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core_ae.F
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core_ae.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 Calculation of the nuclear attraction contribution to the core Hamiltonian
!> <a|erfc|b> :we only calculate the non-screened part
!> \par History
!> - core_ppnl refactored from qs_core_hamiltonian [Joost VandeVondele, 2008-11-01]
!> - adapted for nuclear attraction [jhu, 2009-02-24]
! **************************************************************************************************
MODULE core_ae
USE ai_verfc, ONLY: verfc
USE ao_util, ONLY: exp_radius
USE atomic_kind_types, ONLY: atomic_kind_type,&
get_atomic_kind_set
USE basis_set_types, ONLY: gto_basis_set_p_type,&
gto_basis_set_type
USE cp_dbcsr_api, ONLY: dbcsr_add,&
dbcsr_get_block_p,&
dbcsr_p_type
USE external_potential_types, ONLY: all_potential_type,&
get_potential,&
sgp_potential_type
USE kinds, ONLY: dp,&
int_8
USE orbital_pointers, ONLY: coset,&
indco,&
init_orbital_pointers,&
ncoset
USE particle_types, ONLY: particle_type
USE qs_force_types, ONLY: qs_force_type
USE qs_kind_types, ONLY: get_qs_kind,&
get_qs_kind_set,&
qs_kind_type
USE qs_neighbor_list_types, ONLY: get_iterator_info,&
neighbor_list_iterator_create,&
neighbor_list_iterator_p_type,&
neighbor_list_iterator_release,&
neighbor_list_set_p_type,&
nl_set_sub_iterator,&
nl_sub_iterate
USE virial_methods, ONLY: virial_pair_force
USE virial_types, ONLY: virial_type
!$ USE OMP_LIB, ONLY: omp_get_max_threads, omp_get_thread_num, omp_get_num_threads
!$ USE OMP_LIB, ONLY: omp_lock_kind, &
!$ omp_init_lock, omp_set_lock, &
!$ omp_unset_lock, omp_destroy_lock
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'core_ae'
PUBLIC :: build_core_ae, build_erfc
CONTAINS
! **************************************************************************************************
!> \brief ...
!> \param matrix_h ...
!> \param matrix_p ...
!> \param force ...
!> \param virial ...
!> \param calculate_forces ...
!> \param use_virial ...
!> \param nder ...
!> \param qs_kind_set ...
!> \param atomic_kind_set ...
!> \param particle_set ...
!> \param sab_orb ...
!> \param sac_ae ...
!> \param nimages ...
!> \param cell_to_index ...
!> \param atcore ...
! **************************************************************************************************
SUBROUTINE build_core_ae(matrix_h, matrix_p, force, virial, calculate_forces, use_virial, nder, &
qs_kind_set, atomic_kind_set, particle_set, sab_orb, sac_ae, &
nimages, cell_to_index, atcore)
TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER :: matrix_h, matrix_p
TYPE(qs_force_type), DIMENSION(:), POINTER :: force
TYPE(virial_type), POINTER :: virial
LOGICAL, INTENT(IN) :: calculate_forces
LOGICAL :: use_virial
INTEGER :: nder
TYPE(qs_kind_type), DIMENSION(:), POINTER :: qs_kind_set
TYPE(atomic_kind_type), DIMENSION(:), POINTER :: atomic_kind_set
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
TYPE(neighbor_list_set_p_type), DIMENSION(:), &
POINTER :: sab_orb, sac_ae
INTEGER, INTENT(IN) :: nimages
INTEGER, DIMENSION(:, :, :), POINTER :: cell_to_index
REAL(KIND=dp), DIMENSION(:), INTENT(INOUT), &
OPTIONAL :: atcore
CHARACTER(LEN=*), PARAMETER :: routineN = 'build_core_ae'
INTEGER :: atom_a, handle, iatom, icol, ikind, img, irow, iset, jatom, jkind, jset, katom, &
kkind, ldai, ldsab, maxco, maxl, maxnset, maxsgf, mepos, na_plus, natom, nb_plus, ncoa, &
ncob, nij, nkind, nseta, nsetb, nthread, sgfa, sgfb, slot
INTEGER, ALLOCATABLE, DIMENSION(:) :: atom_of_kind, kind_of
INTEGER, DIMENSION(3) :: cellind
INTEGER, DIMENSION(:), POINTER :: la_max, la_min, lb_max, lb_min, npgfa, &
npgfb, nsgfa, nsgfb
INTEGER, DIMENSION(:, :), POINTER :: first_sgfa, first_sgfb
LOGICAL :: doat, dokp, found
REAL(KIND=dp) :: alpha_c, atk0, atk1, core_charge, &
core_radius, dab, dac, dbc, f0, rab2, &
rac2, rbc2, zeta_c
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: ff
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: habd, work
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: hab, pab, verf, vnuc
REAL(KIND=dp), DIMENSION(3) :: force_a, force_b, rab, rac, rbc
REAL(KIND=dp), DIMENSION(3, 3) :: pv_thread
TYPE(neighbor_list_iterator_p_type), &
DIMENSION(:), POINTER :: ap_iterator
TYPE(gto_basis_set_type), POINTER :: basis_set_a, basis_set_b
TYPE(gto_basis_set_p_type), DIMENSION(:), POINTER :: basis_set_list
TYPE(all_potential_type), POINTER :: all_potential
REAL(KIND=dp), DIMENSION(SIZE(particle_set)) :: at_thread
REAL(KIND=dp), DIMENSION(:, :), POINTER :: h_block, p_block, rpgfa, rpgfb, sphi_a, &
sphi_b, zeta, zetb
REAL(KIND=dp), DIMENSION(:), POINTER :: set_radius_a, set_radius_b
REAL(KIND=dp), DIMENSION(3, SIZE(particle_set)) :: force_thread
TYPE(sgp_potential_type), POINTER :: sgp_potential
!$ INTEGER(kind=omp_lock_kind), &
!$ ALLOCATABLE, DIMENSION(:) :: locks
!$ INTEGER :: lock_num, hash, hash1, hash2
!$ INTEGER(KIND=int_8) :: iatom8
!$ INTEGER, PARAMETER :: nlock = 501
MARK_USED(int_8)
IF (calculate_forces) THEN
CALL timeset(routineN//"_forces", handle)
ELSE
CALL timeset(routineN, handle)
END IF
nkind = SIZE(atomic_kind_set)
natom = SIZE(particle_set)
doat = PRESENT(atcore)
dokp = (nimages > 1)
IF (calculate_forces .OR. doat) THEN
IF (SIZE(matrix_p, 1) == 2) THEN
DO img = 1, nimages
CALL dbcsr_add(matrix_p(1, img)%matrix, matrix_p(2, img)%matrix, &
alpha_scalar=1.0_dp, beta_scalar=1.0_dp)
CALL dbcsr_add(matrix_p(2, img)%matrix, matrix_p(1, img)%matrix, &
alpha_scalar=-2.0_dp, beta_scalar=1.0_dp)
END DO
END IF
END IF
force_thread = 0.0_dp
at_thread = 0.0_dp
pv_thread = 0.0_dp
ALLOCATE (basis_set_list(nkind))
DO ikind = 1, nkind
CALL get_qs_kind(qs_kind_set(ikind), basis_set=basis_set_a)
IF (ASSOCIATED(basis_set_a)) THEN
basis_set_list(ikind)%gto_basis_set => basis_set_a
ELSE
NULLIFY (basis_set_list(ikind)%gto_basis_set)
END IF
END DO
CALL get_qs_kind_set(qs_kind_set, &
maxco=maxco, maxlgto=maxl, maxsgf=maxsgf, maxnset=maxnset)
CALL init_orbital_pointers(maxl + nder + 1)
ldsab = MAX(maxco, maxsgf)
ldai = ncoset(maxl + nder + 1)
nthread = 1
!$ nthread = omp_get_max_threads()
! iterator for basis/potential list
CALL neighbor_list_iterator_create(ap_iterator, sac_ae, search=.TRUE., nthread=nthread)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP SHARED (ap_iterator, basis_set_list, calculate_forces, use_virial, &
!$OMP matrix_h, matrix_p, atomic_kind_set, qs_kind_set, particle_set, &
!$OMP sab_orb, sac_ae, nthread, ncoset, nkind, cell_to_index, &
!$OMP slot, ldsab, maxnset, ldai, nder, maxl, maxco, dokp, doat, locks, natom) &
!$OMP PRIVATE (ikind, jkind, iatom, jatom, rab, basis_set_a, basis_set_b, &
!$OMP first_sgfa, la_max, la_min, npgfa, nsgfa, sphi_a, &
!$OMP zeta, first_sgfb, lb_max, lb_min, npgfb, nsetb, rpgfb, set_radius_b, sphi_b, &
!$OMP zetb, zeta_c, alpha_c, core_charge, dab, irow, icol, h_block, found, iset, ncoa, &
!$OMP sgfa, jset, ncob, sgfb, nsgfb, p_block, work, pab, hab, kkind, nseta, &
!$OMP rac, dac, rbc, rab2, rac2, rbc2, dbc, na_plus, nb_plus, verf, vnuc, &
!$OMP set_radius_a, core_radius, rpgfa, force_a, force_b, mepos, &
!$OMP atk0, atk1, habd, f0, katom, cellind, img, nij, ff, &
!$OMP sgp_potential, all_potential, hash, hash1, hash2, iatom8) &
!$OMP REDUCTION (+ : pv_thread, force_thread, at_thread )
!$OMP SINGLE
!$ ALLOCATE (locks(nlock))
!$OMP END SINGLE
!$OMP DO
!$ DO lock_num = 1, nlock
!$ call omp_init_lock(locks(lock_num))
!$ END DO
!$OMP END DO
mepos = 0
!$ mepos = omp_get_thread_num()
ALLOCATE (hab(ldsab, ldsab, maxnset*maxnset), work(ldsab, ldsab))
ALLOCATE (verf(ldai, ldai, 2*maxl + nder + 1), vnuc(ldai, ldai, 2*maxl + nder + 1), ff(0:2*maxl + nder))
IF (calculate_forces .OR. doat) THEN
ALLOCATE (pab(maxco, maxco, maxnset*maxnset))
END IF
!$OMP DO SCHEDULE(GUIDED)
DO slot = 1, sab_orb(1)%nl_size
ikind = sab_orb(1)%nlist_task(slot)%ikind
jkind = sab_orb(1)%nlist_task(slot)%jkind
iatom = sab_orb(1)%nlist_task(slot)%iatom
jatom = sab_orb(1)%nlist_task(slot)%jatom
cellind(:) = sab_orb(1)%nlist_task(slot)%cell(:)
rab(1:3) = sab_orb(1)%nlist_task(slot)%r(1:3)
basis_set_a => basis_set_list(ikind)%gto_basis_set
IF (.NOT. ASSOCIATED(basis_set_a)) CYCLE
basis_set_b => basis_set_list(jkind)%gto_basis_set
IF (.NOT. ASSOCIATED(basis_set_b)) CYCLE
!$ iatom8 = INT(iatom - 1, int_8)*INT(natom, int_8) + INT(jatom, int_8)
!$ hash1 = INT(MOD(iatom8, INT(nlock, int_8)) + 1)
! basis ikind
first_sgfa => basis_set_a%first_sgf
la_max => basis_set_a%lmax
la_min => basis_set_a%lmin
npgfa => basis_set_a%npgf
nseta = basis_set_a%nset
nsgfa => basis_set_a%nsgf_set
rpgfa => basis_set_a%pgf_radius
set_radius_a => basis_set_a%set_radius
sphi_a => basis_set_a%sphi
zeta => basis_set_a%zet
! basis jkind
first_sgfb => basis_set_b%first_sgf
lb_max => basis_set_b%lmax
lb_min => basis_set_b%lmin
npgfb => basis_set_b%npgf
nsetb = basis_set_b%nset
nsgfb => basis_set_b%nsgf_set
rpgfb => basis_set_b%pgf_radius
set_radius_b => basis_set_b%set_radius
sphi_b => basis_set_b%sphi
zetb => basis_set_b%zet
dab = SQRT(SUM(rab*rab))
IF (dokp) THEN
img = cell_to_index(cellind(1), cellind(2), cellind(3))
ELSE
img = 1
END IF
! *** Use the symmetry of the first derivatives ***
IF (iatom == jatom) THEN
f0 = 1.0_dp
ELSE
f0 = 2.0_dp
END IF
! *** Create matrix blocks for a new matrix block column ***
IF (iatom <= jatom) THEN
irow = iatom
icol = jatom
ELSE
irow = jatom
icol = iatom
END IF
NULLIFY (h_block)
CALL dbcsr_get_block_p(matrix=matrix_h(1, img)%matrix, &
row=irow, col=icol, BLOCK=h_block, found=found)
IF (calculate_forces .OR. doat) THEN
NULLIFY (p_block)
CALL dbcsr_get_block_p(matrix=matrix_p(1, img)%matrix, &
row=irow, col=icol, BLOCK=p_block, found=found)
CPASSERT(ASSOCIATED(p_block))
! *** Decontract density matrix block ***
DO iset = 1, nseta
ncoa = npgfa(iset)*ncoset(la_max(iset))
sgfa = first_sgfa(1, iset)
DO jset = 1, nsetb
ncob = npgfb(jset)*ncoset(lb_max(jset))
sgfb = first_sgfb(1, jset)
nij = jset + (iset - 1)*maxnset
! *** Decontract density matrix block ***
IF (iatom <= jatom) THEN
work(1:ncoa, 1:nsgfb(jset)) = MATMUL(sphi_a(1:ncoa, sgfa:sgfa + nsgfa(iset) - 1), &
p_block(sgfa:sgfa + nsgfa(iset) - 1, sgfb:sgfb + nsgfb(jset) - 1))
ELSE
work(1:ncoa, 1:nsgfb(jset)) = MATMUL(sphi_a(1:ncoa, sgfa:sgfa + nsgfa(iset) - 1), &
TRANSPOSE(p_block(sgfb:sgfb + nsgfb(jset) - 1, sgfa:sgfa + nsgfa(iset) - 1)))
END IF
pab(1:ncoa, 1:ncob, nij) = MATMUL(work(1:ncoa, 1:nsgfb(jset)), &
TRANSPOSE(sphi_b(1:ncob, sgfb:sgfb + nsgfb(jset) - 1)))
END DO
END DO
END IF
! loop over all kinds for pseudopotential atoms
hab = 0._dp
DO kkind = 1, nkind
CALL get_qs_kind(qs_kind_set(kkind), all_potential=all_potential, &
sgp_potential=sgp_potential)
IF (ASSOCIATED(all_potential)) THEN
CALL get_potential(potential=all_potential, &
alpha_core_charge=alpha_c, zeff=zeta_c, &
ccore_charge=core_charge, core_charge_radius=core_radius)
ELSE IF (ASSOCIATED(sgp_potential)) THEN
CALL get_potential(potential=sgp_potential, &
alpha_core_charge=alpha_c, zeff=zeta_c, &
ccore_charge=core_charge, core_charge_radius=core_radius)
ELSE
CYCLE
END IF
CALL nl_set_sub_iterator(ap_iterator, ikind, kkind, iatom, mepos=mepos)
DO WHILE (nl_sub_iterate(ap_iterator, mepos=mepos) == 0)
CALL get_iterator_info(ap_iterator, jatom=katom, r=rac, mepos=mepos)
dac = SQRT(SUM(rac*rac))
rbc(:) = rac(:) - rab(:)
dbc = SQRT(SUM(rbc*rbc))
IF ((MAXVAL(set_radius_a(:)) + core_radius < dac) .OR. &
(MAXVAL(set_radius_b(:)) + core_radius < dbc)) THEN
CYCLE
END IF
DO iset = 1, nseta
IF (set_radius_a(iset) + core_radius < dac) CYCLE
ncoa = npgfa(iset)*ncoset(la_max(iset))
sgfa = first_sgfa(1, iset)
DO jset = 1, nsetb
IF (set_radius_b(jset) + core_radius < dbc) CYCLE
ncob = npgfb(jset)*ncoset(lb_max(jset))
sgfb = first_sgfb(1, jset)
IF (set_radius_a(iset) + set_radius_b(jset) < dab) CYCLE
rab2 = dab*dab
rac2 = dac*dac
rbc2 = dbc*dbc
nij = jset + (iset - 1)*maxnset
! *** Calculate the GTH pseudo potential forces ***
IF (doat) THEN
atk0 = f0*SUM(hab(1:ncoa, 1:ncob, nij)*pab(1:ncoa, 1:ncob, nij))
END IF
IF (calculate_forces) THEN
na_plus = npgfa(iset)*ncoset(la_max(iset) + nder)
nb_plus = npgfb(jset)*ncoset(lb_max(jset))
ALLOCATE (habd(na_plus, nb_plus))
habd = 0._dp
CALL verfc( &
la_max(iset) + nder, npgfa(iset), zeta(:, iset), rpgfa(:, iset), la_min(iset), &
lb_max(jset), npgfb(jset), zetb(:, jset), rpgfb(:, jset), lb_min(jset), &
alpha_c, core_radius, zeta_c, core_charge, &
rab, rab2, rac, rac2, rbc2, hab(:, :, nij), verf, vnuc, ff(0:), &
nder, habd)
! *** The derivatives w.r.t. atomic center c are ***
! *** calculated using the translational invariance ***
! *** of the first derivatives ***
CALL verfc_force(habd, pab(:, :, nij), force_a, force_b, nder, &
la_max(iset), la_min(iset), npgfa(iset), zeta(:, iset), &
lb_max(jset), lb_min(jset), npgfb(jset), zetb(:, jset), rab)
DEALLOCATE (habd)
force_thread(1, iatom) = force_thread(1, iatom) + f0*force_a(1)
force_thread(2, iatom) = force_thread(2, iatom) + f0*force_a(2)
force_thread(3, iatom) = force_thread(3, iatom) + f0*force_a(3)
force_thread(1, jatom) = force_thread(1, jatom) + f0*force_b(1)
force_thread(2, jatom) = force_thread(2, jatom) + f0*force_b(2)
force_thread(3, jatom) = force_thread(3, jatom) + f0*force_b(3)
force_thread(1, katom) = force_thread(1, katom) - f0*force_a(1) - f0*force_b(1)
force_thread(2, katom) = force_thread(2, katom) - f0*force_a(2) - f0*force_b(2)
force_thread(3, katom) = force_thread(3, katom) - f0*force_a(3) - f0*force_b(3)
IF (use_virial) THEN
CALL virial_pair_force(pv_thread, f0, force_a, rac)
CALL virial_pair_force(pv_thread, f0, force_b, rbc)
END IF
ELSE
CALL verfc( &
la_max(iset), npgfa(iset), zeta(:, iset), rpgfa(:, iset), la_min(iset), &
lb_max(jset), npgfb(jset), zetb(:, jset), rpgfb(:, jset), lb_min(jset), &
alpha_c, core_radius, zeta_c, core_charge, &
rab, rab2, rac, rac2, rbc2, hab(:, :, nij), verf, vnuc, ff(0:))
END IF
! calculate atomic contributions
IF (doat) THEN
atk1 = f0*SUM(hab(1:ncoa, 1:ncob, nij)*pab(1:ncoa, 1:ncob, nij))
at_thread(katom) = at_thread(katom) + (atk1 - atk0)
END IF
END DO
END DO
END DO
END DO
! *** Contract nuclear attraction integrals
DO iset = 1, nseta
ncoa = npgfa(iset)*ncoset(la_max(iset))
sgfa = first_sgfa(1, iset)
DO jset = 1, nsetb
ncob = npgfb(jset)*ncoset(lb_max(jset))
sgfb = first_sgfb(1, jset)
nij = jset + (iset - 1)*maxnset
!$ hash2 = MOD((iset - 1)*nsetb + jset, nlock) + 1
!$ hash = MOD(hash1 + hash2, nlock) + 1
work(1:ncoa, 1:nsgfb(jset)) = MATMUL(hab(1:ncoa, 1:ncob, nij), &
sphi_b(1:ncob, sgfb:sgfb + nsgfb(jset) - 1))
!$ CALL omp_set_lock(locks(hash))
IF (iatom <= jatom) THEN
h_block(sgfa:sgfa + nsgfa(iset) - 1, sgfb:sgfb + nsgfb(jset) - 1) = &
h_block(sgfa:sgfa + nsgfa(iset) - 1, sgfb:sgfb + nsgfb(jset) - 1) + &
MATMUL(TRANSPOSE(sphi_a(1:ncoa, sgfa:sgfa + nsgfa(iset) - 1)), work(1:ncoa, 1:nsgfb(jset)))
ELSE
h_block(sgfb:sgfb + nsgfb(jset) - 1, sgfa:sgfa + nsgfa(iset) - 1) = &
h_block(sgfb:sgfb + nsgfb(jset) - 1, sgfa:sgfa + nsgfa(iset) - 1) + &
MATMUL(TRANSPOSE(work(1:ncoa, 1:nsgfb(jset))), sphi_a(1:ncoa, sgfa:sgfa + nsgfa(iset) - 1))
END IF
!$ CALL omp_unset_lock(locks(hash))
END DO
END DO
END DO
DEALLOCATE (hab, work, verf, vnuc, ff)
IF (calculate_forces .OR. doat) THEN
DEALLOCATE (pab)
END IF
!$OMP DO
!$ DO lock_num = 1, nlock
!$ call omp_destroy_lock(locks(lock_num))
!$ END DO
!$OMP END DO
!$OMP SINGLE
!$ DEALLOCATE (locks)
!$OMP END SINGLE NOWAIT
!$OMP END PARALLEL
CALL neighbor_list_iterator_release(ap_iterator)
DEALLOCATE (basis_set_list)
IF (calculate_forces .OR. doat) THEN
! *** If LSD, then recover alpha density and beta density ***
! *** from the total density (1) and the spin density (2) ***
IF (SIZE(matrix_p, 1) == 2) THEN
DO img = 1, nimages
CALL dbcsr_add(matrix_p(1, img)%matrix, matrix_p(2, img)%matrix, &
alpha_scalar=0.5_dp, beta_scalar=0.5_dp)
CALL dbcsr_add(matrix_p(2, img)%matrix, matrix_p(1, img)%matrix, &
alpha_scalar=-1.0_dp, beta_scalar=1.0_dp)
END DO
END IF
END IF
IF (calculate_forces) THEN
CALL get_atomic_kind_set(atomic_kind_set, atom_of_kind=atom_of_kind, kind_of=kind_of)
!$OMP DO
DO iatom = 1, natom
atom_a = atom_of_kind(iatom)
ikind = kind_of(iatom)
force(ikind)%all_potential(:, atom_a) = force(ikind)%all_potential(:, atom_a) + force_thread(:, iatom)
END DO
!$OMP END DO
END IF
IF (doat) THEN
atcore(1:natom) = atcore(1:natom) + at_thread(1:natom)
END IF
IF (calculate_forces .AND. use_virial) THEN
virial%pv_ppl = virial%pv_ppl + pv_thread
virial%pv_virial = virial%pv_virial + pv_thread
END IF
CALL timestop(handle)
END SUBROUTINE build_core_ae
! **************************************************************************************************
!> \brief ...
!> \param habd ...
!> \param pab ...
!> \param fa ...
!> \param fb ...
!> \param nder ...
!> \param la_max ...
!> \param la_min ...
!> \param npgfa ...
!> \param zeta ...
!> \param lb_max ...
!> \param lb_min ...
!> \param npgfb ...
!> \param zetb ...
!> \param rab ...
! **************************************************************************************************
SUBROUTINE verfc_force(habd, pab, fa, fb, nder, la_max, la_min, npgfa, zeta, lb_max, lb_min, npgfb, zetb, rab)
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: habd, pab
REAL(KIND=dp), DIMENSION(3), INTENT(OUT) :: fa, fb
INTEGER, INTENT(IN) :: nder, la_max, la_min, npgfa
REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: zeta
INTEGER, INTENT(IN) :: lb_max, lb_min, npgfb
REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: zetb
REAL(KIND=dp), DIMENSION(3), INTENT(IN) :: rab
INTEGER :: ic_a, ic_b, icam1, icam2, icam3, icap1, &
icap2, icap3, icax, icbm1, icbm2, &
icbm3, icbx, icoa, icob, ipgfa, ipgfb, &
na, nap, nb
INTEGER, DIMENSION(3) :: la, lb
REAL(KIND=dp) :: zax2, zbx2
fa = 0.0_dp
fb = 0.0_dp
na = ncoset(la_max)
nap = ncoset(la_max + nder)
nb = ncoset(lb_max)
DO ipgfa = 1, npgfa
zax2 = zeta(ipgfa)*2.0_dp
DO ipgfb = 1, npgfb
zbx2 = zetb(ipgfb)*2.0_dp
DO ic_a = ncoset(la_min - 1) + 1, ncoset(la_max)
la(1:3) = indco(1:3, ic_a)
icap1 = coset(la(1) + 1, la(2), la(3))
icap2 = coset(la(1), la(2) + 1, la(3))
icap3 = coset(la(1), la(2), la(3) + 1)
icam1 = coset(la(1) - 1, la(2), la(3))
icam2 = coset(la(1), la(2) - 1, la(3))
icam3 = coset(la(1), la(2), la(3) - 1)
icoa = ic_a + (ipgfa - 1)*na
icax = (ipgfa - 1)*nap
DO ic_b = ncoset(lb_min - 1) + 1, ncoset(lb_max)
lb(1:3) = indco(1:3, ic_b)
icbm1 = coset(lb(1) - 1, lb(2), lb(3))
icbm2 = coset(lb(1), lb(2) - 1, lb(3))
icbm3 = coset(lb(1), lb(2), lb(3) - 1)
icob = ic_b + (ipgfb - 1)*nb
icbx = (ipgfb - 1)*nb
fa(1) = fa(1) - pab(icoa, icob)*(-zax2*habd(icap1 + icax, icob) + &
REAL(la(1), KIND=dp)*habd(icam1 + icax, icob))
fa(2) = fa(2) - pab(icoa, icob)*(-zax2*habd(icap2 + icax, icob) + &
REAL(la(2), KIND=dp)*habd(icam2 + icax, icob))
fa(3) = fa(3) - pab(icoa, icob)*(-zax2*habd(icap3 + icax, icob) + &
REAL(la(3), KIND=dp)*habd(icam3 + icax, icob))
fb(1) = fb(1) - pab(icoa, icob)*( &
-zbx2*(habd(icap1 + icax, icob) - rab(1)*habd(ic_a + icax, icob)) + &
REAL(lb(1), KIND=dp)*habd(ic_a + icax, icbm1 + icbx))
fb(2) = fb(2) - pab(icoa, icob)*( &
-zbx2*(habd(icap2 + icax, icob) - rab(2)*habd(ic_a + icax, icob)) + &
REAL(lb(2), KIND=dp)*habd(ic_a + icax, icbm2 + icbx))
fb(3) = fb(3) - pab(icoa, icob)*( &
-zbx2*(habd(icap3 + icax, icob) - rab(3)*habd(ic_a + icax, icob)) + &
REAL(lb(3), KIND=dp)*habd(ic_a + icax, icbm3 + icbx))
END DO ! ic_b
END DO ! ic_a
END DO ! ipgfb
END DO ! ipgfa
END SUBROUTINE verfc_force
! **************************************************************************************************
!> \brief Integrals = -Z*erfc(a*r)/r
!> \param matrix_h ...
!> \param matrix_p ...
!> \param qs_kind_set ...
!> \param atomic_kind_set ...
!> \param particle_set ...
!> \param calpha ...
!> \param ccore ...
!> \param eps_core_charge ...
!> \param sab_orb ...
!> \param sac_ae ...
!> \param atcore ...
! **************************************************************************************************
SUBROUTINE build_erfc(matrix_h, matrix_p, qs_kind_set, atomic_kind_set, particle_set, &
calpha, ccore, eps_core_charge, sab_orb, sac_ae, atcore)
TYPE(dbcsr_p_type) :: matrix_h
TYPE(dbcsr_p_type), DIMENSION(:) :: matrix_p
TYPE(qs_kind_type), DIMENSION(:), POINTER :: qs_kind_set
TYPE(atomic_kind_type), DIMENSION(:), POINTER :: atomic_kind_set
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: calpha, ccore
REAL(KIND=dp), INTENT(IN) :: eps_core_charge
TYPE(neighbor_list_set_p_type), DIMENSION(:), &
POINTER :: sab_orb, sac_ae
REAL(KIND=dp), DIMENSION(:), INTENT(INOUT), &
OPTIONAL :: atcore
CHARACTER(LEN=*), PARAMETER :: routineN = 'build_erfc'
INTEGER :: handle, iatom, icol, ikind, img, irow, iset, jatom, jkind, jset, katom, kkind, &
ldai, ldsab, maxco, maxl, maxnset, maxsgf, mepos, na_plus, natom, nb_plus, ncoa, ncob, &
nij, nkind, nseta, nsetb, nthread, sgfa, sgfb, slot
INTEGER, DIMENSION(3) :: cellind
INTEGER, DIMENSION(:), POINTER :: la_max, la_min, lb_max, lb_min, npgfa, &
npgfb, nsgfa, nsgfb
INTEGER, DIMENSION(:, :), POINTER :: first_sgfa, first_sgfb
LOGICAL :: doat, found
REAL(KIND=dp) :: alpha_c, atk0, atk1, core_charge, &
core_radius, dab, dac, dbc, f0, rab2, &
rac2, rbc2, zeta_c
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: ff
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: habd, work
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: hab, pab, verf, vnuc
REAL(KIND=dp), DIMENSION(3) :: rab, rac, rbc
REAL(KIND=dp), DIMENSION(:), POINTER :: set_radius_a, set_radius_b
REAL(KIND=dp), DIMENSION(:, :), POINTER :: h_block, p_block, rpgfa, rpgfb, sphi_a, &
sphi_b, zeta, zetb
TYPE(neighbor_list_iterator_p_type), &
DIMENSION(:), POINTER :: ap_iterator
TYPE(gto_basis_set_type), POINTER :: basis_set_a, basis_set_b
TYPE(gto_basis_set_p_type), DIMENSION(:), POINTER :: basis_set_list
TYPE(all_potential_type), POINTER :: all_potential
REAL(KIND=dp), DIMENSION(SIZE(particle_set)) :: at_thread
TYPE(sgp_potential_type), POINTER :: sgp_potential
!$ INTEGER(kind=omp_lock_kind), &
!$ ALLOCATABLE, DIMENSION(:) :: locks
!$ INTEGER :: lock_num, hash, hash1, hash2
!$ INTEGER(KIND=int_8) :: iatom8
!$ INTEGER, PARAMETER :: nlock = 501
MARK_USED(int_8)
CALL timeset(routineN, handle)
nkind = SIZE(atomic_kind_set)
natom = SIZE(particle_set)
doat = PRESENT(atcore)
IF (doat) THEN
IF (SIZE(matrix_p, 1) == 2) THEN
CALL dbcsr_add(matrix_p(1)%matrix, matrix_p(2)%matrix, &
alpha_scalar=1.0_dp, beta_scalar=1.0_dp)
CALL dbcsr_add(matrix_p(2)%matrix, matrix_p(1)%matrix, &
alpha_scalar=-2.0_dp, beta_scalar=1.0_dp)
END IF
END IF
at_thread = 0.0_dp
ALLOCATE (basis_set_list(nkind))
DO ikind = 1, nkind
CALL get_qs_kind(qs_kind_set(ikind), basis_set=basis_set_a)
IF (ASSOCIATED(basis_set_a)) THEN
basis_set_list(ikind)%gto_basis_set => basis_set_a
ELSE
NULLIFY (basis_set_list(ikind)%gto_basis_set)
END IF
END DO
CALL get_qs_kind_set(qs_kind_set, &
maxco=maxco, maxlgto=maxl, maxsgf=maxsgf, maxnset=maxnset)
CALL init_orbital_pointers(maxl + 1)
ldsab = MAX(maxco, maxsgf)
ldai = ncoset(maxl + 1)
nthread = 1
!$ nthread = omp_get_max_threads()
! iterator for basis/potential list
CALL neighbor_list_iterator_create(ap_iterator, sac_ae, search=.TRUE., nthread=nthread)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP SHARED (ap_iterator, basis_set_list, &
!$OMP matrix_h, matrix_p, atomic_kind_set, qs_kind_set, particle_set, &
!$OMP sab_orb, sac_ae, nthread, ncoset, nkind, calpha, ccore, eps_core_charge, &
!$OMP slot, ldsab, maxnset, ldai, maxl, maxco, doat, locks, natom) &
!$OMP PRIVATE (ikind, jkind, iatom, jatom, rab, basis_set_a, basis_set_b, &
!$OMP first_sgfa, la_max, la_min, npgfa, nsgfa, sphi_a, &
!$OMP zeta, first_sgfb, lb_max, lb_min, npgfb, nsetb, rpgfb, set_radius_b, sphi_b, &
!$OMP zetb, zeta_c, alpha_c, core_charge, dab, irow, icol, h_block, found, iset, ncoa, &
!$OMP sgfa, jset, ncob, sgfb, nsgfb, p_block, work, pab, hab, kkind, nseta, &
!$OMP rac, dac, rbc, rab2, rac2, rbc2, dbc, na_plus, nb_plus, verf, vnuc, &
!$OMP set_radius_a, core_radius, rpgfa, mepos, &
!$OMP atk0, atk1, habd, f0, katom, cellind, img, nij, ff, &
!$OMP sgp_potential, all_potential, hash, hash1, hash2, iatom8) &
!$OMP REDUCTION (+ : at_thread )
!$OMP SINGLE
!$ ALLOCATE (locks(nlock))
!$OMP END SINGLE
!$OMP DO
!$ DO lock_num = 1, nlock
!$ call omp_init_lock(locks(lock_num))
!$ END DO
!$OMP END DO
mepos = 0
!$ mepos = omp_get_thread_num()
ALLOCATE (hab(ldsab, ldsab, maxnset*maxnset), work(ldsab, ldsab))
ALLOCATE (verf(ldai, ldai, 2*maxl + 1), vnuc(ldai, ldai, 2*maxl + 1), ff(0:2*maxl))
IF (doat) THEN
ALLOCATE (pab(maxco, maxco, maxnset*maxnset))
END IF
!$OMP DO SCHEDULE(GUIDED)
DO slot = 1, sab_orb(1)%nl_size
ikind = sab_orb(1)%nlist_task(slot)%ikind
jkind = sab_orb(1)%nlist_task(slot)%jkind
iatom = sab_orb(1)%nlist_task(slot)%iatom
jatom = sab_orb(1)%nlist_task(slot)%jatom
cellind(:) = sab_orb(1)%nlist_task(slot)%cell(:)
rab(1:3) = sab_orb(1)%nlist_task(slot)%r(1:3)
basis_set_a => basis_set_list(ikind)%gto_basis_set
IF (.NOT. ASSOCIATED(basis_set_a)) CYCLE
basis_set_b => basis_set_list(jkind)%gto_basis_set
IF (.NOT. ASSOCIATED(basis_set_b)) CYCLE
!$ iatom8 = INT(iatom - 1, int_8)*INT(natom, int_8) + INT(jatom, int_8)
!$ hash1 = INT(MOD(iatom8, INT(nlock, int_8)) + 1)
! basis ikind
first_sgfa => basis_set_a%first_sgf
la_max => basis_set_a%lmax
la_min => basis_set_a%lmin
npgfa => basis_set_a%npgf
nseta = basis_set_a%nset
nsgfa => basis_set_a%nsgf_set
rpgfa => basis_set_a%pgf_radius
set_radius_a => basis_set_a%set_radius
sphi_a => basis_set_a%sphi
zeta => basis_set_a%zet
! basis jkind
first_sgfb => basis_set_b%first_sgf
lb_max => basis_set_b%lmax
lb_min => basis_set_b%lmin
npgfb => basis_set_b%npgf
nsetb = basis_set_b%nset
nsgfb => basis_set_b%nsgf_set
rpgfb => basis_set_b%pgf_radius
set_radius_b => basis_set_b%set_radius
sphi_b => basis_set_b%sphi
zetb => basis_set_b%zet
dab = SQRT(SUM(rab*rab))
img = 1
! *** Use the symmetry of the first derivatives ***
IF (iatom == jatom) THEN
f0 = 1.0_dp
ELSE
f0 = 2.0_dp
END IF
! *** Create matrix blocks for a new matrix block column ***
IF (iatom <= jatom) THEN
irow = iatom
icol = jatom
ELSE
irow = jatom
icol = iatom
END IF
NULLIFY (h_block)
CALL dbcsr_get_block_p(matrix=matrix_h%matrix, &
row=irow, col=icol, BLOCK=h_block, found=found)
IF (doat) THEN
NULLIFY (p_block)
CALL dbcsr_get_block_p(matrix=matrix_p(1)%matrix, &
row=irow, col=icol, BLOCK=p_block, found=found)
CPASSERT(ASSOCIATED(p_block))
! *** Decontract density matrix block ***
DO iset = 1, nseta
ncoa = npgfa(iset)*ncoset(la_max(iset))
sgfa = first_sgfa(1, iset)
DO jset = 1, nsetb
ncob = npgfb(jset)*ncoset(lb_max(jset))
sgfb = first_sgfb(1, jset)
nij = jset + (iset - 1)*maxnset
! *** Decontract density matrix block ***
IF (iatom <= jatom) THEN
work(1:ncoa, 1:nsgfb(jset)) = MATMUL(sphi_a(1:ncoa, sgfa:sgfa + nsgfa(iset) - 1), &
p_block(sgfa:sgfa + nsgfa(iset) - 1, sgfb:sgfb + nsgfb(jset) - 1))
ELSE
work(1:ncoa, 1:nsgfb(jset)) = MATMUL(sphi_a(1:ncoa, sgfa:sgfa + nsgfa(iset) - 1), &
TRANSPOSE(p_block(sgfb:sgfb + nsgfb(jset) - 1, sgfa:sgfa + nsgfa(iset) - 1)))
END IF
pab(1:ncoa, 1:ncob, nij) = MATMUL(work(1:ncoa, 1:nsgfb(jset)), &
TRANSPOSE(sphi_b(1:ncob, sgfb:sgfb + nsgfb(jset) - 1)))
END DO
END DO
END IF
! loop over all kinds of atoms
hab = 0._dp
DO kkind = 1, nkind
CALL get_qs_kind(qs_kind_set(kkind), zeff=zeta_c)
alpha_c = calpha(kkind)
core_charge = ccore(kkind)
core_radius = exp_radius(0, alpha_c, eps_core_charge, core_charge)
core_radius = MAX(core_radius, 10.0_dp)
CALL nl_set_sub_iterator(ap_iterator, ikind, kkind, iatom, mepos=mepos)
DO WHILE (nl_sub_iterate(ap_iterator, mepos=mepos) == 0)
CALL get_iterator_info(ap_iterator, jatom=katom, r=rac, mepos=mepos)
dac = SQRT(SUM(rac*rac))
rbc(:) = rac(:) - rab(:)
dbc = SQRT(SUM(rbc*rbc))
IF ((MAXVAL(set_radius_a(:)) + core_radius < dac) .OR. &
(MAXVAL(set_radius_b(:)) + core_radius < dbc)) THEN
CYCLE
END IF
DO iset = 1, nseta
IF (set_radius_a(iset) + core_radius < dac) CYCLE
ncoa = npgfa(iset)*ncoset(la_max(iset))
sgfa = first_sgfa(1, iset)
DO jset = 1, nsetb
IF (set_radius_b(jset) + core_radius < dbc) CYCLE
ncob = npgfb(jset)*ncoset(lb_max(jset))
sgfb = first_sgfb(1, jset)
IF (set_radius_a(iset) + set_radius_b(jset) < dab) CYCLE
rab2 = dab*dab
rac2 = dac*dac
rbc2 = dbc*dbc
nij = jset + (iset - 1)*maxnset
IF (doat) THEN
atk0 = f0*SUM(hab(1:ncoa, 1:ncob, nij)*pab(1:ncoa, 1:ncob, nij))
END IF
!
CALL verfc( &
la_max(iset), npgfa(iset), zeta(:, iset), rpgfa(:, iset), la_min(iset), &
lb_max(jset), npgfb(jset), zetb(:, jset), rpgfb(:, jset), lb_min(jset), &
alpha_c, core_radius, zeta_c, core_charge, &
rab, rab2, rac, rac2, rbc2, hab(:, :, nij), verf, vnuc, ff(0:))
!
IF (doat) THEN
atk1 = f0*SUM(hab(1:ncoa, 1:ncob, nij)*pab(1:ncoa, 1:ncob, nij))
at_thread(katom) = at_thread(katom) + (atk1 - atk0)
END IF
END DO
END DO
END DO
END DO
! *** Contract nuclear attraction integrals
DO iset = 1, nseta
ncoa = npgfa(iset)*ncoset(la_max(iset))
sgfa = first_sgfa(1, iset)
DO jset = 1, nsetb
ncob = npgfb(jset)*ncoset(lb_max(jset))
sgfb = first_sgfb(1, jset)
nij = jset + (iset - 1)*maxnset
!$ hash2 = MOD((iset - 1)*nsetb + jset, nlock) + 1
!$ hash = MOD(hash1 + hash2, nlock) + 1
work(1:ncoa, 1:nsgfb(jset)) = MATMUL(hab(1:ncoa, 1:ncob, nij), &
sphi_b(1:ncob, sgfb:sgfb + nsgfb(jset) - 1))
!$ CALL omp_set_lock(locks(hash))
IF (iatom <= jatom) THEN
h_block(sgfa:sgfa + nsgfa(iset) - 1, sgfb:sgfb + nsgfb(jset) - 1) = &
h_block(sgfa:sgfa + nsgfa(iset) - 1, sgfb:sgfb + nsgfb(jset) - 1) + &
MATMUL(TRANSPOSE(sphi_a(1:ncoa, sgfa:sgfa + nsgfa(iset) - 1)), work(1:ncoa, 1:nsgfb(jset)))
ELSE
h_block(sgfb:sgfb + nsgfb(jset) - 1, sgfa:sgfa + nsgfa(iset) - 1) = &
h_block(sgfb:sgfb + nsgfb(jset) - 1, sgfa:sgfa + nsgfa(iset) - 1) + &
MATMUL(TRANSPOSE(work(1:ncoa, 1:nsgfb(jset))), sphi_a(1:ncoa, sgfa:sgfa + nsgfa(iset) - 1))
END IF
!$ CALL omp_unset_lock(locks(hash))
END DO
END DO
END DO
DEALLOCATE (hab, work, verf, vnuc, ff)
!$OMP DO
!$ DO lock_num = 1, nlock
!$ call omp_destroy_lock(locks(lock_num))
!$ END DO
!$OMP END DO
!$OMP SINGLE
!$ DEALLOCATE (locks)
!$OMP END SINGLE NOWAIT
!$OMP END PARALLEL
CALL neighbor_list_iterator_release(ap_iterator)
DEALLOCATE (basis_set_list)
IF (doat) THEN
! *** If LSD, then recover alpha density and beta density ***
! *** from the total density (1) and the spin density (2) ***
IF (SIZE(matrix_p, 1) == 2) THEN
CALL dbcsr_add(matrix_p(1)%matrix, matrix_p(2)%matrix, &
alpha_scalar=0.5_dp, beta_scalar=0.5_dp)
CALL dbcsr_add(matrix_p(2)%matrix, matrix_p(1)%matrix, &
alpha_scalar=-1.0_dp, beta_scalar=1.0_dp)
END IF
END IF
IF (doat) THEN
atcore(1:natom) = atcore(1:natom) + at_thread(1:natom)
END IF
CALL timestop(handle)
END SUBROUTINE build_erfc
! **************************************************************************************************
END MODULE core_ae