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semi_empirical_int_gks.F
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semi_empirical_int_gks.F
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!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief Integral GKS scheme: The order of the integrals in makeCoul reflects
!> the standard order by MOPAC
!> \par History
!> Teodoro Laino [tlaino] - 04.2009 : Adapted size arrays to d-orbitals and
!> get rid of the alternative ordering. Using the
!> CP2K one.
!> Teodoro Laino [tlaino] - 04.2009 : Skip nullification (speed-up)
!> Teodoro Laino [tlaino] - 04.2009 : Speed-up due to fortran arrays order
!> optimization and collection of common pieces of
!> code
! **************************************************************************************************
MODULE semi_empirical_int_gks
USE dg_rho0_types, ONLY: dg_rho0_type
USE dg_types, ONLY: dg_get,&
dg_type
USE kinds, ONLY: dp
USE mathconstants, ONLY: fourpi,&
oorootpi
USE multipole_types, ONLY: do_multipole_none
USE pw_grid_types, ONLY: pw_grid_type
USE pw_pool_types, ONLY: pw_pool_type
USE semi_empirical_int_arrays, ONLY: indexb,&
rij_threshold
USE semi_empirical_mpole_types, ONLY: semi_empirical_mpole_type
USE semi_empirical_types, ONLY: se_int_control_type,&
semi_empirical_type,&
setup_se_int_control_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'semi_empirical_int_gks'
LOGICAL, PARAMETER, PRIVATE :: debug_this_module = .FALSE.
PUBLIC :: corecore_gks, rotnuc_gks, drotnuc_gks, rotint_gks, drotint_gks
CONTAINS
! **************************************************************************************************
!> \brief Computes the electron-nuclei integrals
!> \param sepi ...
!> \param sepj ...
!> \param rij ...
!> \param e1b ...
!> \param e2a ...
!> \param se_int_control ...
! **************************************************************************************************
SUBROUTINE rotnuc_gks(sepi, sepj, rij, e1b, e2a, se_int_control)
TYPE(semi_empirical_type), POINTER :: sepi, sepj
REAL(dp), DIMENSION(3), INTENT(IN) :: rij
REAL(dp), DIMENSION(45), INTENT(OUT), OPTIONAL :: e1b, e2a
TYPE(se_int_control_type), INTENT(IN) :: se_int_control
INTEGER :: i, mu, nu
REAL(KIND=dp), DIMENSION(3) :: rab
REAL(kind=dp), DIMENSION(45, 45) :: Coul
rab = -rij
IF (se_int_control%do_ewald_gks) THEN
IF (DOT_PRODUCT(rij, rij) > rij_threshold) THEN
CALL makeCoulE(rab, sepi, sepj, Coul, se_int_control)
ELSE
CALL makeCoulE0(sepi, Coul, se_int_control)
END IF
ELSE
CALL makeCoul(rab, sepi, sepj, Coul, se_int_control)
END IF
i = 0
DO mu = 1, sepi%natorb
DO nu = 1, mu
i = i + 1
e1b(i) = -Coul(i, 1)*sepj%zeff
END DO
END DO
i = 0
DO mu = 1, sepj%natorb
DO nu = 1, mu
i = i + 1
e2a(i) = -Coul(1, i)*sepi%zeff
END DO
END DO
END SUBROUTINE rotnuc_gks
! **************************************************************************************************
!> \brief Computes the electron-electron integrals
!> \param sepi ...
!> \param sepj ...
!> \param rij ...
!> \param w ...
!> \param se_int_control ...
! **************************************************************************************************
SUBROUTINE rotint_gks(sepi, sepj, rij, w, se_int_control)
TYPE(semi_empirical_type), POINTER :: sepi, sepj
REAL(dp), DIMENSION(3), INTENT(IN) :: rij
REAL(dp), DIMENSION(2025), INTENT(OUT), OPTIONAL :: w
TYPE(se_int_control_type), INTENT(IN) :: se_int_control
INTEGER :: i, ind1, ind2, lam, mu, nu, sig
REAL(KIND=dp), DIMENSION(3) :: rab
REAL(kind=dp), DIMENSION(45, 45) :: Coul
rab = -rij
IF (se_int_control%do_ewald_gks) THEN
IF (DOT_PRODUCT(rij, rij) > rij_threshold) THEN
CALL makeCoulE(rab, sepi, sepj, Coul, se_int_control)
ELSE
CALL makeCoulE0(sepi, Coul, se_int_control)
END IF
ELSE
CALL makeCoul(rab, sepi, sepj, Coul, se_int_control)
END IF
i = 0
ind1 = 0
DO mu = 1, sepi%natorb
DO nu = 1, mu
ind1 = ind1 + 1
ind2 = 0
DO lam = 1, sepj%natorb
DO sig = 1, lam
i = i + 1
ind2 = ind2 + 1
w(i) = Coul(ind1, ind2)
END DO
END DO
END DO
END DO
END SUBROUTINE rotint_gks
! **************************************************************************************************
!> \brief Computes the derivatives of the electron-nuclei integrals
!> \param sepi ...
!> \param sepj ...
!> \param rij ...
!> \param de1b ...
!> \param de2a ...
!> \param se_int_control ...
! **************************************************************************************************
SUBROUTINE drotnuc_gks(sepi, sepj, rij, de1b, de2a, se_int_control)
TYPE(semi_empirical_type), POINTER :: sepi, sepj
REAL(dp), DIMENSION(3), INTENT(IN) :: rij
REAL(dp), DIMENSION(3, 45), INTENT(OUT), OPTIONAL :: de1b, de2a
TYPE(se_int_control_type), INTENT(IN) :: se_int_control
INTEGER :: i, mu, nu
REAL(KIND=dp), DIMENSION(3) :: rab
REAL(kind=dp), DIMENSION(3, 45, 45) :: dCoul
rab = -rij
IF (se_int_control%do_ewald_gks) THEN
CALL makedCoulE(rab, sepi, sepj, dCoul, se_int_control)
ELSE
CALL makedCoul(rab, sepi, sepj, dCoul, se_int_control)
END IF
i = 0
DO mu = 1, sepi%natorb
DO nu = 1, mu
i = i + 1
de1b(1, i) = dCoul(1, i, 1)*sepj%zeff
de1b(2, i) = dCoul(2, i, 1)*sepj%zeff
de1b(3, i) = dCoul(3, i, 1)*sepj%zeff
END DO
END DO
i = 0
DO mu = 1, sepj%natorb
DO nu = 1, mu
i = i + 1
de2a(1, i) = dCoul(1, 1, i)*sepi%zeff
de2a(2, i) = dCoul(2, 1, i)*sepi%zeff
de2a(3, i) = dCoul(3, 1, i)*sepi%zeff
END DO
END DO
END SUBROUTINE drotnuc_gks
! **************************************************************************************************
!> \brief Computes the derivatives of the electron-electron integrals
!> \param sepi ...
!> \param sepj ...
!> \param rij ...
!> \param dw ...
!> \param se_int_control ...
! **************************************************************************************************
SUBROUTINE drotint_gks(sepi, sepj, rij, dw, se_int_control)
TYPE(semi_empirical_type), POINTER :: sepi, sepj
REAL(dp), DIMENSION(3), INTENT(IN) :: rij
REAL(dp), DIMENSION(3, 2025), INTENT(OUT) :: dw
TYPE(se_int_control_type), INTENT(IN) :: se_int_control
INTEGER :: i, ind1, ind2, lam, mu, nu, sig
REAL(KIND=dp), DIMENSION(3) :: rab
REAL(kind=dp), DIMENSION(3, 45, 45) :: dCoul
rab = -rij
IF (se_int_control%do_ewald_gks) THEN
CALL makedCoulE(rab, sepi, sepj, dCoul, se_int_control)
ELSE
CALL makedCoul(rab, sepi, sepj, dCoul, se_int_control)
END IF
i = 0
ind1 = 0
DO mu = 1, sepi%natorb
DO nu = 1, mu
ind1 = ind1 + 1
ind2 = 0
DO lam = 1, sepj%natorb
DO sig = 1, lam
i = i + 1
ind2 = ind2 + 1
dw(1, i) = -dCoul(1, ind1, ind2)
dw(2, i) = -dCoul(2, ind1, ind2)
dw(3, i) = -dCoul(3, ind1, ind2)
END DO
END DO
END DO
END DO
END SUBROUTINE drotint_gks
! **************************************************************************************************
!> \brief Computes the primitives of the integrals (non-periodic case)
!> \param RAB ...
!> \param sepi ...
!> \param sepj ...
!> \param Coul ...
!> \param se_int_control ...
! **************************************************************************************************
SUBROUTINE makeCoul(RAB, sepi, sepj, Coul, se_int_control)
REAL(kind=dp), DIMENSION(3) :: RAB
TYPE(semi_empirical_type), POINTER :: sepi, sepj
REAL(kind=dp), DIMENSION(45, 45), INTENT(OUT) :: Coul
TYPE(se_int_control_type), INTENT(IN) :: se_int_control
INTEGER :: iA, iB, imA, imB, jA, jB, k1, k2, k3, k4
LOGICAL :: shortrange
REAL(kind=dp) :: a2, ACOULA, ACOULB, d1, d1f(3), d2, &
d2f(3, 3), d3, d3f(3, 3, 3), d4, &
d4f(3, 3, 3, 3), f, rr, w, w0, w1, w2, &
w3, w4, w5
REAL(kind=dp), DIMENSION(3) :: v
REAL(kind=dp), DIMENSION(3, 3, 45) :: M2A, M2B
REAL(kind=dp), DIMENSION(3, 45) :: M1A, M1B
REAL(kind=dp), DIMENSION(45) :: M0A, M0B
shortrange = se_int_control%shortrange
CALL get_se_slater_multipole(sepi, M0A, M1A, M2A, ACOULA)
CALL get_se_slater_multipole(sepj, M0B, M1B, M2B, ACOULB)
v(1) = RAB(1)
v(2) = RAB(2)
v(3) = RAB(3)
rr = SQRT(DOT_PRODUCT(v, v))
a2 = 0.5_dp*(1.0_dp/ACOULA + 1.0_dp/ACOULB)
w0 = a2*rr
w = EXP(-w0)
w1 = (1.0_dp + 0.5_dp*w0)
w2 = (w1 + 0.5_dp*w0 + 0.5_dp*w0**2)
w3 = (w2 + w0**3/6.0_dp)
w4 = (w3 + w0**4/30.0_dp)
w5 = (w3 + 8.0_dp*w0**4/210.0_dp + w0**5/210.0_dp)
IF (shortrange) THEN
f = (-w*w1)/rr
d1 = -1.0_dp*(-w*w2)/rr**3
d2 = 3.0_dp*(-w*w3)/rr**5
d3 = -15.0_dp*(-w*w4)/rr**7
d4 = 105.0_dp*(-w*w5)/rr**9
ELSE
f = (1.0_dp - w*w1)/rr
d1 = -1.0_dp*(1.0_dp - w*w2)/rr**3
d2 = 3.0_dp*(1.0_dp - w*w3)/rr**5
d3 = -15.0_dp*(1.0_dp - w*w4)/rr**7
d4 = 105.0_dp*(1.0_dp - w*w5)/rr**9
END IF
CALL build_d_tensor_gks(d1f, d2f, d3f, d4f, v=v, d1=d1, d2=d2, d3=d3, d4=d4)
imA = 0
DO iA = 1, sepi%natorb
DO jA = 1, iA
imA = imA + 1
imB = 0
DO iB = 1, sepj%natorb
DO jB = 1, iB
imB = imB + 1
w = M0A(imA)*M0B(imB)*f
DO k1 = 1, 3
w = w + (M1A(k1, imA)*M0B(imB) - M0A(imA)*M1B(k1, imB))*d1f(k1)
END DO
DO k2 = 1, 3
DO k1 = 1, 3
w = w + (M2A(k1, k2, imA)*M0B(imB) - M1A(k1, imA)*M1B(k2, imB) + M0A(imA)*M2B(k1, k2, imB))*d2f(k1, k2)
END DO
END DO
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
w = w + (-M2A(k1, k2, imA)*M1B(k3, imB) + M1A(k1, imA)*M2B(k2, k3, imB))*d3f(k1, k2, k3)
END DO
END DO
END DO
DO k4 = 1, 3
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
w = w + M2A(k1, k2, imA)*M2B(k3, k4, imB)*d4f(k1, k2, k3, k4)
END DO
END DO
END DO
END DO
Coul(imA, imB) = w
END DO
END DO
END DO
END DO
END SUBROUTINE makeCoul
! **************************************************************************************************
!> \brief Computes the derivatives of the primitives of the integrals
!> (non-periodic case)
!> \param RAB ...
!> \param sepi ...
!> \param sepj ...
!> \param dCoul ...
!> \param se_int_control ...
! **************************************************************************************************
SUBROUTINE makedCoul(RAB, sepi, sepj, dCoul, se_int_control)
REAL(kind=dp), DIMENSION(3) :: RAB
TYPE(semi_empirical_type), POINTER :: sepi, sepj
REAL(kind=dp), DIMENSION(3, 45, 45), INTENT(OUT) :: dCoul
TYPE(se_int_control_type), INTENT(IN) :: se_int_control
INTEGER :: iA, iB, imA, imB, jA, jB, k1, k2, k3, k4
LOGICAL :: shortrange
REAL(kind=dp) :: a2, ACOULA, ACOULB, d1, d1f(3), d2, d2f(3, 3), d3, d3f(3, 3, 3), d4, &
d4f(3, 3, 3, 3), d5, d5f(3, 3, 3, 3, 3), f, rr, tmp, w, w0, w1, w2, w3, w4, w5, w6
REAL(kind=dp), DIMENSION(3) :: v, wv
REAL(kind=dp), DIMENSION(3, 3, 45) :: M2A, M2B
REAL(kind=dp), DIMENSION(3, 45) :: M1A, M1B
REAL(kind=dp), DIMENSION(45) :: M0A, M0B
shortrange = se_int_control%shortrange
CALL get_se_slater_multipole(sepi, M0A, M1A, M2A, ACOULA)
CALL get_se_slater_multipole(sepj, M0B, M1B, M2B, ACOULB)
v(1) = RAB(1)
v(2) = RAB(2)
v(3) = RAB(3)
rr = SQRT(DOT_PRODUCT(v, v))
a2 = 0.5_dp*(1.0_dp/ACOULA + 1.0_dp/ACOULB)
w0 = a2*rr
w = EXP(-w0)
w1 = (1.0_dp + 0.5_dp*w0)
w2 = (w1 + 0.5_dp*w0 + 0.5_dp*w0**2)
w3 = (w2 + w0**3/6.0_dp)
w4 = (w3 + w0**4/30.0_dp)
w5 = (w3 + 4.0_dp*w0**4/105.0_dp + w0**5/210.0_dp)
w6 = (w3 + 15.0_dp*w0**4/378.0_dp + 2.0_dp*w0**5/315.0_dp + w0**6/1890.0_dp)
IF (shortrange) THEN
f = (-w*w1)/rr
d1 = -1.0_dp*(-w*w2)/rr**3
d2 = 3.0_dp*(-w*w3)/rr**5
d3 = -15.0_dp*(-w*w4)/rr**7
d4 = 105.0_dp*(-w*w5)/rr**9
d5 = -945.0_dp*(-w*w6)/rr**11
ELSE
f = (1.0_dp - w*w1)/rr
d1 = -1.0_dp*(1.0_dp - w*w2)/rr**3
d2 = 3.0_dp*(1.0_dp - w*w3)/rr**5
d3 = -15.0_dp*(1.0_dp - w*w4)/rr**7
d4 = 105.0_dp*(1.0_dp - w*w5)/rr**9
d5 = -945.0_dp*(1.0_dp - w*w6)/rr**11
END IF
CALL build_d_tensor_gks(d1f, d2f, d3f, d4f, d5f, v, d1, d2, d3, d4, d5)
imA = 0
DO iA = 1, sepi%natorb
DO jA = 1, iA
imA = imA + 1
imB = 0
DO iB = 1, sepj%natorb
DO jB = 1, iB
imB = imB + 1
tmp = M0A(imA)*M0B(imB)
wv(1) = tmp*d1f(1)
wv(2) = tmp*d1f(2)
wv(3) = tmp*d1f(3)
DO k1 = 1, 3
tmp = M1A(k1, imA)*M0B(imB) - M0A(imA)*M1B(k1, imB)
wv(1) = wv(1) + tmp*d2f(1, k1)
wv(2) = wv(2) + tmp*d2f(2, k1)
wv(3) = wv(3) + tmp*d2f(3, k1)
END DO
DO k2 = 1, 3
DO k1 = 1, 3
tmp = M2A(k1, k2, imA)*M0B(imB) - M1A(k1, imA)*M1B(k2, imB) + M0A(imA)*M2B(k1, k2, imB)
wv(1) = wv(1) + tmp*d3f(1, k1, k2)
wv(2) = wv(2) + tmp*d3f(2, k1, k2)
wv(3) = wv(3) + tmp*d3f(3, k1, k2)
END DO
END DO
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
tmp = -M2A(k1, k2, imA)*M1B(k3, imB) + M1A(k1, imA)*M2B(k2, k3, imB)
wv(1) = wv(1) + tmp*d4f(1, k1, k2, k3)
wv(2) = wv(2) + tmp*d4f(2, k1, k2, k3)
wv(3) = wv(3) + tmp*d4f(3, k1, k2, k3)
END DO
END DO
END DO
DO k4 = 1, 3
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
tmp = M2A(k1, k2, imA)*M2B(k3, k4, imB)
wv(1) = wv(1) + tmp*d5f(1, k1, k2, k3, k4)
wv(2) = wv(2) + tmp*d5f(2, k1, k2, k3, k4)
wv(3) = wv(3) + tmp*d5f(3, k1, k2, k3, k4)
END DO
END DO
END DO
END DO
dCoul(1, imA, imB) = wv(1)
dCoul(2, imA, imB) = wv(2)
dCoul(3, imA, imB) = wv(3)
END DO
END DO
END DO
END DO
END SUBROUTINE makedCoul
! **************************************************************************************************
!> \brief Computes nuclei-nuclei interactions
!> \param sepi ...
!> \param sepj ...
!> \param rijv ...
!> \param enuc ...
!> \param denuc ...
!> \param se_int_control ...
! **************************************************************************************************
SUBROUTINE corecore_gks(sepi, sepj, rijv, enuc, denuc, se_int_control)
TYPE(semi_empirical_type), POINTER :: sepi, sepj
REAL(dp), DIMENSION(3), INTENT(IN) :: rijv
REAL(dp), INTENT(OUT), OPTIONAL :: enuc
REAL(dp), DIMENSION(3), INTENT(OUT), OPTIONAL :: denuc
TYPE(se_int_control_type), INTENT(IN) :: se_int_control
LOGICAL :: l_denuc, l_enuc
REAL(dp) :: alpi, alpj, dscale, rij, scale, zz
REAL(kind=dp), DIMENSION(3, 45, 45) :: dCoul, dCoulE
REAL(kind=dp), DIMENSION(45, 45) :: Coul, CoulE
TYPE(se_int_control_type) :: se_int_control_off
rij = DOT_PRODUCT(rijv, rijv)
l_enuc = PRESENT(enuc)
l_denuc = PRESENT(denuc)
IF ((rij > rij_threshold) .AND. (l_enuc .OR. l_denuc)) THEN
rij = SQRT(rij)
IF (se_int_control%shortrange) THEN
CALL setup_se_int_control_type(se_int_control_off, shortrange=.FALSE., do_ewald_r3=.FALSE., &
do_ewald_gks=.FALSE., integral_screening=se_int_control%integral_screening, &
max_multipole=do_multipole_none, pc_coulomb_int=.FALSE.)
CALL makeCoul(rijv, sepi, sepj, Coul, se_int_control_off)
IF (l_denuc) CALL makedCoul(rijv, sepi, sepj, dCoul, se_int_control_off)
IF (se_int_control%do_ewald_gks) THEN
CALL makeCoulE(rijv, sepi, sepj, CoulE, se_int_control)
IF (l_denuc) CALL makedCoulE(rijv, sepi, sepj, dCoulE, se_int_control)
ELSE
CALL makeCoul(rijv, sepi, sepj, CoulE, se_int_control)
IF (l_denuc) CALL makedCoul(rijv, sepi, sepj, dCoulE, se_int_control)
END IF
ELSE
CALL makeCoul(rijv, sepi, sepj, Coul, se_int_control)
CoulE = Coul
IF (l_denuc) CALL makedCoul(rijv, sepi, sepj, dCoul, se_int_control)
IF (l_denuc) dCoulE = dCoul
END IF
scale = 0.0_dp
dscale = 0.0_dp
zz = sepi%zeff*sepj%zeff
alpi = sepi%alp
alpj = sepj%alp
scale = EXP(-alpi*rij) + EXP(-alpj*rij)
IF (l_enuc) THEN
enuc = zz*CoulE(1, 1) + scale*zz*Coul(1, 1)
END IF
IF (l_denuc) THEN
dscale = -alpi*EXP(-alpi*rij) - alpj*EXP(-alpj*rij)
denuc(1) = zz*dCoulE(1, 1, 1) + dscale*(rijv(1)/rij)*zz*Coul(1, 1) + scale*zz*dCoul(1, 1, 1)
denuc(2) = zz*dCoulE(2, 1, 1) + dscale*(rijv(2)/rij)*zz*Coul(1, 1) + scale*zz*dCoul(2, 1, 1)
denuc(3) = zz*dCoulE(3, 1, 1) + dscale*(rijv(3)/rij)*zz*Coul(1, 1) + scale*zz*dCoul(3, 1, 1)
END IF
ELSE
IF (se_int_control%do_ewald_gks) THEN
zz = sepi%zeff*sepi%zeff
CALL makeCoulE0(sepi, CoulE, se_int_control)
IF (l_enuc) THEN
enuc = zz*CoulE(1, 1)
END IF
IF (l_denuc) THEN
denuc = 0._dp
END IF
END IF
END IF
END SUBROUTINE corecore_gks
! **************************************************************************************************
!> \brief Computes the primitives of the integrals (periodic case)
!> \param RAB ...
!> \param sepi ...
!> \param sepj ...
!> \param Coul ...
!> \param se_int_control ...
! **************************************************************************************************
SUBROUTINE makeCoulE(RAB, sepi, sepj, Coul, se_int_control)
REAL(KIND=dp), DIMENSION(3) :: RAB
TYPE(semi_empirical_type), POINTER :: sepi, sepj
REAL(KIND=dp), DIMENSION(45, 45), INTENT(OUT) :: Coul
TYPE(se_int_control_type), INTENT(IN) :: se_int_control
INTEGER :: gpt, imA, imB, k1, k2, k3, k4, lp, mp, np
INTEGER, DIMENSION(:, :), POINTER :: bds
REAL(KIND=dp) :: a2, ACOULA, ACOULB, alpha, cc, d1, d1f(3), d2, d2f(3, 3), d3, d3f(3, 3, 3), &
d4, d4f(3, 3, 3, 3), f, ff, kr, kr2, r1, r2, r3, r5, r7, r9, rr, ss, w, w0, w1, w2, w3, &
w4, w5
REAL(KIND=dp), DIMENSION(3) :: kk, v
REAL(KIND=dp), DIMENSION(3, 3, 45) :: M2A, M2B
REAL(KIND=dp), DIMENSION(3, 45) :: M1A, M1B
REAL(KIND=dp), DIMENSION(45) :: M0A, M0B
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: rho0
TYPE(dg_rho0_type), POINTER :: dg_rho0
TYPE(dg_type), POINTER :: dg
TYPE(pw_grid_type), POINTER :: pw_grid
TYPE(pw_pool_type), POINTER :: pw_pool
alpha = se_int_control%ewald_gks%alpha
pw_pool => se_int_control%ewald_gks%pw_pool
dg => se_int_control%ewald_gks%dg
CALL dg_get(dg, dg_rho0=dg_rho0)
rho0 => dg_rho0%density%array
pw_grid => pw_pool%pw_grid
bds => pw_grid%bounds
CALL get_se_slater_multipole(sepi, M0A, M1A, M2A, ACOULA)
CALL get_se_slater_multipole(sepj, M0B, M1B, M2B, ACOULB)
v(1) = RAB(1)
v(2) = RAB(2)
v(3) = RAB(3)
rr = SQRT(DOT_PRODUCT(v, v))
r1 = 1.0_dp/rr
r2 = r1*r1
r3 = r2*r1
r5 = r3*r2
r7 = r5*r2
r9 = r7*r2
a2 = 0.5_dp*(1.0_dp/ACOULA + 1.0_dp/ACOULB)
w0 = a2*rr
w = EXP(-w0)
w1 = (1.0_dp + 0.5_dp*w0)
w2 = (w1 + 0.5_dp*w0 + 0.5_dp*w0**2)
w3 = (w2 + w0**3/6.0_dp)
w4 = (w3 + w0**4/30.0_dp)
w5 = (w3 + 8.0_dp*w0**4/210.0_dp + w0**5/210.0_dp)
f = (1.0_dp - w*w1)*r1
d1 = -1.0_dp*(1.0_dp - w*w2)*r3
d2 = 3.0_dp*(1.0_dp - w*w3)*r5
d3 = -15.0_dp*(1.0_dp - w*w4)*r7
d4 = 105.0_dp*(1.0_dp - w*w5)*r9
kr = alpha*rr
kr2 = kr*kr
w0 = 1.0_dp - erfc(kr)
w1 = 2.0_dp*oorootpi*EXP(-kr2)
w2 = w1*kr
f = f - w0*r1
d1 = d1 + (-w2 + w0)*r3
d2 = d2 + (w2*(3.0_dp + kr2*2.0_dp) - 3.0_dp*w0)*r5
d3 = d3 + (-w2*(15.0_dp + kr2*(10.0_dp + kr2*4.0_dp)) + 15.0_dp*w0)*r7
d4 = d4 + (w2*(105.0_dp + kr2*(70.0_dp + kr2*(28.0_dp + kr2*8.0_dp))) - 105.0_dp*w0)*r9
CALL build_d_tensor_gks(d1f, d2f, d3f, d4f, v=v, d1=d1, d2=d2, d3=d3, d4=d4)
DO imA = 1, (sepi%natorb*(sepi%natorb + 1))/2
DO imB = 1, (sepj%natorb*(sepj%natorb + 1))/2
w = M0A(imA)*M0B(imB)*f
DO k1 = 1, 3
w = w + (M1A(k1, imA)*M0B(imB) - M0A(imA)*M1B(k1, imB))*d1f(k1)
END DO
DO k2 = 1, 3
DO k1 = 1, 3
w = w + (M2A(k1, k2, imA)*M0B(imB) - M1A(k1, imA)*M1B(k2, imB) + M0A(imA)*M2B(k1, k2, imB))*d2f(k1, k2)
END DO
END DO
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
w = w + (-M2A(k1, k2, imA)*M1B(k3, imB) + M1A(k1, imA)*M2B(k2, k3, imB))*d3f(k1, k2, k3)
END DO
END DO
END DO
DO k4 = 1, 3
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
w = w + M2A(k1, k2, imA)*M2B(k3, k4, imB)*d4f(k1, k2, k3, k4)
END DO
END DO
END DO
END DO
Coul(imA, imB) = w
END DO
END DO
v(1) = RAB(1)
v(2) = RAB(2)
v(3) = RAB(3)
f = 0.0_dp
d1f = 0.0_dp
d2f = 0.0_dp
d3f = 0.0_dp
d4f = 0.0_dp
DO gpt = 1, pw_grid%ngpts_cut_local
lp = pw_grid%mapl%pos(pw_grid%g_hat(1, gpt))
mp = pw_grid%mapm%pos(pw_grid%g_hat(2, gpt))
np = pw_grid%mapn%pos(pw_grid%g_hat(3, gpt))
lp = lp + bds(1, 1)
mp = mp + bds(1, 2)
np = np + bds(1, 3)
IF (pw_grid%gsq(gpt) == 0.0_dp) CYCLE
kk(:) = pw_grid%g(:, gpt)
ff = 2.0_dp*fourpi*rho0(lp, mp, np)**2*pw_grid%vol/pw_grid%gsq(gpt)
kr = DOT_PRODUCT(kk, v)
cc = COS(kr)
ss = SIN(kr)
f = f + cc*ff
DO k1 = 1, 3
d1f(k1) = d1f(k1) - kk(k1)*ss*ff
END DO
DO k2 = 1, 3
DO k1 = 1, 3
d2f(k1, k2) = d2f(k1, k2) - kk(k1)*kk(k2)*cc*ff
END DO
END DO
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
d3f(k1, k2, k3) = d3f(k1, k2, k3) + kk(k1)*kk(k2)*kk(k3)*ss*ff
END DO
END DO
END DO
DO k4 = 1, 3
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
d4f(k1, k2, k3, k4) = d4f(k1, k2, k3, k4) + kk(k1)*kk(k2)*kk(k3)*kk(k4)*cc*ff
END DO
END DO
END DO
END DO
END DO
DO imA = 1, (sepi%natorb*(sepi%natorb + 1))/2
DO imB = 1, (sepj%natorb*(sepj%natorb + 1))/2
w = M0A(imA)*M0B(imB)*f
DO k1 = 1, 3
w = w + (M1A(k1, imA)*M0B(imB) - M0A(imA)*M1B(k1, imB))*d1f(k1)
END DO
DO k2 = 1, 3
DO k1 = 1, 3
w = w + (M2A(k1, k2, imA)*M0B(imB) - M1A(k1, imA)*M1B(k2, imB) + M0A(imA)*M2B(k1, k2, imB))*d2f(k1, k2)
END DO
END DO
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
w = w + (-M2A(k1, k2, imA)*M1B(k3, imB) + M1A(k1, imA)*M2B(k2, k3, imB))*d3f(k1, k2, k3)
END DO
END DO
END DO
DO k4 = 1, 3
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
w = w + M2A(k1, k2, imA)*M2B(k3, k4, imB)*d4f(k1, k2, k3, k4)
END DO
END DO
END DO
END DO
Coul(imA, imB) = Coul(imA, imB) + w
END DO
END DO
DO imA = 1, (sepi%natorb*(sepi%natorb + 1))/2
DO imB = 1, (sepj%natorb*(sepj%natorb + 1))/2
w = -M0A(imA)*M0B(imB)*0.25_dp*fourpi/(pw_grid%vol*alpha**2)
Coul(imA, imB) = Coul(imA, imB) + w
END DO
END DO
END SUBROUTINE makeCoulE
! **************************************************************************************************
!> \brief Computes the derivatives of the primitives of the integrals
!> (periodic case)
!> \param RAB ...
!> \param sepi ...
!> \param sepj ...
!> \param dCoul ...
!> \param se_int_control ...
! **************************************************************************************************
SUBROUTINE makedCoulE(RAB, sepi, sepj, dCoul, se_int_control)
REAL(KIND=dp), DIMENSION(3) :: RAB
TYPE(semi_empirical_type), POINTER :: sepi, sepj
REAL(KIND=dp), DIMENSION(3, 45, 45), INTENT(OUT) :: dCoul
TYPE(se_int_control_type), INTENT(IN) :: se_int_control
INTEGER :: gpt, imA, imB, k1, k2, k3, k4, k5, lp, &
mp, np
INTEGER, DIMENSION(:, :), POINTER :: bds
REAL(KIND=dp) :: a2, ACOULA, ACOULB, alpha, cc, d1, d1f(3), d2, d2f(3, 3), d3, d3f(3, 3, 3), &
d4, d4f(3, 3, 3, 3), d5, d5f(3, 3, 3, 3, 3), f, ff, kr, kr2, r1, r11, r2, r3, r5, r7, r9, &
rr, ss, tmp, w, w0, w1, w2, w3, w4, w5, w6
REAL(KIND=dp), DIMENSION(3) :: kk, v, wv
REAL(kind=dp), DIMENSION(3, 3, 45) :: M2A, M2B
REAL(kind=dp), DIMENSION(3, 45) :: M1A, M1B
REAL(kind=dp), DIMENSION(45) :: M0A, M0B
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: rho0
TYPE(dg_rho0_type), POINTER :: dg_rho0
TYPE(dg_type), POINTER :: dg
TYPE(pw_grid_type), POINTER :: pw_grid
TYPE(pw_pool_type), POINTER :: pw_pool
alpha = se_int_control%ewald_gks%alpha
pw_pool => se_int_control%ewald_gks%pw_pool
dg => se_int_control%ewald_gks%dg
CALL dg_get(dg, dg_rho0=dg_rho0)
rho0 => dg_rho0%density%array
pw_grid => pw_pool%pw_grid
bds => pw_grid%bounds
CALL get_se_slater_multipole(sepi, M0A, M1A, M2A, ACOULA)
CALL get_se_slater_multipole(sepj, M0B, M1B, M2B, ACOULB)
v(1) = RAB(1)
v(2) = RAB(2)
v(3) = RAB(3)
rr = SQRT(DOT_PRODUCT(v, v))
a2 = 0.5_dp*(1.0_dp/ACOULA + 1.0_dp/ACOULB)
r1 = 1.0_dp/rr
r2 = r1*r1
r3 = r2*r1
r5 = r3*r2
r7 = r5*r2
r9 = r7*r2
r11 = r9*r2
w0 = a2*rr
w = EXP(-w0)
w1 = (1.0_dp + 0.5_dp*w0)
w2 = (w1 + 0.5_dp*w0 + 0.5_dp*w0**2)
w3 = (w2 + w0**3/6.0_dp)
w4 = (w3 + w0**4/30.0_dp)
w5 = (w3 + 8.0_dp*w0**4/210.0_dp + w0**5/210.0_dp)
w6 = (w3 + 5.0_dp*w0**4/126.0_dp + 2.0_dp*w0**5/315.0_dp + w0**6/1890.0_dp)
f = (1.0_dp - w*w1)*r1
d1 = -1.0_dp*(1.0_dp - w*w2)*r3
d2 = 3.0_dp*(1.0_dp - w*w3)*r5
d3 = -15.0_dp*(1.0_dp - w*w4)*r7
d4 = 105.0_dp*(1.0_dp - w*w5)*r9
d5 = -945.0_dp*(1.0_dp - w*w6)*r11
kr = alpha*rr
kr2 = kr*kr
w0 = 1.0_dp - erfc(kr)
w1 = 2.0_dp*oorootpi*EXP(-kr2)
w2 = w1*kr
f = f - w0*r1
d1 = d1 + (-w2 + w0)*r3
d2 = d2 + (w2*(3.0_dp + kr2*2.0_dp) - 3.0_dp*w0)*r5
d3 = d3 + (-w2*(15.0_dp + kr2*(10.0_dp + kr2*4.0_dp)) + 15.0_dp*w0)*r7
d4 = d4 + (w2*(105.0_dp + kr2*(70.0_dp + kr2*(28.0_dp + kr2*8.0_dp))) - 105.0_dp*w0)*r9
d5 = d5 + (-w2*(945.0_dp + kr2*(630.0_dp + kr2*(252.0_dp + kr2*(72.0_dp + kr2*16.0_dp)))) + 945.0_dp*w0)*r11
CALL build_d_tensor_gks(d1f, d2f, d3f, d4f, d5f, v, d1, d2, d3, d4, d5)
DO imA = 1, (sepi%natorb*(sepi%natorb + 1))/2
DO imB = 1, (sepj%natorb*(sepj%natorb + 1))/2
tmp = M0A(imA)*M0B(imB)
wv(1) = tmp*d1f(1)
wv(2) = tmp*d1f(2)
wv(3) = tmp*d1f(3)
DO k1 = 1, 3
tmp = M1A(k1, imA)*M0B(imB) - M0A(imA)*M1B(k1, imB)
wv(1) = wv(1) + tmp*d2f(1, k1)
wv(2) = wv(2) + tmp*d2f(2, k1)
wv(3) = wv(3) + tmp*d2f(3, k1)
END DO
DO k2 = 1, 3
DO k1 = 1, 3
tmp = M2A(k1, k2, imA)*M0B(imB) - M1A(k1, imA)*M1B(k2, imB) + M0A(imA)*M2B(k1, k2, imB)
wv(1) = wv(1) + tmp*d3f(1, k1, k2)
wv(2) = wv(2) + tmp*d3f(2, k1, k2)
wv(3) = wv(3) + tmp*d3f(3, k1, k2)
END DO
END DO
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
tmp = -M2A(k1, k2, imA)*M1B(k3, imB) + M1A(k1, imA)*M2B(k2, k3, imB)
wv(1) = wv(1) + tmp*d4f(1, k1, k2, k3)
wv(2) = wv(2) + tmp*d4f(2, k1, k2, k3)
wv(3) = wv(3) + tmp*d4f(3, k1, k2, k3)
END DO
END DO
END DO
DO k4 = 1, 3
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
tmp = M2A(k1, k2, imA)*M2B(k3, k4, imB)
wv(1) = wv(1) + tmp*d5f(1, k1, k2, k3, k4)
wv(2) = wv(2) + tmp*d5f(2, k1, k2, k3, k4)
wv(3) = wv(3) + tmp*d5f(3, k1, k2, k3, k4)
END DO
END DO
END DO
END DO
dCoul(1, imA, imB) = wv(1)
dCoul(2, imA, imB) = wv(2)
dCoul(3, imA, imB) = wv(3)
END DO
END DO
v(1) = RAB(1)
v(2) = RAB(2)
v(3) = RAB(3)
f = 0.0_dp
d1f = 0.0_dp
d2f = 0.0_dp
d3f = 0.0_dp
d4f = 0.0_dp
d5f = 0.0_dp
DO gpt = 1, pw_grid%ngpts_cut_local
lp = pw_grid%mapl%pos(pw_grid%g_hat(1, gpt))
mp = pw_grid%mapm%pos(pw_grid%g_hat(2, gpt))
np = pw_grid%mapn%pos(pw_grid%g_hat(3, gpt))
lp = lp + bds(1, 1)
mp = mp + bds(1, 2)
np = np + bds(1, 3)
IF (pw_grid%gsq(gpt) == 0.0_dp) CYCLE
kk(:) = pw_grid%g(:, gpt)
ff = 2.0_dp*fourpi*rho0(lp, mp, np)**2*pw_grid%vol/pw_grid%gsq(gpt)
kr = DOT_PRODUCT(kk, v)
cc = COS(kr)
ss = SIN(kr)
f = f + cc*ff
DO k1 = 1, 3
d1f(k1) = d1f(k1) - kk(k1)*ss*ff
END DO
DO k2 = 1, 3
DO k1 = 1, 3
d2f(k1, k2) = d2f(k1, k2) - kk(k1)*kk(k2)*cc*ff
END DO
END DO
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
d3f(k1, k2, k3) = d3f(k1, k2, k3) + kk(k1)*kk(k2)*kk(k3)*ss*ff
END DO
END DO
END DO
DO k4 = 1, 3
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
d4f(k1, k2, k3, k4) = d4f(k1, k2, k3, k4) + kk(k1)*kk(k2)*kk(k3)*kk(k4)*cc*ff
END DO
END DO
END DO
END DO
DO k5 = 1, 3
DO k4 = 1, 3
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
d5f(k1, k2, k3, k4, k5) = d5f(k1, k2, k3, k4, k5) - kk(k1)*kk(k2)*kk(k3)*kk(k4)*kk(k5)*ss*ff
END DO
END DO
END DO
END DO
END DO
END DO
DO imA = 1, (sepi%natorb*(sepi%natorb + 1))/2
DO imB = 1, (sepj%natorb*(sepj%natorb + 1))/2
tmp = M0A(imA)*M0B(imB)
wv(1) = tmp*d1f(1)
wv(2) = tmp*d1f(2)
wv(3) = tmp*d1f(3)
DO k1 = 1, 3
tmp = M1A(k1, imA)*M0B(imB) - M0A(imA)*M1B(k1, imB)
wv(1) = wv(1) + tmp*d2f(1, k1)
wv(2) = wv(2) + tmp*d2f(2, k1)
wv(3) = wv(3) + tmp*d2f(3, k1)
END DO
DO k2 = 1, 3
DO k1 = 1, 3
tmp = M2A(k1, k2, imA)*M0B(imB) - M1A(k1, imA)*M1B(k2, imB) + M0A(imA)*M2B(k1, k2, imB)
wv(1) = wv(1) + tmp*d3f(1, k1, k2)
wv(2) = wv(2) + tmp*d3f(2, k1, k2)
wv(3) = wv(3) + tmp*d3f(3, k1, k2)
END DO
END DO
DO k3 = 1, 3
DO k2 = 1, 3
DO k1 = 1, 3
tmp = -M2A(k1, k2, imA)*M1B(k3, imB) + M1A(k1, imA)*M2B(k2, k3, imB)
wv(1) = wv(1) + tmp*d4f(1, k1, k2, k3)
wv(2) = wv(2) + tmp*d4f(2, k1, k2, k3)
wv(3) = wv(3) + tmp*d4f(3, k1, k2, k3)
END DO
END DO
END DO