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1st version of grad + lapl of Jmu_modif

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AbdAmmar 2022-10-12 11:24:09 +02:00
parent 6513358da3
commit 7a4f732e15
7 changed files with 1230 additions and 348 deletions
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343
src/ao_many_one_e_ints/ao_erf_gauss.irp.f
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@ -1,4 +1,6 @@
! ---
subroutine phi_j_erf_mu_r_xyz_phi(i,j,mu_in, C_center, xyz_ints)
implicit none
BEGIN_DOC
@ -49,45 +51,58 @@ subroutine phi_j_erf_mu_r_xyz_phi(i,j,mu_in, C_center, xyz_ints)
enddo
end
! ---
double precision function phi_j_erf_mu_r_phi(i,j,mu_in, C_center)
implicit none
BEGIN_DOC
! phi_j_erf_mu_r_phi = int dr phi_j(r) [erf(mu |r - C|)/|r-C|] phi_i(r)
END_DOC
integer, intent(in) :: i,j
double precision, intent(in) :: mu_in, C_center(3)
integer :: num_A,power_A(3), num_b, power_B(3)
double precision :: alpha, beta, A_center(3), B_center(3),contrib,NAI_pol_mult_erf
integer :: n_pt_in,l,m
phi_j_erf_mu_r_phi = 0.d0
if(ao_overlap_abs(j,i).lt.1.d-12)then
return
endif
n_pt_in = n_pt_max_integrals
! j
num_A = ao_nucl(j)
power_A(1:3)= ao_power(j,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
! i
num_B = ao_nucl(i)
power_B(1:3)= ao_power(i,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
double precision function phi_j_erf_mu_r_phi(i, j, mu_in, C_center)
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)
contrib = NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in)
phi_j_erf_mu_r_phi += contrib * ao_coef_normalized_ordered_transp(l,j) &
* ao_coef_normalized_ordered_transp(m,i)
BEGIN_DOC
! phi_j_erf_mu_r_phi = int dr phi_j(r) [erf(mu |r - C|)/|r-C|] phi_i(r)
END_DOC
implicit none
integer, intent(in) :: i,j
double precision, intent(in) :: mu_in, C_center(3)
integer :: num_A, power_A(3), num_b, power_B(3)
integer :: n_pt_in, l, m
double precision :: alpha, beta, A_center(3), B_center(3), contrib
double precision :: NAI_pol_mult_erf
phi_j_erf_mu_r_phi = 0.d0
if(ao_overlap_abs(j,i).lt.1.d-12) then
return
endif
n_pt_in = n_pt_max_integrals
! j
num_A = ao_nucl(j)
power_A(1:3) = ao_power(j,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
! i
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)
contrib = NAI_pol_mult_erf(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in, mu_in)
phi_j_erf_mu_r_phi += contrib * ao_coef_normalized_ordered_transp(l,j) * ao_coef_normalized_ordered_transp(m,i)
enddo
enddo
enddo
end
end function phi_j_erf_mu_r_phi
! ---
subroutine erfc_mu_gauss_xyz_ij_ao(i,j,mu, C_center, delta,gauss_ints)
subroutine erfc_mu_gauss_xyz_ij_ao(i, j, mu, C_center, delta, gauss_ints)
implicit none
BEGIN_DOC
! gauss_ints(m) = \int dr exp(-delta (r - C)^2 ) x/y/z * ( 1 - erf(mu |r-r'|))/ |r-r'| * AO_i(r') * AO_j(r')
@ -132,95 +147,204 @@ subroutine erfc_mu_gauss_xyz_ij_ao(i,j,mu, C_center, delta,gauss_ints)
enddo
end
subroutine erf_mu_gauss_ij_ao(i,j,mu, C_center, delta,gauss_ints)
implicit none
BEGIN_DOC
! gauss_ints(m) = \int dr exp(-delta (r - C)^2 ) * erf(mu |r-r'|)/ |r-r'| * AO_i(r') * AO_j(r')
!
END_DOC
integer, intent(in) :: i,j
double precision, intent(in) :: mu, C_center(3),delta
double precision, intent(out):: gauss_ints
! ---
integer :: num_A,power_A(3), num_b, power_B(3)
double precision :: alpha, beta, A_center(3), B_center(3),contrib,NAI_pol_mult_erf
double precision :: integral , erf_mu_gauss
integer :: n_pt_in,l,m,mm
gauss_ints = 0.d0
if(ao_overlap_abs(j,i).lt.1.d-12)then
return
endif
n_pt_in = n_pt_max_integrals
! j
num_A = ao_nucl(j)
power_A(1:3)= ao_power(j,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
! i
num_B = ao_nucl(i)
power_B(1:3)= ao_power(i,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
subroutine erf_mu_gauss_ij_ao(i, j, mu, C_center, delta, gauss_ints)
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)
if(dabs(ao_coef_normalized_ordered_transp(l,j) * ao_coef_normalized_ordered_transp(m,i)).lt.1.d-12)cycle
integral = erf_mu_gauss(C_center,delta,mu,A_center,B_center,power_A,power_B,alpha,beta,n_pt_in)
gauss_ints += integral * ao_coef_normalized_ordered_transp(l,j) &
* ao_coef_normalized_ordered_transp(m,i)
enddo
enddo
end
subroutine NAI_pol_x_mult_erf_ao(i_ao,j_ao,mu_in,C_center,ints)
implicit none
BEGIN_DOC
!
! gauss_ints = \int dr exp(-delta (r - C)^2) * erf(mu |r-C|) / |r-C| * AO_i(r) * AO_j(r)
!
END_DOC
implicit none
integer, intent(in) :: i, j
double precision, intent(in) :: mu, C_center(3), delta
double precision, intent(out) :: gauss_ints
integer :: n_pt_in, l, m
integer :: num_A, power_A(3), num_b, power_B(3)
double precision :: alpha, beta, A_center(3), B_center(3), coef
double precision :: integral
double precision :: erf_mu_gauss
gauss_ints = 0.d0
if(ao_overlap_abs(j,i).lt.1.d-12) then
return
endif
n_pt_in = n_pt_max_integrals
! j
num_A = ao_nucl(j)
power_A(1:3) = ao_power(j,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
! i
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)
coef = ao_coef_normalized_ordered_transp(l,j) * ao_coef_normalized_ordered_transp(m,i)
if(dabs(coef) .lt. 1.d-12) cycle
integral = erf_mu_gauss(C_center, delta, mu, A_center, B_center, power_A, power_B, alpha, beta, n_pt_in)
gauss_ints += integral * coef
enddo
enddo
end subroutine erf_mu_gauss_ij_ao
! ---
subroutine NAI_pol_x_mult_erf_ao(i_ao, j_ao, mu_in, C_center, ints)
BEGIN_DOC
!
! Computes the following integral :
!
! $\int_{-\infty}^{infty} dr x * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
!
! $\int_{-\infty}^{infty} dr y * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
!
! $\int_{-\infty}^{infty} dr z * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
!
END_DOC
include 'utils/constants.include.F'
integer, intent(in) :: i_ao,j_ao
double precision, intent(in) :: mu_in, C_center(3)
double precision, intent(out):: ints(3)
double precision :: A_center(3), B_center(3),integral, alpha,beta
double precision :: NAI_pol_mult_erf
integer :: i,j,num_A,num_B, power_A(3), power_B(3), n_pt_in, power_xA(3),m
ints = 0.d0
if(ao_overlap_abs(j_ao,i_ao).lt.1.d-12)then
return
endif
num_A = ao_nucl(i_ao)
power_A(1:3)= ao_power(i_ao,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
num_B = ao_nucl(j_ao)
power_B(1:3)= ao_power(j_ao,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
n_pt_in = n_pt_max_integrals
include 'utils/constants.include.F'
do i = 1, ao_prim_num(i_ao)
alpha = ao_expo_ordered_transp(i,i_ao)
do m = 1, 3
power_xA = power_A
! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
power_xA(m) += 1
do j = 1, ao_prim_num(j_ao)
beta = ao_expo_ordered_transp(j,j_ao)
! First term = (x-Ax)**(ax+1)
integral = NAI_pol_mult_erf(A_center,B_center,power_xA,power_B,alpha,beta,C_center,n_pt_in,mu_in)
ints(m) += integral * ao_coef_normalized_ordered_transp(j,j_ao)*ao_coef_normalized_ordered_transp(i,i_ao)
! Second term = Ax * (x-Ax)**(ax)
integral = NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in)
ints(m) += A_center(m) * integral * ao_coef_normalized_ordered_transp(j,j_ao)*ao_coef_normalized_ordered_transp(i,i_ao)
implicit none
integer, intent(in) :: i_ao, j_ao
double precision, intent(in) :: mu_in, C_center(3)
double precision, intent(out) :: ints(3)
integer :: i, j, num_A, num_B, power_A(3), power_B(3), n_pt_in, power_xA(3), m
double precision :: A_center(3), B_center(3), integral, alpha, beta, coef
double precision :: NAI_pol_mult_erf
ints = 0.d0
if(ao_overlap_abs(j_ao,i_ao).lt.1.d-12) then
return
endif
num_A = ao_nucl(i_ao)
power_A(1:3) = ao_power(i_ao,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
num_B = ao_nucl(j_ao)
power_B(1:3) = ao_power(j_ao,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
n_pt_in = n_pt_max_integrals
do i = 1, ao_prim_num(i_ao)
alpha = ao_expo_ordered_transp(i,i_ao)
do m = 1, 3
power_xA = power_A
! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
power_xA(m) += 1
do j = 1, ao_prim_num(j_ao)
beta = ao_expo_ordered_transp(j,j_ao)
coef = ao_coef_normalized_ordered_transp(j,j_ao) * ao_coef_normalized_ordered_transp(i,i_ao)
! First term = (x-Ax)**(ax+1)
integral = NAI_pol_mult_erf(A_center, B_center, power_xA, power_B, alpha, beta, C_center, n_pt_in, mu_in)
ints(m) += integral * coef
! Second term = Ax * (x-Ax)**(ax)
integral = NAI_pol_mult_erf(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in, mu_in)
ints(m) += A_center(m) * integral * coef
enddo
enddo
enddo
enddo
end
end subroutine NAI_pol_x_mult_erf_ao
! ---
subroutine NAI_pol_x_mult_erf_ao_with1s(i_ao, j_ao, beta, B_center, mu_in, C_center, ints)
BEGIN_DOC
!
! Computes the following integral :
!
! $\int_{-\infty}^{infty} dr x * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
!
! $\int_{-\infty}^{infty} dr y * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
!
! $\int_{-\infty}^{infty} dr z * \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
!
END_DOC
include 'utils/constants.include.F'
implicit none
integer, intent(in) :: i_ao, j_ao
double precision, intent(in) :: beta, B_center(3), mu_in, C_center(3)
double precision, intent(out) :: ints(3)
integer :: i, j, power_Ai(3), power_Aj(3), n_pt_in, power_xA(3), m
double precision :: Ai_center(3), Aj_center(3), integral, alphai, alphaj, coef
double precision, external :: NAI_pol_mult_erf_with1s
ints = 0.d0
if(ao_overlap_abs(j_ao,i_ao) .lt. 1.d-12) then
return
endif
power_Ai(1:3) = ao_power(i_ao,1:3)
power_Aj(1:3) = ao_power(j_ao,1:3)
Ai_center(1:3) = nucl_coord(ao_nucl(i_ao),1:3)
Aj_center(1:3) = nucl_coord(ao_nucl(j_ao),1:3)
n_pt_in = n_pt_max_integrals
do i = 1, ao_prim_num(i_ao)
alphai = ao_expo_ordered_transp(i,i_ao)
do m = 1, 3
power_xA = power_Ai
! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
power_xA(m) += 1
do j = 1, ao_prim_num(j_ao)
alphaj = ao_expo_ordered_transp(j,j_ao)
coef = ao_coef_normalized_ordered_transp(j,j_ao) * ao_coef_normalized_ordered_transp(i,i_ao)
! First term = (x-Ax)**(ax+1)
integral = NAI_pol_mult_erf_with1s( Ai_center, Aj_center, power_xA, power_Aj, alphai, alphaj &
, beta, b_center, c_center, n_pt_in, mu_in )
ints(m) += integral * coef
! Second term = Ax * (x-Ax)**(ax)
integral = NAI_pol_mult_erf_with1s( Ai_center, Aj_center, power_Ai, power_Aj, alphai, alphaj &
, beta, b_center, c_center, n_pt_in, mu_in )
ints(m) += Ai_center(m) * integral * coef
enddo
enddo
enddo
end subroutine NAI_pol_x_mult_erf_ao_with1s
! ---
subroutine NAI_pol_x_specify_mult_erf_ao(i_ao,j_ao,mu_in,C_center,m,ints)
implicit none
@ -249,7 +373,6 @@ subroutine NAI_pol_x_specify_mult_erf_ao(i_ao,j_ao,mu_in,C_center,m,ints)
B_center(1:3) = nucl_coord(num_B,1:3)
n_pt_in = n_pt_max_integrals
do i = 1, ao_prim_num(i_ao)
alpha = ao_expo_ordered_transp(i,i_ao)
power_xA = power_A
@ -267,3 +390,5 @@ subroutine NAI_pol_x_specify_mult_erf_ao(i_ao,j_ao,mu_in,C_center,m,ints)
enddo
end
! ---

142
src/ao_many_one_e_ints/ao_gaus_gauss.irp.f
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@ -102,36 +102,118 @@ subroutine overlap_gauss_r12_all_ao(D_center,delta,aos_ints)
enddo
end
double precision function overlap_gauss_r12_ao(D_center,delta,i,j)
implicit none
BEGIN_DOC
! \int dr AO_i(r) AO_j(r) e^{-delta |r-D_center|^2}
END_DOC
integer, intent(in) :: i,j
double precision, intent(in) :: D_center(3), delta
! ---
integer :: num_a,num_b,power_A(3), power_B(3),l,k
double precision :: A_center(3), B_center(3),overlap_gauss_r12,alpha,beta,analytical_j
overlap_gauss_r12_ao = 0.d0
if(ao_overlap_abs(j,i).lt.1.d-12)then
return
endif
! TODO :: PUT CYCLES IN LOOPS
num_A = ao_nucl(i)
power_A(1:3)= ao_power(i,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
num_B = ao_nucl(j)
power_B(1:3)= ao_power(j,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
do l=1,ao_prim_num(i)
alpha = ao_expo_ordered_transp(l,i)
do k=1,ao_prim_num(j)
beta = ao_expo_ordered_transp(k,j)
analytical_j = overlap_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta)
overlap_gauss_r12_ao += analytical_j * ao_coef_normalized_ordered_transp(l,i) &
* ao_coef_normalized_ordered_transp(k,j)
enddo
enddo
end
! TODO :: PUT CYCLES IN LOOPS
double precision function overlap_gauss_r12_ao(D_center, delta, i, j)
BEGIN_DOC
! \int dr AO_i(r) AO_j(r) e^{-delta |r-D_center|^2}
END_DOC
implicit none
integer, intent(in) :: i, j
double precision, intent(in) :: D_center(3), delta
integer :: power_A(3), power_B(3), l, k
double precision :: A_center(3), B_center(3), alpha, beta, coef, analytical_j
double precision, external :: overlap_gauss_r12
overlap_gauss_r12_ao = 0.d0
if(ao_overlap_abs(j,i).lt.1.d-12) then
return
endif
power_A(1:3) = ao_power(i,1:3)
power_B(1:3) = ao_power(j,1:3)
A_center(1:3) = nucl_coord(ao_nucl(i),1:3)
B_center(1:3) = nucl_coord(ao_nucl(j),1:3)
do l = 1, ao_prim_num(i)
alpha = ao_expo_ordered_transp(l,i)
do k = 1, ao_prim_num(j)
beta = ao_expo_ordered_transp(k,j)
coef = ao_coef_normalized_ordered_transp(l,i) * ao_coef_normalized_ordered_transp(k,j)
if(dabs(coef) .lt. 1d-12) cycle
analytical_j = overlap_gauss_r12(D_center, delta, A_center, B_center, power_A, power_B, alpha, beta)
overlap_gauss_r12_ao += coef * analytical_j
enddo
enddo
end function overlap_gauss_r12_ao
! ---
double precision function overlap_gauss_r12_ao_with1s(B_center, beta, D_center, delta, i, j)
BEGIN_DOC
! \int dr AO_i(r) AO_j(r) e^{-beta |r-B_center^2|} e^{-delta |r-D_center|^2}
END_DOC
implicit none
integer, intent(in) :: i, j
double precision, intent(in) :: B_center(3), beta, D_center(3), delta
integer :: power_A1(3), power_A2(3), l, k
double precision :: A1_center(3), A2_center(3), alpha1, alpha2, coef12, analytical_j
double precision :: G_center(3), gama, fact_g, gama_inv
double precision, external :: overlap_gauss_r12, overlap_gauss_r12_ao
ASSERT(beta .gt. 0.d0)
if(beta .lt. 1d-10) then
overlap_gauss_r12_ao_with1s = overlap_gauss_r12_ao(D_center, delta, i, j)
return
endif
overlap_gauss_r12_ao_with1s = 0.d0
if(ao_overlap_abs(j,i) .lt. 1.d-12) then
return
endif
! e^{-beta |r-B_center^2|} e^{-delta |r-D_center|^2} = fact_g e^{-gama |r - G|^2}
gama = beta + delta
gama_inv = 1.d0 / gama
G_center(1) = (beta * B_center(1) + delta * D_center(1)) * gama_inv
G_center(2) = (beta * B_center(2) + delta * D_center(2)) * gama_inv
G_center(3) = (beta * B_center(3) + delta * D_center(3)) * gama_inv
fact_g = beta * delta * gama_inv * ( (B_center(1) - D_center(1)) * (B_center(1) - D_center(1)) &
+ (B_center(2) - D_center(2)) * (B_center(2) - D_center(2)) &
+ (B_center(3) - D_center(3)) * (B_center(3) - D_center(3)) )
fact_g = dexp(-fact_g)
if(fact_g .lt. 1.d-12) return
! ---
power_A1(1:3) = ao_power(i,1:3)
power_A2(1:3) = ao_power(j,1:3)
A1_center(1:3) = nucl_coord(ao_nucl(i),1:3)
A2_center(1:3) = nucl_coord(ao_nucl(j),1:3)
do l = 1, ao_prim_num(i)
alpha1 = ao_expo_ordered_transp(l,i)
do k = 1, ao_prim_num(j)
alpha2 = ao_expo_ordered_transp(k,j)
coef12 = fact_g * ao_coef_normalized_ordered_transp(l,i) * ao_coef_normalized_ordered_transp(k,j)
if(dabs(coef12) .lt. 1d-12) cycle
analytical_j = overlap_gauss_r12(G_center, gama, A1_center, A2_center, power_A1, power_A2, alpha1, alpha2)
overlap_gauss_r12_ao_with1s += coef12 * analytical_j
enddo
enddo
end function overlap_gauss_r12_ao_with1s
! ---

398
src/ao_many_one_e_ints/grad_J1b_ints.irp.f Normal file
View File

@ -0,0 +1,398 @@
! ---
BEGIN_PROVIDER [ integer, List_all_comb_size]
implicit none
List_all_comb_size = 2**nucl_num
END_PROVIDER
! ---
BEGIN_PROVIDER [ integer, List_all_comb, (nucl_num, List_all_comb_size)]
implicit none
integer :: i, j
if(nucl_num .gt. 32) then
print *, ' nucl_num = ', nucl_num, '> 32'
stop
endif
List_all_comb = 0
do i = 0, List_all_comb_size-1
do j = 0, nucl_num-1
if (btest(i,j)) then
List_all_comb(j+1,i+1) = 1
endif
enddo
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, List_all_j1b1s_coef, ( List_all_comb_size)]
&BEGIN_PROVIDER [ double precision, List_all_j1b1s_expo, ( List_all_comb_size)]
&BEGIN_PROVIDER [ double precision, List_all_j1b1s_cent, (3, List_all_comb_size)]
implicit none
integer :: i, j, k, phase
double precision :: tmp_alphaj, tmp_alphak
provide j1b_pen
List_all_j1b1s_coef = 0.d0
List_all_j1b1s_expo = 0.d0
List_all_j1b1s_cent = 0.d0
do i = 1, List_all_comb_size
do j = 1, nucl_num
tmp_alphaj = dble(List_all_comb(j,i)) * j1b_pen(j)
List_all_j1b1s_expo(i) += tmp_alphaj
List_all_j1b1s_cent(1,i) += tmp_alphaj * nucl_coord(j,1)
List_all_j1b1s_cent(2,i) += tmp_alphaj * nucl_coord(j,2)
List_all_j1b1s_cent(3,i) += tmp_alphaj * nucl_coord(j,3)
enddo
ASSERT(List_all_j1b1s_expo(i) .gt. 0d0)
if(List_all_j1b1s_expo(i) .lt. 1d-10) cycle
List_all_j1b1s_cent(1,i) = List_all_j1b1s_cent(1,i) / List_all_j1b1s_expo(i)
List_all_j1b1s_cent(2,i) = List_all_j1b1s_cent(2,i) / List_all_j1b1s_expo(i)
List_all_j1b1s_cent(3,i) = List_all_j1b1s_cent(3,i) / List_all_j1b1s_expo(i)
enddo
! ---
do i = 1, List_all_comb_size
do j = 2, nucl_num, 1
tmp_alphaj = dble(List_all_comb(j,i)) * j1b_pen(j)
do k = 1, j-1, 1
tmp_alphak = dble(List_all_comb(k,i)) * j1b_pen(k)
List_all_j1b1s_coef(i) += tmp_alphaj * tmp_alphak * ( (nucl_coord(j,1) - nucl_coord(k,1)) * (nucl_coord(j,1) - nucl_coord(k,1)) &
+ (nucl_coord(j,2) - nucl_coord(k,2)) * (nucl_coord(j,2) - nucl_coord(k,2)) &
+ (nucl_coord(j,3) - nucl_coord(k,3)) * (nucl_coord(j,3) - nucl_coord(k,3)) )
enddo
enddo
if(List_all_j1b1s_expo(i) .lt. 1d-10) cycle
List_all_j1b1s_coef(i) = List_all_j1b1s_coef(i) / List_all_j1b1s_expo(i)
enddo
! ---
do i = 1, List_all_comb_size
phase = 0
do j = 1, nucl_num
phase += List_all_comb(j,i)
enddo
List_all_j1b1s_coef(i) = (-1.d0)**dble(phase) * dexp(-List_all_j1b1s_coef(i))
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, v_ij_erf_rk_cst_mu_j1b, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr phi_i(r) phi_j(r) 1s_j1b(r) (erf(mu(R) |r - R| - 1) / |r - R|
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s
double precision :: r(3), int_mu, int_coulomb
double precision :: coef, beta, B_center(3)
double precision :: wall0, wall1
double precision, allocatable :: tmp(:,:,:)
double precision, external :: NAI_pol_mult_erf_ao_with1s
provide mu_erf final_grid_points j1b_pen
call wall_time(wall0)
v_ij_erf_rk_cst_mu_j1b = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, r, coef, beta, B_center, int_mu, int_coulomb, tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_size, final_grid_points, &
!$OMP List_all_j1b1s_coef, List_all_j1b1s_expo, List_all_j1b1s_cent, &
!$OMP v_ij_erf_rk_cst_mu_j1b, mu_erf)
allocate( tmp(ao_num,ao_num,n_points_final_grid) )
tmp = 0.d0
!$OMP DO
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i_1s = 1, List_all_comb_size
coef = List_all_j1b1s_coef (i_1s)
beta = List_all_j1b1s_expo (i_1s)
B_center(1) = List_all_j1b1s_cent(1,i_1s)
B_center(2) = List_all_j1b1s_cent(2,i_1s)
B_center(3) = List_all_j1b1s_cent(3,i_1s)
int_mu = NAI_pol_mult_erf_ao_with1s(i, j, beta, B_center, mu_erf, r)
int_coulomb = NAI_pol_mult_erf_ao_with1s(i, j, beta, B_center, 1.d+9, r)
tmp(j,i,ipoint) += coef * (int_mu - int_coulomb)
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP CRITICAL
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
v_ij_erf_rk_cst_mu_j1b(j,i,ipoint) += tmp(j,i,ipoint)
enddo
enddo
enddo
!$OMP END CRITICAL
deallocate( tmp )
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, i-1
v_ij_erf_rk_cst_mu_j1b(j,i,ipoint) = v_ij_erf_rk_cst_mu_j1b(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for v_ij_erf_rk_cst_mu_j1b', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, x_v_ij_erf_rk_cst_mu_j1b, (ao_num, ao_num, n_points_final_grid, 3)]
BEGIN_DOC
! int dr x * phi_i(r) phi_j(r) 1s_j1b(r) (erf(mu(R) |r - R|) - 1)/|r - R|
END_DOC
implicit none
integer :: i, j, ipoint
double precision :: wall0, wall1
call wall_time(wall0)
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, ao_num
x_v_ij_erf_rk_cst_mu_j1b(j,i,ipoint,1) = x_v_ij_erf_rk_cst_mu_tmp_j1b(1,j,i,ipoint)
x_v_ij_erf_rk_cst_mu_j1b(j,i,ipoint,2) = x_v_ij_erf_rk_cst_mu_tmp_j1b(2,j,i,ipoint)
x_v_ij_erf_rk_cst_mu_j1b(j,i,ipoint,3) = x_v_ij_erf_rk_cst_mu_tmp_j1b(3,j,i,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for x_v_ij_erf_rk_cst_mu_j1b', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, x_v_ij_erf_rk_cst_mu_tmp_j1b, (3, ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
! int dr x * phi_i(r) phi_j(r) 1s_j1b(r) (erf(mu(R) |r - R|) - 1)/|r - R|
END_DOC
implicit none
integer :: i, j, ipoint, i_1s
double precision :: coef, beta, B_center(3), r(3), ints(3), ints_coulomb(3)
double precision :: wall0, wall1
double precision, allocatable :: tmp(:,:,:,:)
call wall_time(wall0)
x_v_ij_erf_rk_cst_mu_tmp_j1b = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, r, coef, beta, B_center, ints, ints_coulomb, tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_size, final_grid_points, &
!$OMP List_all_j1b1s_coef, List_all_j1b1s_expo, List_all_j1b1s_cent, &
!$OMP x_v_ij_erf_rk_cst_mu_tmp_j1b, mu_erf)
allocate( tmp(3,ao_num,ao_num,n_points_final_grid) )
tmp = 0.d0
!$OMP DO
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i_1s = 1, List_all_comb_size
coef = List_all_j1b1s_coef (i_1s)
beta = List_all_j1b1s_expo (i_1s)
B_center(1) = List_all_j1b1s_cent(1,i_1s)
B_center(2) = List_all_j1b1s_cent(2,i_1s)
B_center(3) = List_all_j1b1s_cent(3,i_1s)
call NAI_pol_x_mult_erf_ao_with1s(i, j, beta, B_center, mu_erf, r, ints )
call NAI_pol_x_mult_erf_ao_with1s(i, j, beta, B_center, 1.d+9, r, ints_coulomb)
tmp(1,j,i,ipoint) += coef * (ints(1) - ints_coulomb(1))
tmp(2,j,i,ipoint) += coef * (ints(2) - ints_coulomb(2))
tmp(3,j,i,ipoint) += coef * (ints(3) - ints_coulomb(3))
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP CRITICAL
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
x_v_ij_erf_rk_cst_mu_tmp_j1b(1,j,i,ipoint) += tmp(1,j,i,ipoint)
x_v_ij_erf_rk_cst_mu_tmp_j1b(2,j,i,ipoint) += tmp(2,j,i,ipoint)
x_v_ij_erf_rk_cst_mu_tmp_j1b(3,j,i,ipoint) += tmp(3,j,i,ipoint)
enddo
enddo
enddo
!$OMP END CRITICAL
deallocate( tmp )
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, i-1
x_v_ij_erf_rk_cst_mu_tmp(1,j,i,ipoint) = x_v_ij_erf_rk_cst_mu_tmp(1,i,j,ipoint)
x_v_ij_erf_rk_cst_mu_tmp(2,j,i,ipoint) = x_v_ij_erf_rk_cst_mu_tmp(2,i,j,ipoint)
x_v_ij_erf_rk_cst_mu_tmp(3,j,i,ipoint) = x_v_ij_erf_rk_cst_mu_tmp(3,i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for x_v_ij_erf_rk_cst_mu_tmp', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, v_ij_u_cst_mu_j1b, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2) u(mu, r12)
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), int_fit, expo_fit, coef_fit
double precision :: coef, beta, B_center(3)
double precision :: wall0, wall1
double precision, allocatable :: tmp(:,:,:)
double precision, external :: overlap_gauss_r12_ao_with1s
provide mu_erf final_grid_points j1b_pen
call wall_time(wall0)
v_ij_u_cst_mu_j1b = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_size, &
!$OMP final_grid_points, n_max_fit_slat, &
!$OMP expo_gauss_j_mu_x, coef_gauss_j_mu_x, &
!$OMP List_all_j1b1s_coef, List_all_j1b1s_expo, &
!$OMP List_all_j1b1s_cent, v_ij_u_cst_mu_j1b)
allocate( tmp(ao_num,ao_num,n_points_final_grid) )
tmp = 0.d0
!$OMP DO
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i_1s = 1, List_all_comb_size
coef = List_all_j1b1s_coef (i_1s)
beta = List_all_j1b1s_expo (i_1s)
B_center(1) = List_all_j1b1s_cent(1,i_1s)
B_center(2) = List_all_j1b1s_cent(2,i_1s)
B_center(3) = List_all_j1b1s_cent(3,i_1s)
do i_fit = 1, n_max_fit_slat
expo_fit = expo_gauss_j_mu_x(i_fit)
coef_fit = coef_gauss_j_mu_x(i_fit)
int_fit = overlap_gauss_r12_ao_with1s(B_center, beta, r, expo_fit, i, j)
tmp(j,i,ipoint) += coef * coef_fit * int_fit
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP CRITICAL
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
v_ij_u_cst_mu_j1b(j,i,ipoint) += tmp(j,i,ipoint)
enddo
enddo
enddo
!$OMP END CRITICAL
deallocate( tmp )
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, i-1
v_ij_u_cst_mu_j1b(j,i,ipoint) = v_ij_u_cst_mu_j1b(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for v_ij_u_cst_mu_j1b', wall1 - wall0
END_PROVIDER
! ---

161
src/ao_many_one_e_ints/grad_related_ints.irp.f
View File

@ -1,47 +1,64 @@
BEGIN_PROVIDER [ double precision, v_ij_erf_rk_cst_mu, ( ao_num, ao_num,n_points_final_grid)]
implicit none
BEGIN_DOC
! int dr phi_i(r) phi_j(r) (erf(mu(R) |r - R| - 1)/|r - R|
END_DOC
integer :: i,j,ipoint
double precision :: mu,r(3),NAI_pol_mult_erf_ao
double precision :: int_mu, int_coulomb
provide mu_erf final_grid_points
double precision :: wall0, wall1
call wall_time(wall0)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,ipoint,mu,r,int_mu,int_coulomb) &
!$OMP SHARED (ao_num,n_points_final_grid,v_ij_erf_rk_cst_mu,final_grid_points,mu_erf)
! ---
BEGIN_PROVIDER [ double precision, v_ij_erf_rk_cst_mu, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr phi_i(r) phi_j(r) (erf(mu(R) |r - R| - 1) / |r - R|
!
END_DOC
implicit none
integer :: i, j, ipoint
double precision :: r(3)
double precision :: int_mu, int_coulomb
double precision :: wall0, wall1
double precision :: NAI_pol_mult_erf_ao
provide mu_erf final_grid_points
call wall_time(wall0)
v_ij_erf_rk_cst_mu = 0.d0
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i, j, ipoint, r, int_mu, int_coulomb) &
!$OMP SHARED (ao_num, n_points_final_grid, v_ij_erf_rk_cst_mu, final_grid_points, mu_erf)
!$OMP DO SCHEDULE (dynamic)
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
mu = mu_erf
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
int_mu = NAI_pol_mult_erf_ao(i,j,mu,r)
int_coulomb = NAI_pol_mult_erf_ao(i,j,1.d+9,r)
v_ij_erf_rk_cst_mu(j,i,ipoint)= (int_mu - int_coulomb )
enddo
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
int_mu = NAI_pol_mult_erf_ao(i, j, mu_erf, r)
int_coulomb = NAI_pol_mult_erf_ao(i, j, 1.d+9, r)
v_ij_erf_rk_cst_mu(j,i,ipoint) = int_mu - int_coulomb
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, i-1
v_ij_erf_rk_cst_mu(j,i,ipoint)= v_ij_erf_rk_cst_mu(i,j,ipoint)
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, i-1
v_ij_erf_rk_cst_mu(j,i,ipoint) = v_ij_erf_rk_cst_mu(i,j,ipoint)
enddo
enddo
enddo
enddo
call wall_time(wall1)
print*, 'wall time for v_ij_erf_rk_cst_mu ', wall1 - wall0
call wall_time(wall1)
print*,'wall time for v_ij_erf_rk_cst_mu ',wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, v_ij_erf_rk_cst_mu_transp, (n_points_final_grid, ao_num, ao_num)]
implicit none
BEGIN_DOC
@ -86,54 +103,62 @@ BEGIN_PROVIDER [ double precision, v_ij_erf_rk_cst_mu_transp, (n_points_final_gr
print*,'wall time for v_ij_erf_rk_cst_mu_transp ',wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, x_v_ij_erf_rk_cst_mu_tmp, (3, ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
! int dr x * phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/|r - R|
END_DOC
implicit none
integer :: i, j, ipoint, m
double precision :: r(3), ints(3), ints_coulomb(3)
double precision :: wall0, wall1
call wall_time(wall0)
BEGIN_PROVIDER [ double precision, x_v_ij_erf_rk_cst_mu_tmp, (3,ao_num, ao_num,n_points_final_grid)]
implicit none
BEGIN_DOC
! int dr x * phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/|r - R|
END_DOC
integer :: i,j,ipoint,m
double precision :: mu,r(3),ints(3),ints_coulomb(3)
double precision :: wall0, wall1
call wall_time(wall0)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,ipoint,mu,r,ints,m,ints_coulomb) &
!$OMP PRIVATE (i,j,ipoint,r,ints,m,ints_coulomb) &
!$OMP SHARED (ao_num,n_points_final_grid,x_v_ij_erf_rk_cst_mu_tmp,final_grid_points,mu_erf)
!$OMP DO SCHEDULE (dynamic)
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
mu = mu_erf
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
call NAI_pol_x_mult_erf_ao(i,j,mu,r,ints)
call NAI_pol_x_mult_erf_ao(i,j,1.d+9,r,ints_coulomb)
do m = 1, 3
x_v_ij_erf_rk_cst_mu_tmp(m,j,i,ipoint) = ( ints(m) - ints_coulomb(m))
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
call NAI_pol_x_mult_erf_ao(i, j, mu_erf, r, ints )
call NAI_pol_x_mult_erf_ao(i, j, 1.d+9 , r, ints_coulomb)
do m = 1, 3
x_v_ij_erf_rk_cst_mu_tmp(m,j,i,ipoint) = (ints(m) - ints_coulomb(m))
enddo
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, i-1
do m = 1, 3
x_v_ij_erf_rk_cst_mu_tmp(m,j,i,ipoint)= x_v_ij_erf_rk_cst_mu_tmp(m,i,j,ipoint)
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, i-1
do m = 1, 3
x_v_ij_erf_rk_cst_mu_tmp(m,j,i,ipoint) = x_v_ij_erf_rk_cst_mu_tmp(m,i,j,ipoint)
enddo
enddo
enddo
enddo
enddo
enddo
call wall_time(wall1)
print*,'wall time for x_v_ij_erf_rk_cst_mu_tmp',wall1 - wall0
call wall_time(wall1)
print*,'wall time for x_v_ij_erf_rk_cst_mu_tmp',wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, x_v_ij_erf_rk_cst_mu, (ao_num, ao_num,n_points_final_grid,3)]
implicit none
BEGIN_DOC

373
src/ao_one_e_ints/pot_ao_erf_ints.irp.f
View File

@ -1,3 +1,6 @@
! ---
subroutine give_all_erf_kl_ao(integrals_ao,mu_in,C_center)
implicit none
BEGIN_DOC
@ -15,142 +18,328 @@ subroutine give_all_erf_kl_ao(integrals_ao,mu_in,C_center)
enddo
end
! ---
double precision function NAI_pol_mult_erf_ao(i_ao, j_ao, mu_in, C_center)
double precision function NAI_pol_mult_erf_ao(i_ao,j_ao,mu_in,C_center)
implicit none
BEGIN_DOC
!
! Computes the following integral :
! $\int_{-\infty}^{infty} dr \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
! $\int_{-\infty}^{infty} dr \chi_i(r) \chi_j(r) \frac{\erf(\mu |r - R_C|)}{|r - R_C|}$.
!
END_DOC
integer, intent(in) :: i_ao,j_ao
implicit none
integer, intent(in) :: i_ao, j_ao
double precision, intent(in) :: mu_in, C_center(3)
integer :: i,j,num_A,num_B, power_A(3), power_B(3), n_pt_in
double precision :: A_center(3), B_center(3),integral, alpha,beta
integer :: i, j, num_A, num_B, power_A(3), power_B(3), n_pt_in
double precision :: A_center(3), B_center(3), integral, alpha, beta
double precision :: NAI_pol_mult_erf
num_A = ao_nucl(i_ao)
power_A(1:3)= ao_power(i_ao,1:3)
num_A = ao_nucl(i_ao)
power_A(1:3) = ao_power(i_ao,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
num_B = ao_nucl(j_ao)
power_B(1:3)= ao_power(j_ao,1:3)
num_B = ao_nucl(j_ao)
power_B(1:3) = ao_power(j_ao,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
n_pt_in = n_pt_max_integrals
NAI_pol_mult_erf_ao = 0.d0
do i = 1, ao_prim_num(i_ao)
alpha = ao_expo_ordered_transp(i,i_ao)
do j = 1, ao_prim_num(j_ao)
beta = ao_expo_ordered_transp(j,j_ao)
integral = NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in)
NAI_pol_mult_erf_ao += integral * ao_coef_normalized_ordered_transp(j,j_ao)*ao_coef_normalized_ordered_transp(i,i_ao)
integral = NAI_pol_mult_erf(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in,mu_in)
NAI_pol_mult_erf_ao += integral * ao_coef_normalized_ordered_transp(j,j_ao) * ao_coef_normalized_ordered_transp(i,i_ao)
enddo
enddo
end
end function NAI_pol_mult_erf_ao
! ---
double precision function NAI_pol_mult_erf_ao_with1s(i_ao, j_ao, beta, B_center, mu_in, C_center)
double precision function NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in)
BEGIN_DOC
!
! Computes the following integral :
! $\int_{-\infty}^{infty} dr \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu |r - R_C|)}{|r - R_C|}$.
!
END_DOC
implicit none
integer, intent(in) :: i_ao, j_ao
double precision, intent(in) :: beta, B_center(3)
double precision, intent(in) :: mu_in, C_center(3)
integer :: i, j, power_A1(3), power_A2(3), n_pt_in
double precision :: A1_center(3), A2_center(3), alpha1, alpha2, coef12, integral
double precision, external :: NAI_pol_mult_erf_with1s, NAI_pol_mult_erf_ao
ASSERT(beta .lt. 0.d0)
if(beta .lt. 1d-10) then
NAI_pol_mult_erf_ao_with1s = NAI_pol_mult_erf_ao(i_ao, j_ao, mu_in, C_center)
return
endif
power_A1(1:3) = ao_power(i_ao,1:3)
power_A2(1:3) = ao_power(j_ao,1:3)
A1_center(1:3) = nucl_coord(ao_nucl(i_ao),1:3)
A2_center(1:3) = nucl_coord(ao_nucl(j_ao),1:3)
n_pt_in = n_pt_max_integrals
NAI_pol_mult_erf_ao_with1s = 0.d0
do i = 1, ao_prim_num(i_ao)
alpha1 = ao_expo_ordered_transp(i,i_ao)
do j = 1, ao_prim_num(j_ao)
alpha2 = ao_expo_ordered_transp(j,j_ao)
coef12 = ao_coef_normalized_ordered_transp(j,j_ao) * ao_coef_normalized_ordered_transp(i,i_ao)
if(coef12 .lt. 1d-14) cycle
integral = NAI_pol_mult_erf_with1s( A1_center, A2_center, power_A1, power_A2, alpha1, alpha2 &
, beta, B_center, C_center, n_pt_in, mu_in )
NAI_pol_mult_erf_ao_with1s += integral * coef12
enddo
enddo
end function NAI_pol_mult_erf_ao_with1s
! ---
double precision function NAI_pol_mult_erf(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in, mu_in)
BEGIN_DOC
!
! Computes the following integral :
!
! .. 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 | }$.
! \frac{\erf(\mu |r - R_C |)}{| r - R_C |}$.
!
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,mu_in
integer, intent(in) :: 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,dist,const,pouet_2,factor
double precision :: I_n_special_exact,integrate_bourrin,I_n_bibi
double precision :: V_e_n,const_factor,dist_integral,tmp
double precision :: accu,rint,p_inv,p,rho,p_inv_2
integer :: n_pt_out,lmax
include 'utils/constants.include.F'
p = alpha + beta
p_inv = 1.d0/p
p_inv_2 = 0.5d0 * p_inv
rho = alpha * beta * p_inv
dist = 0.d0
implicit none
integer, intent(in) :: n_pt_in
integer, intent(in) :: power_A(3), power_B(3)
double precision, intent(in) :: C_center(3), A_center(3), B_center(3), alpha, beta, mu_in
integer :: i, n_pt, n_pt_out
double precision :: P_center(3)
double precision :: d(0:n_pt_in), coeff, dist, const, factor
double precision :: const_factor, dist_integral
double precision :: accu, p_inv, p, rho, p_inv_2
double precision :: p_new
double precision :: rint
p = alpha + beta
p_inv = 1.d0 / p
p_inv_2 = 0.5d0 * p_inv
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))
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
if(const_factor > 80.d0)then
const_factor = dist * rho
if(const_factor > 80.d0) then
NAI_pol_mult_erf = 0.d0
return
endif
double precision :: p_new
p_new = mu_in/dsqrt(p+ mu_in * mu_in)
factor = dexp(-const_factor)
coeff = dtwo_pi * factor * p_inv * p_new
lmax = 20
! print*, "b"
p_new = mu_in / dsqrt(p + mu_in * mu_in)
factor = dexp(-const_factor)
coeff = dtwo_pi * factor * p_inv * p_new
n_pt = 2 * ( (power_A(1) + power_B(1)) + (power_A(2) + power_B(2)) + (power_A(3) + power_B(3)) )
const = p * dist_integral * p_new * p_new
if(n_pt == 0) then
NAI_pol_mult_erf = coeff * rint(0, const)
return
endif
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)) )
const = p * dist_integral * p_new * p_new
if (n_pt == 0) then
pouet = rint(0,const)
NAI_pol_mult_erf = coeff * pouet
return
endif
! call give_polynomial_mult_center_one_e_erf(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in)
p_new = p_new * p_new
call give_polynomial_mult_center_one_e_erf_opt(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in,p,p_inv,p_inv_2,p_new,P_center)
call give_polynomial_mult_center_one_e_erf_opt( A_center, B_center, power_A, power_B, C_center &
, n_pt_in, d, n_pt_out, p_inv_2, p_new, P_center)
if(n_pt_out<0)then
if(n_pt_out < 0) then
NAI_pol_mult_erf = 0.d0
return
endif
accu = 0.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)
accu = 0.d0
do i = 0, n_pt_out, 2
accu += d(i) * rint(i/2, const)
enddo
NAI_pol_mult_erf = accu * coeff
end
end function NAI_pol_mult_erf
! ---
double precision function NAI_pol_mult_erf_with1s( A1_center, A2_center, power_A1, power_A2, alpha1, alpha2 &
, beta, B_center, C_center, n_pt_in, mu_in )
BEGIN_DOC
!
! Computes the following integral :
!
! .. math::
!
! \int dx (x - A1_x)^a_1 (x - B1_x)^a_2 \exp(-\alpha_1 (x - A1_x)^2 - \alpha_2 (x - A2_x)^2)
! \int dy (y - A1_y)^b_1 (y - B1_y)^b_2 \exp(-\alpha_1 (y - A1_y)^2 - \alpha_2 (y - A2_y)^2)
! \int dz (x - A1_z)^c_1 (z - B1_z)^c_2 \exp(-\alpha_1 (z - A1_z)^2 - \alpha_2 (z - A2_z)^2)
! \exp(-\beta (r - B)^2)
! \frac{\erf(\mu |r - R_C|)}{|r - R_C|}$.
!
END_DOC
include 'utils/constants.include.F'
implicit none
integer, intent(in) :: n_pt_in
integer, intent(in) :: power_A1(3), power_A2(3)
double precision, intent(in) :: C_center(3), A1_center(3), A2_center(3), B_center(3)
double precision, intent(in) :: alpha1, alpha2, beta, mu_in
integer :: i, n_pt, n_pt_out
double precision :: alpha12, alpha12_inv, alpha12_inv_2, rho12, A12_center(3), dist12, const_factor12
double precision :: p, p_inv, p_inv_2, rho, P_center(3), dist, const_factor
double precision :: dist_integral
double precision :: d(0:n_pt_in), coeff, const, factor
double precision :: accu
double precision :: p_new
double precision :: rint
subroutine give_polynomial_mult_center_one_e_erf_opt(A_center,B_center,alpha,beta,&
power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in,p,p_inv,p_inv_2,p_new,P_center)
! e^{-alpha1 (r - A1)^2} e^{-alpha2 (r - A2)^2} = e^{K12} e^{-alpha12 (r - A12)^2}
alpha12 = alpha1 + alpha2
alpha12_inv = 1.d0 / alpha12
alpha12_inv_2 = 0.5d0 * alpha12_inv
rho12 = alpha1 * alpha2 * alpha12_inv
dist12 = 0.d0
do i = 1, 3
A12_center(i) = (alpha1 * A1_center(i) + alpha2 * A2_center(i)) * alpha12_inv
dist12 += (A1_center(i) - A2_center(i)) * (A1_center(i) - A2_center(i))
enddo
const_factor12 = dist12 * rho12
if(const_factor12 > 80.d0) then
NAI_pol_mult_erf_with1s = 0.d0
return
endif
! ---
! e^{K12} e^{-alpha12 (r - A12)^2} e^{-beta (r - B)^2} = e^{K} e^{-p (r - P)^2}
p = alpha12 + beta
p_inv = 1.d0 / p
p_inv_2 = 0.5d0 * p_inv
rho = alpha12 * beta * p_inv
dist = 0.d0
dist_integral = 0.d0
do i = 1, 3
P_center(i) = (alpha12 * A12_center(i) + beta * B_center(i)) * p_inv
dist += (A12_center(i) - B_center(i)) * (A12_center(i) - B_center(i))
dist_integral += (P_center(i) - C_center(i)) * (P_center(i) - C_center(i))
enddo
const_factor = const_factor12 + dist * rho
if(const_factor > 80.d0) then
NAI_pol_mult_erf_with1s = 0.d0
return
endif
! ---
p_new = mu_in / dsqrt(p + mu_in * mu_in)
factor = dexp(-const_factor)
coeff = dtwo_pi * factor * p_inv * p_new
n_pt = 2 * ( (power_A1(1) + power_A2(1)) + (power_A1(2) + power_A2(2)) + (power_A1(3) + power_A2(3)) )
const = p * dist_integral * p_new * p_new
if(n_pt == 0) then
NAI_pol_mult_erf_with1s = coeff * rint(0, const)
return
endif
do i = 0, n_pt_in
d(i) = 0.d0
enddo
p_new = p_new * p_new
call give_polynomial_mult_center_one_e_erf_opt( A1_center, A2_center, power_A1, power_A2, C_center &
, n_pt_in, d, n_pt_out, p_inv_2, p_new, P_center)
if(n_pt_out < 0) then
NAI_pol_mult_erf_with1s = 0.d0
return
endif
! sum of integrals of type : int {t,[0,1]} exp-(rho.(P-Q)^2 * t^2) * t^i
accu = 0.d0
do i = 0, n_pt_out, 2
accu += d(i) * rint(i/2, const)
enddo
NAI_pol_mult_erf_with1s = accu * coeff
end function NAI_pol_mult_erf_with1s
! ---
subroutine give_polynomial_mult_center_one_e_erf_opt( A_center, B_center, power_A, power_B, C_center &
, n_pt_in, d, n_pt_out, p_inv_2, p_new, P_center)
BEGIN_DOC
! Returns the explicit polynomial in terms of the $t$ variable of the
! following polynomial:
!
! $I_{x1}(a_x, d_x,p,q) \times I_{x1}(a_y, d_y,p,q) \times I_{x1}(a_z, d_z,p,q)$.
END_DOC
implicit none
integer, intent(in) :: n_pt_in
integer,intent(out) :: n_pt_out
double precision, intent(in) :: A_center(3), B_center(3),C_center(3),p,p_inv,p_inv_2,p_new,P_center(3)
double precision, intent(in) :: alpha,beta,mu_in
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
integer, intent(in) :: n_pt_in
integer, intent(in) :: power_A(3), power_B(3)
double precision, intent(in) :: A_center(3), B_center(3), C_center(3), p_inv_2, p_new, P_center(3)
integer, intent(out) :: n_pt_out
double precision, 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
integer :: n_pt_tmp
double precision :: d1(0:n_pt_in)
double precision :: d2(0:n_pt_in)
double precision :: d3(0:n_pt_in)
double precision :: accu
double precision :: R1x(0:2), B01(0:2), R1xp(0:2), R2x(0:2)
accu = 0.d0
ASSERT (n_pt_in > 1)
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))* p_new
@ -161,27 +350,22 @@ subroutine give_polynomial_mult_center_one_e_erf_opt(A_center,B_center,alpha,bet
!R1xp = (P_x - B_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
R2x(0) = p_inv_2
R2x(1) = 0.d0
R2x(2) = -p_inv_2* p_new
R2x(2) = -p_inv_2 * p_new
!R2x = 0.5 / p - 0.5/p ( t * mu/sqrt(p+mu^2) )^2
do i = 0,n_pt_in
d(i) = 0.d0
enddo
do i = 0,n_pt_in
do i = 0, n_pt_in
d (i) = 0.d0
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)
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
@ -200,7 +384,7 @@ subroutine give_polynomial_mult_center_one_e_erf_opt(A_center,B_center,alpha,bet
!R1xp = (P_x - B_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^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)
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
@ -209,41 +393,40 @@ subroutine give_polynomial_mult_center_one_e_erf_opt(A_center,B_center,alpha,bet
return
endif
R1x(0) = (P_center(3) - A_center(3))
R1x(1) = 0.d0
R1x(2) = -(P_center(3) - C_center(3))* p_new
R1x(2) = -(P_center(3) - C_center(3)) * p_new
! R1x = (P_x - A_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
R1xp(0) = (P_center(3) - B_center(3))
R1xp(1) = 0.d0
R1xp(2) =-(P_center(3) - C_center(3))* p_new
R1xp(2) =-(P_center(3) - C_center(3)) * p_new
!R2x = 0.5 / p - 0.5/p ( t * mu/sqrt(p+mu^2) )^2
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
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
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)
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
end subroutine give_polynomial_mult_center_one_e_erf_opt
! ---
subroutine give_polynomial_mult_center_one_e_erf(A_center,B_center,alpha,beta,&

61
src/non_h_ints_mu/fit_j.irp.f
View File

@ -12,33 +12,45 @@ BEGIN_PROVIDER [ double precision, expo_j_xmu, (n_fit_1_erf_x) ]
END_PROVIDER
! ---
BEGIN_PROVIDER [double precision, expo_gauss_j_mu_x, (n_max_fit_slat)]
&BEGIN_PROVIDER [double precision, coef_gauss_j_mu_x, (n_max_fit_slat)]
implicit none
BEGIN_DOC
! J(mu,r12) = 1/2 r12 * (1 - erf(mu*r12)) - 1/(2 sqrt(pi)*mu) exp(-(mu*r12)^2) is expressed as
!
! J(mu,r12) = 0.5/mu * F(r12*mu) where F(x) = x * (1 - erf(x)) - 1/sqrt(pi) * exp(-x**2)
!
! F(x) is fitted by - 1/sqrt(pi) * exp(-alpha * x) exp(-beta*mu^2x^2) (see expo_j_xmu)
!
! The slater function exp(-alpha * x) is fitted with n_max_fit_slat gaussians
!
! See Appendix 2 of JCP 154, 084119 (2021)
!
END_DOC
integer :: i
double precision :: expos(n_max_fit_slat),alpha,beta
alpha = expo_j_xmu(1) * mu_erf
call expo_fit_slater_gam(alpha,expos)
beta = expo_j_xmu(2) * mu_erf**2.d0
do i = 1, n_max_fit_slat
expo_gauss_j_mu_x(i) = expos(i) + beta
coef_gauss_j_mu_x(i) = coef_fit_slat_gauss(i) / (2.d0 * mu_erf) * (- 1/dsqrt(dacos(-1.d0)))
enddo
BEGIN_DOC
!
! J(mu,r12) = 1/2 r12 * (1 - erf(mu*r12)) - 1/(2 sqrt(pi)*mu) exp(-(mu*r12)^2) is expressed as
!
! J(mu,r12) = 0.5/mu * F(r12*mu) where F(x) = x * (1 - erf(x)) - 1/sqrt(pi) * exp(-x**2)
!
! F(x) is fitted by - 1/sqrt(pi) * exp(-alpha * x) exp(-beta*mu^2x^2) (see expo_j_xmu)
!
! The slater function exp(-alpha * x) is fitted with n_max_fit_slat gaussians
!
! See Appendix 2 of JCP 154, 084119 (2021)
!
END_DOC
implicit none
integer :: i
double precision :: tmp
double precision :: expos(n_max_fit_slat), alpha, beta
tmp = -0.5d0 / (mu_erf * sqrt(dacos(-1.d0)))
alpha = expo_j_xmu(1) * mu_erf
call expo_fit_slater_gam(alpha, expos)
beta = expo_j_xmu(2) * mu_erf * mu_erf
do i = 1, n_max_fit_slat
expo_gauss_j_mu_x(i) = expos(i) + beta
coef_gauss_j_mu_x(i) = tmp * coef_fit_slat_gauss(i)
enddo
END_PROVIDER
! ---
double precision function F_x_j(x)
implicit none
BEGIN_DOC
@ -89,3 +101,6 @@ double precision function j_mu_fit_gauss(x)
enddo
end
! ---

100
src/non_h_ints_mu/new_grad_tc.irp.f
View File

@ -1,30 +1,84 @@
BEGIN_PROVIDER [ double precision, grad_1_u_ij_mu, ( ao_num, ao_num,n_points_final_grid,3)]
implicit none
BEGIN_DOC
! grad_1_u_ij_mu(i,j,ipoint) = -1 * \int dr2 \grad_r1 u(r1,r2) \phi_i(r2) \phi_j(r2)
!
! where r1 = r(ipoint)
!
! grad_1_u_ij_mu(i,j,ipoint) = \int dr2 (r1 - r2) (erf(mu * r12)-1)/2 r_12 \phi_i(r2) \phi_j(r2)
END_DOC
integer :: ipoint,i,j,m
double precision :: r(3)
do m = 1, 3
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do j = 1, ao_num
do i = 1, ao_num
grad_1_u_ij_mu(i,j,ipoint,m) = v_ij_erf_rk_cst_mu(i,j,ipoint) * r(m) - x_v_ij_erf_rk_cst_mu(i,j,ipoint,m)
! ---
BEGIN_PROVIDER [ double precision, grad_1_u_ij_mu, (ao_num, ao_num,n_points_final_grid, 3)]
BEGIN_DOC
!
! grad_1_u_ij_mu(i,j,ipoint) = \int dr2 [-1 * \grad_r1 u(r1,r2)] \phi_i(r2) \phi_j(r2) x 1s_j1b(r2)
! = \int dr2 [(r1 - r2) (erf(mu * r12)-1)/2 r_12] \phi_i(r2) \phi_j(r2) x 1s_j1b(r2)
!
! where r1 = r(ipoint)
!
END_DOC
implicit none
integer :: ipoint, i, j, i_1s
double precision :: r(3)
double precision :: a, d, e, tmp1, tmp2, fact_r, fact_xyz(3)
PROVIDE j1b_type j1b_pen
if(j1b_type .eq. 3) then
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
fact_r = 1.d0
fact_xyz(1) = 1.d0
fact_xyz(2) = 1.d0
fact_xyz(3) = 1.d0
do i_1s = 1, nucl_num
a = j1b_pen(i_1s)
d = (r(1) - nucl_coord(i_1s,1)) * (r(1) - nucl_coord(i_1s,1)) &
+ (r(2) - nucl_coord(i_1s,2)) * (r(2) - nucl_coord(i_1s,2)) &
+ (r(3) - nucl_coord(i_1s,3)) * (r(3) - nucl_coord(i_1s,3))
e = dexp(-a*d)
fact_r = fact_r * (1.d0 - e)
fact_xyz(1) = fact_xyz(1) * (2.d0 * a * (r(1) - nucl_coord(i_1s,1)) * e)
fact_xyz(2) = fact_xyz(2) * (2.d0 * a * (r(2) - nucl_coord(i_1s,2)) * e)
fact_xyz(3) = fact_xyz(3) * (2.d0 * a * (r(3) - nucl_coord(i_1s,3)) * e)
enddo
do j = 1, ao_num
do i = 1, ao_num
tmp1 = fact_r * v_ij_erf_rk_cst_mu_j1b(i,j,ipoint)
tmp2 = v_ij_u_cst_mu_j1b (i,j,ipoint)
grad_1_u_ij_mu(i,j,ipoint,1) = tmp1 * r(1) - fact_r * x_v_ij_erf_rk_cst_mu_j1b(i,j,ipoint,1) + fact_xyz(1) * tmp2
grad_1_u_ij_mu(i,j,ipoint,2) = tmp1 * r(2) - fact_r * x_v_ij_erf_rk_cst_mu_j1b(i,j,ipoint,2) + fact_xyz(2) * tmp2
grad_1_u_ij_mu(i,j,ipoint,3) = tmp1 * r(3) - fact_r * x_v_ij_erf_rk_cst_mu_j1b(i,j,ipoint,3) + fact_xyz(3) * tmp2
enddo
enddo
enddo
enddo
enddo
enddo
grad_1_u_ij_mu *= 0.5d0
else
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do j = 1, ao_num
do i = 1, ao_num
grad_1_u_ij_mu(i,j,ipoint,1) = v_ij_erf_rk_cst_mu(i,j,ipoint) * r(1) - x_v_ij_erf_rk_cst_mu(i,j,ipoint,1)
grad_1_u_ij_mu(i,j,ipoint,2) = v_ij_erf_rk_cst_mu(i,j,ipoint) * r(2) - x_v_ij_erf_rk_cst_mu(i,j,ipoint,2)
grad_1_u_ij_mu(i,j,ipoint,3) = v_ij_erf_rk_cst_mu(i,j,ipoint) * r(3) - x_v_ij_erf_rk_cst_mu(i,j,ipoint,3)
enddo
enddo
enddo
endif
grad_1_u_ij_mu *= 0.5d0
END_PROVIDER
! ---
BEGIN_PROVIDER [double precision, tc_grad_and_lapl_ao, (ao_num, ao_num, ao_num, ao_num)]
implicit none
BEGIN_DOC