)/=C_center(2)).or. &
(A_center(3)/=C_center(3))) then
continue
else
NAI_pol_mult = V_n_e(power_A(1),power_A(2),power_A(3), &
power_B(1),power_B(2),power_B(3),alpha,beta)
return
endif
p = alpha + beta
p_inv = 1.d0/p
rho = alpha * beta * p_inv
dist = 0.d0
dist_integral = 0.d0
do i = 1, 3
P_center(i) = (alpha * A_center(i) + beta * B_center(i)) * p_inv
dist += (A_center(i) - B_center(i))*(A_center(i) - B_center(i))
dist_integral += (P_center(i) - C_center(i))*(P_center(i) - C_center(i))
enddo
const_factor = dist*rho
const = p * dist_integral
if(const_factor > 80.d0)then
NAI_pol_mult = 0.d0
return
endif
factor = dexp(-const_factor)
coeff = dtwo_pi * factor * p_inv
lmax = 20
! print*, "b"
do i = 0, n_pt_in
d(i) = 0.d0
enddo
n_pt = 2 * ( (power_A(1) + power_B(1)) +(power_A(2) + power_B(2)) +(power_A(3) + power_B(3)) )
if (n_pt == 0) then
epsilo = 1.d0
pouet = rint(0,const)
NAI_pol_mult = coeff * pouet
return
endif
call give_polynomial_mult_center_one_e(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out)
if(n_pt_out<0)then
NAI_pol_mult = 0.d0
return
endif
accu = 0.d0
! 1/r1 standard attraction integral
epsilo = 1.d0
! sum of integrals of type : int {t,[0,1]} exp-(rho.(P-Q)^2 * t^2) * t^i
do i =0 ,n_pt_out,2
accu += d(i) * rint(i/2,const)
enddo
NAI_pol_mult = accu * coeff
end
subroutine give_polynomial_mult_center_one_e(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out)
implicit none
BEGIN_DOC
! Returns the explicit polynomial in terms of the "t" variable of the following
!
! $I_{x1}(a_x, d_x,p,q) \times I_{x1}(a_y, d_y,p,q) \times I_{x1}(a_z, d_z,p,q)$.
END_DOC
integer, intent(in) :: n_pt_in
integer,intent(out) :: n_pt_out
double precision, intent(in) :: A_center(3), B_center(3),C_center(3)
double precision, intent(in) :: alpha,beta
integer, intent(in) :: power_A(3), power_B(3)
integer :: a_x,b_x,a_y,b_y,a_z,b_z
double precision :: d(0:n_pt_in)
double precision :: d1(0:n_pt_in)
double precision :: d2(0:n_pt_in)
double precision :: d3(0:n_pt_in)
double precision :: accu, pq_inv, p10_1, p10_2, p01_1, p01_2
double precision :: p,P_center(3),rho,p_inv,p_inv_2
accu = 0.d0
ASSERT (n_pt_in > 1)
p = alpha+beta
p_inv = 1.d0/p
p_inv_2 = 0.5d0/p
do i =1, 3
P_center(i) = (alpha * A_center(i) + beta * B_center(i)) * p_inv
enddo
double precision :: R1x(0:2), B01(0:2), R1xp(0:2),R2x(0:2)
R1x(0) = (P_center(1) - A_center(1))
R1x(1) = 0.d0
R1x(2) = -(P_center(1) - C_center(1))
R1xp(0) = (P_center(1) - B_center(1))
R1xp(1) = 0.d0
R1xp(2) =-(P_center(1) - C_center(1))
R2x(0) = p_inv_2
R2x(1) = 0.d0
R2x(2) = -p_inv_2
do i = 0,n_pt_in
d(i) = 0.d0
enddo
do i = 0,n_pt_in
d1(i) = 0.d0
enddo
do i = 0,n_pt_in
d2(i) = 0.d0
enddo
do i = 0,n_pt_in
d3(i) = 0.d0
enddo
integer :: n_pt1,n_pt2,n_pt3,dim,i
n_pt1 = n_pt_in
n_pt2 = n_pt_in
n_pt3 = n_pt_in
a_x = power_A(1)
b_x = power_B(1)
call I_x1_pol_mult_one_e(a_x,b_x,R1x,R1xp,R2x,d1,n_pt1,n_pt_in)
if(n_pt1<0)then
n_pt_out = -1
do i = 0,n_pt_in
d(i) = 0.d0
enddo
return
endif
R1x(0) = (P_center(2) - A_center(2))
R1x(1) = 0.d0
R1x(2) = -(P_center(2) - C_center(2))
R1xp(0) = (P_center(2) - B_center(2))
R1xp(1) = 0.d0
R1xp(2) =-(P_center(2) - C_center(2))
a_y = power_A(2)
b_y = power_B(2)
call I_x1_pol_mult_one_e(a_y,b_y,R1x,R1xp,R2x,d2,n_pt2,n_pt_in)
if(n_pt2<0)then
n_pt_out = -1
do i = 0,n_pt_in
d(i) = 0.d0
enddo
return
endif
R1x(0) = (P_center(3) - A_center(3))
R1x(1) = 0.d0
R1x(2) = -(P_center(3) - C_center(3))
R1xp(0) = (P_center(3) - B_center(3))
R1xp(1) = 0.d0
R1xp(2) =-(P_center(3) - C_center(3))
a_z = power_A(3)
b_z = power_B(3)
call I_x1_pol_mult_one_e(a_z,b_z,R1x,R1xp,R2x,d3,n_pt3,n_pt_in)
if(n_pt3<0)then
n_pt_out = -1
do i = 0,n_pt_in
d(i) = 0.d0
enddo
return
endif
integer :: n_pt_tmp
n_pt_tmp = 0
call multiply_poly(d1,n_pt1,d2,n_pt2,d,n_pt_tmp)
do i = 0,n_pt_tmp
d1(i) = 0.d0
enddo
n_pt_out = 0
call multiply_poly(d ,n_pt_tmp ,d3,n_pt3,d1,n_pt_out)
do i = 0, n_pt_out
d(i) = d1(i)
enddo
end
recursive subroutine I_x1_pol_mult_one_e(a,c,R1x,R1xp,R2x,d,nd,n_pt_in)
implicit none
BEGIN_DOC
! Recursive routine involved in the electron-nucleus potential
END_DOC
integer , intent(in) :: n_pt_in
double precision,intent(inout) :: d(0:n_pt_in)
integer,intent(inout) :: nd
integer, intent(in) :: a,c
double precision, intent(in) :: R1x(0:2),R1xp(0:2),R2x(0:2)
include 'utils/constants.include.F'
double precision :: X(0:max_dim)
double precision :: Y(0:max_dim)
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: X, Y
integer :: nx, ix,dim,iy,ny
dim = n_pt_in
! print*,'a,c = ',a,c
! print*,'nd_in = ',nd
if( (a==0) .and. (c==0))then
nd = 0
d(0) = 1.d0
return
elseif( (c<0).or.(nd<0) )then
nd = -1
return
else if ((a==0).and.(c.ne.0)) then
call I_x2_pol_mult_one_e(c,R1x,R1xp,R2x,d,nd,n_pt_in)
else if (a==1) then
nx = nd
do ix=0,n_pt_in
X(ix) = 0.d0
Y(ix) = 0.d0
enddo
call I_x2_pol_mult_one_e(c-1,R1x,R1xp,R2x,X,nx,n_pt_in)
do ix=0,nx
X(ix) *= dble(c)
enddo
call multiply_poly(X,nx,R2x,2,d,nd)
ny=0
call I_x2_pol_mult_one_e(c,R1x,R1xp,R2x,Y,ny,n_pt_in)
call multiply_poly(Y,ny,R1x,2,d,nd)
else
do ix=0,n_pt_in
X(ix) = 0.d0
Y(ix) = 0.d0
enddo
nx = 0
call I_x1_pol_mult_one_e(a-2,c,R1x,R1xp,R2x,X,nx,n_pt_in)
do ix=0,nx
X(ix) *= dble(a-1)
enddo
call multiply_poly(X,nx,R2x,2,d,nd)
nx = nd
do ix=0,n_pt_in
X(ix) = 0.d0
enddo
call I_x1_pol_mult_one_e(a-1,c-1,R1x,R1xp,R2x,X,nx,n_pt_in)
do ix=0,nx
X(ix) *= dble(c)
enddo
call multiply_poly(X,nx,R2x,2,d,nd)
ny=0
call I_x1_pol_mult_one_e(a-1,c,R1x,R1xp,R2x,Y,ny,n_pt_in)
call multiply_poly(Y,ny,R1x,2,d,nd)
endif
end
recursive subroutine I_x2_pol_mult_one_e(c,R1x,R1xp,R2x,d,nd,dim)
implicit none
BEGIN_DOC
! Recursive routine involved in the electron-nucleus potential
END_DOC
integer , intent(in) :: dim
include 'utils/constants.include.F'
double precision :: d(0:max_dim)
integer,intent(inout) :: nd
integer, intent(in) :: c
double precision, intent(in) :: R1x(0:2),R1xp(0:2),R2x(0:2)
integer :: i
if(c==0) then
nd = 0
d(0) = 1.d0
return
elseif ((nd<0).or.(c<0))then
nd = -1
return
else
integer :: nx, ix,ny
double precision :: X(0:max_dim),Y(0:max_dim)
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: X, Y
do ix=0,dim
X(ix) = 0.d0
Y(ix) = 0.d0
enddo
nx = 0
call I_x1_pol_mult_one_e(0,c-2,R1x,R1xp,R2x,X,nx,dim)
do ix=0,nx
X(ix) *= dble(c-1)
enddo
call multiply_poly(X,nx,R2x,2,d,nd)
ny = 0
do ix=0,dim
Y(ix) = 0.d0
enddo
call I_x1_pol_mult_one_e(0,c-1,R1x,R1xp,R2x,Y,ny,dim)
if(ny.ge.0)then
call multiply_poly(Y,ny,R1xp,2,d,nd)
endif
endif
end
double precision function V_n_e(a_x,a_y,a_z,b_x,b_y,b_z,alpha,beta)
implicit none
BEGIN_DOC
! Primitve nuclear attraction between the two primitves centered on the same atom.
!
! $p_1 = x^{a_x} y^{a_y} z^{a_z} \exp(-\alpha r^2)$
!
! $p_2 = x^{b_x} y^{b_y} z^{b_z} \exp(-\beta r^2)$
END_DOC
integer :: a_x,a_y,a_z,b_x,b_y,b_z
double precision :: alpha,beta
double precision :: V_r, V_phi, V_theta
if(iand((a_x+b_x),1)==1.or.iand(a_y+b_y,1)==1.or.iand((a_z+b_z),1)==1)then
V_n_e = 0.d0
else
V_n_e = V_r(a_x+b_x+a_y+b_y+a_z+b_z+1,alpha+beta) &
* V_phi(a_x+b_x,a_y+b_y) &
* V_theta(a_z+b_z,a_x+b_x+a_y+b_y+1)
endif
end
double precision function int_gaus_pol(alpha,n)
implicit none
BEGIN_DOC
! Computes the integral:
!
! $\int_{-\infty}^{\infty} x^n \exp(-\alpha x^2) dx$.
END_DOC
double precision :: alpha
integer :: n
double precision :: dble_fact
include 'utils/constants.include.F'
int_gaus_pol = 0.d0
if(iand(n,1).eq.0)then
int_gaus_pol = dsqrt(alpha/pi)
double precision :: two_alpha
two_alpha = alpha+alpha
integer :: i
do i=1,n,2
int_gaus_pol = int_gaus_pol * two_alpha
enddo
int_gaus_pol = dble_fact(n -1) / int_gaus_pol
endif
end
double precision function V_r(n,alpha)
implicit none
BEGIN_DOC
! Computes the radial part of the nuclear attraction integral:
!
! $\int_{0}^{\infty} r^n \exp(-\alpha r^2) dr$
!
END_DOC
double precision :: alpha, fact
integer :: n
include 'utils/constants.include.F'
if(iand(n,1).eq.1)then
V_r = 0.5d0 * fact(shiftr(n,1)) / (alpha ** (shiftr(n,1) + 1))
else
V_r = sqpi * fact(n) / fact(shiftr(n,1)) * (0.5d0/sqrt(alpha)) ** (n+1)
endif
end
double precision function V_phi(n,m)
implicit none
BEGIN_DOC
! Computes the angular $\phi$ part of the nuclear attraction integral:
!
! $\int_{0}^{2 \pi} \cos(\phi)^n \sin(\phi)^m d\phi$.
END_DOC
integer :: n,m, i
double precision :: prod, Wallis
prod = 1.d0
do i = 0,shiftr(n,1)-1
prod = prod/ (1.d0 + dfloat(m+1)/dfloat(n-i-i-1))
enddo
V_phi = 4.d0 * prod * Wallis(m)
end
double precision function V_theta(n,m)
implicit none
BEGIN_DOC
! Computes the angular $\theta$ part of the nuclear attraction integral:
!
! $\int_{0}^{\pi} \cos(\theta)^n \sin(\theta)^m d\theta$
END_DOC
integer :: n,m,i
double precision :: Wallis, prod
include 'utils/constants.include.F'
V_theta = 0.d0
prod = 1.d0
do i = 0,shiftr(n,1)-1
prod = prod / (1.d0 + dfloat(m+1)/dfloat(n-i-i-1))
enddo
V_theta = (prod+prod) * Wallis(m)
end
double precision function Wallis(n)
implicit none
BEGIN_DOC
! Wallis integral:
!
! $\int_{0}^{\pi} \cos(\theta)^n d\theta$.
END_DOC
double precision :: fact
integer :: n,p
include 'utils/constants.include.F'
if(iand(n,1).eq.0)then
Wallis = fact(shiftr(n,1))
Wallis = pi * fact(n) / (dble(ibset(0_8,n)) * (Wallis+Wallis)*Wallis)
else
p = shiftr(n,1)
Wallis = fact(p)
Wallis = dble(ibset(0_8,p+p)) * Wallis*Wallis / fact(p+p+1)
endif
end
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