From c619b30fe5ff9c0f6423369c598c1eb3b089ffd2 Mon Sep 17 00:00:00 2001 From: eginer Date: Sun, 23 Oct 2022 20:50:14 +0200 Subject: [PATCH] added cosgtos_ao_int --- src/cosgtos_ao_int/EZFIO.cfg | 19 + src/cosgtos_ao_int/NEED | 1 + src/cosgtos_ao_int/README.rst | 4 + src/cosgtos_ao_int/aos_cosgtos.irp.f | 210 +++ src/cosgtos_ao_int/cosgtos_ao_int.irp.f | 7 + src/cosgtos_ao_int/expoim_opt.py | 172 ++ src/cosgtos_ao_int/gauss_legendre.irp.f | 57 + src/cosgtos_ao_int/one_e_Coul_integrals.irp.f | 535 ++++++ src/cosgtos_ao_int/one_e_kin_integrals.irp.f | 223 +++ src/cosgtos_ao_int/two_e_Coul_integrals.irp.f | 1584 +++++++++++++++++ 10 files changed, 2812 insertions(+) create mode 100644 src/cosgtos_ao_int/EZFIO.cfg create mode 100644 src/cosgtos_ao_int/NEED create mode 100644 src/cosgtos_ao_int/README.rst create mode 100644 src/cosgtos_ao_int/aos_cosgtos.irp.f create mode 100644 src/cosgtos_ao_int/cosgtos_ao_int.irp.f create mode 100644 src/cosgtos_ao_int/expoim_opt.py create mode 100644 src/cosgtos_ao_int/gauss_legendre.irp.f create mode 100644 src/cosgtos_ao_int/one_e_Coul_integrals.irp.f create mode 100644 src/cosgtos_ao_int/one_e_kin_integrals.irp.f create mode 100644 src/cosgtos_ao_int/two_e_Coul_integrals.irp.f diff --git a/src/cosgtos_ao_int/EZFIO.cfg b/src/cosgtos_ao_int/EZFIO.cfg new file mode 100644 index 00000000..8edeecd0 --- /dev/null +++ b/src/cosgtos_ao_int/EZFIO.cfg @@ -0,0 +1,19 @@ +[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 + diff --git a/src/cosgtos_ao_int/NEED b/src/cosgtos_ao_int/NEED new file mode 100644 index 00000000..43553132 --- /dev/null +++ b/src/cosgtos_ao_int/NEED @@ -0,0 +1 @@ +ao_basis diff --git a/src/cosgtos_ao_int/README.rst b/src/cosgtos_ao_int/README.rst new file mode 100644 index 00000000..01f25d6d --- /dev/null +++ b/src/cosgtos_ao_int/README.rst @@ -0,0 +1,4 @@ +============== +cosgtos_ao_int +============== + diff --git a/src/cosgtos_ao_int/aos_cosgtos.irp.f b/src/cosgtos_ao_int/aos_cosgtos.irp.f new file mode 100644 index 00000000..6a4d54fd --- /dev/null +++ b/src/cosgtos_ao_int/aos_cosgtos.irp.f @@ -0,0 +1,210 @@ + +! --- + +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 + +! --- + + + diff --git a/src/cosgtos_ao_int/cosgtos_ao_int.irp.f b/src/cosgtos_ao_int/cosgtos_ao_int.irp.f new file mode 100644 index 00000000..d65dfba5 --- /dev/null +++ b/src/cosgtos_ao_int/cosgtos_ao_int.irp.f @@ -0,0 +1,7 @@ +program cosgtos_ao_int + implicit none + BEGIN_DOC +! TODO : Put the documentation of the program here + END_DOC + print *, 'Hello world' +end diff --git a/src/cosgtos_ao_int/expoim_opt.py b/src/cosgtos_ao_int/expoim_opt.py new file mode 100644 index 00000000..d15b0151 --- /dev/null +++ b/src/cosgtos_ao_int/expoim_opt.py @@ -0,0 +1,172 @@ +#!/usr/bin/env python + +import sys +import os +import subprocess +from datetime import datetime +import time +import numpy as np +from modif_powell_imp import my_fmin_powell + +QP_PATH=os.environ["QP_ROOT"] +sys.path.insert(0, QP_PATH+"external/ezfio/Python") +from ezfio import ezfio + + + + + +#------------------------------------------------------------------------------ +# +def get_expoim(): + + expo_im = np.array(ezfio.get_cosgtos_ao_int_ao_expoim_cosgtos()).T + #print(expo_im.shape) + + x = [] + for i in range(ao_num): + for j in range(ao_prim_num[i]): + x.append(expo_im[i,j]) + + return x + +# --- + +def set_expoim(x): + + expo_im = np.zeros((ao_num, ao_prim_num_max)) + + ii = 0 + for i in range(ao_num): + for j in range(ao_prim_num[i]): + expo_im[i,j] = x[ii] + ii = ii + 1 + + ezfio.set_cosgtos_ao_int_ao_expoim_cosgtos(expo_im.T) +# +#------------------------------------------------------------------------------ + + +#------------------------------------------------------------------------------ +# +def save_res(results, file_output): + + lines = results.splitlines() + with open(file_output, "w") as f: + for line in lines: + f.write(f"{line}\n") + +# +#------------------------------------------------------------------------------ + + + +#------------------------------------------------------------------------------ +# +def get_scfenergy(results): + + scf_energy = 0.0 + + lines = results.splitlines() + for line in lines: + if("SCF energy" in line): + scf_energy = float(line.split()[-1]) + + return scf_energy +# +#------------------------------------------------------------------------------ + + + + +#------------------------------------------------------------------------------ +# +def run_scf(): + + return subprocess.check_output( ['qp_run', 'scf', EZFIO_file] + , encoding = "utf-8" ) +# +#------------------------------------------------------------------------------ + + + +#------------------------------------------------------------------------------ +# +def f_scf(x): + + global i_call + i_call += 1 + + #print(x) + + # set expo + set_expoim(x) + + # run scf + results = run_scf() + #save_res(results, "scf_"+str(i_call)) + + + # get scf_energy + scf_energy = get_scfenergy(results) + print( scf_energy ) + sys.stdout.flush() + + return scf_energy +# +#------------------------------------------------------------------------------ + + + + +if __name__ == '__main__': + + t0 = time.time() + + EZFIO_file = sys.argv[1] + ezfio.set_file(EZFIO_file) + print(" Today's date:", datetime.now() ) + print(" EZFIO file = {}".format(EZFIO_file)) + + + ao_num = ezfio.get_ao_basis_ao_num() + print(f" ao_num = {ao_num}") + + ao_prim_num = ezfio.get_ao_basis_ao_prim_num() + + ao_prim_num_max = np.amax(ao_prim_num) + print(f" ao_prim_num_max = {ao_prim_num_max}") + + ezfio.set_ao_basis_ao_prim_num_max(ao_prim_num_max) + + x = get_expoim() + + n_par = len(x) + print(' nb of parameters = {}'.format(n_par)) + + sys.stdout.flush() + + #x = (np.random.rand(n_par) - 0.5) * 1.0 + x = [ (+0.00) for _ in range(n_par)] + + x_min = [ (-10.0) for _ in range(n_par)] + x_max = [ (+10.0) for _ in range(n_par)] + + i_call = 0 + memo_val = {'fmin': 100.} + + opt = my_fmin_powell( f_scf + , x, x_min, x_max + #, xtol = 1e-1 + #, ftol = 1e-1 + , maxfev = 1e8 + , full_output = 1 + , verbose = 1 ) + + + print(" x = " + str(opt)) + + print(" end after {:.3f} minutes".format((time.time()-t0)/60.) ) + + # !!! +# !!! diff --git a/src/cosgtos_ao_int/gauss_legendre.irp.f b/src/cosgtos_ao_int/gauss_legendre.irp.f new file mode 100644 index 00000000..4bdadb6e --- /dev/null +++ b/src/cosgtos_ao_int/gauss_legendre.irp.f @@ -0,0 +1,57 @@ + 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 + diff --git a/src/cosgtos_ao_int/one_e_Coul_integrals.irp.f b/src/cosgtos_ao_int/one_e_Coul_integrals.irp.f new file mode 100644 index 00000000..7f94f226 --- /dev/null +++ b/src/cosgtos_ao_int/one_e_Coul_integrals.irp.f @@ -0,0 +1,535 @@ + +! --- + +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 + +! --- + diff --git a/src/cosgtos_ao_int/one_e_kin_integrals.irp.f b/src/cosgtos_ao_int/one_e_kin_integrals.irp.f new file mode 100644 index 00000000..710b04d4 --- /dev/null +++ b/src/cosgtos_ao_int/one_e_kin_integrals.irp.f @@ -0,0 +1,223 @@ + +! --- + + 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 + +! --- diff --git a/src/cosgtos_ao_int/two_e_Coul_integrals.irp.f b/src/cosgtos_ao_int/two_e_Coul_integrals.irp.f new file mode 100644 index 00000000..527a98d5 --- /dev/null +++ b/src/cosgtos_ao_int/two_e_Coul_integrals.irp.f @@ -0,0 +1,1584 @@ + +! --- + +double precision function ao_two_e_integral_cosgtos(i, j, k, l) + + BEGIN_DOC + ! integral of the AO basis or (ij|kl) + ! i(r1) j(r1) 1/r12 k(r2) l(r2) + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: i, j, k, l + + integer :: p, q, r, s + integer :: num_i, num_j, num_k, num_l, dim1, I_power(3), J_power(3), K_power(3), L_power(3) + integer :: iorder_p1(3), iorder_p2(3), iorder_p3(3), iorder_p4(3), iorder_q1(3), iorder_q2(3) + double precision :: coef1, coef2, coef3, coef4 + complex*16 :: I_center(3), J_center(3), K_center(3), L_center(3) + complex*16 :: expo1, expo2, expo3, expo4 + complex*16 :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1, p1_inv + complex*16 :: P2_new(0:max_dim,3), P2_center(3), fact_p2, pp2, p2_inv + complex*16 :: P3_new(0:max_dim,3), P3_center(3), fact_p3, pp3, p3_inv + complex*16 :: P4_new(0:max_dim,3), P4_center(3), fact_p4, pp4, p4_inv + complex*16 :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1, q1_inv + complex*16 :: Q2_new(0:max_dim,3), Q2_center(3), fact_q2, qq2, q2_inv + complex*16 :: integral1, integral2, integral3, integral4 + complex*16 :: integral5, integral6, integral7, integral8 + complex*16 :: integral_tot + + double precision :: ao_two_e_integral_cosgtos_schwartz_accel + complex*16 :: ERI_cosgtos + complex*16 :: general_primitive_integral_cosgtos + + if(ao_prim_num(i) * ao_prim_num(j) * ao_prim_num(k) * ao_prim_num(l) > 1024) then + + !print *, ' with shwartz acc ' + ao_two_e_integral_cosgtos = ao_two_e_integral_cosgtos_schwartz_accel(i, j, k, l) + + else + !print *, ' without shwartz acc ' + + dim1 = n_pt_max_integrals + + num_i = ao_nucl(i) + num_j = ao_nucl(j) + num_k = ao_nucl(k) + num_l = ao_nucl(l) + + ao_two_e_integral_cosgtos = 0.d0 + + if(num_i /= num_j .or. num_k /= num_l .or. num_j /= num_k) then + !print *, ' not the same center' + + do p = 1, 3 + I_power(p) = ao_power(i,p) + J_power(p) = ao_power(j,p) + K_power(p) = ao_power(k,p) + L_power(p) = ao_power(l,p) + I_center(p) = nucl_coord(num_i,p) * (1.d0, 0.d0) + J_center(p) = nucl_coord(num_j,p) * (1.d0, 0.d0) + K_center(p) = nucl_coord(num_k,p) * (1.d0, 0.d0) + L_center(p) = nucl_coord(num_l,p) * (1.d0, 0.d0) + enddo + + do p = 1, ao_prim_num(i) + coef1 = ao_coef_norm_ord_transp_cosgtos(p,i) + expo1 = ao_expo_ord_transp_cosgtos(p,i) + + do q = 1, ao_prim_num(j) + coef2 = coef1 * ao_coef_norm_ord_transp_cosgtos(q,j) + expo2 = ao_expo_ord_transp_cosgtos(q,j) + + call give_explicit_cpoly_and_cgaussian( P1_new, P1_center, pp1, fact_p1, iorder_p1 & + , expo1, expo2, I_power, J_power, I_center, J_center, dim1 ) + p1_inv = (1.d0,0.d0) / pp1 + + call give_explicit_cpoly_and_cgaussian( P2_new, P2_center, pp2, fact_p2, iorder_p2 & + , conjg(expo1), expo2, I_power, J_power, I_center, J_center, dim1 ) + p2_inv = (1.d0,0.d0) / pp2 + + call give_explicit_cpoly_and_cgaussian( P3_new, P3_center, pp3, fact_p3, iorder_p3 & + , expo1, conjg(expo2), I_power, J_power, I_center, J_center, dim1 ) + p3_inv = (1.d0,0.d0) / pp3 + + call give_explicit_cpoly_and_cgaussian( P4_new, P4_center, pp4, fact_p4, iorder_p4 & + , conjg(expo1), conjg(expo2), I_power, J_power, I_center, J_center, dim1 ) + p4_inv = (1.d0,0.d0) / pp4 + + !integer :: ii + !do ii = 1, 3 + ! print *, 'fact_p1', fact_p1 + ! print *, 'fact_p2', fact_p2 + ! print *, 'fact_p3', fact_p3 + ! print *, 'fact_p4', fact_p4 + ! !print *, pp1, p1_inv + ! !print *, pp2, p2_inv + ! !print *, pp3, p3_inv + ! !print *, pp4, p4_inv + !enddo + ! if( abs(aimag(P1_center(ii))) .gt. 0.d0 ) then + ! print *, ' P_1 is complex !!' + ! print *, P1_center + ! print *, expo1, expo2 + ! print *, conjg(expo1), conjg(expo2) + ! stop + ! endif + ! if( abs(aimag(P2_center(ii))) .gt. 0.d0 ) then + ! print *, ' P_2 is complex !!' + ! print *, P2_center + ! print *, ' old expos:' + ! print *, expo1, expo2 + ! print *, conjg(expo1), conjg(expo2) + ! print *, ' new expo:' + ! print *, pp2, p2_inv + ! print *, ' factor:' + ! print *, fact_p2 + ! print *, ' old centers:' + ! print *, I_center, J_center + ! print *, ' powers:' + ! print *, I_power, J_power + ! stop + ! endif + ! if( abs(aimag(P3_center(ii))) .gt. 0.d0 ) then + ! print *, ' P_3 is complex !!' + ! print *, P3_center + ! print *, expo1, expo2 + ! print *, conjg(expo1), conjg(expo2) + ! stop + ! endif + ! if( abs(aimag(P4_center(ii))) .gt. 0.d0 ) then + ! print *, ' P_4 is complex !!' + ! print *, P4_center + ! print *, expo1, expo2 + ! print *, conjg(expo1), conjg(expo2) + ! stop + ! endif + !enddo + + do r = 1, ao_prim_num(k) + coef3 = coef2 * ao_coef_norm_ord_transp_cosgtos(r,k) + expo3 = ao_expo_ord_transp_cosgtos(r,k) + + do s = 1, ao_prim_num(l) + coef4 = coef3 * ao_coef_norm_ord_transp_cosgtos(s,l) + expo4 = ao_expo_ord_transp_cosgtos(s,l) + + call give_explicit_cpoly_and_cgaussian( Q1_new, Q1_center, qq1, fact_q1, iorder_q1 & + , expo3, expo4, K_power, L_power, K_center, L_center, dim1 ) + q1_inv = (1.d0,0.d0) / qq1 + + call give_explicit_cpoly_and_cgaussian( Q2_new, Q2_center, qq2, fact_q2, iorder_q2 & + , conjg(expo3), expo4, K_power, L_power, K_center, L_center, dim1 ) + q2_inv = (1.d0,0.d0) / qq2 + + !do ii = 1, 3 + ! !print *, qq1, q1_inv + ! !print *, qq2, q2_inv + ! print *, 'fact_q1', fact_q1 + ! print *, 'fact_q2', fact_q2 + !enddo + ! if( abs(aimag(Q1_center(ii))) .gt. 0.d0 ) then + ! print *, ' Q_1 is complex !!' + ! print *, Q1_center + ! print *, expo3, expo4 + ! print *, conjg(expo3), conjg(expo4) + ! stop + ! endif + ! if( abs(aimag(Q2_center(ii))) .gt. 0.d0 ) then + ! print *, ' Q_2 is complex !!' + ! print *, Q2_center + ! print *, expo3, expo4 + ! print *, conjg(expo3), conjg(expo4) + ! stop + ! endif + !enddo + + + integral1 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 & + , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 ) + + integral2 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 & + , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 ) + + integral3 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 & + , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 ) + + integral4 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 & + , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 ) + + integral5 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 & + , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 ) + + integral6 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 & + , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 ) + + integral7 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 & + , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 ) + + integral8 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 & + , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 ) + + integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8 + + !integral_tot = integral1 + !print*, integral_tot + + ao_two_e_integral_cosgtos = ao_two_e_integral_cosgtos + coef4 * 2.d0 * real(integral_tot) + enddo ! s + enddo ! r + enddo ! q + enddo ! p + + else + !print *, ' the same center' + + do p = 1, 3 + I_power(p) = ao_power(i,p) + J_power(p) = ao_power(j,p) + K_power(p) = ao_power(k,p) + L_power(p) = ao_power(l,p) + enddo + + do p = 1, ao_prim_num(i) + coef1 = ao_coef_norm_ord_transp_cosgtos(p,i) + expo1 = ao_expo_ord_transp_cosgtos(p,i) + + do q = 1, ao_prim_num(j) + coef2 = coef1 * ao_coef_norm_ord_transp_cosgtos(q,j) + expo2 = ao_expo_ord_transp_cosgtos(q,j) + + do r = 1, ao_prim_num(k) + coef3 = coef2 * ao_coef_norm_ord_transp_cosgtos(r,k) + expo3 = ao_expo_ord_transp_cosgtos(r,k) + + do s = 1, ao_prim_num(l) + coef4 = coef3 * ao_coef_norm_ord_transp_cosgtos(s,l) + expo4 = ao_expo_ord_transp_cosgtos(s,l) + + integral1 = ERI_cosgtos( expo1, expo2, expo3, expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral2 = ERI_cosgtos( expo1, expo2, conjg(expo3), expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral3 = ERI_cosgtos( conjg(expo1), expo2, expo3, expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral4 = ERI_cosgtos( conjg(expo1), expo2, conjg(expo3), expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral5 = ERI_cosgtos( expo1, conjg(expo2), expo3, expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral6 = ERI_cosgtos( expo1, conjg(expo2), conjg(expo3), expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral7 = ERI_cosgtos( conjg(expo1), conjg(expo2), expo3, expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral8 = ERI_cosgtos( conjg(expo1), conjg(expo2), conjg(expo3), expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8 + + + ao_two_e_integral_cosgtos = ao_two_e_integral_cosgtos + coef4 * 2.d0 * real(integral_tot) + enddo ! s + enddo ! r + enddo ! q + enddo ! p + + endif + endif + +end function ao_two_e_integral_cosgtos + +! --- + +double precision function ao_two_e_integral_cosgtos_schwartz_accel(i, j, k, l) + + BEGIN_DOC + ! integral of the AO basis or (ij|kl) + ! i(r1) j(r1) 1/r12 k(r2) l(r2) + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: i, j, k, l + + integer :: p, q, r, s + integer :: num_i, num_j, num_k, num_l, dim1, I_power(3), J_power(3), K_power(3), L_power(3) + integer :: iorder_p1(3), iorder_p2(3), iorder_p3(3), iorder_p4(3), iorder_q1(3), iorder_q2(3) + double precision :: coef1, coef2, coef3, coef4 + complex*16 :: I_center(3), J_center(3), K_center(3), L_center(3) + complex*16 :: expo1, expo2, expo3, expo4 + complex*16 :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1, p1_inv + complex*16 :: P2_new(0:max_dim,3), P2_center(3), fact_p2, pp2, p2_inv + complex*16 :: P3_new(0:max_dim,3), P3_center(3), fact_p3, pp3, p3_inv + complex*16 :: P4_new(0:max_dim,3), P4_center(3), fact_p4, pp4, p4_inv + complex*16 :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1, q1_inv + complex*16 :: Q2_new(0:max_dim,3), Q2_center(3), fact_q2, qq2, q2_inv + complex*16 :: integral1, integral2, integral3, integral4 + complex*16 :: integral5, integral6, integral7, integral8 + complex*16 :: integral_tot + + double precision, allocatable :: schwartz_kl(:,:) + double precision :: thr + double precision :: schwartz_ij + + complex*16 :: ERI_cosgtos + complex*16 :: general_primitive_integral_cosgtos + + ao_two_e_integral_cosgtos_schwartz_accel = 0.d0 + + dim1 = n_pt_max_integrals + + num_i = ao_nucl(i) + num_j = ao_nucl(j) + num_k = ao_nucl(k) + num_l = ao_nucl(l) + + + thr = ao_integrals_threshold*ao_integrals_threshold + + allocate( schwartz_kl(0:ao_prim_num(l),0:ao_prim_num(k)) ) + + if(num_i /= num_j .or. num_k /= num_l .or. num_j /= num_k) then + + do p = 1, 3 + I_power(p) = ao_power(i,p) + J_power(p) = ao_power(j,p) + K_power(p) = ao_power(k,p) + L_power(p) = ao_power(l,p) + I_center(p) = nucl_coord(num_i,p) * (1.d0, 0.d0) + J_center(p) = nucl_coord(num_j,p) * (1.d0, 0.d0) + K_center(p) = nucl_coord(num_k,p) * (1.d0, 0.d0) + L_center(p) = nucl_coord(num_l,p) * (1.d0, 0.d0) + enddo + + schwartz_kl(0,0) = 0.d0 + do r = 1, ao_prim_num(k) + coef1 = ao_coef_norm_ord_transp_cosgtos(r,k) * ao_coef_norm_ord_transp_cosgtos(r,k) + expo1 = ao_expo_ord_transp_cosgtos(r,k) + + schwartz_kl(0,r) = 0.d0 + do s = 1, ao_prim_num(l) + coef2 = coef1 * ao_coef_norm_ord_transp_cosgtos(s,l) * ao_coef_norm_ord_transp_cosgtos(s,l) + expo2 = ao_expo_ord_transp_cosgtos(s,l) + + call give_explicit_cpoly_and_cgaussian( P1_new, P1_center, pp1, fact_p1, iorder_p1 & + , expo1, expo2, K_power, L_power, K_center, L_center, dim1 ) + p1_inv = (1.d0,0.d0) / pp1 + + call give_explicit_cpoly_and_cgaussian( P2_new, P2_center, pp2, fact_p2, iorder_p2 & + , conjg(expo1), expo2, K_power, L_power, K_center, L_center, dim1 ) + p2_inv = (1.d0,0.d0) / pp2 + + call give_explicit_cpoly_and_cgaussian( P3_new, P3_center, pp3, fact_p3, iorder_p3 & + , expo1, conjg(expo2), K_power, L_power, K_center, L_center, dim1 ) + p3_inv = (1.d0,0.d0) / pp3 + + call give_explicit_cpoly_and_cgaussian( P4_new, P4_center, pp4, fact_p4, iorder_p4 & + , conjg(expo1), conjg(expo2), K_power, L_power, K_center, L_center, dim1 ) + p4_inv = (1.d0,0.d0) / pp4 + + integral1 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 & + , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 ) + + integral2 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 & + , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 ) + + integral3 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 & + , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 ) + + integral4 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 & + , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 ) + + integral5 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 & + , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 ) + + integral6 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 & + , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 ) + + integral7 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 & + , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 ) + + integral8 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 & + , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 ) + + integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8 + + + schwartz_kl(s,r) = coef2 * 2.d0 * real(integral_tot) + + schwartz_kl(0,r) = max(schwartz_kl(0,r), schwartz_kl(s,r)) + enddo + + schwartz_kl(0,0) = max(schwartz_kl(0,r), schwartz_kl(0,0)) + enddo + + + do p = 1, ao_prim_num(i) + coef1 = ao_coef_norm_ord_transp_cosgtos(p,i) + expo1 = ao_expo_ord_transp_cosgtos(p,i) + + do q = 1, ao_prim_num(j) + coef2 = coef1 * ao_coef_norm_ord_transp_cosgtos(q,j) + expo2 = ao_expo_ord_transp_cosgtos(q,j) + + call give_explicit_cpoly_and_cgaussian( P1_new, P1_center, pp1, fact_p1, iorder_p1 & + , expo1, expo2, I_power, J_power, I_center, J_center, dim1 ) + p1_inv = (1.d0,0.d0) / pp1 + + call give_explicit_cpoly_and_cgaussian( P2_new, P2_center, pp2, fact_p2, iorder_p2 & + , conjg(expo1), expo2, I_power, J_power, I_center, J_center, dim1 ) + p2_inv = (1.d0,0.d0) / pp2 + + call give_explicit_cpoly_and_cgaussian( P3_new, P3_center, pp3, fact_p3, iorder_p3 & + , expo1, conjg(expo2), I_power, J_power, I_center, J_center, dim1 ) + p3_inv = (1.d0,0.d0) / pp3 + + call give_explicit_cpoly_and_cgaussian( P4_new, P4_center, pp4, fact_p4, iorder_p4 & + , conjg(expo1), conjg(expo2), I_power, J_power, I_center, J_center, dim1 ) + p4_inv = (1.d0,0.d0) / pp4 + + integral1 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 & + , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 ) + + integral2 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 & + , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 ) + + integral3 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 & + , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 ) + + integral4 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 & + , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 ) + + integral5 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 & + , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 ) + + integral6 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 & + , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 ) + + integral7 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 & + , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 ) + + integral8 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 & + , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 ) + + integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8 + + schwartz_ij = coef2 * coef2 * 2.d0 * real(integral_tot) + + if(schwartz_kl(0,0)*schwartz_ij < thr) cycle + + do r = 1, ao_prim_num(k) + if(schwartz_kl(0,r)*schwartz_ij < thr) cycle + + coef3 = coef2 * ao_coef_norm_ord_transp_cosgtos(r,k) + expo3 = ao_expo_ord_transp_cosgtos(r,k) + + do s = 1, ao_prim_num(l) + if(schwartz_kl(s,r)*schwartz_ij < thr) cycle + + coef4 = coef3 * ao_coef_norm_ord_transp_cosgtos(s,l) + expo4 = ao_expo_ord_transp_cosgtos(s,l) + + call give_explicit_cpoly_and_cgaussian( Q1_new, Q1_center, qq1, fact_q1, iorder_q1 & + , expo3, expo4, K_power, L_power, K_center, L_center, dim1 ) + q1_inv = (1.d0,0.d0) / qq1 + + call give_explicit_cpoly_and_cgaussian( Q2_new, Q2_center, qq2, fact_q2, iorder_q2 & + , conjg(expo3), expo4, K_power, L_power, K_center, L_center, dim1 ) + q2_inv = (1.d0,0.d0) / qq2 + + integral1 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 & + , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 ) + + integral2 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 & + , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 ) + + integral3 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 & + , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 ) + + integral4 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 & + , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 ) + + + integral5 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 & + , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 ) + + integral6 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 & + , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 ) + + integral7 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 & + , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 ) + + integral8 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 & + , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 ) + + integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8 + + ao_two_e_integral_cosgtos_schwartz_accel = ao_two_e_integral_cosgtos_schwartz_accel & + + coef4 * 2.d0 * real(integral_tot) + enddo ! s + enddo ! r + enddo ! q + enddo ! p + + else + + do p = 1, 3 + I_power(p) = ao_power(i,p) + J_power(p) = ao_power(j,p) + K_power(p) = ao_power(k,p) + L_power(p) = ao_power(l,p) + enddo + + schwartz_kl(0,0) = 0.d0 + do r = 1, ao_prim_num(k) + coef1 = ao_coef_norm_ord_transp_cosgtos(r,k) * ao_coef_norm_ord_transp_cosgtos(r,k) + expo1 = ao_expo_ord_transp_cosgtos(r,k) + + schwartz_kl(0,r) = 0.d0 + do s = 1, ao_prim_num(l) + coef2 = coef1 * ao_coef_norm_ord_transp_cosgtos(s,l) * ao_coef_norm_ord_transp_cosgtos(s,l) + expo2 = ao_expo_ord_transp_cosgtos(s,l) + + integral1 = ERI_cosgtos( expo1, expo2, expo1, expo2 & + , K_power(1), L_power(1), K_power(1), L_power(1) & + , K_power(2), L_power(2), K_power(2), L_power(2) & + , K_power(3), L_power(3), K_power(3), L_power(3) ) + integral2 = ERI_cosgtos( expo1, expo2, conjg(expo1), expo2 & + , K_power(1), L_power(1), K_power(1), L_power(1) & + , K_power(2), L_power(2), K_power(2), L_power(2) & + , K_power(3), L_power(3), K_power(3), L_power(3) ) + + integral3 = ERI_cosgtos( conjg(expo1), expo2, expo1, expo2 & + , K_power(1), L_power(1), K_power(1), L_power(1) & + , K_power(2), L_power(2), K_power(2), L_power(2) & + , K_power(3), L_power(3), K_power(3), L_power(3) ) + integral4 = ERI_cosgtos( conjg(expo1), expo2, conjg(expo1), expo2 & + , K_power(1), L_power(1), K_power(1), L_power(1) & + , K_power(2), L_power(2), K_power(2), L_power(2) & + , K_power(3), L_power(3), K_power(3), L_power(3) ) + + integral5 = ERI_cosgtos( expo1, conjg(expo2), expo1, expo2 & + , K_power(1), L_power(1), K_power(1), L_power(1) & + , K_power(2), L_power(2), K_power(2), L_power(2) & + , K_power(3), L_power(3), K_power(3), L_power(3) ) + integral6 = ERI_cosgtos( expo1, conjg(expo2), conjg(expo1), expo2 & + , K_power(1), L_power(1), K_power(1), L_power(1) & + , K_power(2), L_power(2), K_power(2), L_power(2) & + , K_power(3), L_power(3), K_power(3), L_power(3) ) + + integral7 = ERI_cosgtos( conjg(expo1), conjg(expo2), expo1, expo2 & + , K_power(1), L_power(1), K_power(1), L_power(1) & + , K_power(2), L_power(2), K_power(2), L_power(2) & + , K_power(3), L_power(3), K_power(3), L_power(3) ) + integral8 = ERI_cosgtos( conjg(expo1), conjg(expo2), conjg(expo1), expo2 & + , K_power(1), L_power(1), K_power(1), L_power(1) & + , K_power(2), L_power(2), K_power(2), L_power(2) & + , K_power(3), L_power(3), K_power(3), L_power(3) ) + + integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8 + + + schwartz_kl(s,r) = coef2 * 2.d0 * real(integral_tot) + + schwartz_kl(0,r) = max(schwartz_kl(0,r), schwartz_kl(s,r)) + enddo + schwartz_kl(0,0) = max(schwartz_kl(0,r), schwartz_kl(0,0)) + enddo + + do p = 1, ao_prim_num(i) + coef1 = ao_coef_norm_ord_transp_cosgtos(p,i) + expo1 = ao_expo_ord_transp_cosgtos(p,i) + + do q = 1, ao_prim_num(j) + coef2 = coef1 * ao_coef_norm_ord_transp_cosgtos(q,j) + expo2 = ao_expo_ord_transp_cosgtos(q,j) + + integral1 = ERI_cosgtos( expo1, expo2, expo1, expo2 & + , I_power(1), J_power(1), I_power(1), J_power(1) & + , I_power(2), J_power(2), I_power(2), J_power(2) & + , I_power(3), J_power(3), I_power(3), J_power(3) ) + + integral2 = ERI_cosgtos( expo1, expo2, conjg(expo1), expo2 & + , I_power(1), J_power(1), I_power(1), J_power(1) & + , I_power(2), J_power(2), I_power(2), J_power(2) & + , I_power(3), J_power(3), I_power(3), J_power(3) ) + + integral3 = ERI_cosgtos( conjg(expo1), expo2, expo1, expo2 & + , I_power(1), J_power(1), I_power(1), J_power(1) & + , I_power(2), J_power(2), I_power(2), J_power(2) & + , I_power(3), J_power(3), I_power(3), J_power(3) ) + + integral4 = ERI_cosgtos( conjg(expo1), expo2, conjg(expo1), expo2 & + , I_power(1), J_power(1), I_power(1), J_power(1) & + , I_power(2), J_power(2), I_power(2), J_power(2) & + , I_power(3), J_power(3), I_power(3), J_power(3) ) + + integral5 = ERI_cosgtos( expo1, conjg(expo2), expo1, expo2 & + , I_power(1), J_power(1), I_power(1), J_power(1) & + , I_power(2), J_power(2), I_power(2), J_power(2) & + , I_power(3), J_power(3), I_power(3), J_power(3) ) + + integral6 = ERI_cosgtos( expo1, conjg(expo2), conjg(expo1), expo2 & + , I_power(1), J_power(1), I_power(1), J_power(1) & + , I_power(2), J_power(2), I_power(2), J_power(2) & + , I_power(3), J_power(3), I_power(3), J_power(3) ) + + integral7 = ERI_cosgtos( conjg(expo1), conjg(expo2), expo1, expo2 & + , I_power(1), J_power(1), I_power(1), J_power(1) & + , I_power(2), J_power(2), I_power(2), J_power(2) & + , I_power(3), J_power(3), I_power(3), J_power(3) ) + + integral8 = ERI_cosgtos( conjg(expo1), conjg(expo2), conjg(expo1), expo2 & + , I_power(1), J_power(1), I_power(1), J_power(1) & + , I_power(2), J_power(2), I_power(2), J_power(2) & + , I_power(3), J_power(3), I_power(3), J_power(3) ) + + integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8 + + schwartz_ij = coef2 * coef2 * 2.d0 * real(integral_tot) + + if(schwartz_kl(0,0)*schwartz_ij < thr) cycle + do r = 1, ao_prim_num(k) + if(schwartz_kl(0,r)*schwartz_ij < thr) cycle + + coef3 = coef2 * ao_coef_norm_ord_transp_cosgtos(r,k) + expo3 = ao_expo_ord_transp_cosgtos(r,k) + + do s = 1, ao_prim_num(l) + if(schwartz_kl(s,r)*schwartz_ij < thr) cycle + + coef4 = coef3 * ao_coef_norm_ord_transp_cosgtos(s,l) + expo4 = ao_expo_ord_transp_cosgtos(s,l) + + integral1 = ERI_cosgtos( expo1, expo2, expo3, expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral2 = ERI_cosgtos( expo1, expo2, conjg(expo3), expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral3 = ERI_cosgtos( conjg(expo1), expo2, expo3, expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral4 = ERI_cosgtos( conjg(expo1), expo2, conjg(expo3), expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral5 = ERI_cosgtos( expo1, conjg(expo2), expo3, expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral6 = ERI_cosgtos( expo1, conjg(expo2), conjg(expo3), expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral7 = ERI_cosgtos( conjg(expo1), conjg(expo2), expo3, expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral8 = ERI_cosgtos( conjg(expo1), conjg(expo2), conjg(expo3), expo4 & + , I_power(1), J_power(1), K_power(1), L_power(1) & + , I_power(2), J_power(2), K_power(2), L_power(2) & + , I_power(3), J_power(3), K_power(3), L_power(3) ) + + integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8 + + ao_two_e_integral_cosgtos_schwartz_accel = ao_two_e_integral_cosgtos_schwartz_accel & + + coef4 * 2.d0 * real(integral_tot) + enddo ! s + enddo ! r + enddo ! q + enddo ! p + + endif + + deallocate(schwartz_kl) + +end function ao_two_e_integral_cosgtos_schwartz_accel + +! --- + +BEGIN_PROVIDER [ double precision, ao_two_e_integral_cosgtos_schwartz, (ao_num,ao_num) ] + + BEGIN_DOC + ! Needed to compute Schwartz inequalities + END_DOC + + implicit none + integer :: i, k + double precision :: ao_two_e_integral_cosgtos + + ao_two_e_integral_cosgtos_schwartz(1,1) = ao_two_e_integral_cosgtos(1, 1, 1, 1) + + !$OMP PARALLEL DO PRIVATE(i,k) & + !$OMP DEFAULT(NONE) & + !$OMP SHARED(ao_num, ao_two_e_integral_cosgtos_schwartz) & + !$OMP SCHEDULE(dynamic) + do i = 1, ao_num + do k = 1, i + ao_two_e_integral_cosgtos_schwartz(i,k) = dsqrt(ao_two_e_integral_cosgtos(i, i, k, k)) + ao_two_e_integral_cosgtos_schwartz(k,i) = ao_two_e_integral_cosgtos_schwartz(i,k) + enddo + enddo + !$OMP END PARALLEL DO + +END_PROVIDER + +! --- + +complex*16 function general_primitive_integral_cosgtos( dim, P_new, P_center, fact_p, p, p_inv, iorder_p & + , Q_new, Q_center, fact_q, q, q_inv, iorder_q ) + + BEGIN_DOC + ! + ! Computes the integral where p,q,r,s are cos-cGTOS primitives + ! + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: dim + integer, intent(in) :: iorder_p(3), iorder_q(3) + complex*16, intent(in) :: P_new(0:max_dim,3), P_center(3), fact_p, p, p_inv + complex*16, intent(in) :: Q_new(0:max_dim,3), Q_center(3), fact_q, q, q_inv + + integer :: i, j, nx, ny, nz, n_Ix, n_Iy, n_Iz, iorder, n_pt_tmp, n_pt_out + double precision :: tmp_mod + double precision :: ppq_re, ppq_im, ppq_mod, sq_ppq_re, sq_ppq_im + complex*16 :: pq, pq_inv, pq_inv_2, p01_1, p01_2, p10_1, p10_2, ppq, sq_ppq + complex*16 :: rho, dist, const + complex*16 :: accu, tmp_p, tmp_q + complex*16 :: dx(0:max_dim), Ix_pol(0:max_dim), dy(0:max_dim), Iy_pol(0:max_dim), dz(0:max_dim), Iz_pol(0:max_dim) + complex*16 :: d1(0:max_dim), d_poly(0:max_dim) + + complex*16 :: crint_sum + + + !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: dx, Ix_pol, dy, Iy_pol, dz, Iz_pol + !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: d1, d_poly + + general_primitive_integral_cosgtos = (0.d0, 0.d0) + + pq = (0.5d0, 0.d0) * p_inv * q_inv + pq_inv = (0.5d0, 0.d0) / (p + q) + pq_inv_2 = pq_inv + pq_inv + p10_1 = q * pq ! 1/(2p) + p01_1 = p * pq ! 1/(2q) + p10_2 = pq_inv_2 * p10_1 * q ! 0.5d0*q/(pq + p*p) + p01_2 = pq_inv_2 * p01_1 * p ! 0.5d0*p/(q*q + pq) + + ! get \sqrt(p + q) + !ppq = p + q + !ppq_re = REAL (ppq) + !ppq_im = AIMAG(ppq) + !ppq_mod = dsqrt(ppq_re*ppq_re + ppq_im*ppq_im) + !sq_ppq_re = sq_op5 * dsqrt(ppq_re + ppq_mod) + !sq_ppq_im = 0.5d0 * ppq_im / sq_ppq_re + !sq_ppq = sq_ppq_re + (0.d0, 1.d0) * sq_ppq_im + sq_ppq = zsqrt(p + q) + + ! --- + + iorder = iorder_p(1) + iorder_q(1) + iorder_p(1) + iorder_q(1) + + do i = 0, iorder + Ix_pol(i) = (0.d0, 0.d0) + enddo + + n_Ix = 0 + do i = 0, iorder_p(1) + + tmp_p = P_new(i,1) + tmp_mod = dsqrt(REAL(tmp_p)*REAL(tmp_p) + AIMAG(tmp_p)*AIMAG(tmp_p)) + if(tmp_mod < thresh) cycle + + do j = 0, iorder_q(1) + + tmp_q = tmp_p * Q_new(j,1) + tmp_mod = dsqrt(REAL(tmp_q)*REAL(tmp_q) + AIMAG(tmp_q)*AIMAG(tmp_q)) + if(tmp_mod < thresh) cycle + + !DIR$ FORCEINLINE + call give_cpolynom_mult_center_x(P_center(1), Q_center(1), i, j, p, q, iorder, pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, dx, nx) + !DIR$ FORCEINLINE + call add_cpoly_multiply(dx, nx, tmp_q, Ix_pol, n_Ix) + enddo + enddo + if(n_Ix == -1) then + return + endif + + ! --- + + iorder = iorder_p(2) + iorder_q(2) + iorder_p(2) + iorder_q(2) + + do i = 0, iorder + Iy_pol(i) = (0.d0, 0.d0) + enddo + + n_Iy = 0 + do i = 0, iorder_p(2) + + tmp_p = P_new(i,2) + tmp_mod = dsqrt(REAL(tmp_p)*REAL(tmp_p) + AIMAG(tmp_p)*AIMAG(tmp_p)) + if(tmp_mod < thresh) cycle + + do j = 0, iorder_q(2) + + tmp_q = tmp_p * Q_new(j,2) + tmp_mod = dsqrt(REAL(tmp_q)*REAL(tmp_q) + AIMAG(tmp_q)*AIMAG(tmp_q)) + if(tmp_mod < thresh) cycle + + !DIR$ FORCEINLINE + call give_cpolynom_mult_center_x(P_center(2), Q_center(2), i, j, p, q, iorder, pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, dy, ny) + !DIR$ FORCEINLINE + call add_cpoly_multiply(dy, ny, tmp_q, Iy_pol, n_Iy) + enddo + enddo + + if(n_Iy == -1) then + return + endif + + ! --- + + iorder = iorder_p(3) + iorder_q(3) + iorder_p(3) + iorder_q(3) + + do i = 0, iorder + Iz_pol(i) = (0.d0, 0.d0) + enddo + + n_Iz = 0 + do i = 0, iorder_p(3) + + tmp_p = P_new(i,3) + tmp_mod = dsqrt(REAL(tmp_p)*REAL(tmp_p) + AIMAG(tmp_p)*AIMAG(tmp_p)) + if(tmp_mod < thresh) cycle + + do j = 0, iorder_q(3) + + tmp_q = tmp_p * Q_new(j,3) + tmp_mod = dsqrt(REAL(tmp_q)*REAL(tmp_q) + AIMAG(tmp_q)*AIMAG(tmp_q)) + if(tmp_mod < thresh) cycle + + !DIR$ FORCEINLINE + call give_cpolynom_mult_center_x(P_center(3), Q_center(3), i, j, p, q, iorder, pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, dz, nz) + !DIR$ FORCEINLINE + call add_cpoly_multiply(dz, nz, tmp_q, Iz_pol, n_Iz) + enddo + enddo + + if(n_Iz == -1) then + return + endif + + ! --- + + rho = p * q * pq_inv_2 + dist = (P_center(1) - Q_center(1)) * (P_center(1) - Q_center(1)) & + + (P_center(2) - Q_center(2)) * (P_center(2) - Q_center(2)) & + + (P_center(3) - Q_center(3)) * (P_center(3) - Q_center(3)) + const = dist * rho + + n_pt_tmp = n_Ix + n_Iy + do i = 0, n_pt_tmp + d_poly(i) = (0.d0, 0.d0) + enddo + + !DIR$ FORCEINLINE + call multiply_cpoly(Ix_pol, n_Ix, Iy_pol, n_Iy, d_poly, n_pt_tmp) + if(n_pt_tmp == -1) then + return + endif + n_pt_out = n_pt_tmp + n_Iz + do i = 0, n_pt_out + d1(i) = (0.d0, 0.d0) + enddo + + !DIR$ FORCEINLINE + call multiply_cpoly(d_poly, n_pt_tmp, Iz_pol, n_Iz, d1, n_pt_out) + + accu = crint_sum(n_pt_out, const, d1) +! print *, n_pt_out, real(d1(0:n_pt_out)) +! print *, real(accu) + + general_primitive_integral_cosgtos = fact_p * fact_q * accu * pi_5_2 * p_inv * q_inv / sq_ppq + +end function general_primitive_integral_cosgtos + +! --- + +complex*16 function ERI_cosgtos(alpha, beta, delta, gama, a_x, b_x, c_x, d_x, a_y, b_y, c_y, d_y, a_z, b_z, c_z, d_z) + + BEGIN_DOC + ! ATOMIC PRIMTIVE two-electron integral between the 4 primitives :: + ! primitive_1 = x1**(a_x) y1**(a_y) z1**(a_z) exp(-alpha * r1**2) + ! primitive_2 = x1**(b_x) y1**(b_y) z1**(b_z) exp(- beta * r1**2) + ! primitive_3 = x2**(c_x) y2**(c_y) z2**(c_z) exp(-delta * r2**2) + ! primitive_4 = x2**(d_x) y2**(d_y) z2**(d_z) exp(- gama * r2**2) + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: a_x, b_x, c_x, d_x, a_y, b_y, c_y, d_y, a_z, b_z, c_z, d_z + complex*16, intent(in) :: delta, gama, alpha, beta + + integer :: a_x_2, b_x_2, c_x_2, d_x_2, a_y_2, b_y_2, c_y_2, d_y_2, a_z_2, b_z_2, c_z_2, d_z_2 + integer :: i, j, k, l, n_pt + integer :: nx, ny, nz + double precision :: ppq_re, ppq_im, ppq_mod, sq_ppq_re, sq_ppq_im + complex*16 :: p, q, ppq, sq_ppq, coeff, I_f + + ERI_cosgtos = (0.d0, 0.d0) + + ASSERT (REAL(alpha) >= 0.d0) + ASSERT (REAL(beta ) >= 0.d0) + ASSERT (REAL(delta) >= 0.d0) + ASSERT (REAL(gama ) >= 0.d0) + + nx = a_x + b_x + c_x + d_x + if(iand(nx,1) == 1) then + ERI_cosgtos = (0.d0, 0.d0) + return + endif + + ny = a_y + b_y + c_y + d_y + if(iand(ny,1) == 1) then + ERI_cosgtos = (0.d0, 0.d0) + return + endif + + nz = a_z + b_z + c_z + d_z + if(iand(nz,1) == 1) then + ERI_cosgtos = (0.d0, 0.d0) + return + endif + + n_pt = shiftl(nx+ny+nz, 1) + + p = alpha + beta + q = delta + gama + + ! get \sqrt(p + q) + !ppq = p + q + !ppq_re = REAL (ppq) + !ppq_im = AIMAG(ppq) + !ppq_mod = dsqrt(ppq_re*ppq_re + ppq_im*ppq_im) + !sq_ppq_re = sq_op5 * dsqrt(ppq_re + ppq_mod) + !sq_ppq_im = 0.5d0 * ppq_im / sq_ppq_re + !sq_ppq = sq_ppq_re + (0.d0, 1.d0) * sq_ppq_im + sq_ppq = zsqrt(p + q) + + coeff = pi_5_2 / (p * q * sq_ppq) + if(n_pt == 0) then + ERI_cosgtos = coeff + return + endif + + call integrale_new_cosgtos(I_f, a_x, b_x, c_x, d_x, a_y, b_y, c_y, d_y, a_z, b_z, c_z, d_z, p, q, n_pt) + + ERI_cosgtos = I_f * coeff + +end function ERI_cosgtos + +! --- + +subroutine integrale_new_cosgtos(I_f, a_x, b_x, c_x, d_x, a_y, b_y, c_y, d_y, a_z, b_z, c_z, d_z, p, q, n_pt) + + BEGIN_DOC + ! Calculates the integral of the polynomial : + ! + ! $I_{x_1}(a_x+b_x, c_x+d_x, p, q) \, I_{x_1}(a_y+b_y, c_y+d_y, p, q) \, I_{x_1}(a_z+b_z, c_z+d_z, p, q)$ + ! in $( 0 ; 1)$ + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: n_pt + integer, intent(in) :: a_x, b_x, c_x, d_x, a_y, b_y, c_y, d_y, a_z, b_z, c_z, d_z + complex*16, intent(out) :: I_f + + integer :: i, j, ix, iy, iz, jx, jy, jz, sx, sy, sz + complex*16 :: p, q + complex*16 :: pq_inv, p10_1, p10_2, p01_1, p01_2, pq_inv_2 + complex*16 :: B00(n_pt_max_integrals), B10(n_pt_max_integrals), B01(n_pt_max_integrals) + complex*16 :: t1(n_pt_max_integrals), t2(n_pt_max_integrals) + + + ASSERT (n_pt > 1) + + j = shiftr(n_pt, 1) + + pq_inv = (0.5d0, 0.d0) / (p + q) + p10_1 = (0.5d0, 0.d0) / p + p01_1 = (0.5d0, 0.d0) / q + p10_2 = (0.5d0, 0.d0) * q /(p * q + p * p) + p01_2 = (0.5d0, 0.d0) * p /(q * q + q * p) + pq_inv_2 = pq_inv + pq_inv + + !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: t1, t2, B10, B01, B00 + ix = a_x + b_x + jx = c_x + d_x + iy = a_y + b_y + jy = c_y + d_y + iz = a_z + b_z + jz = c_z + d_z + sx = ix + jx + sy = iy + jy + sz = iz + jz + + do i = 1, n_pt + B10(i) = p10_1 - gauleg_t2(i, j) * p10_2 + B01(i) = p01_1 - gauleg_t2(i, j) * p01_2 + B00(i) = gauleg_t2(i, j) * pq_inv + enddo + + if(sx > 0) then + call I_x1_new_cosgtos(ix, jx, B10, B01, B00, t1, n_pt) + else + do i = 1, n_pt + t1(i) = (1.d0, 0.d0) + enddo + endif + + if(sy > 0) then + call I_x1_new_cosgtos(iy, jy, B10, B01, B00, t2, n_pt) + do i = 1, n_pt + t1(i) = t1(i) * t2(i) + enddo + endif + + if(sz > 0) then + call I_x1_new_cosgtos(iz, jz, B10, B01, B00, t2, n_pt) + do i = 1, n_pt + t1(i) = t1(i) * t2(i) + enddo + endif + + I_f = (0.d0, 0.d0) + do i = 1, n_pt + I_f += gauleg_w(i, j) * t1(i) + enddo + +end subroutine integrale_new_cosgtos + +! --- + +recursive subroutine I_x1_new_cosgtos(a, c, B_10, B_01, B_00, res, n_pt) + + BEGIN_DOC + ! recursive function involved in the two-electron integral + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: a, c, n_pt + complex*16, intent(in) :: B_10(n_pt_max_integrals), B_01(n_pt_max_integrals), B_00(n_pt_max_integrals) + complex*16, intent(out) :: res(n_pt_max_integrals) + + integer :: i + complex*16 :: res2(n_pt_max_integrals) + + if(c < 0) then + + do i = 1, n_pt + res(i) = (0.d0, 0.d0) + enddo + + else if (a == 0) then + + call I_x2_new_cosgtos(c, B_10, B_01, B_00, res, n_pt) + + else if (a == 1) then + + call I_x2_new_cosgtos(c-1, B_10, B_01, B_00, res, n_pt) + do i = 1, n_pt + res(i) = dble(c) * B_00(i) * res(i) + enddo + + else + + call I_x1_new_cosgtos(a-2, c , B_10, B_01, B_00, res , n_pt) + call I_x1_new_cosgtos(a-1, c-1, B_10, B_01, B_00, res2, n_pt) + do i = 1, n_pt + res(i) = dble(a-1) * B_10(i) * res(i) + dble(c) * B_00(i) * res2(i) + enddo + + endif + +end subroutine I_x1_new_cosgtos + +! --- + +recursive subroutine I_x2_new_cosgtos(c, B_10, B_01, B_00, res, n_pt) + + BEGIN_DOC + ! recursive function involved in the two-electron integral + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: c, n_pt + complex*16, intent(in) :: B_10(n_pt_max_integrals), B_01(n_pt_max_integrals), B_00(n_pt_max_integrals) + complex*16, intent(out) :: res(n_pt_max_integrals) + + integer :: i + + if(c == 1) then + + do i = 1, n_pt + res(i) = (0.d0, 0.d0) + enddo + + elseif(c == 0) then + + do i = 1, n_pt + res(i) = (1.d0, 0.d0) + enddo + + else + + call I_x1_new_cosgtos(0, c-2, B_10, B_01, B_00, res, n_pt) + do i = 1, n_pt + res(i) = dble(c-1) * B_01(i) * res(i) + enddo + + endif + +end subroutine I_x2_new_cosgtos + +! --- + +subroutine give_cpolynom_mult_center_x( P_center, Q_center, a_x, d_x, p, q, n_pt_in & + , pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, d, n_pt_out) + + BEGIN_DOC + ! subroutine that returns the explicit polynom in term of the "t" + ! variable of the following polynoms : + ! + ! $I_{x_1}(a_x,d_x,p,q) \, I_{x_1}(a_y,d_y,p,q) \ I_{x_1}(a_z,d_z,p,q)$ + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: n_pt_in, a_x, d_x + complex*16, intent(in) :: P_center, Q_center, p, q, pq_inv, p10_1, p01_1, p10_2, p01_2, pq_inv_2 + integer, intent(out) :: n_pt_out + complex*16, intent(out) :: d(0:max_dim) + + integer :: n_pt1, i + complex*16 :: B10(0:2), B01(0:2), B00(0:2), C00(0:2), D00(0:2) + + ASSERT (n_pt_in >= 0) + + B10(0) = p10_1 + B10(1) = (0.d0, 0.d0) + B10(2) = -p10_2 + + B01(0) = p01_1 + B01(1) = (0.d0, 0.d0) + B01(2) = -p01_2 + + B00(0) = (0.d0, 0.d0) + B00(1) = (0.d0, 0.d0) + B00(2) = pq_inv + + C00(0) = (0.d0, 0.d0) + C00(1) = (0.d0, 0.d0) + C00(2) = -q * (P_center - Q_center) * pq_inv_2 + + D00(0) = (0.d0, 0.d0) + D00(1) = (0.d0, 0.d0) + D00(2) = -p * (Q_center - P_center) * pq_inv_2 + + do i = 0, n_pt_in + d(i) = (0.d0, 0.d0) + enddo + + n_pt1 = n_pt_in + + !DIR$ FORCEINLINE + call I_x1_pol_mult_cosgtos(a_x, d_x, B10, B01, B00, C00, D00, d, n_pt1, n_pt_in) + n_pt_out = n_pt1 + +! print *, ' ' +! print *, a_x, d_x +! print *, real(B10), real(B01), real(B00), real(C00), real(D00) +! print *, n_pt1, real(d(0:n_pt1)) +! print *, ' ' + + if(n_pt1 < 0) then + n_pt_out = -1 + do i = 0, n_pt_in + d(i) = (0.d0, 0.d0) + enddo + return + endif + +end subroutine give_cpolynom_mult_center_x + +! --- + +subroutine I_x1_pol_mult_cosgtos(a, c, B_10, B_01, B_00, C_00, D_00, d, nd, n_pt_in) + + BEGIN_DOC + ! Recursive function involved in the two-electron integral + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: n_pt_in, a, c + complex*16, intent(in) :: B_10(0:2), B_01(0:2), B_00(0:2), C_00(0:2), D_00(0:2) + integer, intent(inout) :: nd + complex*16, intent(inout) :: d(0:max_dim) + + if( (c >= 0) .and. (nd >= 0) ) then + + if(a == 1) then + call I_x1_pol_mult_a1_cosgtos(c, B_10, B_01, B_00, C_00, D_00, d, nd, n_pt_in) + else if(a == 2) then + call I_x1_pol_mult_a2_cosgtos(c, B_10, B_01, B_00, C_00, D_00, d, nd, n_pt_in) + else if(a > 2) then + call I_x1_pol_mult_recurs_cosgtos(a, c, B_10, B_01, B_00, C_00, D_00, d, nd, n_pt_in) + else ! a == 0 + + if(c == 0)then + nd = 0 + d(0) = (1.d0, 0.d0) + return + endif + + call I_x2_pol_mult_cosgtos(c, B_10, B_01, B_00, C_00, D_00, d, nd, n_pt_in) + endif + + else + + nd = -1 + + endif + +end subroutine I_x1_pol_mult_cosgtos + +! --- + +recursive subroutine I_x1_pol_mult_recurs_cosgtos(a, c, B_10, B_01, B_00, C_00, D_00, d, nd, n_pt_in) + + BEGIN_DOC + ! Recursive function involved in the two-electron integral + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: n_pt_in, a, c + complex*16, intent(in) :: B_10(0:2), B_01(0:2), B_00(0:2), C_00(0:2), D_00(0:2) + integer, intent(inout) :: nd + complex*16, intent(inout) :: d(0:max_dim) + + integer :: nx, ix, iy, ny + complex*16 :: X(0:max_dim) + complex*16 :: Y(0:max_dim) + !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: X,Y + + ASSERT (a > 2) + + !DIR$ LOOP COUNT(8) + do ix = 0, n_pt_in + X(ix) = (0.d0, 0.d0) + enddo + + nx = 0 + if(a == 3) then + call I_x1_pol_mult_a1_cosgtos(c, B_10, B_01, B_00, C_00, D_00, X, nx, n_pt_in) + elseif(a == 4) then + call I_x1_pol_mult_a2_cosgtos(c, B_10, B_01, B_00, C_00, D_00, X, nx, n_pt_in) + else + ASSERT (a >= 5) + call I_x1_pol_mult_recurs_cosgtos(a-2, c, B_10, B_01, B_00, C_00, D_00, X, nx, n_pt_in) + endif + + !DIR$ LOOP COUNT(8) + do ix = 0, nx + X(ix) *= dble(a-1) + enddo + + !DIR$ FORCEINLINE + call multiply_cpoly(X, nx, B_10, 2, d, nd) + nx = nd + + !DIR$ LOOP COUNT(8) + do ix = 0, n_pt_in + X(ix) = (0.d0, 0.d0) + enddo + + if(c > 0) then + + if(a == 3) then + call I_x1_pol_mult_a2_cosgtos(c-1, B_10, B_01, B_00, C_00, D_00, X, nx, n_pt_in) + else + ASSERT(a >= 4) + call I_x1_pol_mult_recurs_cosgtos(a-1, c-1, B_10, B_01, B_00, C_00, D_00, X, nx, n_pt_in) + endif + + if(c > 1) then + !DIR$ LOOP COUNT(8) + do ix = 0, nx + X(ix) *= dble(c) + enddo + endif + !DIR$ FORCEINLINE + call multiply_cpoly(X, nx, B_00, 2, d, nd) + + endif + + ny = 0 + + !DIR$ LOOP COUNT(8) + do ix = 0, n_pt_in + Y(ix) = (0.d0, 0.d0) + enddo + + ASSERT (a > 2) + + if(a == 3) then + call I_x1_pol_mult_a2_cosgtos(c, B_10, B_01, B_00, C_00, D_00, Y, ny, n_pt_in) + else + ASSERT(a >= 4) + call I_x1_pol_mult_recurs_cosgtos(a-1, c, B_10, B_01, B_00, C_00, D_00, Y, ny, n_pt_in) + endif + + !DIR$ FORCEINLINE + call multiply_cpoly(Y, ny, C_00, 2, d, nd) + +end subroutine I_x1_pol_mult_recurs_cosgtos + +! --- + +recursive subroutine I_x1_pol_mult_a1_cosgtos(c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in) + + BEGIN_DOC + ! Recursive function involved in the two-electron integral + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: n_pt_in, c + complex*16, intent(in) :: B_10(0:2), B_01(0:2), B_00(0:2), C_00(0:2), D_00(0:2) + integer, intent(inout) :: nd + complex*16, intent(inout) :: d(0:max_dim) + + integer :: nx, ix, iy, ny + complex*16 :: X(0:max_dim) + complex*16 :: Y(0:max_dim) + !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: X,Y + + if( (c < 0) .or. (nd < 0) ) then + nd = -1 + return + endif + + nx = nd + !DIR$ LOOP COUNT(8) + do ix = 0, n_pt_in + X(ix) = (0.d0, 0.d0) + enddo + call I_x2_pol_mult_cosgtos(c-1, B_10, B_01, B_00, C_00, D_00, X, nx, n_pt_in) + + if(c > 1) then + !DIR$ LOOP COUNT(8) + do ix = 0, nx + X(ix) *= dble(c) + enddo + endif + + !DIR$ FORCEINLINE + call multiply_cpoly(X, nx, B_00, 2, d, nd) + + ny = 0 + + !DIR$ LOOP COUNT(8) + do ix = 0, n_pt_in + Y(ix) = (0.d0, 0.d0) + enddo + call I_x2_pol_mult_cosgtos(c, B_10, B_01, B_00, C_00, D_00, Y, ny, n_pt_in) + + !DIR$ FORCEINLINE + call multiply_cpoly(Y, ny, C_00, 2, d, nd) + +end subroutine I_x1_pol_mult_a1_cosgtos + +! --- + +recursive subroutine I_x1_pol_mult_a2_cosgtos(c, B_10, B_01, B_00, C_00, D_00, d, nd, n_pt_in) + + BEGIN_DOC + ! Recursive function involved in the two-electron integral + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: n_pt_in, c + complex*16, intent(in) :: B_10(0:2), B_01(0:2), B_00(0:2), C_00(0:2), D_00(0:2) + integer, intent(inout) :: nd + complex*16, intent(inout) :: d(0:max_dim) + + integer :: nx, ix, iy, ny + complex*16 :: X(0:max_dim) + complex*16 :: Y(0:max_dim) + !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: X,Y + + !DIR$ LOOP COUNT(8) + do ix = 0, n_pt_in + X(ix) = (0.d0, 0.d0) + enddo + + nx = 0 + call I_x2_pol_mult_cosgtos(c, B_10, B_01, B_00, C_00, D_00, X, nx, n_pt_in) + + !DIR$ FORCEINLINE + call multiply_cpoly(X, nx, B_10, 2, d, nd) + + nx = nd + !DIR$ LOOP COUNT(8) + do ix = 0, n_pt_in + X(ix) = (0.d0, 0.d0) + enddo + + !DIR$ FORCEINLINE + call I_x1_pol_mult_a1_cosgtos(c-1, B_10, B_01, B_00, C_00, D_00, X, nx, n_pt_in) + + if (c>1) then + !DIR$ LOOP COUNT(8) + do ix = 0, nx + X(ix) *= dble(c) + enddo + endif + + !DIR$ FORCEINLINE + call multiply_cpoly(X, nx, B_00, 2, d, nd) + + ny = 0 + !DIR$ LOOP COUNT(8) + do ix = 0, n_pt_in + Y(ix) = 0.d0 + enddo + !DIR$ FORCEINLINE + call I_x1_pol_mult_a1_cosgtos(c, B_10, B_01, B_00, C_00, D_00, Y, ny, n_pt_in) + + !DIR$ FORCEINLINE + call multiply_cpoly(Y, ny, C_00, 2, d, nd) + +end subroutine I_x1_pol_mult_a2_cosgtos + +! --- + +recursive subroutine I_x2_pol_mult_cosgtos(c, B_10, B_01, B_00, C_00, D_00, d, nd, dim) + + BEGIN_DOC + ! Recursive function involved in the two-electron integral + END_DOC + + implicit none + include 'utils/constants.include.F' + + integer, intent(in) :: dim, c + complex*16, intent(in) :: B_10(0:2), B_01(0:2), B_00(0:2), C_00(0:2), D_00(0:2) + integer, intent(inout) :: nd + complex*16, intent(inout) :: d(0:max_dim) + + integer :: i + integer :: nx, ix, ny + complex*16 :: X(0:max_dim), Y(0:max_dim) + !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: X, Y + + select case (c) + + case (0) + nd = 0 + d(0) = (1.d0, 0.d0) + return + + case (:-1) + nd = -1 + return + + case (1) + nd = 2 + d(0) = D_00(0) + d(1) = D_00(1) + d(2) = D_00(2) + return + + case (2) + nd = 2 + d(0) = B_01(0) + d(1) = B_01(1) + d(2) = B_01(2) + + ny = 2 + Y(0) = D_00(0) + Y(1) = D_00(1) + Y(2) = D_00(2) + + !DIR$ FORCEINLINE + call multiply_cpoly(Y, ny, D_00, 2, d, nd) + return + + case default + + !DIR$ LOOP COUNT(6) + do ix = 0, c+c + X(ix) = (0.d0, 0.d0) + enddo + nx = 0 + call I_x2_pol_mult_cosgtos(c-2, B_10, B_01, B_00, C_00, D_00, X, nx, dim) + + !DIR$ LOOP COUNT(6) + do ix = 0, nx + X(ix) *= dble(c-1) + enddo + + !DIR$ FORCEINLINE + call multiply_cpoly(X, nx, B_01, 2, d, nd) + + ny = 0 + !DIR$ LOOP COUNT(6) + do ix = 0, c+c + Y(ix) = 0.d0 + enddo + call I_x2_pol_mult_cosgtos(c-1, B_10, B_01, B_00, C_00, D_00, Y, ny, dim) + + !DIR$ FORCEINLINE + call multiply_cpoly(Y, ny, D_00, 2, d, nd) + + end select + +end subroutine I_x2_pol_mult_cosgtos + +! --- + +