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atom_electronic_structure.F
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atom_electronic_structure.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 !
!--------------------------------------------------------------------------------------------------!
MODULE atom_electronic_structure
USE atom_optimization, ONLY: atom_history_init,&
atom_history_release,&
atom_history_type,&
atom_history_update,&
atom_opt_fmat
USE atom_output, ONLY: atom_print_energies,&
atom_print_iteration,&
atom_print_state,&
atom_print_zmp_iteration
USE atom_types, ONLY: &
atom_type, create_opgrid, create_opmat, ecp_pseudo, gth_pseudo, lmat, no_pseudo, &
opgrid_type, opmat_type, release_opgrid, release_opmat, set_atom, setup_hf_section, &
sgp_pseudo, upf_pseudo
USE atom_utils, ONLY: &
atom_denmat, atom_density, atom_read_external_density, atom_read_external_vxc, &
atom_read_zmp_restart, atom_solve, atom_trace, ceri_contract, coulomb_potential_analytic, &
coulomb_potential_numeric, eeri_contract, err_matrix, exchange_numeric, &
exchange_semi_analytic, numpot_matrix, slater_density, wigner_slater_functional
USE atom_xc, ONLY: calculate_atom_ext_vxc,&
calculate_atom_vxc_lda,&
calculate_atom_vxc_lsd,&
calculate_atom_zmp
USE input_constants, ONLY: &
do_analytic, do_dkh0_atom, do_dkh1_atom, do_dkh2_atom, do_dkh3_atom, do_nonrel_atom, &
do_numeric, do_rhf_atom, do_rks_atom, do_rohf_atom, do_sczoramp_atom, do_semi_analytic, &
do_uhf_atom, do_uks_atom, do_zoramp_atom
USE input_section_types, ONLY: section_vals_get,&
section_vals_get_subs_vals,&
section_vals_type
USE kinds, ONLY: dp
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
PUBLIC :: calculate_atom
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'atom_electronic_structure'
CONTAINS
! **************************************************************************************************
!> \brief General routine to perform electronic structure atomic calculations.
!> \param atom information about the atomic kind
!> \param iw output file unit
!> \param noguess skip initial guess
!> \param converged whether SCF iterations have been converged
!> \par History
!> * 06.2017 disable XC input options [Juerg Hutter]
!> * 11.2009 created from the subroutine calculate_atom() [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE calculate_atom(atom, iw, noguess, converged)
TYPE(atom_type), POINTER :: atom
INTEGER, INTENT(IN) :: iw
LOGICAL, INTENT(IN), OPTIONAL :: noguess
LOGICAL, INTENT(OUT), OPTIONAL :: converged
CHARACTER(len=*), PARAMETER :: routineN = 'calculate_atom'
INTEGER :: handle, method
LOGICAL :: explicit
TYPE(section_vals_type), POINTER :: sub_section
CALL timeset(routineN, handle)
! test for not supported methods and functionals
IF (ASSOCIATED(atom%xc_section)) THEN
!
sub_section => section_vals_get_subs_vals(atom%xc_section, "ADIABATIC_RESCALING")
CALL section_vals_get(sub_section, explicit=explicit)
IF (explicit) CALL cp_abort(__LOCATION__, "ADIABATIC_RESCALING not supported in ATOM code")
!
sub_section => section_vals_get_subs_vals(atom%xc_section, "VDW_POTENTIAL")
CALL section_vals_get(sub_section, explicit=explicit)
IF (explicit) CALL cp_abort(__LOCATION__, "VDW_POTENTIAL not supported in ATOM code")
!
sub_section => section_vals_get_subs_vals(atom%xc_section, "XC_POTENTIAL")
CALL section_vals_get(sub_section, explicit=explicit)
IF (explicit) CALL cp_abort(__LOCATION__, "XC_POTENTIAL not supported in ATOM code")
!
sub_section => section_vals_get_subs_vals(atom%xc_section, "WF_CORRELATION")
CALL section_vals_get(sub_section, explicit=explicit)
IF (explicit) CALL cp_abort(__LOCATION__, "WF_CORRELATION methods not supported in ATOM code")
!
END IF
method = atom%method_type
SELECT CASE (method)
CASE (do_rks_atom, do_rhf_atom)
CALL calculate_atom_restricted(atom, iw, noguess, converged)
CASE (do_uks_atom, do_uhf_atom)
CALL calculate_atom_unrestricted(atom, iw, noguess, converged)
CASE (do_rohf_atom)
CPABORT("")
CASE DEFAULT
CPABORT("")
END SELECT
CALL timestop(handle)
END SUBROUTINE calculate_atom
! **************************************************************************************************
!> \brief Perform restricted (closed shell) electronic structure atomic calculations.
!> \param atom information about the atomic kind
!> \param iw output file unit
!> \param noguess skip initial guess
!> \param converged whether SCF iterations have been converged
!> \par History
!> * 02.2016 support UPF files and ECP potentials [Juerg Hutter]
!> * 09.2015 Polarized Atomic Orbitals (PAO) method [Ole Schuett]
!> * 11.2013 Zhao, Morrison, and Parr (ZMP) potential [Daniele Varsano]
!> * 07.2013 scaled ZORA with model potential [Juerg Hutter]
!> * 11.2009 split into three subroutines calculate_atom(), calculate_atom_restricted(),
!> and calculate_atom_unrestricted() [Juerg Hutter]
!> * 12.2008 refactored and renamed to calculate_atom() [Juerg Hutter]
!> * 08.2008 created as atom_electronic_structure() [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE calculate_atom_restricted(atom, iw, noguess, converged)
TYPE(atom_type), POINTER :: atom
INTEGER, INTENT(IN) :: iw
LOGICAL, INTENT(IN), OPTIONAL :: noguess
LOGICAL, INTENT(OUT), OPTIONAL :: converged
CHARACTER(len=*), PARAMETER :: routineN = 'calculate_atom_restricted'
INTEGER :: handle, i, iter, l, max_iter, method, &
reltyp
LOGICAL :: do_hfx, doguess, is_converged, need_vxc, &
need_x, need_xc, need_zmp
REAL(KIND=dp) :: deps, eps_scf, hf_frac
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: ext_density, ext_vxc, tmp_dens
TYPE(atom_history_type) :: history
TYPE(opgrid_type), POINTER :: cpot, density
TYPE(opmat_type), POINTER :: fmat, hcore, jmat, kmat, xcmat
TYPE(section_vals_type), POINTER :: xc_section
CALL timeset(routineN, handle)
IF (PRESENT(noguess)) THEN
doguess = .NOT. noguess
ELSE
doguess = .TRUE.
END IF
CALL setup_hf_section(hf_frac, do_hfx, atom, xc_section, atom%exchange_integral_type)
method = atom%method_type
max_iter = atom%optimization%max_iter
eps_scf = atom%optimization%eps_scf
SELECT CASE (method)
CASE DEFAULT
CPABORT("")
CASE (do_rks_atom)
need_x = do_hfx
need_xc = .TRUE.
CASE (do_uks_atom)
CPABORT("")
CASE (do_rhf_atom)
need_x = .TRUE.
need_xc = .FALSE.
hf_frac = 1._dp
CASE (do_uhf_atom)
CPABORT("")
CASE (do_rohf_atom)
need_x = .TRUE.
need_xc = .FALSE.
hf_frac = 1._dp
CPABORT("")
END SELECT
! ZMP starting to read external density for the zmp calculation
need_zmp = atom%do_zmp
IF (need_zmp) THEN
need_x = .FALSE.
need_xc = .FALSE.
ALLOCATE (ext_density(atom%basis%grid%nr))
ext_density = 0._dp
CALL atom_read_external_density(ext_density, atom, iw)
END IF
! ZMP starting to read external vxc for the zmp calculation
need_vxc = atom%read_vxc
IF (need_vxc) THEN
need_x = .FALSE.
need_xc = .FALSE.
need_zmp = .FALSE.
ALLOCATE (ext_vxc(atom%basis%grid%nr))
ext_vxc = 0._dp
CALL atom_read_external_vxc(ext_vxc, atom, iw)
END IF
! check for relativistic method
reltyp = atom%relativistic
IF (iw > 0) CALL atom_print_state(atom%state, iw)
NULLIFY (hcore)
CALL create_opmat(hcore, atom%basis%nbas)
! Pseudopotentials
SELECT CASE (atom%potential%ppot_type)
CASE DEFAULT
CPABORT("")
CASE (NO_PSEUDO)
SELECT CASE (reltyp)
CASE DEFAULT
CPABORT("")
CASE (do_nonrel_atom)
hcore%op = atom%integrals%kin - atom%zcore*atom%integrals%core
CASE (do_zoramp_atom, do_sczoramp_atom)
hcore%op = atom%integrals%kin + atom%integrals%tzora - atom%zcore*atom%integrals%core
CASE (do_dkh0_atom, do_dkh1_atom, do_dkh2_atom, do_dkh3_atom)
hcore%op = atom%integrals%hdkh
END SELECT
CASE (gth_pseudo, upf_pseudo, sgp_pseudo, ecp_pseudo)
hcore%op = atom%integrals%kin + atom%integrals%core + atom%integrals%hnl
END SELECT
! add confinement potential (not included in relativistic transformations)
IF (atom%potential%confinement) THEN
hcore%op = hcore%op + atom%potential%acon*atom%integrals%conf
END IF
NULLIFY (fmat, jmat, kmat, xcmat)
CALL create_opmat(fmat, atom%basis%nbas)
CALL create_opmat(jmat, atom%basis%nbas)
CALL create_opmat(kmat, atom%basis%nbas)
CALL create_opmat(xcmat, atom%basis%nbas)
NULLIFY (density, cpot)
CALL create_opgrid(density, atom%basis%grid)
CALL create_opgrid(cpot, atom%basis%grid)
! ZMP reading the file to restart
IF (atom%doread) CALL atom_read_zmp_restart(atom, doguess, iw)
IF (doguess) THEN
! initial guess
ALLOCATE (tmp_dens(SIZE(density%op)))
CALL slater_density(density%op, tmp_dens, atom%z, atom%state, atom%basis%grid)
density%op = density%op + tmp_dens
DEALLOCATE (tmp_dens)
CALL coulomb_potential_numeric(cpot%op, density%op, density%grid)
CALL numpot_matrix(jmat%op, cpot%op, atom%basis, 0)
CALL wigner_slater_functional(density%op, cpot%op)
CALL numpot_matrix(xcmat%op, cpot%op, atom%basis, 0)
fmat%op = hcore%op + jmat%op + xcmat%op
CALL atom_solve(fmat%op, atom%integrals%utrans, atom%orbitals%wfn, atom%orbitals%ener, &
atom%basis%nbas, atom%integrals%nne, atom%state%maxl_calc)
END IF
CALL atom_denmat(atom%orbitals%pmat, atom%orbitals%wfn, atom%basis%nbas, atom%state%occupation, &
atom%state%maxl_occ, atom%state%maxn_occ)
! wavefunction history
NULLIFY (history%dmat, history%hmat)
CALL atom_history_init(history, atom%optimization, fmat%op)
is_converged = .FALSE.
iter = 0
DO !SCF Loop
! Kinetic energy
atom%energy%ekin = atom_trace(atom%integrals%kin, atom%orbitals%pmat)
! Band energy
atom%energy%eband = 0._dp
DO l = 0, lmat
DO i = 1, MIN(SIZE(atom%state%occupation, 2), SIZE(atom%orbitals%ener, 1))
atom%energy%eband = atom%energy%eband + atom%orbitals%ener(i, l)*atom%state%occupation(l, i)
END DO
END DO
! Pseudopotential energy
SELECT CASE (atom%potential%ppot_type)
CASE DEFAULT
CPABORT("")
CASE (no_pseudo)
atom%energy%eploc = 0._dp
atom%energy%epnl = 0._dp
CASE (gth_pseudo, upf_pseudo, sgp_pseudo, ecp_pseudo)
atom%energy%eploc = atom_trace(atom%integrals%core, atom%orbitals%pmat)
atom%energy%epnl = atom_trace(atom%integrals%hnl, atom%orbitals%pmat)
END SELECT
atom%energy%epseudo = atom%energy%eploc + atom%energy%epnl
! Core energy
atom%energy%ecore = atom_trace(hcore%op, atom%orbitals%pmat)
! Confinement energy
IF (atom%potential%confinement) THEN
atom%energy%econfinement = atom_trace(atom%integrals%conf, atom%orbitals%pmat)
ELSE
atom%energy%econfinement = 0._dp
END IF
! Hartree Term
jmat%op = 0._dp
SELECT CASE (atom%coulomb_integral_type)
CASE DEFAULT
CPABORT("")
CASE (do_analytic)
CALL ceri_contract(jmat%op, atom%integrals%ceri, atom%orbitals%pmat, atom%integrals%n)
CASE (do_semi_analytic)
CALL coulomb_potential_analytic(cpot%op, atom%orbitals%pmat, atom%basis, atom%basis%grid, &
atom%state%maxl_occ)
CALL numpot_matrix(jmat%op, cpot%op, atom%basis, 0)
CASE (do_numeric)
CALL atom_density(density%op, atom%orbitals%pmat, atom%basis, atom%state%maxl_occ, typ="RHO")
CALL coulomb_potential_numeric(cpot%op, density%op, density%grid)
CALL numpot_matrix(jmat%op, cpot%op, atom%basis, 0)
END SELECT
atom%energy%ecoulomb = 0.5_dp*atom_trace(jmat%op, atom%orbitals%pmat)
! Exchange Term
IF (need_x) THEN
kmat%op = 0._dp
SELECT CASE (atom%exchange_integral_type)
CASE DEFAULT
CPABORT("")
CASE (do_analytic)
CALL eeri_contract(kmat%op, atom%integrals%eeri, atom%orbitals%pmat, atom%integrals%n)
CASE (do_semi_analytic)
CALL exchange_semi_analytic(kmat%op, atom%state, atom%state%occupation, atom%orbitals%wfn, atom%basis, atom%hfx_pot)
CASE (do_numeric)
CALL exchange_numeric(kmat%op, atom%state, atom%state%occupation, atom%orbitals%wfn, atom%basis, atom%hfx_pot)
END SELECT
atom%energy%eexchange = hf_frac*0.5_dp*atom_trace(kmat%op, atom%orbitals%pmat)
kmat%op = hf_frac*kmat%op
ELSE
kmat%op = 0._dp
atom%energy%eexchange = 0._dp
END IF
! XC
IF (need_xc) THEN
xcmat%op = 0._dp
CALL calculate_atom_vxc_lda(xcmat, atom, xc_section)
! ZMP added options for the zmp calculations, building external density and vxc potential
ELSEIF (need_zmp) THEN
xcmat%op = 0._dp
CALL calculate_atom_zmp(ext_density=ext_density, atom=atom, lprint=.FALSE., xcmat=xcmat)
ELSEIF (need_vxc) THEN
xcmat%op = 0._dp
CALL calculate_atom_ext_vxc(vxc=ext_vxc, atom=atom, lprint=.FALSE., xcmat=xcmat)
ELSE
xcmat%op = 0._dp
atom%energy%exc = 0._dp
END IF
! Zero this contribution
atom%energy%elsd = 0._dp
! Total energy
atom%energy%etot = atom%energy%ecore + atom%energy%ecoulomb + atom%energy%eexchange + atom%energy%exc
! Potential energy
atom%energy%epot = atom%energy%etot - atom%energy%ekin
! Total HF/KS matrix
fmat%op = hcore%op + jmat%op + kmat%op + xcmat%op
! calculate error matrix
CALL err_matrix(jmat%op, deps, fmat%op, atom%orbitals%pmat, atom%integrals%utrans, &
atom%integrals%uptrans, atom%basis%nbas, atom%integrals%nne)
iter = iter + 1
IF (iw > 0) THEN
IF (need_zmp) THEN
CALL atom_print_zmp_iteration(iter, deps, atom, iw)
ELSE
CALL atom_print_iteration(iter, deps, atom%energy%etot, iw)
END IF
END IF
IF (deps < eps_scf) THEN
is_converged = .TRUE.
EXIT
END IF
IF (iter >= max_iter) THEN
IF (iw > 0) THEN
WRITE (iw, "(A)") " No convergence within maximum number of iterations "
END IF
EXIT
END IF
! update history container and extrapolate KS matrix
CALL atom_history_update(history, atom%orbitals%pmat, fmat%op, jmat%op, atom%energy%etot, deps)
CALL atom_opt_fmat(fmat%op, history, deps)
! Solve HF/KS equations
CALL atom_solve(fmat%op, atom%integrals%utrans, atom%orbitals%wfn, atom%orbitals%ener, &
atom%basis%nbas, atom%integrals%nne, atom%state%maxl_calc)
CALL atom_denmat(atom%orbitals%pmat, atom%orbitals%wfn, atom%basis%nbas, atom%state%occupation, &
atom%state%maxl_occ, atom%state%maxn_occ)
END DO !SCF Loop
IF (iw > 0) THEN
CALL atom_print_energies(atom, iw)
END IF
CALL atom_history_release(history)
! conserve fmat within atom_type
CALL set_atom(atom, fmat=fmat)
CALL release_opmat(jmat)
CALL release_opmat(kmat)
CALL release_opmat(xcmat)
CALL release_opmat(hcore)
CALL release_opgrid(density)
CALL release_opgrid(cpot)
! ZMP deallocating ext_density ext_vxc
IF (need_zmp) DEALLOCATE (ext_density)
IF (need_vxc) DEALLOCATE (ext_vxc)
IF (PRESENT(converged)) THEN
converged = is_converged
END IF
CALL timestop(handle)
END SUBROUTINE calculate_atom_restricted
! **************************************************************************************************
!> \brief Perform unrestricted (spin-polarised) electronic structure atomic calculations.
!> \param atom information about the atomic kind
!> \param iw output file unit
!> \param noguess skip initial guess
!> \param converged whether SCF iterations have been converged
!> \par History
!> * identical to the subroutine calculate_atom_restricted()
! **************************************************************************************************
SUBROUTINE calculate_atom_unrestricted(atom, iw, noguess, converged)
TYPE(atom_type), POINTER :: atom
INTEGER, INTENT(IN) :: iw
LOGICAL, INTENT(IN), OPTIONAL :: noguess
LOGICAL, INTENT(OUT), OPTIONAL :: converged
CHARACTER(len=*), PARAMETER :: routineN = 'calculate_atom_unrestricted'
INTEGER :: handle, i, iter, k, l, max_iter, method, &
reltyp
LOGICAL :: do_hfx, doguess, is_converged, lsdpot, &
need_x, need_xc
REAL(KIND=dp) :: deps, depsa, depsb, eps_scf, hf_frac, &
ne, nm
TYPE(atom_history_type) :: historya, historyb
TYPE(opgrid_type), POINTER :: cpot, density, rhoa, rhob
TYPE(opmat_type), POINTER :: fmata, fmatb, hcore, hlsd, jmat, kmata, &
kmatb, xcmata, xcmatb
TYPE(section_vals_type), POINTER :: xc_section
CALL timeset(routineN, handle)
IF (PRESENT(noguess)) THEN
doguess = .NOT. noguess
ELSE
doguess = .TRUE.
END IF
CALL setup_hf_section(hf_frac, do_hfx, atom, xc_section, atom%exchange_integral_type)
method = atom%method_type
max_iter = atom%optimization%max_iter
eps_scf = atom%optimization%eps_scf
SELECT CASE (method)
CASE DEFAULT
CPABORT("")
CASE (do_rks_atom)
CPABORT("")
CASE (do_uks_atom)
need_x = do_hfx
need_xc = .TRUE.
CASE (do_rhf_atom)
CPABORT("")
CASE (do_uhf_atom)
need_x = .TRUE.
need_xc = .FALSE.
hf_frac = 1._dp
CASE (do_rohf_atom)
need_x = .TRUE.
need_xc = .FALSE.
hf_frac = 1._dp
CPABORT("")
END SELECT
! set alpha and beta occupations
IF (SUM(ABS(atom%state%occa) + ABS(atom%state%occb)) == 0.0_dp) THEN
DO l = 0, 3
nm = REAL((2*l + 1), KIND=dp)
DO k = 1, 10
ne = atom%state%occupation(l, k)
IF (ne == 0._dp) THEN !empty shell
EXIT !assume there are no holes
ELSEIF (ne == 2._dp*nm) THEN !closed shell
atom%state%occa(l, k) = nm
atom%state%occb(l, k) = nm
ELSEIF (atom%state%multiplicity == -2) THEN !High spin case
atom%state%occa(l, k) = MIN(ne, nm)
atom%state%occb(l, k) = MAX(0._dp, ne - nm)
ELSE
atom%state%occa(l, k) = 0.5_dp*(ne + atom%state%multiplicity - 1._dp)
atom%state%occb(l, k) = ne - atom%state%occa(l, k)
END IF
END DO
END DO
END IF
! check for relativistic method
reltyp = atom%relativistic
IF (iw > 0) CALL atom_print_state(atom%state, iw)
NULLIFY (hcore, hlsd)
CALL create_opmat(hcore, atom%basis%nbas)
CALL create_opmat(hlsd, atom%basis%nbas)
hlsd%op = 0._dp
! Pseudopotentials
lsdpot = .FALSE.
SELECT CASE (atom%potential%ppot_type)
CASE DEFAULT
CPABORT("")
CASE (no_pseudo)
SELECT CASE (reltyp)
CASE DEFAULT
CPABORT("")
CASE (do_nonrel_atom)
hcore%op = atom%integrals%kin - atom%zcore*atom%integrals%core
CASE (do_zoramp_atom, do_sczoramp_atom)
hcore%op = atom%integrals%kin + atom%integrals%tzora - atom%zcore*atom%integrals%core
CASE (do_dkh0_atom, do_dkh1_atom, do_dkh2_atom, do_dkh3_atom)
hcore%op = atom%integrals%hdkh
END SELECT
CASE (gth_pseudo)
hcore%op = atom%integrals%kin + atom%integrals%core + atom%integrals%hnl
IF (atom%potential%gth_pot%lsdpot) THEN
lsdpot = .TRUE.
hlsd%op = atom%integrals%clsd
END IF
CASE (upf_pseudo, sgp_pseudo, ecp_pseudo)
hcore%op = atom%integrals%kin + atom%integrals%core + atom%integrals%hnl
END SELECT
! add confinement potential (not included in relativistic transformations)
IF (atom%potential%confinement) THEN
hcore%op = hcore%op + atom%potential%acon*atom%integrals%conf
END IF
NULLIFY (fmata, fmatb, jmat, kmata, kmatb, xcmata, xcmatb)
CALL create_opmat(fmata, atom%basis%nbas)
CALL create_opmat(fmatb, atom%basis%nbas)
CALL create_opmat(jmat, atom%basis%nbas)
CALL create_opmat(kmata, atom%basis%nbas)
CALL create_opmat(kmatb, atom%basis%nbas)
CALL create_opmat(xcmata, atom%basis%nbas)
CALL create_opmat(xcmatb, atom%basis%nbas)
NULLIFY (density, rhoa, rhob, cpot)
CALL create_opgrid(density, atom%basis%grid)
CALL create_opgrid(rhoa, atom%basis%grid)
CALL create_opgrid(rhob, atom%basis%grid)
CALL create_opgrid(cpot, atom%basis%grid)
IF (doguess) THEN
! initial guess
CALL slater_density(rhoa%op, rhob%op, atom%z, atom%state, atom%basis%grid)
density%op = rhoa%op + rhob%op
CALL coulomb_potential_numeric(cpot%op, density%op, density%grid)
CALL numpot_matrix(jmat%op, cpot%op, atom%basis, 0)
! alpha spin
density%op = 2._dp*rhoa%op
CALL wigner_slater_functional(density%op, cpot%op)
CALL numpot_matrix(xcmata%op, cpot%op, atom%basis, 0)
fmata%op = hcore%op + hlsd%op + jmat%op + xcmata%op
CALL atom_solve(fmata%op, atom%integrals%utrans, atom%orbitals%wfna, atom%orbitals%enera, &
atom%basis%nbas, atom%integrals%nne, atom%state%maxl_calc)
! beta spin
density%op = 2._dp*rhob%op
CALL wigner_slater_functional(density%op, cpot%op)
CALL numpot_matrix(xcmatb%op, cpot%op, atom%basis, 0)
fmatb%op = hcore%op - hlsd%op + jmat%op + xcmatb%op
CALL atom_solve(fmatb%op, atom%integrals%utrans, atom%orbitals%wfnb, atom%orbitals%enerb, &
atom%basis%nbas, atom%integrals%nne, atom%state%maxl_calc)
END IF
CALL atom_denmat(atom%orbitals%pmata, atom%orbitals%wfna, atom%basis%nbas, atom%state%occa, &
atom%state%maxl_occ, atom%state%maxn_occ)
CALL atom_denmat(atom%orbitals%pmatb, atom%orbitals%wfnb, atom%basis%nbas, atom%state%occb, &
atom%state%maxl_occ, atom%state%maxn_occ)
atom%orbitals%pmat = atom%orbitals%pmata + atom%orbitals%pmatb
! wavefunction history
NULLIFY (historya%dmat, historya%hmat)
CALL atom_history_init(historya, atom%optimization, fmata%op)
NULLIFY (historyb%dmat, historyb%hmat)
CALL atom_history_init(historyb, atom%optimization, fmatb%op)
is_converged = .FALSE.
iter = 0
DO !SCF Loop
! Kinetic energy
atom%energy%ekin = atom_trace(atom%integrals%kin, atom%orbitals%pmat)
! Band energy
atom%energy%eband = 0._dp
DO l = 0, 3
DO i = 1, MIN(SIZE(atom%state%occupation, 2), SIZE(atom%orbitals%ener, 1))
atom%energy%eband = atom%energy%eband + atom%orbitals%enera(i, l)*atom%state%occa(l, i)
atom%energy%eband = atom%energy%eband + atom%orbitals%enerb(i, l)*atom%state%occb(l, i)
END DO
END DO
! Pseudopotential energy
SELECT CASE (atom%potential%ppot_type)
CASE DEFAULT
CPABORT("")
CASE (no_pseudo)
atom%energy%eploc = 0._dp
atom%energy%epnl = 0._dp
CASE (gth_pseudo, upf_pseudo, sgp_pseudo, ecp_pseudo)
atom%energy%eploc = atom_trace(atom%integrals%core, atom%orbitals%pmat)
atom%energy%epnl = atom_trace(atom%integrals%hnl, atom%orbitals%pmat)
END SELECT
atom%energy%epseudo = atom%energy%eploc + atom%energy%epnl
! Core energy
atom%energy%ecore = atom_trace(hcore%op, atom%orbitals%pmat)
! Confinement energy
IF (atom%potential%confinement) THEN
atom%energy%econfinement = atom_trace(atom%integrals%conf, atom%orbitals%pmat)
ELSE
atom%energy%econfinement = 0._dp
END IF
! Hartree Term
jmat%op = 0._dp
SELECT CASE (atom%coulomb_integral_type)
CASE DEFAULT
CPABORT("")
CASE (do_analytic)
CALL ceri_contract(jmat%op, atom%integrals%ceri, atom%orbitals%pmat, atom%integrals%n)
CASE (do_semi_analytic)
CALL coulomb_potential_analytic(cpot%op, atom%orbitals%pmat, atom%basis, atom%basis%grid, &
atom%state%maxl_occ)
CALL numpot_matrix(jmat%op, cpot%op, atom%basis, 0)
CASE (do_numeric)
CALL atom_density(density%op, atom%orbitals%pmat, atom%basis, atom%state%maxl_occ, typ="RHO")
CALL coulomb_potential_numeric(cpot%op, density%op, density%grid)
CALL numpot_matrix(jmat%op, cpot%op, atom%basis, 0)
END SELECT
atom%energy%ecoulomb = 0.5_dp*atom_trace(jmat%op, atom%orbitals%pmat)
! Exchange Term
IF (need_x) THEN
kmata%op = 0._dp
kmatb%op = 0._dp
SELECT CASE (atom%exchange_integral_type)
CASE DEFAULT
CPABORT("")
CASE (do_analytic)
CALL eeri_contract(kmata%op, atom%integrals%eeri, atom%orbitals%pmata, atom%integrals%n)
CALL eeri_contract(kmatb%op, atom%integrals%eeri, atom%orbitals%pmatb, atom%integrals%n)
CASE (do_semi_analytic)
CALL exchange_semi_analytic(kmata%op, atom%state, atom%state%occa, atom%orbitals%wfna, atom%basis, atom%hfx_pot)
CALL exchange_semi_analytic(kmatb%op, atom%state, atom%state%occb, atom%orbitals%wfnb, atom%basis, atom%hfx_pot)
CASE (do_numeric)
CALL exchange_numeric(kmata%op, atom%state, atom%state%occa, atom%orbitals%wfna, atom%basis, atom%hfx_pot)
CALL exchange_numeric(kmatb%op, atom%state, atom%state%occb, atom%orbitals%wfnb, atom%basis, atom%hfx_pot)
END SELECT
atom%energy%eexchange = hf_frac*(atom_trace(kmata%op, atom%orbitals%pmata) + &
atom_trace(kmatb%op, atom%orbitals%pmatb))
kmata%op = 2._dp*hf_frac*kmata%op
kmatb%op = 2._dp*hf_frac*kmatb%op
ELSE
kmata%op = 0._dp
kmatb%op = 0._dp
atom%energy%eexchange = 0._dp
END IF
! XC
IF (need_xc) THEN
xcmata%op = 0._dp
xcmatb%op = 0._dp
CALL calculate_atom_vxc_lsd(xcmata, xcmatb, atom, xc_section)
ELSE
xcmata%op = 0._dp
xcmatb%op = 0._dp
atom%energy%exc = 0._dp
END IF
IF (lsdpot) THEN
atom%energy%elsd = atom_trace(hlsd%op, atom%orbitals%pmata) - &
atom_trace(hlsd%op, atom%orbitals%pmatb)
atom%energy%epseudo = atom%energy%epseudo + atom%energy%elsd
atom%energy%ecore = atom%energy%ecore + atom%energy%elsd
ELSE
atom%energy%elsd = 0._dp
END IF
! Total energy
atom%energy%etot = atom%energy%ecore + atom%energy%ecoulomb + atom%energy%eexchange + atom%energy%exc
! Potential energy
atom%energy%epot = atom%energy%etot - atom%energy%ekin
! Total HF/KS matrix
fmata%op = hcore%op + hlsd%op + jmat%op + kmata%op + xcmata%op
fmatb%op = hcore%op - hlsd%op + jmat%op + kmatb%op + xcmatb%op
! calculate error matrix
CALL err_matrix(xcmata%op, depsa, fmata%op, atom%orbitals%pmata, atom%integrals%utrans, &
atom%integrals%uptrans, atom%basis%nbas, atom%integrals%nne)
CALL err_matrix(xcmatb%op, depsb, fmatb%op, atom%orbitals%pmatb, atom%integrals%utrans, &
atom%integrals%uptrans, atom%basis%nbas, atom%integrals%nne)
deps = 2._dp*MAX(depsa, depsb)
iter = iter + 1
IF (iw > 0) THEN
CALL atom_print_iteration(iter, deps, atom%energy%etot, iw)
END IF
IF (deps < eps_scf) THEN
is_converged = .TRUE.
EXIT
END IF
IF (iter >= max_iter) THEN
IF (iw > 0) THEN
WRITE (iw, "(A)") " No convergence within maximum number of iterations "
END IF
EXIT
END IF
! update history container and extrapolate KS matrix
CALL atom_history_update(historya, atom%orbitals%pmata, fmata%op, xcmata%op, atom%energy%etot, deps)
CALL atom_history_update(historyb, atom%orbitals%pmatb, fmatb%op, xcmatb%op, atom%energy%etot, deps)
CALL atom_opt_fmat(fmata%op, historya, depsa)
CALL atom_opt_fmat(fmatb%op, historyb, depsb)
! Solve HF/KS equations
CALL atom_solve(fmata%op, atom%integrals%utrans, atom%orbitals%wfna, atom%orbitals%enera, &
atom%basis%nbas, atom%integrals%nne, atom%state%maxl_calc)
CALL atom_denmat(atom%orbitals%pmata, atom%orbitals%wfna, atom%basis%nbas, atom%state%occa, &
atom%state%maxl_occ, atom%state%maxn_occ)
CALL atom_solve(fmatb%op, atom%integrals%utrans, atom%orbitals%wfnb, atom%orbitals%enerb, &
atom%basis%nbas, atom%integrals%nne, atom%state%maxl_calc)
CALL atom_denmat(atom%orbitals%pmatb, atom%orbitals%wfnb, atom%basis%nbas, atom%state%occb, &
atom%state%maxl_occ, atom%state%maxn_occ)
atom%orbitals%pmat = atom%orbitals%pmata + atom%orbitals%pmatb
END DO !SCF Loop
IF (iw > 0) THEN
CALL atom_print_energies(atom, iw)
END IF
CALL atom_history_release(historya)
CALL atom_history_release(historyb)
CALL release_opgrid(density)
CALL release_opgrid(rhoa)
CALL release_opgrid(rhob)
CALL release_opgrid(cpot)
! conserve fmata as fmat within atom_type.
CALL set_atom(atom, fmat=fmata)
CALL release_opmat(fmatb)
CALL release_opmat(jmat)
CALL release_opmat(kmata)
CALL release_opmat(kmatb)
CALL release_opmat(xcmata)
CALL release_opmat(xcmatb)
CALL release_opmat(hlsd)
CALL release_opmat(hcore)
IF (PRESENT(converged)) THEN
converged = is_converged
END IF
CALL timestop(handle)
END SUBROUTINE calculate_atom_unrestricted
END MODULE atom_electronic_structure