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added cosgtos_ao_int

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eginer 2022-10-24 21:10:56 +02:00
parent 1c614a389b
commit 7ebc9da4ce
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19
src/cosgtos_ao_int/EZFIO.cfg Normal file
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[ao_expoim_cosgtos]
type: double precision
doc: imag part for Exponents for each primitive of each cosGTOs |AO|
size: (ao_basis.ao_num,ao_basis.ao_prim_num_max)
interface: ezfio, provider
[use_cosgtos]
type: logical
doc: If true, use cosgtos for AO integrals
interface: ezfio,provider,ocaml
default: False
[ao_integrals_threshold]
type: Threshold
doc: If | (pq|rs) | < `ao_integrals_threshold` then (pq|rs) is zero
interface: ezfio,provider,ocaml
default: 1.e-15
ezfio_name: threshold_ao

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src/cosgtos_ao_int/NEED Normal file
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ao_basis

4
src/cosgtos_ao_int/README.rst Normal file
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==============
cosgtos_ao_int
==============

210
src/cosgtos_ao_int/aos_cosgtos.irp.f Normal file
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! ---
BEGIN_PROVIDER [ double precision, ao_coef_norm_ord_transp_cosgtos, (ao_prim_num_max, ao_num) ]
implicit none
integer :: i, j
do j = 1, ao_num
do i = 1, ao_prim_num_max
ao_coef_norm_ord_transp_cosgtos(i,j) = ao_coef_norm_ord_cosgtos(j,i)
enddo
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ complex*16, ao_expo_ord_transp_cosgtos, (ao_prim_num_max, ao_num) ]
implicit none
integer :: i, j
do j = 1, ao_num
do i = 1, ao_prim_num_max
ao_expo_ord_transp_cosgtos(i,j) = ao_expo_ord_cosgtos(j,i)
enddo
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, ao_coef_norm_cosgtos, (ao_num, ao_prim_num_max) ]
implicit none
integer :: i, j, powA(3), nz
double precision :: norm
complex*16 :: overlap_x, overlap_y, overlap_z, C_A(3)
complex*16 :: integ1, integ2, expo
nz = 100
C_A(1) = (0.d0, 0.d0)
C_A(2) = (0.d0, 0.d0)
C_A(3) = (0.d0, 0.d0)
ao_coef_norm_cosgtos = 0.d0
do i = 1, ao_num
powA(1) = ao_power(i,1)
powA(2) = ao_power(i,2)
powA(3) = ao_power(i,3)
! Normalization of the primitives
if(primitives_normalized) then
do j = 1, ao_prim_num(i)
expo = ao_expo(i,j) + (0.d0, 1.d0) * ao_expoim_cosgtos(i,j)
call overlap_cgaussian_xyz(C_A, C_A, expo, expo, powA, powA, overlap_x, overlap_y, overlap_z, integ1, nz)
call overlap_cgaussian_xyz(C_A, C_A, conjg(expo), expo, powA, powA, overlap_x, overlap_y, overlap_z, integ2, nz)
norm = 2.d0 * real( integ1 + integ2 )
ao_coef_norm_cosgtos(i,j) = ao_coef(i,j) / dsqrt(norm)
enddo
else
do j = 1, ao_prim_num(i)
ao_coef_norm_cosgtos(i,j) = ao_coef(i,j)
enddo
endif
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, ao_coef_norm_ord_cosgtos, (ao_num, ao_prim_num_max) ]
&BEGIN_PROVIDER [ complex*16 , ao_expo_ord_cosgtos, (ao_num, ao_prim_num_max) ]
implicit none
integer :: i, j
integer :: iorder(ao_prim_num_max)
double precision :: d(ao_prim_num_max,3)
d = 0.d0
do i = 1, ao_num
do j = 1, ao_prim_num(i)
iorder(j) = j
d(j,1) = ao_expo(i,j)
d(j,2) = ao_coef_norm_cosgtos(i,j)
d(j,3) = ao_expoim_cosgtos(i,j)
enddo
call dsort (d(1,1), iorder, ao_prim_num(i))
call dset_order(d(1,2), iorder, ao_prim_num(i))
call dset_order(d(1,3), iorder, ao_prim_num(i))
do j = 1, ao_prim_num(i)
ao_expo_ord_cosgtos (i,j) = d(j,1) + (0.d0, 1.d0) * d(j,3)
ao_coef_norm_ord_cosgtos(i,j) = d(j,2)
enddo
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, ao_overlap_cosgtos, (ao_num, ao_num) ]
&BEGIN_PROVIDER [ double precision, ao_overlap_cosgtos_x, (ao_num, ao_num) ]
&BEGIN_PROVIDER [ double precision, ao_overlap_cosgtos_y, (ao_num, ao_num) ]
&BEGIN_PROVIDER [ double precision, ao_overlap_cosgtos_z, (ao_num, ao_num) ]
implicit none
integer :: i, j, n, l, dim1, power_A(3), power_B(3)
double precision :: c, overlap, overlap_x, overlap_y, overlap_z
complex*16 :: alpha, beta, A_center(3), B_center(3)
complex*16 :: overlap1, overlap_x1, overlap_y1, overlap_z1
complex*16 :: overlap2, overlap_x2, overlap_y2, overlap_z2
ao_overlap_cosgtos = 0.d0
ao_overlap_cosgtos_x = 0.d0
ao_overlap_cosgtos_y = 0.d0
ao_overlap_cosgtos_z = 0.d0
dim1 = 100
!$OMP PARALLEL DO SCHEDULE(GUIDED) &
!$OMP DEFAULT(NONE) &
!$OMP PRIVATE( A_center, B_center, power_A, power_B, alpha, beta, i, j, n, l, c &
!$OMP , overlap_x , overlap_y , overlap_z , overlap &
!$OMP , overlap_x1, overlap_y1, overlap_z1, overlap1 &
!$OMP , overlap_x2, overlap_y2, overlap_z2, overlap2 ) &
!$OMP SHARED( nucl_coord, ao_power, ao_prim_num, ao_num, ao_nucl, dim1 &
!$OMP , ao_overlap_cosgtos_x, ao_overlap_cosgtos_y, ao_overlap_cosgtos_z, ao_overlap_cosgtos &
!$OMP , ao_coef_norm_ord_transp_cosgtos, ao_expo_ord_transp_cosgtos )
do j = 1, ao_num
A_center(1) = nucl_coord(ao_nucl(j),1) * (1.d0, 0.d0)
A_center(2) = nucl_coord(ao_nucl(j),2) * (1.d0, 0.d0)
A_center(3) = nucl_coord(ao_nucl(j),3) * (1.d0, 0.d0)
power_A(1) = ao_power(j,1)
power_A(2) = ao_power(j,2)
power_A(3) = ao_power(j,3)
do i = 1, ao_num
B_center(1) = nucl_coord(ao_nucl(i),1) * (1.d0, 0.d0)
B_center(2) = nucl_coord(ao_nucl(i),2) * (1.d0, 0.d0)
B_center(3) = nucl_coord(ao_nucl(i),3) * (1.d0, 0.d0)
power_B(1) = ao_power(i,1)
power_B(2) = ao_power(i,2)
power_B(3) = ao_power(i,3)
do n = 1, ao_prim_num(j)
alpha = ao_expo_ord_transp_cosgtos(n,j)
do l = 1, ao_prim_num(i)
c = ao_coef_norm_ord_transp_cosgtos(n,j) * ao_coef_norm_ord_transp_cosgtos(l,i)
beta = ao_expo_ord_transp_cosgtos(l,i)
call overlap_cgaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
, overlap_x1, overlap_y1, overlap_z1, overlap1, dim1 )
call overlap_cgaussian_xyz( A_center, B_center, conjg(alpha), beta, power_A, power_B &
, overlap_x2, overlap_y2, overlap_z2, overlap2, dim1 )
overlap_x = 2.d0 * real( overlap_x1 + overlap_x2 )
overlap_y = 2.d0 * real( overlap_y1 + overlap_y2 )
overlap_z = 2.d0 * real( overlap_z1 + overlap_z2 )
overlap = 2.d0 * real( overlap1 + overlap2 )
ao_overlap_cosgtos(i,j) = ao_overlap_cosgtos(i,j) + c * overlap
if( isnan(ao_overlap_cosgtos(i,j)) ) then
print*,'i, j', i, j
print*,'l, n', l, n
print*,'c, overlap', c, overlap
print*, overlap_x, overlap_y, overlap_z
stop
endif
ao_overlap_cosgtos_x(i,j) = ao_overlap_cosgtos_x(i,j) + c * overlap_x
ao_overlap_cosgtos_y(i,j) = ao_overlap_cosgtos_y(i,j) + c * overlap_y
ao_overlap_cosgtos_z(i,j) = ao_overlap_cosgtos_z(i,j) + c * overlap_z
enddo
enddo
enddo
enddo
!$OMP END PARALLEL DO
END_PROVIDER
! ---

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src/cosgtos_ao_int/cosgtos_ao_int.irp.f Normal file
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program cosgtos_ao_int
implicit none
BEGIN_DOC
! TODO : Put the documentation of the program here
END_DOC
print *, 'Hello world'
end

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src/cosgtos_ao_int/gauss_legendre.irp.f Normal file
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BEGIN_PROVIDER [ double precision, gauleg_t2, (n_pt_max_integrals,n_pt_max_integrals/2) ]
&BEGIN_PROVIDER [ double precision, gauleg_w, (n_pt_max_integrals,n_pt_max_integrals/2) ]
implicit none
BEGIN_DOC
! t_w(i,1,k) = w(i)
! t_w(i,2,k) = t(i)
END_DOC
integer :: i,j,l
l=0
do i = 2,n_pt_max_integrals,2
l = l+1
call gauleg(0.d0,1.d0,gauleg_t2(1,l),gauleg_w(1,l),i)
do j=1,i
gauleg_t2(j,l) *= gauleg_t2(j,l)
enddo
enddo
END_PROVIDER
subroutine gauleg(x1,x2,x,w,n)
implicit none
BEGIN_DOC
! Gauss-Legendre
END_DOC
integer, intent(in) :: n
double precision, intent(in) :: x1, x2
double precision, intent (out) :: x(n),w(n)
double precision, parameter :: eps=3.d-14
integer :: m,i,j
double precision :: xm, xl, z, z1, p1, p2, p3, pp, dn
m=(n+1)/2
xm=0.5d0*(x2+x1)
xl=0.5d0*(x2-x1)
dn = dble(n)
do i=1,m
z=dcos(3.141592654d0*(dble(i)-.25d0)/(dble(n)+.5d0))
z1 = z+1.d0
do while (dabs(z-z1) > eps)
p1=1.d0
p2=0.d0
do j=1,n
p3=p2
p2=p1
p1=(dble(j+j-1)*z*p2-dble(j-1)*p3)/j
enddo
pp=dn*(z*p1-p2)/(z*z-1.d0)
z1=z
z=z1-p1/pp
end do
x(i)=xm-xl*z
x(n+1-i)=xm+xl*z
w(i)=(xl+xl)/((1.d0-z*z)*pp*pp)
w(n+1-i)=w(i)
enddo
end

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src/cosgtos_ao_int/one_e_Coul_integrals.irp.f Normal file
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! ---
BEGIN_PROVIDER [ double precision, ao_integrals_n_e_cosgtos, (ao_num, ao_num)]
BEGIN_DOC
!
! Nucleus-electron interaction, in the cosgtos |AO| basis set.
!
! :math:`\langle \chi_i | -\sum_A \frac{1}{|r-R_A|} | \chi_j \rangle`
!
END_DOC
implicit none
integer :: num_A, num_B, power_A(3), power_B(3)
integer :: i, j, k, l, n_pt_in, m
double precision :: c, Z, A_center(3), B_center(3), C_center(3)
complex*16 :: alpha, beta, c1, c2
complex*16 :: NAI_pol_mult_cosgtos
ao_integrals_n_e_cosgtos = 0.d0
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE ( i, j, k, l, m, alpha, beta, A_center, B_center, C_center &
!$OMP , power_A, power_B, num_A, num_B, Z, c, c1, c2, n_pt_in ) &
!$OMP SHARED ( ao_num, ao_prim_num, ao_nucl, nucl_coord, ao_power, nucl_num, nucl_charge &
!$OMP , ao_expo_ord_transp_cosgtos, ao_coef_norm_ord_transp_cosgtos &
!$OMP , n_pt_max_integrals, ao_integrals_n_e_cosgtos )
n_pt_in = n_pt_max_integrals
!$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_ord_transp_cosgtos(l,j)
do m = 1, ao_prim_num(i)
beta = ao_expo_ord_transp_cosgtos(m,i)
c = 0.d0
do k = 1, nucl_num
Z = nucl_charge(k)
C_center(1:3) = nucl_coord(k,1:3)
!print *, ' '
!print *, A_center, B_center, C_center, power_A, power_B
!print *, real(alpha), real(beta)
c1 = NAI_pol_mult_cosgtos( A_center, B_center, power_A, power_B &
, alpha, beta, C_center, n_pt_in )
!c2 = c1
c2 = NAI_pol_mult_cosgtos( A_center, B_center, power_A, power_B &
, conjg(alpha), beta, C_center, n_pt_in )
!print *, ' c1 = ', real(c1)
!print *, ' c2 = ', real(c2)
c = c - Z * 2.d0 * real(c1 + c2)
enddo
ao_integrals_n_e_cosgtos(i,j) = ao_integrals_n_e_cosgtos(i,j) &
+ ao_coef_norm_ord_transp_cosgtos(l,j) &
* ao_coef_norm_ord_transp_cosgtos(m,i) * c
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
END_PROVIDER
! ---
complex*16 function NAI_pol_mult_cosgtos(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 cosgtos.
!
! :math:`\langle g_i | \frac{1}{|r-R_c|} | g_j \rangle`
!
END_DOC
implicit none
include 'utils/constants.include.F'
integer, intent(in) :: n_pt_in, power_A(3), power_B(3)
double precision, intent(in) :: C_center(3), A_center(3), B_center(3)
complex*16, intent(in) :: alpha, beta
integer :: i, n_pt, n_pt_out
double precision :: dist, const_mod
complex*16 :: p, p_inv, rho, dist_integral, const, const_factor, coeff, factor
complex*16 :: accu, P_center(3)
complex*16 :: d(0:n_pt_in)
complex*16 :: V_n_e_cosgtos
complex*16 :: crint
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_cosgtos = V_n_e_cosgtos( 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, 0.d0) / p
rho = alpha * beta * p_inv
dist = 0.d0
dist_integral = (0.d0, 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
const_mod = dsqrt(real(const_factor)*real(const_factor) + aimag(const_factor)*aimag(const_factor))
if(const_mod > 80.d0) then
NAI_pol_mult_cosgtos = (0.d0, 0.d0)
return
endif
factor = zexp(-const_factor)
coeff = dtwo_pi * factor * p_inv
do i = 0, n_pt_in
d(i) = (0.d0, 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
NAI_pol_mult_cosgtos = coeff * crint(0, const)
return
endif
call give_cpolynomial_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_cosgtos = (0.d0, 0.d0)
return
endif
accu = (0.d0, 0.d0)
do i = 0, n_pt_out, 2
accu += crint(shiftr(i, 1), const) * d(i)
! print *, shiftr(i, 1), real(const), real(d(i)), real(crint(shiftr(i, 1), const))
enddo
NAI_pol_mult_cosgtos = accu * coeff
end function NAI_pol_mult_cosgtos
! ---
subroutine give_cpolynomial_mult_center_one_e( A_center, B_center, alpha, beta &
, power_A, power_B, C_center, n_pt_in, d, n_pt_out)
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
implicit none
integer, intent(in) :: n_pt_in, power_A(3), power_B(3)
double precision, intent(in) :: A_center(3), B_center(3), C_center(3)
complex*16, intent(in) :: alpha, beta
integer, intent(out) :: n_pt_out
complex*16, intent(out) :: d(0:n_pt_in)
integer :: a_x, b_x, a_y, b_y, a_z, b_z
integer :: n_pt1, n_pt2, n_pt3, dim, i, n_pt_tmp
complex*16 :: p, P_center(3), rho, p_inv, p_inv_2
complex*16 :: R1x(0:2), B01(0:2), R1xp(0:2),R2x(0:2)
complex*16 :: d1(0:n_pt_in), d2(0:n_pt_in), d3(0:n_pt_in)
ASSERT (n_pt_in > 1)
p = alpha + beta
p_inv = (1.d0, 0.d0) / p
p_inv_2 = 0.5d0 * p_inv
do i = 1, 3
P_center(i) = (alpha * A_center(i) + beta * B_center(i)) * p_inv
enddo
do i = 0, n_pt_in
d(i) = (0.d0, 0.d0)
d1(i) = (0.d0, 0.d0)
d2(i) = (0.d0, 0.d0)
d3(i) = (0.d0, 0.d0)
enddo
! ---
n_pt1 = n_pt_in
R1x(0) = (P_center(1) - A_center(1))
R1x(1) = (0.d0, 0.d0)
R1x(2) = -(P_center(1) - C_center(1))
R1xp(0) = (P_center(1) - B_center(1))
R1xp(1) = (0.d0, 0.d0)
R1xp(2) = -(P_center(1) - C_center(1))
R2x(0) = p_inv_2
R2x(1) = (0.d0, 0.d0)
R2x(2) = -p_inv_2
a_x = power_A(1)
b_x = power_B(1)
call I_x1_pol_mult_one_e_cosgtos(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, 0.d0)
enddo
return
endif
! ---
n_pt2 = n_pt_in
R1x(0) = (P_center(2) - A_center(2))
R1x(1) = (0.d0, 0.d0)
R1x(2) = -(P_center(2) - C_center(2))
R1xp(0) = (P_center(2) - B_center(2))
R1xp(1) = (0.d0, 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_cosgtos(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, 0.d0)
enddo
return
endif
! ---
n_pt3 = n_pt_in
R1x(0) = (P_center(3) - A_center(3))
R1x(1) = (0.d0, 0.d0)
R1x(2) = -(P_center(3) - C_center(3))
R1xp(0) = (P_center(3) - B_center(3))
R1xp(1) = (0.d0, 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_cosgtos(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, 0.d0)
enddo
return
endif
! ---
n_pt_tmp = 0
call multiply_cpoly(d1, n_pt1, d2, n_pt2, d, n_pt_tmp)
do i = 0, n_pt_tmp
d1(i) = (0.d0, 0.d0)
enddo
n_pt_out = 0
call multiply_cpoly(d, n_pt_tmp, d3, n_pt3, d1, n_pt_out)
do i = 0, n_pt_out
d(i) = d1(i)
enddo
end subroutine give_cpolynomial_mult_center_one_e
! ---
recursive subroutine I_x1_pol_mult_one_e_cosgtos(a, c, R1x, R1xp, R2x, d, nd, n_pt_in)
BEGIN_DOC
! Recursive routine involved in the electron-nucleus potential
END_DOC
implicit none
include 'utils/constants.include.F'
integer, intent(in) :: a, c, n_pt_in
complex*16, intent(in) :: R1x(0:2), R1xp(0:2), R2x(0:2)
integer, intent(inout) :: nd
complex*16, intent(inout) :: d(0:n_pt_in)
integer :: nx, ix, dim, iy, ny
complex*16 :: X(0:max_dim)
complex*16 :: Y(0:max_dim)
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: X, Y
dim = n_pt_in
if( (a==0) .and. (c==0)) then
nd = 0
d(0) = (1.d0, 0.d0)
return
elseif( (c < 0) .or. (nd < 0) ) then
nd = -1
return
elseif((a == 0) .and. (c .ne. 0)) then
call I_x2_pol_mult_one_e_cosgtos(c, R1x, R1xp, R2x, d, nd, n_pt_in)
elseif(a == 1) then
nx = nd
do ix = 0, n_pt_in
X(ix) = (0.d0, 0.d0)
Y(ix) = (0.d0, 0.d0)
enddo
call I_x2_pol_mult_one_e_cosgtos(c-1, R1x, R1xp, R2x, X, nx, n_pt_in)
do ix = 0, nx
X(ix) *= dble(c)
enddo
call multiply_cpoly(X, nx, R2x, 2, d, nd)
ny = 0
call I_x2_pol_mult_one_e_cosgtos(c, R1x, R1xp, R2x, Y, ny, n_pt_in)
call multiply_cpoly(Y, ny, R1x, 2, d, nd)
else
nx = 0
do ix = 0, n_pt_in
X(ix) = (0.d0, 0.d0)
Y(ix) = (0.d0, 0.d0)
enddo
call I_x1_pol_mult_one_e_cosgtos(a-2, c, R1x, R1xp, R2x, X, nx, n_pt_in)
do ix = 0, nx
X(ix) *= dble(a-1)
enddo
call multiply_cpoly(X, nx, R2x, 2, d, nd)
nx = nd
do ix = 0, n_pt_in
X(ix) = (0.d0, 0.d0)
enddo
call I_x1_pol_mult_one_e_cosgtos(a-1, c-1, R1x, R1xp, R2x, X, nx, n_pt_in)
do ix = 0, nx
X(ix) *= dble(c)
enddo
call multiply_cpoly(X, nx, R2x, 2, d, nd)
ny = 0
call I_x1_pol_mult_one_e_cosgtos(a-1, c, R1x, R1xp, R2x, Y, ny, n_pt_in)
call multiply_cpoly(Y, ny, R1x, 2, d, nd)
endif
end subroutine I_x1_pol_mult_one_e_cosgtos
! ---
recursive subroutine I_x2_pol_mult_one_e_cosgtos(c, R1x, R1xp, R2x, d, nd, dim)
BEGIN_DOC
! Recursive routine involved in the electron-nucleus potential
END_DOC
implicit none
include 'utils/constants.include.F'
integer, intent(in) :: dim, c
complex*16, intent(in) :: R1x(0:2), R1xp(0:2), R2x(0:2)
integer, intent(inout) :: nd
complex*16, intent(out) :: d(0:max_dim)
integer :: i, nx, ix, ny
complex*16 :: X(0:max_dim), Y(0:max_dim)
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: X, Y
if(c == 0) then
nd = 0
d(0) = (1.d0, 0.d0)
return
elseif((nd < 0) .or. (c < 0)) then
nd = -1
return
else
nx = 0
do ix = 0, dim
X(ix) = (0.d0, 0.d0)
Y(ix) = (0.d0, 0.d0)
enddo
call I_x1_pol_mult_one_e_cosgtos(0, c-2, R1x, R1xp, R2x, X, nx, dim)
do ix = 0, nx
X(ix) *= dble(c-1)
enddo
call multiply_cpoly(X, nx, R2x, 2, d, nd)
ny = 0
do ix = 0, dim
Y(ix) = (0.d0, 0.d0)
enddo
call I_x1_pol_mult_one_e_cosgtos(0, c-1, R1x, R1xp, R2x, Y, ny, dim)
if(ny .ge. 0) then
call multiply_cpoly(Y, ny, R1xp, 2, d, nd)
endif
endif
end subroutine I_x2_pol_mult_one_e_cosgtos
! ---
complex*16 function V_n_e_cosgtos(a_x, a_y, a_z, b_x, b_y, b_z, alpha, beta)
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
implicit none
integer, intent(in) :: a_x, a_y, a_z, b_x, b_y, b_z
complex*16, intent(in) :: alpha, beta
double precision :: V_phi, V_theta
complex*16 :: V_r_cosgtos
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_cosgtos = (0.d0, 0.d0)
else
V_n_e_cosgtos = V_r_cosgtos(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 function V_n_e_cosgtos
! ---
complex*16 function V_r_cosgtos(n, alpha)
BEGIN_DOC
! Computes the radial part of the nuclear attraction integral:
!
! $\int_{0}^{\infty} r^n \exp(-\alpha r^2) dr$
!
END_DOC
implicit none
include 'utils/constants.include.F'
integer , intent(in) :: n
complex*16, intent(in) :: alpha
double precision :: fact
if(iand(n, 1) .eq. 1) then
V_r_cosgtos = 0.5d0 * fact(shiftr(n, 1)) / (alpha**(shiftr(n, 1) + 1))
else
V_r_cosgtos = sqpi * fact(n) / fact(shiftr(n, 1)) * (0.5d0/zsqrt(alpha))**(n+1)
endif
end function V_r_cosgtos
! ---

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! ---
BEGIN_PROVIDER [ double precision, ao_deriv2_cosgtos_x, (ao_num, ao_num) ]
&BEGIN_PROVIDER [ double precision, ao_deriv2_cosgtos_y, (ao_num, ao_num) ]
&BEGIN_PROVIDER [ double precision, ao_deriv2_cosgtos_z, (ao_num, ao_num) ]
implicit none
integer :: i, j, n, l, dim1, power_A(3), power_B(3)
double precision :: c, deriv_tmp
complex*16 :: alpha, beta, A_center(3), B_center(3)
complex*16 :: overlap_x, overlap_y, overlap_z, overlap
complex*16 :: overlap_x0_1, overlap_y0_1, overlap_z0_1
complex*16 :: overlap_x0_2, overlap_y0_2, overlap_z0_2
complex*16 :: overlap_m2_1, overlap_p2_1
complex*16 :: overlap_m2_2, overlap_p2_2
complex*16 :: deriv_tmp_1, deriv_tmp_2
dim1 = 100
! -- Dummy call to provide everything
A_center(:) = (0.0d0, 0.d0)
B_center(:) = (1.0d0, 0.d0)
alpha = (1.0d0, 0.d0)
beta = (0.1d0, 0.d0)
power_A = 1
power_B = 0
call overlap_cgaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
, overlap_x0_1, overlap_y0_1, overlap_z0_1, overlap, dim1 )
! ---
!$OMP PARALLEL DO SCHEDULE(GUIDED) &
!$OMP DEFAULT(NONE) &
!$OMP PRIVATE( A_center, B_center, power_A, power_B, alpha, beta, i, j, l, n, c &
!$OMP , deriv_tmp, deriv_tmp_1, deriv_tmp_2 &
!$OMP , overlap_x, overlap_y, overlap_z, overlap &
!$OMP , overlap_m2_1, overlap_p2_1, overlap_m2_2, overlap_p2_2 &
!$OMP , overlap_x0_1, overlap_y0_1, overlap_z0_1, overlap_x0_2, overlap_y0_2, overlap_z0_2 ) &
!$OMP SHARED( nucl_coord, ao_power, ao_prim_num, ao_num, ao_nucl, dim1 &
!$OMP , ao_coef_norm_ord_transp_cosgtos, ao_expo_ord_transp_cosgtos &
!$OMP , ao_deriv2_cosgtos_x, ao_deriv2_cosgtos_y, ao_deriv2_cosgtos_z )
do j = 1, ao_num
A_center(1) = nucl_coord(ao_nucl(j),1) * (1.d0, 0.d0)
A_center(2) = nucl_coord(ao_nucl(j),2) * (1.d0, 0.d0)
A_center(3) = nucl_coord(ao_nucl(j),3) * (1.d0, 0.d0)
power_A(1) = ao_power(j,1)
power_A(2) = ao_power(j,2)
power_A(3) = ao_power(j,3)
do i = 1, ao_num
B_center(1) = nucl_coord(ao_nucl(i),1) * (1.d0, 0.d0)
B_center(2) = nucl_coord(ao_nucl(i),2) * (1.d0, 0.d0)
B_center(3) = nucl_coord(ao_nucl(i),3) * (1.d0, 0.d0)
power_B(1) = ao_power(i,1)
power_B(2) = ao_power(i,2)
power_B(3) = ao_power(i,3)
ao_deriv2_cosgtos_x(i,j) = 0.d0
ao_deriv2_cosgtos_y(i,j) = 0.d0
ao_deriv2_cosgtos_z(i,j) = 0.d0
do n = 1, ao_prim_num(j)
alpha = ao_expo_ord_transp_cosgtos(n,j)
do l = 1, ao_prim_num(i)
c = ao_coef_norm_ord_transp_cosgtos(n,j) * ao_coef_norm_ord_transp_cosgtos(l,i)
beta = ao_expo_ord_transp_cosgtos(l,i)
call overlap_cgaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
, overlap_x0_1, overlap_y0_1, overlap_z0_1, overlap, dim1 )
call overlap_cgaussian_xyz( A_center, B_center, alpha, conjg(beta), power_A, power_B &
, overlap_x0_2, overlap_y0_2, overlap_z0_2, overlap, dim1 )
! ---
power_A(1) = power_A(1) - 2
if(power_A(1) > -1) then
call overlap_cgaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
, overlap_m2_1, overlap_y, overlap_z, overlap, dim1 )
call overlap_cgaussian_xyz( A_center, B_center, alpha, conjg(beta), power_A, power_B &
, overlap_m2_2, overlap_y, overlap_z, overlap, dim1 )
else
overlap_m2_1 = (0.d0, 0.d0)
overlap_m2_2 = (0.d0, 0.d0)
endif
power_A(1) = power_A(1) + 4
call overlap_cgaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
, overlap_p2_1, overlap_y, overlap_z, overlap, dim1 )
call overlap_cgaussian_xyz( A_center, B_center, alpha, conjg(beta), power_A, power_B &
, overlap_p2_2, overlap_y, overlap_z, overlap, dim1 )
power_A(1) = power_A(1) - 2
deriv_tmp_1 = ( -2.d0 * alpha * (2.d0 * power_A(1) + 1.d0) * overlap_x0_1 &
+ power_A(1) * (power_A(1) - 1.d0) * overlap_m2_1 &
+ 4.d0 * alpha * alpha * overlap_p2_1 ) * overlap_y0_1 * overlap_z0_1
deriv_tmp_2 = ( -2.d0 * alpha * (2.d0 * power_A(1) + 1.d0) * overlap_x0_2 &
+ power_A(1) * (power_A(1) - 1.d0) * overlap_m2_2 &
+ 4.d0 * alpha * alpha * overlap_p2_2 ) * overlap_y0_2 * overlap_z0_2
deriv_tmp = 2.d0 * real(deriv_tmp_1 + deriv_tmp_2)
ao_deriv2_cosgtos_x(i,j) += c * deriv_tmp
! ---
power_A(2) = power_A(2) - 2
if(power_A(2) > -1) then
call overlap_cgaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
, overlap_x, overlap_m2_1, overlap_y, overlap, dim1 )
call overlap_cgaussian_xyz( A_center, B_center, alpha, conjg(beta), power_A, power_B &
, overlap_x, overlap_m2_2, overlap_y, overlap, dim1 )
else
overlap_m2_1 = (0.d0, 0.d0)
overlap_m2_2 = (0.d0, 0.d0)
endif
power_A(2) = power_A(2) + 4
call overlap_cgaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
, overlap_x, overlap_p2_1, overlap_y, overlap, dim1 )
call overlap_cgaussian_xyz( A_center, B_center, alpha, conjg(beta), power_A, power_B &
, overlap_x, overlap_p2_2, overlap_y, overlap, dim1 )
power_A(2) = power_A(2) - 2
deriv_tmp_1 = ( -2.d0 * alpha * (2.d0 * power_A(2) + 1.d0) * overlap_y0_1 &
+ power_A(2) * (power_A(2) - 1.d0) * overlap_m2_1 &
+ 4.d0 * alpha * alpha * overlap_p2_1 ) * overlap_x0_1 * overlap_z0_1
deriv_tmp_2 = ( -2.d0 * alpha * (2.d0 * power_A(2) + 1.d0) * overlap_y0_2 &
+ power_A(2) * (power_A(2) - 1.d0) * overlap_m2_2 &
+ 4.d0 * alpha * alpha * overlap_p2_2 ) * overlap_x0_2 * overlap_z0_2
deriv_tmp = 2.d0 * real(deriv_tmp_1 + deriv_tmp_2)
ao_deriv2_cosgtos_y(i,j) += c * deriv_tmp
! ---
power_A(3) = power_A(3) - 2
if(power_A(3) > -1) then
call overlap_cgaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
, overlap_x, overlap_y, overlap_m2_1, overlap, dim1 )
call overlap_cgaussian_xyz( A_center, B_center, alpha, conjg(beta), power_A, power_B &
, overlap_x, overlap_y, overlap_m2_2, overlap, dim1 )
else
overlap_m2_1 = (0.d0, 0.d0)
overlap_m2_2 = (0.d0, 0.d0)
endif
power_A(3) = power_A(3) + 4
call overlap_cgaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
, overlap_x, overlap_y, overlap_p2_1, overlap, dim1 )
call overlap_cgaussian_xyz( A_center, B_center, alpha, conjg(beta), power_A, power_B &
, overlap_x, overlap_y, overlap_p2_2, overlap, dim1 )
power_A(3) = power_A(3) - 2
deriv_tmp_1 = ( -2.d0 * alpha * (2.d0 * power_A(3) + 1.d0) * overlap_z0_1 &
+ power_A(3) * (power_A(3) - 1.d0) * overlap_m2_1 &
+ 4.d0 * alpha * alpha * overlap_p2_1 ) * overlap_x0_1 * overlap_y0_1
deriv_tmp_2 = ( -2.d0 * alpha * (2.d0 * power_A(3) + 1.d0) * overlap_z0_2 &
+ power_A(3) * (power_A(3) - 1.d0) * overlap_m2_2 &
+ 4.d0 * alpha * alpha * overlap_p2_2 ) * overlap_x0_2 * overlap_y0_2
deriv_tmp = 2.d0 * real(deriv_tmp_1 + deriv_tmp_2)
ao_deriv2_cosgtos_z(i,j) += c * deriv_tmp
! ---
enddo
enddo
enddo
enddo
!$OMP END PARALLEL DO
END_PROVIDER
! ---
BEGIN_PROVIDER [double precision, ao_kinetic_integrals_cosgtos, (ao_num, ao_num)]
BEGIN_DOC
!
! Kinetic energy integrals in the cosgtos |AO| basis.
!
! $\langle \chi_i |\hat{T}| \chi_j \rangle$
!
END_DOC
implicit none
integer :: i, j
!$OMP PARALLEL DO DEFAULT(NONE) &
!$OMP PRIVATE(i, j) &
!$OMP SHARED(ao_num, ao_kinetic_integrals_cosgtos, ao_deriv2_cosgtos_x, ao_deriv2_cosgtos_y, ao_deriv2_cosgtos_z)
do j = 1, ao_num
do i = 1, ao_num
ao_kinetic_integrals_cosgtos(i,j) = -0.5d0 * ( ao_deriv2_cosgtos_x(i,j) &
+ ao_deriv2_cosgtos_y(i,j) &
+ ao_deriv2_cosgtos_z(i,j) )
enddo
enddo
!$OMP END PARALLEL DO
END_PROVIDER
! ---

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