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atom_xc.F
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atom_xc.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 routines that build the integrals of the Vxc potential calculated
!> for the atomic code
! **************************************************************************************************
MODULE atom_xc
USE atom_types, ONLY: atom_basis_type,&
atom_type,&
gth_pseudo,&
opmat_type,&
sgp_pseudo,&
upf_pseudo
USE atom_utils, ONLY: atom_core_density,&
atom_density,&
coulomb_potential_numeric,&
integrate_grid,&
numpot_matrix
USE cp_files, ONLY: close_file,&
get_unit_number,&
open_file
USE input_constants, ONLY: xc_none
USE input_section_types, ONLY: section_vals_get_subs_vals,&
section_vals_type,&
section_vals_val_get
USE kinds, ONLY: dp
USE mathconstants, ONLY: fourpi,&
pi
USE xc_atom, ONLY: xc_rho_set_atom_update
USE xc_derivative_desc, ONLY: &
deriv_norm_drho, deriv_norm_drhoa, deriv_norm_drhob, deriv_rho, deriv_rhoa, deriv_rhob, &
deriv_tau, deriv_tau_a, deriv_tau_b
USE xc_derivative_set_types, ONLY: xc_derivative_set_type,&
xc_dset_create,&
xc_dset_get_derivative,&
xc_dset_release,&
xc_dset_zero_all
USE xc_derivative_types, ONLY: xc_derivative_get,&
xc_derivative_type
USE xc_derivatives, ONLY: xc_functionals_eval,&
xc_functionals_get_needs
USE xc_rho_cflags_types, ONLY: xc_rho_cflags_type
USE xc_rho_set_types, ONLY: xc_rho_set_create,&
xc_rho_set_release,&
xc_rho_set_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'atom_xc'
! ZMP added coulomb_potential_numeric
! ZMP added public subroutines calculate_atom_zmp, calculate_atom_ext_vxc
PUBLIC :: calculate_atom_vxc_lda, calculate_atom_vxc_lsd, &
calculate_atom_zmp, calculate_atom_ext_vxc
PUBLIC :: atom_vxc_lda, atom_vxc_lsd, atom_dpot_lda
CONTAINS
! **************************************************************************************************
!> \brief ZMP subroutine for the calculation of the effective constraint
!> potential in the atomic code.
!> \param ext_density external electron density
!> \param atom information about the atomic kind
!> \param lprint save exchange-correlation potential to the file 'linear_potentials.dat'
!> \param xcmat exchange-correlation potential matrix
!> \author D. Varsano [daniele.varsano@nano.cnr.it]
! **************************************************************************************************
SUBROUTINE calculate_atom_zmp(ext_density, atom, lprint, xcmat)
REAL(KIND=dp), DIMENSION(:), INTENT(INOUT) :: ext_density
TYPE(atom_type), INTENT(INOUT) :: atom
LOGICAL :: lprint
TYPE(opmat_type), OPTIONAL, POINTER :: xcmat
CHARACTER(LEN=*), PARAMETER :: routineN = 'calculate_atom_zmp'
INTEGER :: extunit, handle, ir, nr, z
REAL(KIND=dp) :: int1, int2
REAL(KIND=dp), DIMENSION(:), POINTER :: deltarho, rho_dum, vxc, vxc1, vxc2
REAL(KIND=dp), DIMENSION(:, :), POINTER :: rho
CALL timeset(routineN, handle)
nr = atom%basis%grid%nr
z = atom%z
ALLOCATE (rho(nr, 1), vxc(nr), vxc1(nr), vxc2(nr), rho_dum(nr), deltarho(nr))
CALL atom_density(rho(:, 1), atom%orbitals%pmat, atom%basis, atom%state%maxl_occ, typ="RHO")
!Vxc1
int1 = integrate_grid(ext_density, atom%basis%grid)
int1 = fourpi*int1
CALL coulomb_potential_numeric(vxc1, rho(:, 1), atom%basis%grid)
vxc1 = -vxc1/z
!Vxc2
rho_dum = rho(:, 1)*int1/z
deltarho = rho_dum - ext_density
int2 = integrate_grid(deltarho, atom%basis%grid)
CALL coulomb_potential_numeric(vxc2, deltarho, atom%basis%grid)
vxc2 = vxc2*atom%lambda
!Vxc
vxc = vxc1 + vxc2
atom%energy%exc = fourpi*integrate_grid(vxc, rho(:, 1), atom%basis%grid)
atom%rho_diff_integral = fourpi*int2
IF (lprint) THEN
extunit = get_unit_number()
CALL open_file(file_name="linear_potentials.dat", file_status="UNKNOWN", &
file_form="FORMATTED", file_action="WRITE", &
unit_number=extunit)
WRITE (extunit, fmt='("#",T10,"R[bohr]",T36,"Rho[au]",T61,"DRho[au]",T86,"V_XC[au]",T111,"V_XC1[au]",T136,"V_XC2[au]")')
DO ir = 1, nr
WRITE (extunit, fmt='(T1,E24.15,T26,E24.15,T51,E24.15,T76,E24.15,T101,E24.15,T126,E24.15)') &
atom%basis%grid%rad(ir), rho(ir, 1), deltarho(ir), vxc(ir), vxc1(ir), vxc2(ir)
END DO
CALL close_file(unit_number=extunit)
END IF
IF (PRESENT(xcmat)) CALL numpot_matrix(xcmat%op, vxc, atom%basis, 0)
DEALLOCATE (rho, vxc, vxc1, vxc2, rho_dum, deltarho)
CALL timestop(handle)
END SUBROUTINE calculate_atom_zmp
! **************************************************************************************************
!> \brief ZMP subroutine for the scf external density from the external v_xc.
!> \param vxc exchange-correlation potential
!> \param atom information about the atomic kind
!> \param lprint save exchange-correlation potential to the file 'linear_potentials.dat'
!> \param xcmat exchange-correlation potential matrix
!> \author D. Varsano [daniele.varsano@nano.cnr.it]
! **************************************************************************************************
SUBROUTINE calculate_atom_ext_vxc(vxc, atom, lprint, xcmat)
REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: vxc
TYPE(atom_type), INTENT(INOUT) :: atom
LOGICAL, INTENT(in) :: lprint
TYPE(opmat_type), INTENT(inout), OPTIONAL, POINTER :: xcmat
CHARACTER(LEN=*), PARAMETER :: routineN = 'calculate_atom_ext_vxc'
INTEGER :: extunit, handle, ir, nr
REAL(KIND=dp), DIMENSION(:, :), POINTER :: rho
CALL timeset(routineN, handle)
nr = atom%basis%grid%nr
ALLOCATE (rho(nr, 1))
CALL atom_density(rho(:, 1), atom%orbitals%pmat, atom%basis, atom%state%maxl_occ, typ="RHO")
IF (lprint) THEN
extunit = get_unit_number()
CALL open_file(file_name="linear_potentials.dat", file_status="UNKNOWN", &
file_form="FORMATTED", file_action="WRITE", &
unit_number=extunit)
WRITE (extunit, fmt='("#",T10,"R[bohr]",T36,"Rho[au]",T61,"V_XC[au]")')
DO ir = 1, nr
WRITE (extunit, fmt='(T1,E24.15,T26,E24.15,T51,E24.15)') &
atom%basis%grid%rad(ir), rho(ir, 1), vxc(ir)
END DO
CALL close_file(unit_number=extunit)
END IF
atom%energy%exc = fourpi*integrate_grid(vxc, rho(:, 1), atom%basis%grid)
IF (PRESENT(xcmat)) CALL numpot_matrix(xcmat%op, vxc, atom%basis, 0)
DEALLOCATE (rho)
CALL timestop(handle)
END SUBROUTINE calculate_atom_ext_vxc
! **************************************************************************************************
!> \brief Calculate atomic exchange-correlation potential in spin-restricted case.
!> \param xcmat exchange-correlation potential expressed in the atomic basis set
!> \param atom information about the atomic kind
!> \param xc_section XC input section
!> \par History
!> * 03.2010 extension of GTH pseudo-potential definition [Juerg Hutter]
!> * 02.2010 renamed to calculate_atom_vxc_lda() [Juerg Hutter]
!> * 08.2008 created [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE calculate_atom_vxc_lda(xcmat, atom, xc_section)
TYPE(opmat_type), POINTER :: xcmat
TYPE(atom_type), INTENT(INOUT) :: atom
TYPE(section_vals_type), POINTER :: xc_section
CHARACTER(LEN=*), PARAMETER :: routineN = 'calculate_atom_vxc_lda'
INTEGER :: deriv_order, handle, i, l, myfun, n1, &
n2, n3, nr, nspins, unit_nr
INTEGER, DIMENSION(2, 3) :: bounds
LOGICAL :: lsd, nlcc
REAL(KIND=dp) :: density_cut, gradient_cut, tau_cut
REAL(KIND=dp), DIMENSION(:), POINTER :: exc, vxc
REAL(KIND=dp), DIMENSION(:, :), POINTER :: drho, lap, rho, tau
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: taumat, xcpot
TYPE(section_vals_type), POINTER :: xc_fun_section
TYPE(xc_derivative_set_type) :: deriv_set
TYPE(xc_derivative_type), POINTER :: deriv
TYPE(xc_rho_cflags_type) :: needs
TYPE(xc_rho_set_type) :: rho_set
CALL timeset(routineN, handle)
nlcc = .FALSE.
IF (atom%potential%ppot_type == gth_pseudo) THEN
nlcc = atom%potential%gth_pot%nlcc
ELSE IF (atom%potential%ppot_type == upf_pseudo) THEN
nlcc = atom%potential%upf_pot%core_correction
ELSE IF (atom%potential%ppot_type == sgp_pseudo) THEN
nlcc = atom%potential%sgp_pot%has_nlcc
END IF
IF (ASSOCIATED(xc_section)) THEN
xc_fun_section => section_vals_get_subs_vals(xc_section, "XC_FUNCTIONAL")
CALL section_vals_val_get(xc_fun_section, "_SECTION_PARAMETERS_", i_val=myfun)
IF (myfun == xc_none) THEN
atom%energy%exc = 0._dp
ELSE
CALL section_vals_val_get(xc_section, "DENSITY_CUTOFF", r_val=density_cut)
CALL section_vals_val_get(xc_section, "GRADIENT_CUTOFF", r_val=gradient_cut)
CALL section_vals_val_get(xc_section, "TAU_CUTOFF", r_val=tau_cut)
lsd = .FALSE.
nspins = 1
needs = xc_functionals_get_needs(xc_fun_section, lsd=lsd, calc_potential=.FALSE.)
! Prepare the structures needed to calculate and store the xc derivatives
! Array dimension: here anly one dimensional arrays are used,
! i.e. only the first column of deriv_data is read.
! The other to dimensions are set to size equal 1
nr = atom%basis%grid%nr
bounds(1:2, 1:3) = 1
bounds(2, 1) = nr
! create a place where to put the derivatives
CALL xc_dset_create(deriv_set, local_bounds=bounds)
! create the place where to store the argument for the functionals
CALL xc_rho_set_create(rho_set, bounds, rho_cutoff=density_cut, &
drho_cutoff=gradient_cut, tau_cutoff=tau_cut)
! allocate the required 3d arrays where to store rho and drho
CALL xc_rho_set_atom_update(rho_set, needs, nspins, bounds)
NULLIFY (rho, drho, tau)
IF (needs%rho) THEN
ALLOCATE (rho(nr, 1))
CALL atom_density(rho(:, 1), atom%orbitals%pmat, atom%basis, atom%state%maxl_occ, typ="RHO")
IF (nlcc) THEN
CALL atom_core_density(rho(:, 1), atom%potential, typ="RHO", rr=atom%basis%grid%rad)
END IF
END IF
IF (needs%norm_drho) THEN
ALLOCATE (drho(nr, 1))
CALL atom_density(drho(:, 1), atom%orbitals%pmat, atom%basis, atom%state%maxl_occ, typ="DER")
IF (nlcc) THEN
CALL atom_core_density(drho(:, 1), atom%potential, typ="DER", rr=atom%basis%grid%rad)
END IF
END IF
IF (needs%tau) THEN
ALLOCATE (tau(nr, 1))
CALL atom_density(tau(:, 1), atom%orbitals%pmat, atom%basis, atom%state%maxl_occ, &
typ="KIN", rr=atom%basis%grid%rad2)
END IF
IF (needs%laplace_rho) THEN
ALLOCATE (lap(nr, 1))
CALL atom_density(lap(:, 1), atom%orbitals%pmat, atom%basis, atom%state%maxl_occ, &
typ="LAP", rr=atom%basis%grid%rad2)
IF (nlcc) THEN
CALL atom_core_density(lap(:, 1), atom%potential, typ="LAP", rr=atom%basis%grid%rad)
END IF
END IF
CALL fill_rho_set(rho_set, nspins, needs, rho, drho, tau, lap, nr)
CALL xc_dset_zero_all(deriv_set)
deriv_order = 1
CALL xc_functionals_eval(xc_fun_section, lsd=lsd, rho_set=rho_set, deriv_set=deriv_set, &
deriv_order=deriv_order)
! Integration to get the matrix elements and energy
deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
atom%energy%exc = fourpi*integrate_grid(xcpot(:, 1, 1), atom%basis%grid)
! dump grid density and xcpot (xc energy?)
IF (.FALSE.) THEN
CALL open_file(unit_number=unit_nr, file_status="UNKNOWN", file_action="WRITE", file_name="atom.dat")
DO i = 1, SIZE(xcpot(:, 1, 1))
WRITE (unit_nr, *) atom%basis%grid%rad(i), rho(i, 1), xcpot(i, 1, 1)
END DO
CALL close_file(unit_nr)
END IF
IF (needs%rho) THEN
deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmat%op, xcpot(:, 1, 1), atom%basis, 0)
IF (.FALSE.) THEN
CALL open_file(unit_number=unit_nr, file_status="UNKNOWN", file_action="WRITE", file_name="atompot.dat")
DO i = 1, SIZE(xcpot(:, 1, 1))
WRITE (unit_nr, *) atom%basis%grid%rad(i), rho(i, 1), xcpot(i, 1, 1)
END DO
CALL close_file(unit_nr)
END IF
DEALLOCATE (rho)
END IF
IF (needs%norm_drho) THEN
deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmat%op, xcpot(:, 1, 1), atom%basis, 1)
IF (.FALSE.) THEN
CALL open_file(unit_number=unit_nr, file_status="UNKNOWN", file_action="WRITE", file_name="atomdpot.dat")
DO i = 1, SIZE(xcpot(:, 1, 1))
WRITE (unit_nr, *) atom%basis%grid%rad(i), drho(i, 1), xcpot(i, 1, 1)
END DO
CALL close_file(unit_nr)
END IF
DEALLOCATE (drho)
END IF
IF (needs%tau) THEN
deriv => xc_dset_get_derivative(deriv_set, [deriv_tau], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
n1 = SIZE(xcmat%op, 1)
n2 = SIZE(xcmat%op, 2)
n3 = SIZE(xcmat%op, 3)
ALLOCATE (taumat(n1, n2, 0:n3 - 1))
taumat = 0._dp
xcpot(:, 1, 1) = 0.5_dp*xcpot(:, 1, 1)
CALL numpot_matrix(xcmat%op, xcpot(:, 1, 1), atom%basis, 2)
xcpot(:, 1, 1) = xcpot(:, 1, 1)/atom%basis%grid%rad2(:)
CALL numpot_matrix(taumat, xcpot(:, 1, 1), atom%basis, 0)
DO l = 0, 3
xcmat%op(:, :, l) = xcmat%op(:, :, l) + REAL(l*(l + 1), dp)*taumat(:, :, l)
END DO
DEALLOCATE (tau)
DEALLOCATE (taumat)
END IF
! assume lap is not really needed
IF (needs%laplace_rho) THEN
DEALLOCATE (lap)
END IF
! Release the xc structure used to store the xc derivatives
CALL xc_dset_release(deriv_set)
CALL xc_rho_set_release(rho_set)
END IF !xc_none
ELSE
! we don't have an xc_section, use a default setup
nr = atom%basis%grid%nr
ALLOCATE (rho(nr, 1), exc(nr), vxc(nr))
CALL atom_density(rho(:, 1), atom%orbitals%pmat, atom%basis, atom%state%maxl_occ, typ="RHO")
IF (nlcc) THEN
CALL atom_core_density(rho(:, 1), atom%potential, typ="RHO", rr=atom%basis%grid%rad)
END IF
CALL lda_pade(rho(:, 1), exc, vxc)
atom%energy%exc = fourpi*integrate_grid(exc, atom%basis%grid)
CALL numpot_matrix(xcmat%op, vxc, atom%basis, 0)
DEALLOCATE (rho, exc, vxc)
END IF
CALL timestop(handle)
END SUBROUTINE calculate_atom_vxc_lda
! **************************************************************************************************
!> \brief Calculate atomic exchange-correlation potential in spin-polarized case.
!> \param xcmata spin-alpha exchange-correlation potential matrix
!> \param xcmatb spin-beta exchange-correlation potential matrix
!> \param atom information about the atomic kind
!> \param xc_section XC input section
!> \par History
!> * 02.2010 created [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE calculate_atom_vxc_lsd(xcmata, xcmatb, atom, xc_section)
TYPE(opmat_type), POINTER :: xcmata, xcmatb
TYPE(atom_type), INTENT(INOUT) :: atom
TYPE(section_vals_type), POINTER :: xc_section
CHARACTER(LEN=*), PARAMETER :: routineN = 'calculate_atom_vxc_lsd'
INTEGER :: deriv_order, handle, l, myfun, n1, n2, &
n3, nr, nspins
INTEGER, DIMENSION(2, 3) :: bounds
LOGICAL :: lsd, nlcc
REAL(KIND=dp) :: density_cut, gradient_cut, tau_cut
REAL(KIND=dp), DIMENSION(:), POINTER :: exc, vxca, vxcb, xfun
REAL(KIND=dp), DIMENSION(:, :), POINTER :: drho, lap, rho, tau
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: taumat, xcpot
TYPE(section_vals_type), POINTER :: xc_fun_section
TYPE(xc_derivative_set_type) :: deriv_set
TYPE(xc_derivative_type), POINTER :: deriv
TYPE(xc_rho_cflags_type) :: needs
TYPE(xc_rho_set_type) :: rho_set
CALL timeset(routineN, handle)
nlcc = .FALSE.
IF (atom%potential%ppot_type == gth_pseudo) THEN
nlcc = atom%potential%gth_pot%nlcc
ELSE IF (atom%potential%ppot_type == upf_pseudo) THEN
nlcc = atom%potential%upf_pot%core_correction
CPASSERT(.NOT. nlcc)
ELSE IF (atom%potential%ppot_type == sgp_pseudo) THEN
nlcc = atom%potential%sgp_pot%has_nlcc
CPASSERT(.NOT. nlcc)
END IF
IF (ASSOCIATED(xc_section)) THEN
IF (nlcc) THEN
nr = atom%basis%grid%nr
ALLOCATE (xfun(nr))
END IF
xc_fun_section => section_vals_get_subs_vals(xc_section, "XC_FUNCTIONAL")
CALL section_vals_val_get(xc_fun_section, "_SECTION_PARAMETERS_", i_val=myfun)
IF (myfun == xc_none) THEN
atom%energy%exc = 0._dp
ELSE
CALL section_vals_val_get(xc_section, "DENSITY_CUTOFF", r_val=density_cut)
CALL section_vals_val_get(xc_section, "GRADIENT_CUTOFF", r_val=gradient_cut)
CALL section_vals_val_get(xc_section, "TAU_CUTOFF", r_val=tau_cut)
lsd = .TRUE.
nspins = 2
needs = xc_functionals_get_needs(xc_fun_section, lsd=lsd, calc_potential=.FALSE.)
! Prepare the structures needed to calculate and store the xc derivatives
! Array dimension: here anly one dimensional arrays are used,
! i.e. only the first column of deriv_data is read.
! The other to dimensions are set to size equal 1
nr = atom%basis%grid%nr
bounds(1:2, 1:3) = 1
bounds(2, 1) = nr
! create a place where to put the derivatives
CALL xc_dset_create(deriv_set, local_bounds=bounds)
! create the place where to store the argument for the functionals
CALL xc_rho_set_create(rho_set, bounds, rho_cutoff=density_cut, &
drho_cutoff=gradient_cut, tau_cutoff=tau_cut)
! allocate the required 3d arrays where to store rho and drho
CALL xc_rho_set_atom_update(rho_set, needs, nspins, bounds)
NULLIFY (rho, drho, tau)
IF (needs%rho_spin) THEN
ALLOCATE (rho(nr, 2))
CALL atom_density(rho(:, 1), atom%orbitals%pmata, atom%basis, atom%state%maxl_occ, typ="RHO")
CALL atom_density(rho(:, 2), atom%orbitals%pmatb, atom%basis, atom%state%maxl_occ, typ="RHO")
IF (nlcc) THEN
xfun = 0.0_dp
CALL atom_core_density(xfun(:), atom%potential, typ="RHO", rr=atom%basis%grid%rad)
rho(:, 1) = rho(:, 1) + 0.5_dp*xfun(:)
rho(:, 2) = rho(:, 2) + 0.5_dp*xfun(:)
END IF
END IF
IF (needs%norm_drho_spin) THEN
ALLOCATE (drho(nr, 2))
CALL atom_density(drho(:, 1), atom%orbitals%pmata, atom%basis, atom%state%maxl_occ, typ="DER")
CALL atom_density(drho(:, 2), atom%orbitals%pmatb, atom%basis, atom%state%maxl_occ, typ="DER")
IF (nlcc) THEN
xfun = 0.0_dp
CALL atom_core_density(xfun(:), atom%potential, typ="DER", rr=atom%basis%grid%rad)
drho(:, 1) = drho(:, 1) + 0.5_dp*xfun(:)
drho(:, 2) = drho(:, 2) + 0.5_dp*xfun(:)
END IF
END IF
IF (needs%tau_spin) THEN
ALLOCATE (tau(nr, 2))
CALL atom_density(tau(:, 1), atom%orbitals%pmata, atom%basis, atom%state%maxl_occ, &
typ="KIN", rr=atom%basis%grid%rad2)
CALL atom_density(tau(:, 2), atom%orbitals%pmatb, atom%basis, atom%state%maxl_occ, &
typ="KIN", rr=atom%basis%grid%rad2)
END IF
IF (needs%laplace_rho_spin) THEN
ALLOCATE (lap(nr, 2))
CALL atom_density(lap(:, 1), atom%orbitals%pmata, atom%basis, atom%state%maxl_occ, &
typ="LAP", rr=atom%basis%grid%rad2)
CALL atom_density(lap(:, 2), atom%orbitals%pmatb, atom%basis, atom%state%maxl_occ, &
typ="LAP", rr=atom%basis%grid%rad2)
IF (nlcc) THEN
xfun = 0.0_dp
CALL atom_core_density(xfun(:), atom%potential, typ="LAP", rr=atom%basis%grid%rad)
lap(:, 1) = lap(:, 1) + 0.5_dp*xfun(:)
lap(:, 2) = lap(:, 2) + 0.5_dp*xfun(:)
END IF
END IF
CALL fill_rho_set(rho_set, nspins, needs, rho, drho, tau, lap, nr)
CALL xc_dset_zero_all(deriv_set)
deriv_order = 1
CALL xc_functionals_eval(xc_fun_section, lsd=lsd, rho_set=rho_set, deriv_set=deriv_set, &
deriv_order=deriv_order)
! Integration to get the matrix elements and energy
deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
atom%energy%exc = fourpi*integrate_grid(xcpot(:, 1, 1), atom%basis%grid)
IF (needs%rho_spin) THEN
deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmata%op, xcpot(:, 1, 1), atom%basis, 0)
deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmatb%op, xcpot(:, 1, 1), atom%basis, 0)
DEALLOCATE (rho)
END IF
IF (needs%norm_drho_spin) THEN
! drhoa
NULLIFY (deriv)
deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmata%op, xcpot(:, 1, 1), atom%basis, 1)
! drhob
NULLIFY (deriv)
deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmatb%op, xcpot(:, 1, 1), atom%basis, 1)
! Cross Terms
NULLIFY (deriv)
deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho])
IF (ASSOCIATED(deriv)) THEN
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmata%op, xcpot(:, 1, 1), atom%basis, 1)
CALL numpot_matrix(xcmatb%op, xcpot(:, 1, 1), atom%basis, 1)
END IF
DEALLOCATE (drho)
END IF
IF (needs%tau_spin) THEN
n1 = SIZE(xcmata%op, 1)
n2 = SIZE(xcmata%op, 2)
n3 = SIZE(xcmata%op, 3)
ALLOCATE (taumat(n1, n2, 0:n3 - 1))
deriv => xc_dset_get_derivative(deriv_set, [deriv_tau_a], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
taumat = 0._dp
xcpot(:, 1, 1) = 0.5_dp*xcpot(:, 1, 1)
CALL numpot_matrix(xcmata%op, xcpot(:, 1, 1), atom%basis, 2)
xcpot(:, 1, 1) = xcpot(:, 1, 1)/atom%basis%grid%rad2(:)
CALL numpot_matrix(taumat, xcpot(:, 1, 1), atom%basis, 0)
DO l = 0, 3
xcmata%op(:, :, l) = xcmata%op(:, :, l) + REAL(l*(l + 1), dp)*taumat(:, :, l)
END DO
deriv => xc_dset_get_derivative(deriv_set, [deriv_tau_b], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
taumat = 0._dp
xcpot(:, 1, 1) = 0.5_dp*xcpot(:, 1, 1)
CALL numpot_matrix(xcmatb%op, xcpot(:, 1, 1), atom%basis, 2)
xcpot(:, 1, 1) = xcpot(:, 1, 1)/atom%basis%grid%rad2(:)
CALL numpot_matrix(taumat, xcpot(:, 1, 1), atom%basis, 0)
DO l = 0, 3
xcmatb%op(:, :, l) = xcmatb%op(:, :, l) + REAL(l*(l + 1), dp)*taumat(:, :, l)
END DO
DEALLOCATE (tau)
DEALLOCATE (taumat)
END IF
! assume lap is not really needed
IF (needs%laplace_rho_spin) THEN
DEALLOCATE (lap)
END IF
! Release the xc structure used to store the xc derivatives
CALL xc_dset_release(deriv_set)
CALL xc_rho_set_release(rho_set)
END IF !xc_none
IF (nlcc) DEALLOCATE (xfun)
ELSE
! we don't have an xc_section, use a default setup
nr = atom%basis%grid%nr
ALLOCATE (rho(nr, 2), exc(nr), vxca(nr), vxcb(nr))
IF (nlcc) ALLOCATE (xfun(nr))
CALL atom_density(rho(:, 1), atom%orbitals%pmata, atom%basis, atom%state%maxl_occ, typ="RHO")
CALL atom_density(rho(:, 2), atom%orbitals%pmatb, atom%basis, atom%state%maxl_occ, typ="RHO")
IF (nlcc) THEN
xfun(:) = 0.0_dp
CALL atom_core_density(xfun(:), atom%potential, typ="RHO", rr=atom%basis%grid%rad)
rho(:, 1) = rho(:, 1) + 0.5_dp*xfun(:)
rho(:, 2) = rho(:, 2) + 0.5_dp*xfun(:)
END IF
CALL lsd_pade(rho(:, 1), rho(:, 2), exc, vxca, vxcb)
atom%energy%exc = fourpi*integrate_grid(exc, atom%basis%grid)
CALL numpot_matrix(xcmata%op, vxca, atom%basis, 0)
CALL numpot_matrix(xcmatb%op, vxcb, atom%basis, 0)
DEALLOCATE (rho, exc, vxca, vxcb)
IF (nlcc) DEALLOCATE (xfun)
END IF
CALL timestop(handle)
END SUBROUTINE calculate_atom_vxc_lsd
! **************************************************************************************************
!> \brief Alternative subroutine that calculates atomic exchange-correlation potential
!> in spin-restricted case.
!> \param basis atomic basis set
!> \param pmat density matrix
!> \param maxl maximum angular momentum
!> \param xc_section XC input section
!> \param fexc exchange-correlation energy
!> \param xcmat exchange-correlation potential matrix
!> \par History
!> * 07.2016 ADMM analysis [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE atom_vxc_lda(basis, pmat, maxl, xc_section, fexc, xcmat)
TYPE(atom_basis_type), POINTER :: basis
REAL(KIND=dp), DIMENSION(:, :, :), INTENT(IN) :: pmat
INTEGER, INTENT(IN) :: maxl
TYPE(section_vals_type), POINTER :: xc_section
REAL(KIND=dp), INTENT(OUT) :: fexc
REAL(KIND=dp), DIMENSION(:, :, :), INTENT(INOUT) :: xcmat
CHARACTER(LEN=*), PARAMETER :: routineN = 'atom_vxc_lda'
INTEGER :: deriv_order, handle, l, myfun, n1, n2, &
n3, nr, nspins
INTEGER, DIMENSION(2, 3) :: bounds
LOGICAL :: lsd
REAL(KIND=dp) :: density_cut, gradient_cut, tau_cut
REAL(KIND=dp), DIMENSION(:, :), POINTER :: drho, lap, rho, tau
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: taumat, xcpot
TYPE(section_vals_type), POINTER :: xc_fun_section
TYPE(xc_derivative_set_type) :: deriv_set
TYPE(xc_derivative_type), POINTER :: deriv
TYPE(xc_rho_cflags_type) :: needs
TYPE(xc_rho_set_type) :: rho_set
CALL timeset(routineN, handle)
CPASSERT(ASSOCIATED(xc_section))
xc_fun_section => section_vals_get_subs_vals(xc_section, "XC_FUNCTIONAL")
CALL section_vals_val_get(xc_fun_section, "_SECTION_PARAMETERS_", i_val=myfun)
IF (myfun == xc_none) THEN
fexc = 0._dp
ELSE
CALL section_vals_val_get(xc_section, "DENSITY_CUTOFF", r_val=density_cut)
CALL section_vals_val_get(xc_section, "GRADIENT_CUTOFF", r_val=gradient_cut)
CALL section_vals_val_get(xc_section, "TAU_CUTOFF", r_val=tau_cut)
lsd = .FALSE.
nspins = 1
needs = xc_functionals_get_needs(xc_fun_section, lsd=lsd, calc_potential=.FALSE.)
! Prepare the structures needed to calculate and store the xc derivatives
! Array dimension: here anly one dimensional arrays are used,
! i.e. only the first column of deriv_data is read.
! The other to dimensions are set to size equal 1
nr = basis%grid%nr
bounds(1:2, 1:3) = 1
bounds(2, 1) = nr
! create a place where to put the derivatives
CALL xc_dset_create(deriv_set, local_bounds=bounds)
! create the place where to store the argument for the functionals
CALL xc_rho_set_create(rho_set, bounds, rho_cutoff=density_cut, &
drho_cutoff=gradient_cut, tau_cutoff=tau_cut)
! allocate the required 3d arrays where to store rho and drho
CALL xc_rho_set_atom_update(rho_set, needs, nspins, bounds)
NULLIFY (rho, drho, tau)
IF (needs%rho) THEN
ALLOCATE (rho(nr, 1))
CALL atom_density(rho(:, 1), pmat, basis, maxl, typ="RHO")
END IF
IF (needs%norm_drho) THEN
ALLOCATE (drho(nr, 1))
CALL atom_density(drho(:, 1), pmat, basis, maxl, typ="DER")
END IF
IF (needs%tau) THEN
ALLOCATE (tau(nr, 1))
CALL atom_density(tau(:, 1), pmat, basis, maxl, typ="KIN", rr=basis%grid%rad2)
END IF
IF (needs%laplace_rho) THEN
ALLOCATE (lap(nr, 1))
CALL atom_density(lap(:, 1), pmat, basis, maxl, typ="LAP", rr=basis%grid%rad2)
END IF
CALL fill_rho_set(rho_set, nspins, needs, rho, drho, tau, lap, nr)
CALL xc_dset_zero_all(deriv_set)
deriv_order = 1
CALL xc_functionals_eval(xc_fun_section, lsd=lsd, rho_set=rho_set, deriv_set=deriv_set, &
deriv_order=deriv_order)
! Integration to get the matrix elements and energy
deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
fexc = fourpi*integrate_grid(xcpot(:, 1, 1), basis%grid)
IF (needs%rho) THEN
deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmat, xcpot(:, 1, 1), basis, 0)
DEALLOCATE (rho)
END IF
IF (needs%norm_drho) THEN
deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmat, xcpot(:, 1, 1), basis, 1)
DEALLOCATE (drho)
END IF
IF (needs%tau) THEN
deriv => xc_dset_get_derivative(deriv_set, [deriv_tau], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
n1 = SIZE(xcmat, 1)
n2 = SIZE(xcmat, 2)
n3 = SIZE(xcmat, 3)
ALLOCATE (taumat(n1, n2, 0:n3 - 1))
taumat = 0._dp
xcpot(:, 1, 1) = 0.5_dp*xcpot(:, 1, 1)
CALL numpot_matrix(xcmat, xcpot(:, 1, 1), basis, 2)
xcpot(:, 1, 1) = xcpot(:, 1, 1)/basis%grid%rad2(:)
CALL numpot_matrix(taumat, xcpot(:, 1, 1), basis, 0)
DO l = 0, 3
xcmat(:, :, l) = xcmat(:, :, l) + REAL(l*(l + 1), dp)*taumat(:, :, l)
END DO
DEALLOCATE (tau)
DEALLOCATE (taumat)
END IF
! we assume lap is not really needed
IF (needs%laplace_rho) THEN
DEALLOCATE (lap)
END IF
! Release the xc structure used to store the xc derivatives
CALL xc_dset_release(deriv_set)
CALL xc_rho_set_release(rho_set)
END IF !xc_none
CALL timestop(handle)
END SUBROUTINE atom_vxc_lda
! **************************************************************************************************
!> \brief Alternative subroutine that calculates atomic exchange-correlation potential
!> in spin-polarized case.
!> \param basis atomic basis set
!> \param pmata spin-alpha density matrix
!> \param pmatb spin-beta density matrix
!> \param maxl maximum angular momentum
!> \param xc_section XC input section
!> \param fexc exchange-correlation energy
!> \param xcmata spin-alpha exchange-correlation potential matrix
!> \param xcmatb spin-beta exchange-correlation potential matrix
!> \par History
!> * 07.2016 ADMM analysis [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE atom_vxc_lsd(basis, pmata, pmatb, maxl, xc_section, fexc, xcmata, xcmatb)
TYPE(atom_basis_type), POINTER :: basis
REAL(KIND=dp), DIMENSION(:, :, :), INTENT(IN) :: pmata, pmatb
INTEGER, INTENT(IN) :: maxl
TYPE(section_vals_type), POINTER :: xc_section
REAL(KIND=dp), INTENT(OUT) :: fexc
REAL(KIND=dp), DIMENSION(:, :, :), INTENT(INOUT) :: xcmata, xcmatb
CHARACTER(LEN=*), PARAMETER :: routineN = 'atom_vxc_lsd'
INTEGER :: deriv_order, handle, l, myfun, n1, n2, &
n3, nr, nspins
INTEGER, DIMENSION(2, 3) :: bounds
LOGICAL :: lsd
REAL(KIND=dp) :: density_cut, gradient_cut, tau_cut
REAL(KIND=dp), DIMENSION(:, :), POINTER :: drho, lap, rho, tau
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: taumat, xcpot
TYPE(section_vals_type), POINTER :: xc_fun_section
TYPE(xc_derivative_set_type) :: deriv_set
TYPE(xc_derivative_type), POINTER :: deriv
TYPE(xc_rho_cflags_type) :: needs
TYPE(xc_rho_set_type) :: rho_set
CALL timeset(routineN, handle)
CPASSERT(ASSOCIATED(xc_section))
xc_fun_section => section_vals_get_subs_vals(xc_section, "XC_FUNCTIONAL")
CALL section_vals_val_get(xc_fun_section, "_SECTION_PARAMETERS_", i_val=myfun)
IF (myfun == xc_none) THEN
fexc = 0._dp
ELSE
CALL section_vals_val_get(xc_section, "DENSITY_CUTOFF", r_val=density_cut)
CALL section_vals_val_get(xc_section, "GRADIENT_CUTOFF", r_val=gradient_cut)
CALL section_vals_val_get(xc_section, "TAU_CUTOFF", r_val=tau_cut)
lsd = .TRUE.
nspins = 2
needs = xc_functionals_get_needs(xc_fun_section, lsd=lsd, calc_potential=.FALSE.)
! Prepare the structures needed to calculate and store the xc derivatives
! Array dimension: here anly one dimensional arrays are used,
! i.e. only the first column of deriv_data is read.
! The other to dimensions are set to size equal 1
nr = basis%grid%nr
bounds(1:2, 1:3) = 1
bounds(2, 1) = nr
! create a place where to put the derivatives
CALL xc_dset_create(deriv_set, local_bounds=bounds)
! create the place where to store the argument for the functionals
CALL xc_rho_set_create(rho_set, bounds, rho_cutoff=density_cut, &
drho_cutoff=gradient_cut, tau_cutoff=tau_cut)
! allocate the required 3d arrays where to store rho and drho
CALL xc_rho_set_atom_update(rho_set, needs, nspins, bounds)
NULLIFY (rho, drho, tau)
IF (needs%rho_spin) THEN
ALLOCATE (rho(nr, 2))
CALL atom_density(rho(:, 1), pmata, basis, maxl, typ="RHO")
CALL atom_density(rho(:, 2), pmatb, basis, maxl, typ="RHO")
END IF
IF (needs%norm_drho_spin) THEN
ALLOCATE (drho(nr, 2))
CALL atom_density(drho(:, 1), pmata, basis, maxl, typ="DER")
CALL atom_density(drho(:, 2), pmatb, basis, maxl, typ="DER")
END IF
IF (needs%tau_spin) THEN
ALLOCATE (tau(nr, 2))
CALL atom_density(tau(:, 1), pmata, basis, maxl, typ="KIN", rr=basis%grid%rad2)
CALL atom_density(tau(:, 2), pmatb, basis, maxl, typ="KIN", rr=basis%grid%rad2)
END IF
IF (needs%laplace_rho_spin) THEN
ALLOCATE (lap(nr, 2))
CALL atom_density(lap(:, 1), pmata, basis, maxl, typ="LAP", rr=basis%grid%rad2)
CALL atom_density(lap(:, 2), pmatb, basis, maxl, typ="LAP", rr=basis%grid%rad2)
END IF
CALL fill_rho_set(rho_set, nspins, needs, rho, drho, tau, lap, nr)
CALL xc_dset_zero_all(deriv_set)
deriv_order = 1
CALL xc_functionals_eval(xc_fun_section, lsd=lsd, rho_set=rho_set, deriv_set=deriv_set, &
deriv_order=deriv_order)
! Integration to get the matrix elements and energy
deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
fexc = fourpi*integrate_grid(xcpot(:, 1, 1), basis%grid)
IF (needs%rho_spin) THEN
deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmata, xcpot(:, 1, 1), basis, 0)
deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmatb, xcpot(:, 1, 1), basis, 0)
DEALLOCATE (rho)
END IF
IF (needs%norm_drho_spin) THEN
! drhoa
NULLIFY (deriv)
deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmata, xcpot(:, 1, 1), basis, 1)
! drhob
NULLIFY (deriv)
deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmatb, xcpot(:, 1, 1), basis, 1)
! Cross Terms
NULLIFY (deriv)
deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho])
IF (ASSOCIATED(deriv)) THEN
CALL xc_derivative_get(deriv, deriv_data=xcpot)
CALL numpot_matrix(xcmata, xcpot(:, 1, 1), basis, 1)
CALL numpot_matrix(xcmatb, xcpot(:, 1, 1), basis, 1)
END IF
DEALLOCATE (drho)
END IF
IF (needs%tau_spin) THEN
n1 = SIZE(xcmata, 1)
n2 = SIZE(xcmata, 2)
n3 = SIZE(xcmata, 3)
ALLOCATE (taumat(n1, n2, 0:n3 - 1))
deriv => xc_dset_get_derivative(deriv_set, [deriv_tau_a], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
taumat = 0._dp
xcpot(:, 1, 1) = 0.5_dp*xcpot(:, 1, 1)
CALL numpot_matrix(xcmata, xcpot(:, 1, 1), basis, 2)
xcpot(:, 1, 1) = xcpot(:, 1, 1)/basis%grid%rad2(:)
CALL numpot_matrix(taumat, xcpot(:, 1, 1), basis, 0)
DO l = 0, 3
xcmata(:, :, l) = xcmata(:, :, l) + REAL(l*(l + 1), dp)*taumat(:, :, l)
END DO
deriv => xc_dset_get_derivative(deriv_set, [deriv_tau_b], allocate_deriv=.FALSE.)
CALL xc_derivative_get(deriv, deriv_data=xcpot)
taumat = 0._dp
xcpot(:, 1, 1) = 0.5_dp*xcpot(:, 1, 1)
CALL numpot_matrix(xcmatb, xcpot(:, 1, 1), basis, 2)
xcpot(:, 1, 1) = xcpot(:, 1, 1)/basis%grid%rad2(:)
CALL numpot_matrix(taumat, xcpot(:, 1, 1), basis, 0)
DO l = 0, 3
xcmatb(:, :, l) = xcmatb(:, :, l) + REAL(l*(l + 1), dp)*taumat(:, :, l)
END DO
DEALLOCATE (tau)
DEALLOCATE (taumat)
END IF
! Release the xc structure used to store the xc derivatives
CALL xc_dset_release(deriv_set)
CALL xc_rho_set_release(rho_set)
END IF !xc_none
CALL timestop(handle)
END SUBROUTINE atom_vxc_lsd
! **************************************************************************************************
!> \brief Estimate the ADMM exchange energy correction term using a model exchange functional.
!> \param basis0 reference atomic basis set
!> \param pmat0 reference density matrix
!> \param basis1 ADMM basis set
!> \param pmat1 ADMM density matrix
!> \param maxl maxumum angular momentum
!> \param functional name of the model exchange functional:
!> "LINX" -- linear extrapolation of the Slater exchange potential [?]
!> \param dfexc exchange-correlation energy difference
!> \param linxpar LINX parameters
!> \par History
!> * 07.2016 ADMM analysis [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE atom_dpot_lda(basis0, pmat0, basis1, pmat1, maxl, functional, dfexc, linxpar)
TYPE(atom_basis_type), POINTER :: basis0
REAL(KIND=dp), DIMENSION(:, :, :), INTENT(IN) :: pmat0
TYPE(atom_basis_type), POINTER :: basis1
REAL(KIND=dp), DIMENSION(:, :, :), INTENT(IN) :: pmat1
INTEGER, INTENT(IN) :: maxl
CHARACTER(LEN=*), INTENT(IN) :: functional
REAL(KIND=dp), INTENT(OUT) :: dfexc
REAL(KIND=dp), DIMENSION(:), INTENT(IN), OPTIONAL :: linxpar
CHARACTER(LEN=*), PARAMETER :: routineN = 'atom_dpot_lda'
REAL(KIND=dp), PARAMETER :: alx = 0.20_dp, blx = -0.06_dp, &
fs = -0.75_dp*(3._dp/pi)**(1._dp/3._dp)
INTEGER :: handle, ir, nr
REAL(KIND=dp) :: a, b, fx
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: delta, drho0, drho1, pot0, pot1, rho0, &
rho1
CALL timeset(routineN, handle)
nr = basis0%grid%nr