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eginer 2022-10-10 18:20:33 +02:00
parent 70516c8c05
commit 996c09d220
8 changed files with 348 additions and 2 deletions
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1
src/ao_many_one_e_ints/ao_gaus_gauss.irp.f
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@ -116,6 +116,7 @@ double precision function overlap_gauss_r12_ao(D_center,delta,i,j)
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)

2
src/ao_tc_eff_map/map_integrals_eff_pot.irp.f
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@ -78,7 +78,7 @@ double precision function get_ao_tc_sym_two_e_pot(i,j,k,l,map) result(result)
use map_module
implicit none
BEGIN_DOC
! Gets one |AO| two-electron integral from the |AO| map
! Gets one |AO| two-electron integral from the |AO| map in PHYSICIST NOTATION
END_DOC
integer, intent(in) :: i,j,k,l
integer(key_kind) :: idx

4
src/ao_two_e_ints/map_integrals.irp.f
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@ -326,7 +326,9 @@ double precision function get_ao_two_e_integral(i,j,k,l,map) result(result)
use map_module
implicit none
BEGIN_DOC
! Gets one AO bi-electronic integral from the AO map
! Gets one AO bi-electronic integral from the AO map in PHYSICIST NOTATION
!
! <1:k, 2:l |1:i, 2:j>
END_DOC
integer, intent(in) :: i,j,k,l
integer(key_kind) :: idx

91
src/non_h_ints_mu/fit_j.irp.f Normal file
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@ -0,0 +1,91 @@
BEGIN_PROVIDER [ double precision, expo_j_xmu, (n_fit_1_erf_x) ]
implicit none
BEGIN_DOC
! F(x) = x * (1 - erf(x)) - 1/sqrt(pi) * exp(-x**2) is fitted with a gaussian and a Slater
!
! \approx - 1/sqrt(pi) * exp(-alpha * x ) exp(-beta * x**2)
!
! where alpha = expo_j_xmu(1) and beta = expo_j_xmu(2)
END_DOC
expo_j_xmu(1) = 1.7477d0
expo_j_xmu(2) = 0.668662d0
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
END_PROVIDER
double precision function F_x_j(x)
implicit none
BEGIN_DOC
! F_x_j(x) = dimension-less correlation factor = x (1 - erf(x)) - 1/sqrt(pi) exp(-x^2)
END_DOC
double precision, intent(in) :: x
F_x_j = x * (1.d0 - derf(x)) - 1/dsqrt(dacos(-1.d0)) * dexp(-x**2)
end
double precision function j_mu_F_x_j(x)
implicit none
BEGIN_DOC
! j_mu_F_x_j(x) = correlation factor = 1/2 r12 * (1 - erf(mu*r12)) - 1/(2 sqrt(pi)*mu) exp(-(mu*r12)^2)
!
! = 1/(2*mu) * F_x_j(mu*x)
END_DOC
double precision :: F_x_j
double precision, intent(in) :: x
j_mu_F_x_j = 0.5d0/mu_erf * F_x_j(x*mu_erf)
end
double precision function j_mu(x)
implicit none
double precision, intent(in) :: x
BEGIN_DOC
! j_mu(x) = correlation factor = 1/2 r12 * (1 - erf(mu*r12)) - 1/(2 sqrt(pi)*mu) exp(-(mu*r12)^2)
END_DOC
j_mu = 0.5d0* x * (1.d0 - derf(mu_erf*x)) - 0.5d0/( dsqrt(dacos(-1.d0))*mu_erf) * dexp(-(mu_erf*x)*(mu_erf*x))
end
double precision function j_mu_fit_gauss(x)
implicit none
BEGIN_DOC
! j_mu_fit_gauss(x) = correlation factor = 1/2 r12 * (1 - erf(mu*r12)) - 1/(2 sqrt(pi)*mu) exp(-(mu*r12)^2)
!
! but fitted with gaussians
END_DOC
double precision, intent(in) :: x
integer :: i
double precision :: alpha,coef
j_mu_fit_gauss = 0.d0
do i = 1, n_max_fit_slat
alpha = expo_gauss_j_mu_x(i)
coef = coef_gauss_j_mu_x(i)
j_mu_fit_gauss += coef_gauss_j_mu_x(i) * dexp(-expo_gauss_j_mu_x(i)*x*x)
enddo
end

72
src/non_h_ints_mu/grad_squared.irp.f Normal file
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@ -0,0 +1,72 @@
BEGIN_PROVIDER [ double precision, grad_1_squared_u_ij_mu, ( ao_num, ao_num,n_points_final_grid)]
implicit none
integer :: ipoint,i,j,m,igauss
BEGIN_DOC
! grad_1_squared_u_ij_mu(j,i,ipoint) = -1/2 \int dr2 phi_j(r2) phi_i(r2) |\grad_r1 u(r1,r2,\mu)|^2
! |\grad_r1 u(r1,r2,\mu)|^2 = 1/4 * (1 - erf(mu*r12))^2
! ! (1 - erf(mu*r12))^2 = \sum_i coef_gauss_1_erf_x_2(i) * exp(-expo_gauss_1_erf_x_2(i) * r12^2)
END_DOC
double precision :: r(3),delta,coef
double precision :: overlap_gauss_r12_ao,time0,time1
print*,'providing grad_1_squared_u_ij_mu ...'
call wall_time(time0)
!TODO : strong optmization : write the loops in a different way
! : for each couple of AO, the gaussian product are done once for all
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
! \int dr2 phi_j(r2) phi_i(r2) (1 - erf(mu*r12))^2
! = \sum_i coef_gauss_1_erf_x_2(i) \int dr2 phi_j(r2) phi_i(r2) exp(-expo_gauss_1_erf_x_2(i) * (r_1 - r_2)^2)
do igauss = 1, n_max_fit_slat
delta = expo_gauss_1_erf_x_2(igauss)
coef = coef_gauss_1_erf_x_2(igauss)
grad_1_squared_u_ij_mu(j,i,ipoint) += -0.25 * coef * overlap_gauss_r12_ao(r,delta,i,j)
enddo
enddo
enddo
enddo
call wall_time(time1)
print*,'Wall time for grad_1_squared_u_ij_mu = ',time1 - time0
END_PROVIDER
BEGIN_PROVIDER [double precision, tc_grad_square_ao, (ao_num, ao_num, ao_num, ao_num)]
implicit none
BEGIN_DOC
! tc_grad_square_ao(k,i,l,j) = -1/2 <kl | |\grad_1 u(r1,r2)|^2 + |\grad_1 u(r1,r2)|^2 | ij>
!
END_DOC
integer :: ipoint,i,j,k,l
double precision :: contrib,weight1
double precision, allocatable :: ac_mat(:,:,:,:)
allocate(ac_mat(ao_num, ao_num, ao_num, ao_num))
ac_mat = 0.d0
do ipoint = 1, n_points_final_grid
weight1 = final_weight_at_r_vector(ipoint)
do j = 1, ao_num
do l = 1, ao_num
do i = 1, ao_num
do k = 1, ao_num
contrib = weight1 *0.5D0* (aos_in_r_array_transp(ipoint,k) * aos_in_r_array_transp(ipoint,i))
! \int dr1 phi_k(r1) phi_i(r1) . \int dr2 |\grad_1 u(r1,r2)|^2 \phi_l(r2) \phi_j(r2)
ac_mat(k,i,l,j) += grad_1_squared_u_ij_mu(l,j,ipoint) * contrib
enddo
enddo
enddo
enddo
enddo
do j = 1, ao_num
do l = 1, ao_num
do i = 1, ao_num
do k = 1, ao_num
tc_grad_square_ao(k,i,l,j) = ac_mat(k,i,l,j) + ac_mat(l,j,k,i)
enddo
enddo
enddo
enddo
END_PROVIDER

8
src/non_h_ints_mu/grad_tc_int.irp.f
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@ -11,6 +11,8 @@ END_DOC
double precision, allocatable :: b_mat(:,:,:,:),ac_mat(:,:,:,:)
! provide v_ij_erf_rk_cst_mu
provide v_ij_erf_rk_cst_mu x_v_ij_erf_rk_cst_mu
! ao_non_hermit_term_chemist = non_h_ints
! return
call wall_time(wall0)
allocate(b_mat(n_points_final_grid,ao_num,ao_num,3),ac_mat(ao_num, ao_num, ao_num, ao_num))
!$OMP PARALLEL &
@ -35,6 +37,9 @@ END_DOC
!$OMP END DO
!$OMP END PARALLEL
! (A) b_mat(ipoint,k,i,m) X v_ij_erf_rk_cst_mu(j,l,r1)
! 1/2 \int dr1 x1 phi_k(1) d/dx1 phi_i(1) \int dr2 (1 - erf(mu_r12))/r12 phi_j(2) phi_l(2)
ac_mat = 0.d0
do m = 1, 3
! A B^T dim(A,1) dim(B,2) dim(A,2) alpha * A LDA
@ -60,6 +65,8 @@ END_DOC
!$OMP END DO
!$OMP END PARALLEL
! (B) b_mat(ipoint,k,i,m) X x_v_ij_erf_rk_cst_mu(j,l,r1,m)
! 1/2 \int dr1 phi_k(1) d/dx1 phi_i(1) \int dr2 x2(1 - erf(mu_r12))/r12 phi_j(2) phi_l(2)
do m = 1, 3
! A B^T dim(A,1) dim(B,2) dim(A,2) alpha * A LDA
call dgemm("N","N",ao_num*ao_num,ao_num*ao_num,n_points_final_grid,-1.d0,x_v_ij_erf_rk_cst_mu(1,1,1,m),ao_num*ao_num &
@ -75,6 +82,7 @@ END_DOC
do l = 1, ao_num
do i = 1, ao_num
do k = 1, ao_num
! (ki|lj) (ki|lj) (lj|ki)
ao_non_hermit_term_chemist(k,i,l,j) = ac_mat(k,i,l,j) + ac_mat(l,j,k,i)
enddo
enddo

70
src/non_h_ints_mu/new_grad_tc.irp.f Normal file
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@ -0,0 +1,70 @@
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)
enddo
enddo
enddo
enddo
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
! tc_grad_and_lapl_ao(k,i,l,j) = <kl | -1/2 \Delta_1 u(r1,r2) - \grad_1 u(r1,r2) | ij>
!
! = 1/2 \int dr1 (phi_k(r1) \grad_r1 phi_i(r1) - phi_i(r1) \grad_r1 phi_k(r1)) . \int dr2 \grad_r1 u(r1,r2) \phi_l(r2) \phi_j(r2)
!
! This is obtained by integration by parts.
END_DOC
integer :: ipoint,i,j,k,l,m
double precision :: contrib,weight1
double precision, allocatable :: ac_mat(:,:,:,:)
allocate(ac_mat(ao_num, ao_num, ao_num, ao_num))
ac_mat = 0.d0
do m = 1, 3
do ipoint = 1, n_points_final_grid
weight1 = final_weight_at_r_vector(ipoint)
do j = 1, ao_num
do l = 1, ao_num
do i = 1, ao_num
do k = 1, ao_num
contrib = weight1 *0.5D0* (aos_in_r_array_transp(ipoint,k) * aos_grad_in_r_array_transp_bis(ipoint,i,m) &
-aos_in_r_array_transp(ipoint,i) * aos_grad_in_r_array_transp_bis(ipoint,k,m) )
! \int dr1 phi_k(r1) \grad_r1 phi_i(r1) . \int dr2 \grad_r1 u(r1,r2) \phi_l(r2) \phi_j(r2)
ac_mat(k,i,l,j) += grad_1_u_ij_mu(l,j,ipoint,m) * contrib
enddo
enddo
enddo
enddo
enddo
enddo
do j = 1, ao_num
do l = 1, ao_num
do i = 1, ao_num
do k = 1, ao_num
tc_grad_and_lapl_ao(k,i,l,j) = ac_mat(k,i,l,j) + ac_mat(l,j,k,i)
enddo
enddo
enddo
enddo
END_PROVIDER

102
src/non_h_ints_mu/test_non_h_ints.irp.f Normal file
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@ -0,0 +1,102 @@
program test_non_h
implicit none
my_grid_becke = .True.
my_n_pt_r_grid = 50
my_n_pt_a_grid = 74
! my_n_pt_r_grid = 10 ! small grid for quick debug
! my_n_pt_a_grid = 26 ! small grid for quick debug
touch my_grid_becke my_n_pt_r_grid my_n_pt_a_grid
!call routine_grad_squared
call routine_fit
end
subroutine routine_lapl_grad
implicit none
integer :: i,j,k,l
double precision :: grad_lapl, get_ao_tc_sym_two_e_pot,new,accu,contrib
double precision :: ao_two_e_integral_erf,get_ao_two_e_integral,count_n,accu_relat
! !!!!!!!!!!!!!!!!!!!!! WARNING
! THIS ROUTINE MAKES SENSE ONLY IF HAND MODIFIED coef_gauss_eff_pot(1:n_max_fit_slat) = 0. to cancel (1-erf(mu*r12))^2
accu = 0.d0
accu_relat = 0.d0
count_n = 0.d0
do i = 1, ao_num
do j = 1, ao_num
do k = 1, ao_num
do l = 1, ao_num
grad_lapl = get_ao_tc_sym_two_e_pot(i,j,k,l,ao_tc_sym_two_e_pot_map) ! pure gaussian part : comes from Lapl
grad_lapl += ao_two_e_integral_erf(i, k, j, l) ! erf(mu r12)/r12 : comes from Lapl
grad_lapl += ao_non_hermit_term_chemist(k,i,l,j) ! \grad u(r12) . grad
new = tc_grad_and_lapl_ao(k,i,l,j)
new += get_ao_two_e_integral(i,j,k,l,ao_integrals_map)
contrib = dabs(new - grad_lapl)
if(dabs(grad_lapl).gt.1.d-12)then
count_n += 1.d0
accu_relat += 2.0d0 * contrib/dabs(grad_lapl+new)
endif
if(contrib.gt.1.d-10)then
print*,i,j,k,l
print*,grad_lapl,new,contrib
print*,2.0d0*contrib/dabs(grad_lapl+new+1.d-12)
endif
accu += contrib
enddo
enddo
enddo
enddo
print*,'accu = ',accu/count_n
print*,'accu/rel = ',accu_relat/count_n
end
subroutine routine_grad_squared
implicit none
integer :: i,j,k,l
double precision :: grad_squared, get_ao_tc_sym_two_e_pot,new,accu,contrib
double precision :: count_n,accu_relat
! !!!!!!!!!!!!!!!!!!!!! WARNING
! THIS ROUTINE MAKES SENSE ONLY IF HAND MODIFIED coef_gauss_eff_pot(n_max_fit_slat:n_max_fit_slat+1) = 0. to cancel exp(-'mu*r12)^2)
accu = 0.d0
accu_relat = 0.d0
count_n = 0.d0
do i = 1, ao_num
do j = 1, ao_num
do k = 1, ao_num
do l = 1, ao_num
grad_squared = get_ao_tc_sym_two_e_pot(i,j,k,l,ao_tc_sym_two_e_pot_map) ! pure gaussian part : comes from Lapl
new = tc_grad_square_ao(k,i,l,j)
contrib = dabs(new - grad_squared)
if(dabs(grad_squared).gt.1.d-12)then
count_n += 1.d0
accu_relat += 2.0d0 * contrib/dabs(grad_squared+new)
endif
if(contrib.gt.1.d-10)then
print*,i,j,k,l
print*,grad_squared,new,contrib
print*,2.0d0*contrib/dabs(grad_squared+new+1.d-12)
endif
accu += contrib
enddo
enddo
enddo
enddo
print*,'accu = ',accu/count_n
print*,'accu/rel = ',accu_relat/count_n
end
subroutine routine_fit
implicit none
integer :: i,nx
double precision :: dx,xmax,x,j_mu,j_mu_F_x_j,j_mu_fit_gauss
nx = 500
xmax = 5.d0
dx = xmax/dble(nx)
x = 0.d0
print*,'coucou',mu_erf
do i = 1, nx
write(33,'(100(F16.10,X))') x,j_mu(x),j_mu_F_x_j(x),j_mu_fit_gauss(x)
x += dx
enddo
end