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commutator_rpnl.F
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commutator_rpnl.F
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!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2023 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief Calculation of the non-local pseudopotential contribution to the core Hamiltonian
!> <a|V(non-local)|b> = <a|p(l,i)>*h(i,j)*<p(l,j)|b>
!> \par History
!> - refactered from qs_core_hamiltian [Joost VandeVondele, 2008-11-01]
!> - full rewrite [jhu, 2009-01-23]
! **************************************************************************************************
MODULE commutator_rpnl
USE ai_moments, ONLY: moment
USE ai_overlap, ONLY: overlap
USE basis_set_types, ONLY: gto_basis_set_p_type,&
gto_basis_set_type
USE block_p_types, ONLY: block_p_type
USE cell_types, ONLY: cell_type
USE dbcsr_api, ONLY: dbcsr_get_block_p,&
dbcsr_p_type
USE external_potential_types, ONLY: gth_potential_p_type,&
gth_potential_type,&
sgp_potential_p_type,&
sgp_potential_type
USE kinds, ONLY: dp
USE orbital_pointers, ONLY: init_orbital_pointers,&
nco,&
ncoset
USE particle_types, ONLY: particle_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,&
get_neighbor_list_set_p,&
neighbor_list_iterate,&
neighbor_list_iterator_create,&
neighbor_list_iterator_p_type,&
neighbor_list_iterator_release,&
neighbor_list_set_p_type
USE sap_kind_types, ONLY: alist_type,&
build_sap_ints,&
clist_type,&
get_alist,&
release_sap_int,&
sap_int_type,&
sap_sort
!$ 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 = 'commutator_rpnl'
PUBLIC :: build_com_rpnl, build_com_mom_nl, build_com_nl_mag, build_com_vnl_giao
CONTAINS
! **************************************************************************************************
!> \brief ...
!> \param matrix_rv ...
!> \param qs_kind_set ...
!> \param sab_orb ...
!> \param sap_ppnl ...
!> \param eps_ppnl ...
! **************************************************************************************************
SUBROUTINE build_com_rpnl(matrix_rv, qs_kind_set, sab_orb, sap_ppnl, eps_ppnl)
TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: matrix_rv
TYPE(qs_kind_type), DIMENSION(:), POINTER :: qs_kind_set
TYPE(neighbor_list_set_p_type), DIMENSION(:), &
POINTER :: sab_orb, sap_ppnl
REAL(KIND=dp), INTENT(IN) :: eps_ppnl
CHARACTER(LEN=*), PARAMETER :: routineN = 'build_com_rpnl'
INTEGER :: handle, i, iab, iac, iatom, ibc, icol, ikind, ilist, inode, irow, iset, jatom, &
jkind, jneighbor, kac, katom, kbc, kkind, l, lc_max, lc_min, ldai, ldsab, lppnl, maxco, &
maxder, maxl, maxlgto, maxlppnl, maxppnl, maxsgf, mepos, na, nb, ncoa, ncoc, nkind, &
nlist, nneighbor, nnode, np, nppnl, nprjc, nseta, nsgfa, nthread, prjc, sgfa
INTEGER, DIMENSION(3) :: cell_b, cell_c
INTEGER, DIMENSION(:), POINTER :: la_max, la_min, npgfa, nprj_ppnl, &
nsgf_seta
INTEGER, DIMENSION(:, :), POINTER :: first_sgfa
LOGICAL :: found, gpot, ppnl_present, spot
REAL(KIND=dp) :: dac, ppnl_radius
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: ai_work, sab, work
REAL(KIND=dp), DIMENSION(1) :: rprjc, zetc
REAL(KIND=dp), DIMENSION(3) :: rab, rac
REAL(KIND=dp), DIMENSION(:), POINTER :: alpha_ppnl, set_radius_a
REAL(KIND=dp), DIMENSION(:, :), POINTER :: cprj, rpgfa, sphi_a, vprj_ppnl, x_block, &
y_block, z_block, zeta
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: achint, acint, bchint, bcint
TYPE(alist_type), POINTER :: alist_ac, alist_bc
TYPE(clist_type), POINTER :: clist
TYPE(gth_potential_p_type), DIMENSION(:), POINTER :: gpotential
TYPE(gth_potential_type), POINTER :: gth_potential
TYPE(gto_basis_set_p_type), DIMENSION(:), POINTER :: basis_set
TYPE(gto_basis_set_type), POINTER :: orb_basis_set
TYPE(neighbor_list_iterator_p_type), &
DIMENSION(:), POINTER :: nl_iterator
TYPE(sap_int_type), DIMENSION(:), POINTER :: sap_int
TYPE(sgp_potential_p_type), DIMENSION(:), POINTER :: spotential
TYPE(sgp_potential_type), POINTER :: sgp_potential
CALL timeset(routineN, handle)
ppnl_present = ASSOCIATED(sap_ppnl)
IF (ppnl_present) THEN
nkind = SIZE(qs_kind_set)
CALL get_qs_kind_set(qs_kind_set, &
maxco=maxco, &
maxlgto=maxlgto, &
maxsgf=maxsgf, &
maxlppnl=maxlppnl, &
maxppnl=maxppnl)
maxl = MAX(maxlgto, maxlppnl)
CALL init_orbital_pointers(maxl + 1)
ldsab = MAX(maxco, ncoset(maxlppnl), maxsgf, maxppnl)
ldai = ncoset(maxl + 1)
!sap_int needs to be shared as multiple threads need to access this
ALLOCATE (sap_int(nkind*nkind))
DO i = 1, nkind*nkind
NULLIFY (sap_int(i)%alist, sap_int(i)%asort, sap_int(i)%aindex)
sap_int(i)%nalist = 0
END DO
!set up direct access to basis and potential
ALLOCATE (basis_set(nkind), gpotential(nkind), spotential(nkind))
DO ikind = 1, nkind
CALL get_qs_kind(qs_kind_set(ikind), basis_set=orb_basis_set)
IF (ASSOCIATED(orb_basis_set)) THEN
basis_set(ikind)%gto_basis_set => orb_basis_set
ELSE
NULLIFY (basis_set(ikind)%gto_basis_set)
END IF
CALL get_qs_kind(qs_kind_set(ikind), gth_potential=gth_potential, &
sgp_potential=sgp_potential)
IF (ASSOCIATED(gth_potential)) THEN
gpotential(ikind)%gth_potential => gth_potential
NULLIFY (spotential(ikind)%sgp_potential)
ELSE IF (ASSOCIATED(sgp_potential)) THEN
spotential(ikind)%sgp_potential => sgp_potential
NULLIFY (gpotential(ikind)%gth_potential)
ELSE
NULLIFY (gpotential(ikind)%gth_potential)
NULLIFY (spotential(ikind)%sgp_potential)
END IF
END DO
maxder = 4
nthread = 1
!$ nthread = omp_get_max_threads()
!calculate the overlap integrals <a|p>
CALL neighbor_list_iterator_create(nl_iterator, sap_ppnl, nthread=nthread)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP SHARED (nl_iterator, basis_set, spotential, gpotential, maxder, ncoset, &
!$OMP sap_int, nkind, ldsab, ldai, nco ) &
!$OMP PRIVATE (mepos, ikind, kkind, iatom, katom, nlist, ilist, nneighbor, jneighbor, &
!$OMP cell_c, rac, iac, first_sgfa, la_max, la_min, npgfa, nseta, nsgfa, nsgf_seta, &
!$OMP sphi_a, zeta, cprj, lppnl, nppnl, nprj_ppnl, &
!$OMP clist, iset, ncoa, sgfa, prjc, work, sab, ai_work, nprjc, ppnl_radius, &
!$OMP ncoc, rpgfa, vprj_ppnl, i, l, gpot, spot, &
!$OMP set_radius_a, rprjc, dac, lc_max, lc_min, zetc, alpha_ppnl)
mepos = 0
!$ mepos = omp_get_thread_num()
ALLOCATE (sab(ldsab, ldsab, maxder), work(ldsab, ldsab, maxder))
sab = 0.0_dp
ALLOCATE (ai_work(ldai, ldai, 1))
ai_work = 0.0_dp
DO WHILE (neighbor_list_iterate(nl_iterator, mepos=mepos) == 0)
CALL get_iterator_info(nl_iterator, mepos=mepos, ikind=ikind, jkind=kkind, iatom=iatom, &
jatom=katom, nlist=nlist, ilist=ilist, nnode=nneighbor, inode=jneighbor, cell=cell_c, r=rac)
iac = ikind + nkind*(kkind - 1)
IF (.NOT. ASSOCIATED(basis_set(ikind)%gto_basis_set)) CYCLE
gpot = ASSOCIATED(gpotential(kkind)%gth_potential)
spot = ASSOCIATED(spotential(kkind)%sgp_potential)
IF ((.NOT. gpot) .AND. (.NOT. spot)) CYCLE
! get definition of basis set
first_sgfa => basis_set(ikind)%gto_basis_set%first_sgf
la_max => basis_set(ikind)%gto_basis_set%lmax
la_min => basis_set(ikind)%gto_basis_set%lmin
npgfa => basis_set(ikind)%gto_basis_set%npgf
nseta = basis_set(ikind)%gto_basis_set%nset
nsgfa = basis_set(ikind)%gto_basis_set%nsgf
nsgf_seta => basis_set(ikind)%gto_basis_set%nsgf_set
rpgfa => basis_set(ikind)%gto_basis_set%pgf_radius
set_radius_a => basis_set(ikind)%gto_basis_set%set_radius
sphi_a => basis_set(ikind)%gto_basis_set%sphi
zeta => basis_set(ikind)%gto_basis_set%zet
nsgfa = basis_set(ikind)%gto_basis_set%nsgf
! get definition of PP projectors
IF (gpot) THEN
alpha_ppnl => gpotential(kkind)%gth_potential%alpha_ppnl
cprj => gpotential(kkind)%gth_potential%cprj
lppnl = gpotential(kkind)%gth_potential%lppnl
nppnl = gpotential(kkind)%gth_potential%nppnl
nprj_ppnl => gpotential(kkind)%gth_potential%nprj_ppnl
ppnl_radius = gpotential(kkind)%gth_potential%ppnl_radius
vprj_ppnl => gpotential(kkind)%gth_potential%vprj_ppnl
ELSEIF (spot) THEN
CPABORT('SGP not implemented')
ELSE
CPABORT('PPNL unknown')
END IF
!$OMP CRITICAL(sap_int_critical)
IF (.NOT. ASSOCIATED(sap_int(iac)%alist)) THEN
sap_int(iac)%a_kind = ikind
sap_int(iac)%p_kind = kkind
sap_int(iac)%nalist = nlist
ALLOCATE (sap_int(iac)%alist(nlist))
DO i = 1, nlist
NULLIFY (sap_int(iac)%alist(i)%clist)
sap_int(iac)%alist(i)%aatom = 0
sap_int(iac)%alist(i)%nclist = 0
END DO
END IF
IF (.NOT. ASSOCIATED(sap_int(iac)%alist(ilist)%clist)) THEN
sap_int(iac)%alist(ilist)%aatom = iatom
sap_int(iac)%alist(ilist)%nclist = nneighbor
ALLOCATE (sap_int(iac)%alist(ilist)%clist(nneighbor))
DO i = 1, nneighbor
sap_int(iac)%alist(ilist)%clist(i)%catom = 0
END DO
END IF
!$OMP END CRITICAL(sap_int_critical)
dac = SQRT(SUM(rac*rac))
clist => sap_int(iac)%alist(ilist)%clist(jneighbor)
clist%catom = katom
clist%cell = cell_c
clist%rac = rac
ALLOCATE (clist%acint(nsgfa, nppnl, maxder), &
clist%achint(nsgfa, nppnl, maxder))
clist%acint = 0._dp
clist%achint = 0._dp
clist%nsgf_cnt = 0
NULLIFY (clist%sgf_list)
DO iset = 1, nseta
ncoa = npgfa(iset)*ncoset(la_max(iset))
sgfa = first_sgfa(1, iset)
work = 0._dp
prjc = 1
DO l = 0, lppnl
nprjc = nprj_ppnl(l)*nco(l)
IF (nprjc == 0) CYCLE
rprjc(1) = ppnl_radius
IF (set_radius_a(iset) + rprjc(1) < dac) CYCLE
lc_max = l + 2*(nprj_ppnl(l) - 1)
lc_min = l
zetc(1) = alpha_ppnl(l)
ncoc = ncoset(lc_max)
! Calculate the primitive overlap and dipole moment integrals
CALL overlap(la_max(iset), la_min(iset), npgfa(iset), rpgfa(:, iset), zeta(:, iset), &
lc_max, lc_min, 1, rprjc, zetc, rac, dac, sab(:, :, 1), 0, .FALSE., ai_work, ldai)
CALL moment(la_max(iset), npgfa(iset), zeta(:, iset), rpgfa(:, iset), la_min(iset), &
lc_max, 1, zetc, rprjc, 1, rac, (/0._dp, 0._dp, 0._dp/), sab(:, :, 2:4))
! *** Transformation step projector functions (cartesian->spherical) ***
DO i = 1, maxder
CALL dgemm("N", "N", ncoa, nprjc, ncoc, 1.0_dp, sab(1, 1, i), ldsab, &
cprj(1, prjc), SIZE(cprj, 1), 0.0_dp, work(1, 1, i), ldsab)
END DO
prjc = prjc + nprjc
END DO
DO i = 1, maxder
! Contraction step (basis functions)
CALL dgemm("T", "N", nsgf_seta(iset), nppnl, ncoa, 1.0_dp, sphi_a(1, sgfa), SIZE(sphi_a, 1), &
work(1, 1, i), ldsab, 0.0_dp, clist%acint(sgfa, 1, i), nsgfa)
! Multiply with interaction matrix(h)
CALL dgemm("N", "N", nsgf_seta(iset), nppnl, nppnl, 1.0_dp, clist%acint(sgfa, 1, i), nsgfa, &
vprj_ppnl(1, 1), SIZE(vprj_ppnl, 1), 0.0_dp, clist%achint(sgfa, 1, i), nsgfa)
END DO
END DO
clist%maxac = MAXVAL(ABS(clist%acint(:, :, 1)))
clist%maxach = MAXVAL(ABS(clist%achint(:, :, 1)))
END DO
DEALLOCATE (sab, ai_work, work)
!$OMP END PARALLEL
CALL neighbor_list_iterator_release(nl_iterator)
! *** Set up a sorting index
CALL sap_sort(sap_int)
! *** All integrals needed have been calculated and stored in sap_int
! *** We now calculate the Hamiltonian matrix elements
CALL neighbor_list_iterator_create(nl_iterator, sab_orb, nthread=nthread)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP SHARED (nl_iterator, basis_set, matrix_rv, &
!$OMP sap_int, nkind, eps_ppnl ) &
!$OMP PRIVATE (mepos, ikind, jkind, iatom, jatom, nlist, ilist, nnode, inode, cell_b, rab, &
!$OMP iab, irow, icol, x_block, y_block, z_block, &
!$OMP found, iac, ibc, alist_ac, alist_bc, acint, bcint, &
!$OMP achint, bchint, na, np, nb, katom, rac, kkind, kac, kbc, i)
mepos = 0
!$ mepos = omp_get_thread_num()
DO WHILE (neighbor_list_iterate(nl_iterator, mepos=mepos) == 0)
CALL get_iterator_info(nl_iterator, mepos=mepos, ikind=ikind, jkind=jkind, iatom=iatom, &
jatom=jatom, nlist=nlist, ilist=ilist, nnode=nnode, inode=inode, cell=cell_b, r=rab)
IF (.NOT. ASSOCIATED(basis_set(ikind)%gto_basis_set)) CYCLE
IF (.NOT. ASSOCIATED(basis_set(jkind)%gto_basis_set)) CYCLE
iab = ikind + nkind*(jkind - 1)
! *** Create matrix blocks for a new matrix block column ***
IF (iatom <= jatom) THEN
irow = iatom
icol = jatom
ELSE
irow = jatom
icol = iatom
END IF
CALL dbcsr_get_block_p(matrix_rv(1)%matrix, irow, icol, x_block, found)
CALL dbcsr_get_block_p(matrix_rv(2)%matrix, irow, icol, y_block, found)
CALL dbcsr_get_block_p(matrix_rv(3)%matrix, irow, icol, z_block, found)
! loop over all kinds for projector atom
IF (ASSOCIATED(x_block) .AND. ASSOCIATED(y_block) .AND. ASSOCIATED(z_block)) THEN
DO kkind = 1, nkind
iac = ikind + nkind*(kkind - 1)
ibc = jkind + nkind*(kkind - 1)
IF (.NOT. ASSOCIATED(sap_int(iac)%alist)) CYCLE
IF (.NOT. ASSOCIATED(sap_int(ibc)%alist)) CYCLE
CALL get_alist(sap_int(iac), alist_ac, iatom)
CALL get_alist(sap_int(ibc), alist_bc, jatom)
IF (.NOT. ASSOCIATED(alist_ac)) CYCLE
IF (.NOT. ASSOCIATED(alist_bc)) CYCLE
DO kac = 1, alist_ac%nclist
DO kbc = 1, alist_bc%nclist
IF (alist_ac%clist(kac)%catom /= alist_bc%clist(kbc)%catom) CYCLE
IF (ALL(cell_b + alist_bc%clist(kbc)%cell - alist_ac%clist(kac)%cell == 0)) THEN
IF (alist_ac%clist(kac)%maxac*alist_bc%clist(kbc)%maxach < eps_ppnl) CYCLE
acint => alist_ac%clist(kac)%acint
bcint => alist_bc%clist(kbc)%acint
achint => alist_ac%clist(kac)%achint
bchint => alist_bc%clist(kbc)%achint
na = SIZE(acint, 1)
np = SIZE(acint, 2)
nb = SIZE(bcint, 1)
!$OMP CRITICAL(h_block_critical)
IF (iatom <= jatom) THEN
! Vnl*r
CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 1), na, &
bcint(1, 1, 2), nb, 1.0_dp, x_block, SIZE(x_block, 1))
CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 1), na, &
bcint(1, 1, 3), nb, 1.0_dp, y_block, SIZE(y_block, 1))
CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 1), na, &
bcint(1, 1, 4), nb, 1.0_dp, z_block, SIZE(z_block, 1))
! -r*Vnl
CALL dgemm("N", "T", na, nb, np, -1._dp, achint(1, 1, 2), na, &
bcint(1, 1, 1), nb, 1.0_dp, x_block, SIZE(x_block, 1))
CALL dgemm("N", "T", na, nb, np, -1._dp, achint(1, 1, 3), na, &
bcint(1, 1, 1), nb, 1.0_dp, y_block, SIZE(y_block, 1))
CALL dgemm("N", "T", na, nb, np, -1._dp, achint(1, 1, 4), na, &
bcint(1, 1, 1), nb, 1.0_dp, z_block, SIZE(z_block, 1))
ELSE
! Vnl*r
CALL dgemm("N", "T", nb, na, np, 1.0_dp, bchint(1, 1, 2), nb, &
acint(1, 1, 1), na, 1.0_dp, x_block, SIZE(x_block, 1))
CALL dgemm("N", "T", nb, na, np, 1.0_dp, bchint(1, 1, 3), nb, &
acint(1, 1, 1), na, 1.0_dp, y_block, SIZE(y_block, 1))
CALL dgemm("N", "T", nb, na, np, 1.0_dp, bchint(1, 1, 4), nb, &
acint(1, 1, 1), na, 1.0_dp, z_block, SIZE(z_block, 1))
! -r*Vnl
CALL dgemm("N", "T", nb, na, np, -1.0_dp, bchint(1, 1, 1), nb, &
acint(1, 1, 2), na, 1.0_dp, x_block, SIZE(x_block, 1))
CALL dgemm("N", "T", nb, na, np, -1.0_dp, bchint(1, 1, 1), nb, &
acint(1, 1, 3), na, 1.0_dp, y_block, SIZE(y_block, 1))
CALL dgemm("N", "T", nb, na, np, -1.0_dp, bchint(1, 1, 1), nb, &
acint(1, 1, 4), na, 1.0_dp, z_block, SIZE(z_block, 1))
END IF
!$OMP END CRITICAL(h_block_critical)
EXIT ! We have found a match and there can be only one single match
END IF
END DO
END DO
END DO
END IF
END DO
!$OMP END PARALLEL
CALL neighbor_list_iterator_release(nl_iterator)
CALL release_sap_int(sap_int)
DEALLOCATE (basis_set, gpotential, spotential)
END IF !ppnl_present
CALL timestop(handle)
END SUBROUTINE build_com_rpnl
! **************************************************************************************************
!> \brief Calculate [r,Vnl] (matrix_rv), r x [r,Vnl] (matrix_rxrv)
!> or [rr,Vnl] (matrix_rrv) in AO basis.
!> Reference point is required for the two latter options
!> Update: Calculate rxVnlxr (matrix_rvr) and rxrxVnl + Vnlxrxr (matrix_rrv_vrr)
!> in AO basis. Added in the first place for current correction in
!> the VG formalism (first order wrt vector potential).
!> \param qs_kind_set ...
!> \param sab_all ...
!> \param sap_ppnl ...
!> \param eps_ppnl ...
!> \param particle_set ...
!> \param cell ...
!> \param matrix_rv ...
!> \param matrix_rxrv ...
!> \param matrix_rrv ...
!> \param matrix_rvr ...
!> \param matrix_rrv_vrr ...
!> \param matrix_r_rxvr ...
!> \param matrix_rxvr_r ...
!> \param matrix_r_doublecom ...
!> \param pseudoatom ...
!> \param ref_point ...
! **************************************************************************************************
SUBROUTINE build_com_mom_nl(qs_kind_set, sab_all, sap_ppnl, eps_ppnl, particle_set, cell, matrix_rv, matrix_rxrv, &
matrix_rrv, matrix_rvr, matrix_rrv_vrr, matrix_r_rxvr, matrix_rxvr_r, matrix_r_doublecom, pseudoatom, ref_point)
TYPE(qs_kind_type), DIMENSION(:), INTENT(IN), &
POINTER :: qs_kind_set
TYPE(neighbor_list_set_p_type), DIMENSION(:), &
INTENT(IN), POINTER :: sab_all, sap_ppnl
REAL(KIND=dp), INTENT(IN) :: eps_ppnl
TYPE(particle_type), DIMENSION(:), INTENT(IN), &
POINTER :: particle_set
TYPE(cell_type), INTENT(IN), POINTER :: cell
TYPE(dbcsr_p_type), DIMENSION(:), INTENT(INOUT), &
OPTIONAL :: matrix_rv, matrix_rxrv, matrix_rrv, &
matrix_rvr, matrix_rrv_vrr
TYPE(dbcsr_p_type), DIMENSION(:, :), &
INTENT(INOUT), OPTIONAL :: matrix_r_rxvr, matrix_rxvr_r, &
matrix_r_doublecom
INTEGER, INTENT(in), OPTIONAL :: pseudoatom
REAL(KIND=dp), DIMENSION(3), INTENT(IN), OPTIONAL :: ref_point
CHARACTER(LEN=*), PARAMETER :: routineN = 'build_com_mom_nl'
INTEGER, PARAMETER :: i_x = 2, i_xx = 5, i_xy = 6, i_xz = 7, i_y = 3, i_yx = i_xy, i_yy = 8, &
i_yz = 9, i_z = 4, i_zx = i_xz, i_zy = i_yz, i_zz = 10
INTEGER :: handle, i, iab, iac, iatom, ibc, icol, &
ikind, ind, ind2, irow, jatom, jkind, &
kac, kbc, kkind, na, natom, nb, nkind, &
np, order, slot
INTEGER, DIMENSION(3) :: cell_b
LOGICAL :: asso_r_doublecom, asso_r_rxvr, asso_rrv, asso_rrv_vrr, asso_rv, asso_rvr, &
asso_rxrv, asso_rxvr_r, do_symmetric, found, go, my_r_doublecom, my_r_rxvr, my_ref, &
my_rrv, my_rrv_vrr, my_rv, my_rvr, my_rxrv, my_rxvr_r, periodic, ppnl_present
REAL(KIND=dp), DIMENSION(3) :: rab, rf
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: achint, acint, bchint, bcint
TYPE(alist_type), POINTER :: alist_ac, alist_bc
TYPE(block_p_type), ALLOCATABLE, DIMENSION(:) :: blocks_rrv, blocks_rrv_vrr, blocks_rv, &
blocks_rvr, blocks_rxrv
TYPE(block_p_type), ALLOCATABLE, DIMENSION(:, :) :: blocks_r_doublecom, blocks_r_rxvr, &
blocks_rxvr_r
TYPE(gto_basis_set_p_type), ALLOCATABLE, &
DIMENSION(:) :: basis_set
TYPE(gto_basis_set_type), POINTER :: orb_basis_set
TYPE(sap_int_type), DIMENSION(:), POINTER :: sap_int
!$ INTEGER(kind=omp_lock_kind), &
!$ ALLOCATABLE, DIMENSION(:) :: locks
!$ INTEGER :: lock_num, hash
!$ INTEGER, PARAMETER :: nlock = 501
ppnl_present = ASSOCIATED(sap_ppnl)
IF (.NOT. ppnl_present) RETURN
CALL timeset(routineN, handle)
my_r_doublecom = .FALSE.
my_r_rxvr = .FALSE.
my_rxvr_r = .FALSE.
my_rxrv = .FALSE.
my_rrv = .FALSE.
my_rv = .FALSE.
my_rvr = .FALSE.
my_rrv_vrr = .FALSE.
IF (PRESENT(matrix_r_doublecom)) my_r_doublecom = .TRUE.
IF (PRESENT(matrix_r_rxvr)) my_r_rxvr = .TRUE.
IF (PRESENT(matrix_rxvr_r)) my_rxvr_r = .TRUE.
IF (PRESENT(matrix_rxrv)) my_rxrv = .TRUE.
IF (PRESENT(matrix_rrv)) my_rrv = .TRUE.
IF (PRESENT(matrix_rv)) my_rv = .TRUE.
IF (PRESENT(matrix_rvr)) my_rvr = .TRUE.
IF (PRESENT(matrix_rrv_vrr)) my_rrv_vrr = .TRUE.
IF (.NOT. (my_rv .OR. my_rxrv .OR. my_rrv .OR. my_rvr .OR. my_rrv_vrr .OR. my_r_rxvr .OR. my_rxvr_r .OR. my_r_doublecom)) THEN
CPABORT('No dbcsr matrix provided for commutator calculation!')
END IF
natom = SIZE(particle_set)
IF (my_rxrv .OR. my_rrv .OR. my_r_rxvr .OR. my_rxvr_r .OR. my_r_doublecom) THEN
order = 2
CPASSERT(PRESENT(ref_point)) ! need reference point for r x [r,Vnl] and [rr,Vnl]
ELSE IF (my_rvr .OR. my_rrv_vrr) THEN
order = 2
ELSE
order = 1
END IF
! When we want the double commutator [[Vnl, r], r], we also want to fix the pseudoatom
IF (my_r_doublecom) THEN
CPASSERT(PRESENT(pseudoatom))
END IF
periodic = ANY(cell%perd > 0)
my_ref = .FALSE.
IF (PRESENT(ref_point)) THEN
IF (.NOT. periodic) THEN
rf = ref_point
my_ref = .TRUE.
ELSE ! use my_ref = False in periodic case, corresponds to distributed ref point
IF (order .GT. 1) THEN
CPWARN("Not clear how to define reference point for order > 1 in periodic cells.")
END IF
END IF
END IF
nkind = SIZE(qs_kind_set)
!sap_int needs to be shared as multiple threads need to access this
NULLIFY (sap_int)
ALLOCATE (sap_int(nkind*nkind))
DO i = 1, nkind*nkind
NULLIFY (sap_int(i)%alist, sap_int(i)%asort, sap_int(i)%aindex)
sap_int(i)%nalist = 0
END DO
IF (my_ref) THEN
! calculate integrals <a|x^n|p>
CALL build_sap_ints(sap_int, sap_ppnl, qs_kind_set, order, moment_mode=.TRUE., refpoint=rf, &
particle_set=particle_set, cell=cell)
ELSE
CALL build_sap_ints(sap_int, sap_ppnl, qs_kind_set, order, moment_mode=.TRUE.)
END IF
! *** Set up a sorting index
CALL sap_sort(sap_int)
ALLOCATE (basis_set(nkind))
DO ikind = 1, nkind
CALL get_qs_kind(qs_kind_set(ikind), basis_set=orb_basis_set)
IF (ASSOCIATED(orb_basis_set)) THEN
basis_set(ikind)%gto_basis_set => orb_basis_set
ELSE
NULLIFY (basis_set(ikind)%gto_basis_set)
END IF
END DO
! *** All integrals needed have been calculated and stored in sap_int
! *** We now calculate the commutator matrix elements
CALL get_neighbor_list_set_p(neighbor_list_sets=sab_all, symmetric=do_symmetric)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP SHARED (basis_set, matrix_rv, matrix_rxrv, matrix_rrv, &
!$OMP matrix_rvr, matrix_rrv_vrr, matrix_r_doublecom, &
!$OMP sap_int, natom, nkind, eps_ppnl, locks, sab_all, &
!$OMP my_rv, my_rxrv, my_rrv, my_rvr, my_rrv_vrr, &
!$OMP my_r_doublecom, &
!$OMP matrix_r_rxvr, matrix_rxvr_r, my_r_rxvr, my_rxvr_r, &
!$OMP pseudoatom, do_symmetric) &
!$OMP PRIVATE (ikind, jkind, iatom, jatom, cell_b, rab, &
!$OMP iab, irow, icol, &
!$OMP blocks_rv, blocks_rxrv, blocks_rrv, blocks_rvr, blocks_rrv_vrr, &
!$OMP blocks_r_rxvr, blocks_rxvr_r, blocks_r_doublecom, &
!$OMP found, iac, ibc, alist_ac, alist_bc, &
!$OMP na, np, nb, kkind, kac, kbc, i, &
!$OMP go, asso_rv, asso_rxrv, asso_rrv, asso_rvr, asso_rrv_vrr, &
!$OMP asso_r_rxvr, asso_rxvr_r, asso_r_doublecom, hash, &
!$OMP acint, achint, bcint, bchint)
!$OMP SINGLE
!$ ALLOCATE (locks(nlock))
!$OMP END SINGLE
!$OMP DO
!$ DO lock_num = 1, nlock
!$ call omp_init_lock(locks(lock_num))
!$ END DO
!$OMP END DO
!$OMP DO SCHEDULE(GUIDED)
DO slot = 1, sab_all(1)%nl_size
ikind = sab_all(1)%nlist_task(slot)%ikind
jkind = sab_all(1)%nlist_task(slot)%jkind
iatom = sab_all(1)%nlist_task(slot)%iatom
jatom = sab_all(1)%nlist_task(slot)%jatom
cell_b(:) = sab_all(1)%nlist_task(slot)%cell(:)
rab(1:3) = sab_all(1)%nlist_task(slot)%r(1:3)
IF (.NOT. ASSOCIATED(basis_set(ikind)%gto_basis_set)) CYCLE
IF (.NOT. ASSOCIATED(basis_set(jkind)%gto_basis_set)) CYCLE
iab = ikind + nkind*(jkind - 1)
IF (do_symmetric) THEN
IF (iatom <= jatom) THEN
irow = iatom
icol = jatom
ELSE
irow = jatom
icol = iatom
END IF
ELSE
irow = iatom
icol = jatom
END IF
! allocate blocks
IF (my_rv) THEN
ALLOCATE (blocks_rv(3))
END IF
IF (my_rxrv) THEN
ALLOCATE (blocks_rxrv(3))
END IF
IF (my_rrv) THEN
ALLOCATE (blocks_rrv(6))
END IF
IF (my_rvr) THEN
ALLOCATE (blocks_rvr(6))
END IF
IF (my_rrv_vrr) THEN
ALLOCATE (blocks_rrv_vrr(6))
END IF
IF (my_r_rxvr) THEN
ALLOCATE (blocks_r_rxvr(3, 3))
END IF
IF (my_rxvr_r) THEN
ALLOCATE (blocks_rxvr_r(3, 3))
END IF
IF (my_r_doublecom) THEN
ALLOCATE (blocks_r_doublecom(3, 3))
END IF
! get blocks
IF (my_rv) THEN
DO ind = 1, 3
CALL dbcsr_get_block_p(matrix_rv(ind)%matrix, irow, icol, blocks_rv(ind)%block, found)
END DO
END IF
IF (my_rxrv) THEN
DO ind = 1, 3
CALL dbcsr_get_block_p(matrix_rxrv(ind)%matrix, irow, icol, blocks_rxrv(ind)%block, found)
blocks_rxrv(ind)%block(:, :) = 0._dp
END DO
END IF
IF (my_rrv) THEN
DO ind = 1, 6
CALL dbcsr_get_block_p(matrix_rrv(ind)%matrix, irow, icol, blocks_rrv(ind)%block, found)
END DO
END IF
IF (my_rvr) THEN
DO ind = 1, 6
CALL dbcsr_get_block_p(matrix_rvr(ind)%matrix, irow, icol, blocks_rvr(ind)%block, found)
END DO
END IF
IF (my_rrv_vrr) THEN
DO ind = 1, 6
CALL dbcsr_get_block_p(matrix_rrv_vrr(ind)%matrix, irow, icol, blocks_rrv_vrr(ind)%block, found)
END DO
END IF
IF (my_r_rxvr) THEN
DO ind = 1, 3
DO ind2 = 1, 3
CALL dbcsr_get_block_p(matrix_r_rxvr(ind, ind2)%matrix, irow, icol, &
blocks_r_rxvr(ind, ind2)%block, found)
blocks_r_rxvr(ind, ind2)%block(:, :) = 0._dp
END DO
END DO
END IF
IF (my_rxvr_r) THEN
DO ind = 1, 3
DO ind2 = 1, 3
CALL dbcsr_get_block_p(matrix_rxvr_r(ind, ind2)%matrix, irow, icol, &
blocks_rxvr_r(ind, ind2)%block, found)
blocks_rxvr_r(ind, ind2)%block(:, :) = 0._dp
END DO
END DO
END IF
IF (my_r_doublecom) THEN
DO ind = 1, 3
DO ind2 = 1, 3
CALL dbcsr_get_block_p(matrix_r_doublecom(ind, ind2)%matrix, irow, icol, &
blocks_r_doublecom(ind, ind2)%block, found)
blocks_r_doublecom(ind, ind2)%block(:, :) = 0._dp
END DO
END DO
END IF
! check whether all blocks are associated
go = .TRUE.
IF (my_rv) THEN
asso_rv = (ASSOCIATED(blocks_rv(1)%block) .AND. ASSOCIATED(blocks_rv(2)%block) .AND. &
ASSOCIATED(blocks_rv(3)%block))
go = go .AND. asso_rv
END IF
IF (my_rxrv) THEN
asso_rxrv = (ASSOCIATED(blocks_rxrv(1)%block) .AND. ASSOCIATED(blocks_rxrv(2)%block) .AND. &
ASSOCIATED(blocks_rxrv(3)%block))
go = go .AND. asso_rxrv
END IF
IF (my_rrv) THEN
asso_rrv = (ASSOCIATED(blocks_rrv(1)%block) .AND. ASSOCIATED(blocks_rrv(2)%block) .AND. &
ASSOCIATED(blocks_rrv(3)%block) .AND. ASSOCIATED(blocks_rrv(4)%block) .AND. &
ASSOCIATED(blocks_rrv(5)%block) .AND. ASSOCIATED(blocks_rrv(6)%block))
go = go .AND. asso_rrv
END IF
IF (my_rvr) THEN
asso_rvr = (ASSOCIATED(blocks_rvr(1)%block) .AND. ASSOCIATED(blocks_rvr(2)%block) .AND. &
ASSOCIATED(blocks_rvr(3)%block) .AND. ASSOCIATED(blocks_rvr(4)%block) .AND. &
ASSOCIATED(blocks_rvr(5)%block) .AND. ASSOCIATED(blocks_rvr(6)%block))
go = go .AND. asso_rvr
END IF
IF (my_rrv_vrr) THEN
asso_rrv_vrr = (ASSOCIATED(blocks_rrv_vrr(1)%block) .AND. ASSOCIATED(blocks_rrv_vrr(2)%block) .AND. &
ASSOCIATED(blocks_rrv_vrr(3)%block) .AND. ASSOCIATED(blocks_rrv_vrr(4)%block) .AND. &
ASSOCIATED(blocks_rrv_vrr(5)%block) .AND. ASSOCIATED(blocks_rrv_vrr(6)%block))
go = go .AND. asso_rrv_vrr
END IF
IF (my_r_rxvr) THEN
asso_r_rxvr = .TRUE.
DO ind = 1, 3
DO ind2 = 1, 3
asso_r_rxvr = asso_r_rxvr .AND. ASSOCIATED(blocks_r_rxvr(ind, ind2)%block)
END DO
END DO
go = go .AND. asso_r_rxvr
END IF
IF (my_rxvr_r) THEN
asso_rxvr_r = .TRUE.
DO ind = 1, 3
DO ind2 = 1, 3
asso_rxvr_r = asso_rxvr_r .AND. ASSOCIATED(blocks_rxvr_r(ind, ind2)%block)
END DO
END DO
go = go .AND. asso_rxvr_r
END IF
IF (my_r_doublecom) THEN
asso_r_doublecom = .TRUE.
DO ind = 1, 3
DO ind2 = 1, 3
asso_r_doublecom = asso_r_doublecom .AND. ASSOCIATED(blocks_r_doublecom(ind, ind2)%block)
END DO
END DO
go = go .AND. asso_r_doublecom
END IF
! loop over all kinds for projector atom
! < iatom | katom > h < katom | jatom >
IF (go) THEN
DO kkind = 1, nkind
iac = ikind + nkind*(kkind - 1)
ibc = jkind + nkind*(kkind - 1)
IF (.NOT. ASSOCIATED(sap_int(iac)%alist)) CYCLE
IF (.NOT. ASSOCIATED(sap_int(ibc)%alist)) CYCLE
CALL get_alist(sap_int(iac), alist_ac, iatom)
CALL get_alist(sap_int(ibc), alist_bc, jatom)
IF (.NOT. ASSOCIATED(alist_ac)) CYCLE
IF (.NOT. ASSOCIATED(alist_bc)) CYCLE
DO kac = 1, alist_ac%nclist
DO kbc = 1, alist_bc%nclist
IF (alist_ac%clist(kac)%catom /= alist_bc%clist(kbc)%catom) CYCLE
IF (PRESENT(pseudoatom)) THEN
IF (alist_ac%clist(kac)%catom /= pseudoatom) CYCLE
END IF
IF (ALL(cell_b + alist_bc%clist(kbc)%cell - alist_ac%clist(kac)%cell == 0)) THEN
IF (alist_ac%clist(kac)%maxac*alist_bc%clist(kbc)%maxach < eps_ppnl) CYCLE
acint => alist_ac%clist(kac)%acint
bcint => alist_bc%clist(kbc)%acint
achint => alist_ac%clist(kac)%achint
bchint => alist_bc%clist(kbc)%achint
na = SIZE(acint, 1)
np = SIZE(acint, 2)
nb = SIZE(bcint, 1)
!$ hash = MOD((iatom - 1)*natom + jatom, nlock) + 1
!$ CALL omp_set_lock(locks(hash))
IF (my_rv) THEN
! r*Vnl
! with LAPACK
! CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 2), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rv(1)%block, SIZE(blocks_rv(1)%block, 1)) ! xV
! CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 3), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rv(2)%block, SIZE(blocks_rv(2)%block, 1)) ! yV
! CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 4), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rv(3)%block, SIZE(blocks_rv(3)%block, 1)) ! zV
IF (iatom <= jatom) THEN
! with MATMUL
blocks_rv(1)%block(1:na, 1:nb) = blocks_rv(1)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 2), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! xV
blocks_rv(2)%block(1:na, 1:nb) = blocks_rv(2)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 3), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! yV
blocks_rv(3)%block(1:na, 1:nb) = blocks_rv(3)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 4), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! zV
ELSE
blocks_rv(1)%block(1:nb, 1:na) = blocks_rv(1)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 2), TRANSPOSE(acint(1:na, 1:np, 1)))
blocks_rv(2)%block(1:nb, 1:na) = blocks_rv(2)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 3), TRANSPOSE(acint(1:na, 1:np, 1)))
blocks_rv(3)%block(1:nb, 1:na) = blocks_rv(3)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 4), TRANSPOSE(acint(1:na, 1:np, 1)))
END IF
! -Vnl r
! with LAPACK
! CALL dgemm("N", "T", na, nb, np, -1._dp, achint(1, 1, 1), na, &
! bcint(1, 1, 2), nb, 1.0_dp, blocks_rv(1)%block, SIZE(blocks_rv(1)%block, 1)) ! -Vx
! CALL dgemm("N", "T", na, nb, np, -1._dp, achint(1, 1, 1), na, &
! bcint(1, 1, 3), nb, 1.0_dp, blocks_rv(2)%block, SIZE(blocks_rv(2)%block, 1)) ! -Vy
! CALL dgemm("N", "T", na, nb, np, -1._dp, achint(1, 1, 1), na, &
! bcint(1, 1, 4), nb, 1.0_dp, blocks_rv(3)%block, SIZE(blocks_rv(3)%block, 1)) ! -Vz
! with MATMUL
IF (iatom <= jatom) THEN
blocks_rv(1)%block(1:na, 1:nb) = blocks_rv(1)%block(1:na, 1:nb) - &
MATMUL(achint(1:na, 1:np, 1), TRANSPOSE(bcint(1:nb, 1:np, 2))) ! -Vx
blocks_rv(2)%block(1:na, 1:nb) = blocks_rv(2)%block(1:na, 1:nb) - &
MATMUL(achint(1:na, 1:np, 1), TRANSPOSE(bcint(1:nb, 1:np, 3))) ! -Vy
blocks_rv(3)%block(1:na, 1:nb) = blocks_rv(3)%block(1:na, 1:nb) - &
MATMUL(achint(1:na, 1:np, 1), TRANSPOSE(bcint(1:nb, 1:np, 4))) ! -Vz
ELSE
blocks_rv(1)%block(1:nb, 1:na) = blocks_rv(1)%block(1:nb, 1:na) - &
MATMUL(bchint(1:nb, 1:np, 1), TRANSPOSE(acint(1:na, 1:np, 2)))
blocks_rv(2)%block(1:nb, 1:na) = blocks_rv(2)%block(1:nb, 1:na) - &
MATMUL(bchint(1:nb, 1:np, 1), TRANSPOSE(acint(1:na, 1:np, 3)))
blocks_rv(3)%block(1:nb, 1:na) = blocks_rv(3)%block(1:nb, 1:na) - &
MATMUL(bchint(1:nb, 1:np, 1), TRANSPOSE(acint(1:na, 1:np, 4)))
END IF
END IF
IF (my_rxrv) THEN
! x-component (y [z,Vnl] - z [y, Vnl])
! with LAPACK
! CALL dgemm("N", "T", na, nb, np, 1.0_dp, achint(1, 1, 9), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rxrv(1)%block, SIZE(blocks_rxrv(1)%block, 1)) ! yzV
! CALL dgemm("N", "T", na, nb, np, -1.0_dp, achint(1, 1, 3), na, &
! bcint(1, 1, 4), nb, 1.0_dp, blocks_rxrv(1)%block, SIZE(blocks_rxrv(1)%block, 1)) ! -yVz
! CALL dgemm("N", "T", na, nb, np, -1.0_dp, achint(1, 1, 9), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rxrv(1)%block, SIZE(blocks_rxrv(1)%block, 1)) ! -zyV
! CALL dgemm("N", "T", na, nb, np, 1.0_dp, achint(1, 1, 4), na, &
! bcint(1, 1, 3), nb, 1.0_dp, blocks_rxrv(1)%block, SIZE(blocks_rxrv(1)%block, 1)) ! zVy
! with MATMUL
IF (iatom <= jatom) THEN
blocks_rxrv(1)%block(1:na, 1:nb) = blocks_rxrv(1)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 9), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! yzV
blocks_rxrv(1)%block(1:na, 1:nb) = blocks_rxrv(1)%block(1:na, 1:nb) - &
MATMUL(achint(1:na, 1:np, 3), TRANSPOSE(bcint(1:nb, 1:np, 4))) ! -yVz
blocks_rxrv(1)%block(1:na, 1:nb) = blocks_rxrv(1)%block(1:na, 1:nb) - &
MATMUL(achint(1:na, 1:np, 9), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! -zyV
blocks_rxrv(1)%block(1:na, 1:nb) = blocks_rxrv(1)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 4), TRANSPOSE(bcint(1:nb, 1:np, 3))) ! zVy
ELSE
blocks_rxrv(1)%block(1:nb, 1:na) = blocks_rxrv(1)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 9), TRANSPOSE(acint(1:na, 1:np, 1))) ! yzV
blocks_rxrv(1)%block(1:nb, 1:na) = blocks_rxrv(1)%block(1:nb, 1:na) - &
MATMUL(bchint(1:nb, 1:np, 3), TRANSPOSE(acint(1:na, 1:np, 4))) ! -yVz
blocks_rxrv(1)%block(1:nb, 1:na) = blocks_rxrv(1)%block(1:nb, 1:na) - &
MATMUL(bchint(1:nb, 1:np, 9), TRANSPOSE(acint(1:na, 1:np, 1))) ! -zyV
blocks_rxrv(1)%block(1:nb, 1:na) = blocks_rxrv(1)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 4), TRANSPOSE(acint(1:na, 1:np, 3))) ! zVy
END IF
! y-component (z [x,Vnl] - x [z, Vnl])
! with LAPACK
! CALL dgemm("N", "T", na, nb, np, 1.0_dp, achint(1, 1, 7), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rxrv(2)%block, SIZE(blocks_rxrv(2)%block, 1)) ! zxV
! CALL dgemm("N", "T", na, nb, np, -1.0_dp, achint(1, 1, 4), na, &
! bcint(1, 1, 2), nb, 1.0_dp, blocks_rxrv(2)%block, SIZE(blocks_rxrv(2)%block, 1)) ! -zVx
! CALL dgemm("N", "T", na, nb, np, -1.0_dp, achint(1, 1, 7), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rxrv(2)%block, SIZE(blocks_rxrv(2)%block, 1)) ! -xzV
! CALL dgemm("N", "T", na, nb, np, 1.0_dp, achint(1, 1, 2), na, &
! bcint(1, 1, 4), nb, 1.0_dp, blocks_rxrv(2)%block, SIZE(blocks_rxrv(2)%block, 1)) ! xVz
! with MATMUL
IF (iatom <= jatom) THEN
blocks_rxrv(2)%block(1:na, 1:nb) = blocks_rxrv(2)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 7), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! zxV
blocks_rxrv(2)%block(1:na, 1:nb) = blocks_rxrv(2)%block(1:na, 1:nb) - &
MATMUL(achint(1:na, 1:np, 4), TRANSPOSE(bcint(1:nb, 1:np, 2))) ! -zVx
blocks_rxrv(2)%block(1:na, 1:nb) = blocks_rxrv(2)%block(1:na, 1:nb) - &
MATMUL(achint(1:na, 1:np, 7), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! -xzV
blocks_rxrv(2)%block(1:na, 1:nb) = blocks_rxrv(2)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 2), TRANSPOSE(bcint(1:nb, 1:np, 4))) ! xVz
ELSE
blocks_rxrv(2)%block(1:nb, 1:na) = blocks_rxrv(2)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 7), TRANSPOSE(acint(1:na, 1:np, 1))) ! zxV
blocks_rxrv(2)%block(1:nb, 1:na) = blocks_rxrv(2)%block(1:nb, 1:na) - &
MATMUL(bchint(1:nb, 1:np, 4), TRANSPOSE(acint(1:na, 1:np, 2))) ! -zVx
blocks_rxrv(2)%block(1:nb, 1:na) = blocks_rxrv(2)%block(1:nb, 1:na) - &
MATMUL(bchint(1:nb, 1:np, 7), TRANSPOSE(acint(1:na, 1:np, 1))) ! -xzV
blocks_rxrv(2)%block(1:nb, 1:na) = blocks_rxrv(2)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 2), TRANSPOSE(acint(1:na, 1:np, 4))) ! xVz
END IF
! z-component (x [y,Vnl] - y [x, Vnl])
! with LAPACK
! CALL dgemm("N", "T", na, nb, np, 1.0_dp, achint(1, 1, 6), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rxrv(3)%block, SIZE(blocks_rxrv(3)%block, 1)) ! xyV
! CALL dgemm("N", "T", na, nb, np, -1.0_dp, achint(1, 1, 2), na, &
! bcint(1, 1, 3), nb, 1.0_dp, blocks_rxrv(3)%block, SIZE(blocks_rxrv(3)%block, 1)) ! -xVy
! CALL dgemm("N", "T", na, nb, np, -1.0_dp, achint(1, 1, 6), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rxrv(3)%block, SIZE(blocks_rxrv(3)%block, 1)) ! -yxV
! CALL dgemm("N", "T", na, nb, np, 1.0_dp, achint(1, 1, 3), na, &
! bcint(1, 1, 2), nb, 1.0_dp, blocks_rxrv(3)%block, SIZE(blocks_rxrv(3)%block, 1)) ! yVx
! with MATMUL
IF (iatom <= jatom) THEN
blocks_rxrv(3)%block(1:na, 1:nb) = blocks_rxrv(3)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 6), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! xyV
blocks_rxrv(3)%block(1:na, 1:nb) = blocks_rxrv(3)%block(1:na, 1:nb) - &
MATMUL(achint(1:na, 1:np, 2), TRANSPOSE(bcint(1:nb, 1:np, 3))) ! -xVy
blocks_rxrv(3)%block(1:na, 1:nb) = blocks_rxrv(3)%block(1:na, 1:nb) - &
MATMUL(achint(1:na, 1:np, 6), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! -yxV
blocks_rxrv(3)%block(1:na, 1:nb) = blocks_rxrv(3)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 3), TRANSPOSE(bcint(1:nb, 1:np, 2))) ! zVx
ELSE
blocks_rxrv(3)%block(1:nb, 1:na) = blocks_rxrv(3)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 6), TRANSPOSE(acint(1:na, 1:np, 1))) ! xyV
blocks_rxrv(3)%block(1:nb, 1:na) = blocks_rxrv(3)%block(1:nb, 1:na) - &
MATMUL(bchint(1:nb, 1:np, 2), TRANSPOSE(acint(1:na, 1:np, 3))) ! -xVy
blocks_rxrv(3)%block(1:nb, 1:na) = blocks_rxrv(3)%block(1:nb, 1:na) - &
MATMUL(bchint(1:nb, 1:np, 6), TRANSPOSE(acint(1:na, 1:np, 1))) ! -yxV
blocks_rxrv(3)%block(1:nb, 1:na) = blocks_rxrv(3)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 3), TRANSPOSE(acint(1:na, 1:np, 2))) ! zVx
END IF
END IF
IF (my_rrv) THEN
! r_alpha * r_beta * Vnl
! with LAPACK
! CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 5), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rrv(1)%block, SIZE(blocks_rrv(1)%block, 1)) ! xxV
! CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 6), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rrv(2)%block, SIZE(blocks_rrv(2)%block, 1)) ! xyV
! CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 7), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rrv(3)%block, SIZE(blocks_rrv(3)%block, 1)) ! xzV
! CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 8), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rrv(4)%block, SIZE(blocks_rrv(4)%block, 1)) ! yyV
! CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 9), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rrv(5)%block, SIZE(blocks_rrv(5)%block, 1)) ! yzV
! CALL dgemm("N", "T", na, nb, np, 1._dp, achint(1, 1, 10), na, &
! bcint(1, 1, 1), nb, 1.0_dp, blocks_rrv(6)%block, SIZE(blocks_rrv(6)%block, 1)) ! zzV
! with MATMUL
IF (iatom <= jatom) THEN
blocks_rrv(1)%block(1:na, 1:nb) = blocks_rrv(1)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 5), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! xxV
blocks_rrv(2)%block(1:na, 1:nb) = blocks_rrv(2)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 6), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! xyV
blocks_rrv(3)%block(1:na, 1:nb) = blocks_rrv(3)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 7), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! xzV
blocks_rrv(4)%block(1:na, 1:nb) = blocks_rrv(4)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 8), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! yyV
blocks_rrv(5)%block(1:na, 1:nb) = blocks_rrv(5)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 9), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! yzV
blocks_rrv(6)%block(1:na, 1:nb) = blocks_rrv(6)%block(1:na, 1:nb) + &
MATMUL(achint(1:na, 1:np, 10), TRANSPOSE(bcint(1:nb, 1:np, 1))) ! zzV
ELSE
blocks_rrv(1)%block(1:nb, 1:na) = blocks_rrv(1)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 5), TRANSPOSE(acint(1:na, 1:np, 1))) ! xxV
blocks_rrv(2)%block(1:nb, 1:na) = blocks_rrv(2)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 6), TRANSPOSE(acint(1:na, 1:np, 1))) ! xyV
blocks_rrv(3)%block(1:nb, 1:na) = blocks_rrv(3)%block(1:nb, 1:na) + &
MATMUL(bchint(1:nb, 1:np, 7), TRANSPOSE(acint(1:na, 1:np, 1))) ! xzV
blocks_rrv(4)%block(1:nb, 1:na) = blocks_rrv(4)%block(1:nb, 1:na) + &