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atom_types.F
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!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2025 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief Define the atom type and its sub types
!> \author jgh
!> \date 03.03.2008
!> \version 1.0
!>
! **************************************************************************************************
MODULE atom_types
USE atom_upf, ONLY: atom_read_upf,&
atom_release_upf,&
atom_upfpot_type
USE bessel_lib, ONLY: bessel0
USE bibliography, ONLY: Limpanuparb2011,&
cite_reference
USE cp_linked_list_input, ONLY: cp_sll_val_next,&
cp_sll_val_type
USE cp_parser_methods, ONLY: parser_get_next_line,&
parser_get_object,&
parser_read_line,&
parser_search_string,&
parser_test_next_token
USE cp_parser_types, ONLY: cp_parser_type,&
parser_create,&
parser_release
USE input_constants, ONLY: &
barrier_conf, contracted_gto, do_analytic, do_gapw_log, do_nonrel_atom, do_numeric, &
do_potential_coulomb, do_potential_long, do_potential_mix_cl, do_potential_short, &
do_rks_atom, do_semi_analytic, ecp_pseudo, gaussian, geometrical_gto, gth_pseudo, no_conf, &
no_pseudo, numerical, poly_conf, sgp_pseudo, slater, upf_pseudo
USE input_section_types, ONLY: section_vals_get,&
section_vals_get_subs_vals,&
section_vals_list_get,&
section_vals_type,&
section_vals_val_get
USE input_val_types, ONLY: val_get,&
val_type
USE kinds, ONLY: default_string_length,&
dp
USE mathconstants, ONLY: dfac,&
fac,&
pi,&
rootpi
USE periodic_table, ONLY: get_ptable_info,&
ptable
USE qs_grid_atom, ONLY: allocate_grid_atom,&
create_grid_atom,&
deallocate_grid_atom,&
grid_atom_type
USE string_utilities, ONLY: remove_word,&
uppercase
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'atom_types'
! maximum l-quantum number considered in atomic code/basis
INTEGER, PARAMETER :: lmat = 5
INTEGER, PARAMETER :: GTO_BASIS = 100, &
CGTO_BASIS = 101, &
STO_BASIS = 102, &
NUM_BASIS = 103
INTEGER, PARAMETER :: nmax = 25
!> \brief Provides all information about a basis set
! **************************************************************************************************
TYPE atom_basis_type
INTEGER :: basis_type = GTO_BASIS
INTEGER, DIMENSION(0:lmat) :: nbas = 0
INTEGER, DIMENSION(0:lmat) :: nprim = 0
REAL(KIND=dp), DIMENSION(:, :), POINTER :: am => NULL() !GTO exponents
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: cm => NULL() !Contraction coeffs
REAL(KIND=dp), DIMENSION(:, :), POINTER :: as => NULL() !STO exponents
INTEGER, DIMENSION(:, :), POINTER :: ns => NULL() !STO n-quantum numbers
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: bf => NULL() !num. bsf
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: dbf => NULL() !derivatives (num)
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: ddbf => NULL() !2nd derivatives (num)
REAL(KIND=dp) :: eps_eig = 0.0_dp
TYPE(grid_atom_type), POINTER :: grid => NULL()
LOGICAL :: geometrical = .FALSE.
REAL(KIND=dp) :: aval = 0.0_dp, cval = 0.0_dp
INTEGER, DIMENSION(0:lmat) :: start = 0
END TYPE atom_basis_type
!> \brief Provides all information about a pseudopotential
! **************************************************************************************************
TYPE atom_gthpot_type
CHARACTER(LEN=2) :: symbol = ""
CHARACTER(LEN=default_string_length) :: pname = ""
INTEGER, DIMENSION(0:lmat) :: econf = 0
REAL(dp) :: zion = 0.0_dp
REAL(dp) :: rc = 0.0_dp
INTEGER :: ncl = 0
REAL(dp), DIMENSION(5) :: cl = 0.0_dp
INTEGER, DIMENSION(0:lmat) :: nl = 0
REAL(dp), DIMENSION(0:lmat) :: rcnl = 0.0_dp
REAL(dp), DIMENSION(4, 4, 0:lmat) :: hnl = 0.0_dp
! type extensions
! NLCC
LOGICAL :: nlcc = .FALSE.
INTEGER :: nexp_nlcc = 0
REAL(KIND=dp), DIMENSION(10) :: alpha_nlcc = 0.0_dp
INTEGER, DIMENSION(10) :: nct_nlcc = 0
REAL(KIND=dp), DIMENSION(4, 10) :: cval_nlcc = 0.0_dp
! LSD potential
LOGICAL :: lsdpot = .FALSE.
INTEGER :: nexp_lsd = 0
REAL(KIND=dp), DIMENSION(10) :: alpha_lsd = 0.0_dp
INTEGER, DIMENSION(10) :: nct_lsd = 0
REAL(KIND=dp), DIMENSION(4, 10) :: cval_lsd = 0.0_dp
! extended local potential
LOGICAL :: lpotextended = .FALSE.
INTEGER :: nexp_lpot = 0
REAL(KIND=dp), DIMENSION(10) :: alpha_lpot = 0.0_dp
INTEGER, DIMENSION(10) :: nct_lpot = 0
REAL(KIND=dp), DIMENSION(4, 10) :: cval_lpot = 0.0_dp
END TYPE atom_gthpot_type
TYPE atom_ecppot_type
CHARACTER(LEN=2) :: symbol = ""
CHARACTER(LEN=default_string_length) :: pname = ""
INTEGER, DIMENSION(0:lmat) :: econf = 0
REAL(dp) :: zion = 0.0_dp
INTEGER :: lmax = 0
INTEGER :: nloc = 0 ! # terms
INTEGER, DIMENSION(1:15) :: nrloc = 0 ! r**(n-2)
REAL(dp), DIMENSION(1:15) :: aloc = 0.0_dp ! coefficient
REAL(dp), DIMENSION(1:15) :: bloc = 0.0_dp ! exponent
INTEGER, DIMENSION(0:10) :: npot = 0 ! # terms
INTEGER, DIMENSION(1:15, 0:10) :: nrpot = 0 ! r**(n-2)
REAL(dp), DIMENSION(1:15, 0:10) :: apot = 0.0_dp ! coefficient
REAL(dp), DIMENSION(1:15, 0:10) :: bpot = 0.0_dp ! exponent
END TYPE atom_ecppot_type
TYPE atom_sgppot_type
CHARACTER(LEN=2) :: symbol = ""
CHARACTER(LEN=default_string_length) :: pname = ""
INTEGER, DIMENSION(0:lmat) :: econf = 0
REAL(dp) :: zion = 0.0_dp
INTEGER :: lmax = 0
LOGICAL :: has_nonlocal = .FALSE.
INTEGER :: n_nonlocal = 0
LOGICAL, DIMENSION(0:5) :: is_nonlocal = .FALSE.
REAL(KIND=dp), DIMENSION(nmax) :: a_nonlocal = 0.0_dp
REAL(KIND=dp), DIMENSION(nmax, 0:lmat) :: h_nonlocal = 0.0_dp
REAL(KIND=dp), DIMENSION(nmax, nmax, 0:lmat) :: c_nonlocal = 0.0_dp
INTEGER :: n_local = 0
REAL(KIND=dp) :: ac_local = 0.0_dp
REAL(KIND=dp), DIMENSION(nmax) :: a_local = 0.0_dp
REAL(KIND=dp), DIMENSION(nmax) :: c_local = 0.0_dp
LOGICAL :: has_nlcc = .FALSE.
INTEGER :: n_nlcc = 0
REAL(KIND=dp), DIMENSION(nmax) :: a_nlcc = 0.0_dp
REAL(KIND=dp), DIMENSION(nmax) :: c_nlcc = 0.0_dp
END TYPE atom_sgppot_type
TYPE atom_potential_type
INTEGER :: ppot_type = 0
LOGICAL :: confinement = .FALSE.
INTEGER :: conf_type = 0
REAL(dp) :: acon = 0.0_dp
REAL(dp) :: rcon = 0.0_dp
REAL(dp) :: scon = 0.0_dp
TYPE(atom_gthpot_type) :: gth_pot = atom_gthpot_type()
TYPE(atom_ecppot_type) :: ecp_pot = atom_ecppot_type()
TYPE(atom_upfpot_type) :: upf_pot = atom_upfpot_type()
TYPE(atom_sgppot_type) :: sgp_pot = atom_sgppot_type()
END TYPE atom_potential_type
!> \brief Provides info about hartree-fock exchange (For now, we only support potentials that can be represented
!> with Coulomb and longrange-coulomb potential)
! **************************************************************************************************
TYPE atom_hfx_type
REAL(KIND=dp) :: scale_coulomb = 0.0_dp
REAL(KIND=dp) :: scale_longrange = 0.0_dp
REAL(KIND=dp) :: omega = 0.0_dp
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: kernel
LOGICAL :: do_gh = .FALSE.
INTEGER :: nr_gh = 0
END TYPE atom_hfx_type
!> \brief Provides all information on states and occupation
! **************************************************************************************************
TYPE atom_state
REAL(KIND=dp), DIMENSION(0:lmat, 10) :: occ = 0.0_dp
REAL(KIND=dp), DIMENSION(0:lmat, 10) :: core = 0.0_dp
REAL(KIND=dp), DIMENSION(0:lmat, 10) :: occupation = 0.0_dp
INTEGER :: maxl_occ = 0
INTEGER, DIMENSION(0:lmat) :: maxn_occ = 0
INTEGER :: maxl_calc = 0
INTEGER, DIMENSION(0:lmat) :: maxn_calc = 0
INTEGER :: multiplicity = 0
REAL(KIND=dp), DIMENSION(0:lmat, 10) :: occa = 0.0_dp, occb = 0.0_dp
END TYPE atom_state
!> \brief Holds atomic integrals
! **************************************************************************************************
TYPE eri
REAL(KIND=dp), DIMENSION(:, :), POINTER :: int => NULL()
END TYPE eri
TYPE atom_integrals
INTEGER :: status = 0
INTEGER :: ppstat = 0
LOGICAL :: eri_coulomb = .FALSE.
LOGICAL :: eri_exchange = .FALSE.
LOGICAL :: all_nu = .FALSE.
INTEGER, DIMENSION(0:lmat) :: n = 0, nne = 0
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: ovlp => NULL(), kin => NULL(), core => NULL(), clsd => NULL()
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: utrans => NULL(), uptrans => NULL()
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: hnl => NULL()
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: conf => NULL()
TYPE(eri), DIMENSION(100) :: ceri = eri()
TYPE(eri), DIMENSION(100) :: eeri = eri()
INTEGER :: dkhstat = 0
INTEGER :: zorastat = 0
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: tzora => NULL()
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: hdkh => NULL()
END TYPE atom_integrals
!> \brief Holds atomic orbitals and energies
! **************************************************************************************************
TYPE atom_orbitals
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: wfn => NULL(), wfna => NULL(), wfnb => NULL()
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: pmat => NULL(), pmata => NULL(), pmatb => NULL()
REAL(KIND=dp), DIMENSION(:, :), POINTER :: ener => NULL(), enera => NULL(), enerb => NULL()
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: refene => NULL(), refchg => NULL(), refnod => NULL()
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: wrefene => NULL(), wrefchg => NULL(), wrefnod => NULL()
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: crefene => NULL(), crefchg => NULL(), crefnod => NULL()
REAL(KIND=dp), DIMENSION(:, :), POINTER :: wpsir0 => NULL(), tpsir0 => NULL()
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: rcmax => NULL()
CHARACTER(LEN=2), DIMENSION(:, :, :), POINTER :: reftype => NULL()
END TYPE atom_orbitals
!> \brief Operator matrices
! **************************************************************************************************
TYPE opmat_type
INTEGER, DIMENSION(0:lmat) :: n = 0
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: op => NULL()
END TYPE opmat_type
!> \brief Operator grids
! **************************************************************************************************
TYPE opgrid_type
REAL(KIND=dp), DIMENSION(:), POINTER :: op => NULL()
TYPE(grid_atom_type), POINTER :: grid => NULL()
END TYPE opgrid_type
!> \brief All energies
! **************************************************************************************************
TYPE atom_energy_type
REAL(KIND=dp) :: etot = 0.0_dp
REAL(KIND=dp) :: eband = 0.0_dp
REAL(KIND=dp) :: ekin = 0.0_dp
REAL(KIND=dp) :: epot = 0.0_dp
REAL(KIND=dp) :: ecore = 0.0_dp
REAL(KIND=dp) :: elsd = 0.0_dp
REAL(KIND=dp) :: epseudo = 0.0_dp
REAL(KIND=dp) :: eploc = 0.0_dp
REAL(KIND=dp) :: epnl = 0.0_dp
REAL(KIND=dp) :: exc = 0.0_dp
REAL(KIND=dp) :: ecoulomb = 0.0_dp
REAL(KIND=dp) :: eexchange = 0.0_dp
REAL(KIND=dp) :: econfinement = 0.0_dp
END TYPE atom_energy_type
!> \brief Information on optimization procedure
! **************************************************************************************************
TYPE atom_optimization_type
REAL(KIND=dp) :: damping = 0.0_dp
REAL(KIND=dp) :: eps_scf = 0.0_dp
REAL(KIND=dp) :: eps_diis = 0.0_dp
INTEGER :: max_iter = 0
INTEGER :: n_diis = 0
END TYPE atom_optimization_type
!> \brief Provides all information about an atomic kind
! **************************************************************************************************
TYPE atom_type
INTEGER :: z = 0
INTEGER :: zcore = 0
LOGICAL :: pp_calc = .FALSE.
! ZMP adding in type some variables
LOGICAL :: do_zmp = .FALSE., doread = .FALSE., read_vxc = .FALSE., dm = .FALSE.
CHARACTER(LEN=default_string_length) :: ext_file = "", ext_vxc_file = "", &
zmp_restart_file = ""
!
INTEGER :: method_type = do_rks_atom
INTEGER :: relativistic = do_nonrel_atom
INTEGER :: coulomb_integral_type = do_analytic
INTEGER :: exchange_integral_type = do_analytic
! ZMP
REAL(KIND=dp) :: lambda = 0.0_dp
REAL(KIND=dp) :: rho_diff_integral = 0.0_dp
REAL(KIND=dp) :: weight = 0.0_dp, zmpgrid_tol = 0.0_dp, zmpvxcgrid_tol = 0.0_dp
!
TYPE(atom_basis_type), POINTER :: basis => NULL()
TYPE(atom_potential_type), POINTER :: potential => NULL()
TYPE(atom_state), POINTER :: state => NULL()
TYPE(atom_integrals), POINTER :: integrals => NULL()
TYPE(atom_orbitals), POINTER :: orbitals => NULL()
TYPE(atom_energy_type) :: energy = atom_energy_type()
TYPE(atom_optimization_type) :: optimization = atom_optimization_type()
TYPE(section_vals_type), POINTER :: xc_section => NULL(), zmp_section => NULL()
TYPE(opmat_type), POINTER :: fmat => NULL()
TYPE(atom_hfx_type) :: hfx_pot = atom_hfx_type()
END TYPE atom_type
! **************************************************************************************************
TYPE atom_p_type
TYPE(atom_type), POINTER :: atom => NULL()
END TYPE atom_p_type
PUBLIC :: lmat
PUBLIC :: atom_p_type, atom_type, atom_basis_type, atom_state, atom_integrals
PUBLIC :: atom_orbitals, eri, atom_potential_type, atom_hfx_type
PUBLIC :: atom_gthpot_type, atom_ecppot_type, atom_sgppot_type
PUBLIC :: atom_optimization_type
PUBLIC :: atom_compare_grids
PUBLIC :: create_atom_type, release_atom_type, set_atom
PUBLIC :: create_atom_orbs, release_atom_orbs
PUBLIC :: init_atom_basis, init_atom_basis_default_pp, atom_basis_gridrep, release_atom_basis
PUBLIC :: init_atom_potential, release_atom_potential
PUBLIC :: read_atom_opt_section, read_ecp_potential
PUBLIC :: Clementi_geobas
PUBLIC :: GTO_BASIS, CGTO_BASIS, STO_BASIS, NUM_BASIS
PUBLIC :: opmat_type, create_opmat, release_opmat
PUBLIC :: opgrid_type, create_opgrid, release_opgrid
PUBLIC :: no_pseudo, gth_pseudo, sgp_pseudo, upf_pseudo, ecp_pseudo
PUBLIC :: setup_hf_section
! **************************************************************************************************
CONTAINS
! **************************************************************************************************
!> \brief Initialize the basis for the atomic code
!> \param basis ...
!> \param basis_section ...
!> \param zval ...
!> \param btyp ...
!> \note Highly accurate relativistic universal Gaussian basis set: Dirac-Fock-Coulomb calculations
!> for atomic systems up to nobelium
!> J. Chem. Phys. 101, 6829 (1994); DOI:10.1063/1.468311
!> G. L. Malli and A. B. F. Da Silva
!> Department of Chemistry, Simon Fraser University, Burnaby, B.C., Canada
!> Yasuyuki Ishikawa
!> Department of Chemistry, University of Puerto Rico, San Juan, Puerto Rico
!>
!> A universal Gaussian basis set is developed that leads to relativistic Dirac-Fock SCF energies
!> of comparable accuracy as that obtained by the accurate numerical finite-difference method
!> (GRASP2 package) [J. Phys. B 25, 1 (1992)]. The Gaussian-type functions of our universal basis
!> set satisfy the relativistic boundary conditions associated with the finite nuclear model for a
!> finite speed of light and conform to the so-called kinetic balance at the nonrelativistic limit.
!> We attribute the exceptionally high accuracy obtained in our calculations to the fact that the
!> representation of the relativistic dynamics of an electron in a spherical ball finite nucleus
!> near the origin in terms of our universal Gaussian basis set is as accurate as that provided by
!> the numerical finite-difference method. Results of the Dirac-Fock-Coulomb energies for a number
!> of atoms up to No (Z=102) and some negative ions are presented and compared with the recent
!> results obtained with the numerical finite-difference method and geometrical Gaussian basis sets
!> by Parpia, Mohanty, and Clementi [J. Phys. B 25, 1 (1992)]. The accuracy of our calculations is
!> estimated to be within a few parts in 109 for all the atomic systems studied.
! **************************************************************************************************
SUBROUTINE init_atom_basis(basis, basis_section, zval, btyp)
TYPE(atom_basis_type), INTENT(INOUT) :: basis
TYPE(section_vals_type), POINTER :: basis_section
INTEGER, INTENT(IN) :: zval
CHARACTER(LEN=2) :: btyp
INTEGER, PARAMETER :: nua = 40, nup = 16
REAL(KIND=dp), DIMENSION(nua), PARAMETER :: ugbs = (/0.007299_dp, 0.013705_dp, 0.025733_dp, &
0.048316_dp, 0.090718_dp, 0.170333_dp, 0.319819_dp, 0.600496_dp, 1.127497_dp, 2.117000_dp,&
3.974902_dp, 7.463317_dp, 14.013204_dp, 26.311339_dp, 49.402449_dp, 92.758561_dp, &
174.164456_dp, 327.013024_dp, 614.003114_dp, 1152.858743_dp, 2164.619772_dp, &
4064.312984_dp, 7631.197056_dp, 14328.416324_dp, 26903.186074_dp, 50513.706789_dp, &
94845.070265_dp, 178082.107320_dp, 334368.848683_dp, 627814.487663_dp, 1178791.123851_dp, &
2213310.684886_dp, 4155735.557141_dp, 7802853.046713_dp, 14650719.428954_dp, &
27508345.793637_dp, 51649961.080194_dp, 96978513.342764_dp, 182087882.613702_dp, &
341890134.751331_dp/)
CHARACTER(LEN=default_string_length) :: basis_fn, basis_name
INTEGER :: basistype, i, j, k, l, ll, m, ngp, nl, &
nr, nu, quadtype
INTEGER, DIMENSION(0:lmat) :: starti
INTEGER, DIMENSION(:), POINTER :: nqm, num_gto, num_slater, sindex
REAL(KIND=dp) :: al, amax, aval, cval, ear, pf, rk
REAL(KIND=dp), DIMENSION(:), POINTER :: expo
TYPE(section_vals_type), POINTER :: gto_basis_section
! btyp = AE : standard all-electron basis
! btyp = PP : standard pseudopotential basis
! btyp = AA : high accuracy all-electron basis
! btyp = AP : high accuracy pseudopotential basis
NULLIFY (basis%am, basis%cm, basis%as, basis%ns, basis%bf, basis%dbf, basis%ddbf)
! get information on quadrature type and number of grid points
! allocate and initialize the atomic grid
CALL allocate_grid_atom(basis%grid)
CALL section_vals_val_get(basis_section, "QUADRATURE", i_val=quadtype)
CALL section_vals_val_get(basis_section, "GRID_POINTS", i_val=ngp)
IF (ngp <= 0) &
CPABORT("# point radial grid < 0")
CALL create_grid_atom(basis%grid, ngp, 1, 1, 0, quadtype)
basis%grid%nr = ngp
basis%geometrical = .FALSE.
basis%aval = 0._dp
basis%cval = 0._dp
basis%start = 0
CALL section_vals_val_get(basis_section, "BASIS_TYPE", i_val=basistype)
CALL section_vals_val_get(basis_section, "EPS_EIGENVALUE", r_val=basis%eps_eig)
SELECT CASE (basistype)
CASE DEFAULT
CPABORT("")
CASE (gaussian)
basis%basis_type = GTO_BASIS
NULLIFY (num_gto)
CALL section_vals_val_get(basis_section, "NUM_GTO", i_vals=num_gto)
IF (num_gto(1) < 1) THEN
! use default basis
IF (btyp == "AE") THEN
nu = nua
ELSEIF (btyp == "PP") THEN
nu = nup
ELSE
nu = nua
END IF
basis%nbas = nu
basis%nprim = nu
ALLOCATE (basis%am(nu, 0:lmat))
DO i = 0, lmat
basis%am(1:nu, i) = ugbs(1:nu)
END DO
ELSE
basis%nbas = 0
DO i = 1, SIZE(num_gto)
basis%nbas(i - 1) = num_gto(i)
END DO
basis%nprim = basis%nbas
m = MAXVAL(basis%nbas)
ALLOCATE (basis%am(m, 0:lmat))
basis%am = 0._dp
DO l = 0, lmat
IF (basis%nbas(l) > 0) THEN
NULLIFY (expo)
SELECT CASE (l)
CASE DEFAULT
CPABORT("Atom Basis")
CASE (0)
CALL section_vals_val_get(basis_section, "S_EXPONENTS", r_vals=expo)
CASE (1)
CALL section_vals_val_get(basis_section, "P_EXPONENTS", r_vals=expo)
CASE (2)
CALL section_vals_val_get(basis_section, "D_EXPONENTS", r_vals=expo)
CASE (3)
CALL section_vals_val_get(basis_section, "F_EXPONENTS", r_vals=expo)
END SELECT
CPASSERT(SIZE(expo) >= basis%nbas(l))
DO i = 1, basis%nbas(l)
basis%am(i, l) = expo(i)
END DO
END IF
END DO
END IF
! initialize basis function on a radial grid
nr = basis%grid%nr
m = MAXVAL(basis%nbas)
ALLOCATE (basis%bf(nr, m, 0:lmat))
ALLOCATE (basis%dbf(nr, m, 0:lmat))
ALLOCATE (basis%ddbf(nr, m, 0:lmat))
basis%bf = 0._dp
basis%dbf = 0._dp
basis%ddbf = 0._dp
DO l = 0, lmat
DO i = 1, basis%nbas(l)
al = basis%am(i, l)
DO k = 1, nr
rk = basis%grid%rad(k)
ear = EXP(-al*basis%grid%rad(k)**2)
basis%bf(k, i, l) = rk**l*ear
basis%dbf(k, i, l) = (REAL(l, dp)*rk**(l - 1) - 2._dp*al*rk**(l + 1))*ear
basis%ddbf(k, i, l) = (REAL(l*(l - 1), dp)*rk**(l - 2) - &
2._dp*al*REAL(2*l + 1, dp)*rk**(l) + 4._dp*al*rk**(l + 2))*ear
END DO
END DO
END DO
CASE (geometrical_gto)
basis%basis_type = GTO_BASIS
NULLIFY (num_gto)
CALL section_vals_val_get(basis_section, "NUM_GTO", i_vals=num_gto)
IF (num_gto(1) < 1) THEN
IF (btyp == "AE") THEN
! use the Clementi extra large basis
CALL Clementi_geobas(zval, cval, aval, basis%nbas, starti)
ELSEIF (btyp == "PP") THEN
! use the Clementi extra large basis
CALL Clementi_geobas(zval, cval, aval, basis%nbas, starti)
ELSEIF (btyp == "AA") THEN
CALL Clementi_geobas(zval, cval, aval, basis%nbas, starti)
amax = cval**(basis%nbas(0) - 1)
basis%nbas(0) = NINT((LOG(amax)/LOG(1.6_dp)))
cval = 1.6_dp
starti = 0
basis%nbas(1) = basis%nbas(0) - 4
basis%nbas(2) = basis%nbas(0) - 8
basis%nbas(3) = basis%nbas(0) - 12
IF (lmat > 3) basis%nbas(4:lmat) = 0
ELSEIF (btyp == "AP") THEN
CALL Clementi_geobas(zval, cval, aval, basis%nbas, starti)
amax = 500._dp/aval
basis%nbas = NINT((LOG(amax)/LOG(1.6_dp)))
cval = 1.6_dp
starti = 0
ELSE
! use the Clementi extra large basis
CALL Clementi_geobas(zval, cval, aval, basis%nbas, starti)
END IF
basis%nprim = basis%nbas
ELSE
basis%nbas = 0
DO i = 1, SIZE(num_gto)
basis%nbas(i - 1) = num_gto(i)
END DO
basis%nprim = basis%nbas
NULLIFY (sindex)
CALL section_vals_val_get(basis_section, "START_INDEX", i_vals=sindex)
starti = 0
DO i = 1, SIZE(sindex)
starti(i - 1) = sindex(i)
CPASSERT(sindex(i) >= 0)
END DO
CALL section_vals_val_get(basis_section, "GEOMETRICAL_FACTOR", r_val=cval)
CALL section_vals_val_get(basis_section, "GEO_START_VALUE", r_val=aval)
END IF
m = MAXVAL(basis%nbas)
ALLOCATE (basis%am(m, 0:lmat))
basis%am = 0._dp
DO l = 0, lmat
DO i = 1, basis%nbas(l)
ll = i - 1 + starti(l)
basis%am(i, l) = aval*cval**(ll)
END DO
END DO
basis%geometrical = .TRUE.
basis%aval = aval
basis%cval = cval
basis%start = starti
! initialize basis function on a radial grid
nr = basis%grid%nr
m = MAXVAL(basis%nbas)
ALLOCATE (basis%bf(nr, m, 0:lmat))
ALLOCATE (basis%dbf(nr, m, 0:lmat))
ALLOCATE (basis%ddbf(nr, m, 0:lmat))
basis%bf = 0._dp
basis%dbf = 0._dp
basis%ddbf = 0._dp
DO l = 0, lmat
DO i = 1, basis%nbas(l)
al = basis%am(i, l)
DO k = 1, nr
rk = basis%grid%rad(k)
ear = EXP(-al*basis%grid%rad(k)**2)
basis%bf(k, i, l) = rk**l*ear
basis%dbf(k, i, l) = (REAL(l, dp)*rk**(l - 1) - 2._dp*al*rk**(l + 1))*ear
basis%ddbf(k, i, l) = (REAL(l*(l - 1), dp)*rk**(l - 2) - &
2._dp*al*REAL(2*l + 1, dp)*rk**(l) + 4._dp*al*rk**(l + 2))*ear
END DO
END DO
END DO
CASE (contracted_gto)
basis%basis_type = CGTO_BASIS
CALL section_vals_val_get(basis_section, "BASIS_SET_FILE_NAME", c_val=basis_fn)
CALL section_vals_val_get(basis_section, "BASIS_SET", c_val=basis_name)
gto_basis_section => section_vals_get_subs_vals(basis_section, "BASIS")
CALL read_basis_set(ptable(zval)%symbol, basis, basis_name, basis_fn, &
gto_basis_section)
! initialize basis function on a radial grid
nr = basis%grid%nr
m = MAXVAL(basis%nbas)
ALLOCATE (basis%bf(nr, m, 0:lmat))
ALLOCATE (basis%dbf(nr, m, 0:lmat))
ALLOCATE (basis%ddbf(nr, m, 0:lmat))
basis%bf = 0._dp
basis%dbf = 0._dp
basis%ddbf = 0._dp
DO l = 0, lmat
DO i = 1, basis%nprim(l)
al = basis%am(i, l)
DO k = 1, nr
rk = basis%grid%rad(k)
ear = EXP(-al*basis%grid%rad(k)**2)
DO j = 1, basis%nbas(l)
basis%bf(k, j, l) = basis%bf(k, j, l) + rk**l*ear*basis%cm(i, j, l)
basis%dbf(k, j, l) = basis%dbf(k, j, l) &
+ (REAL(l, dp)*rk**(l - 1) - 2._dp*al*rk**(l + 1))*ear*basis%cm(i, j, l)
basis%ddbf(k, j, l) = basis%ddbf(k, j, l) + &
(REAL(l*(l - 1), dp)*rk**(l - 2) - 2._dp*al*REAL(2*l + 1, dp)*rk**(l) + 4._dp*al*rk**(l + 2))* &
ear*basis%cm(i, j, l)
END DO
END DO
END DO
END DO
CASE (slater)
basis%basis_type = STO_BASIS
NULLIFY (num_slater)
CALL section_vals_val_get(basis_section, "NUM_SLATER", i_vals=num_slater)
IF (num_slater(1) < 1) THEN
CPABORT("")
ELSE
basis%nbas = 0
DO i = 1, SIZE(num_slater)
basis%nbas(i - 1) = num_slater(i)
END DO
basis%nprim = basis%nbas
m = MAXVAL(basis%nbas)
ALLOCATE (basis%as(m, 0:lmat), basis%ns(m, 0:lmat))
basis%as = 0._dp
basis%ns = 0
DO l = 0, lmat
IF (basis%nbas(l) > 0) THEN
NULLIFY (expo)
SELECT CASE (l)
CASE DEFAULT
CPABORT("Atom Basis")
CASE (0)
CALL section_vals_val_get(basis_section, "S_EXPONENTS", r_vals=expo)
CASE (1)
CALL section_vals_val_get(basis_section, "P_EXPONENTS", r_vals=expo)
CASE (2)
CALL section_vals_val_get(basis_section, "D_EXPONENTS", r_vals=expo)
CASE (3)
CALL section_vals_val_get(basis_section, "F_EXPONENTS", r_vals=expo)
END SELECT
CPASSERT(SIZE(expo) >= basis%nbas(l))
DO i = 1, basis%nbas(l)
basis%as(i, l) = expo(i)
END DO
NULLIFY (nqm)
SELECT CASE (l)
CASE DEFAULT
CPABORT("Atom Basis")
CASE (0)
CALL section_vals_val_get(basis_section, "S_QUANTUM_NUMBERS", i_vals=nqm)
CASE (1)
CALL section_vals_val_get(basis_section, "P_QUANTUM_NUMBERS", i_vals=nqm)
CASE (2)
CALL section_vals_val_get(basis_section, "D_QUANTUM_NUMBERS", i_vals=nqm)
CASE (3)
CALL section_vals_val_get(basis_section, "F_QUANTUM_NUMBERS", i_vals=nqm)
END SELECT
CPASSERT(SIZE(nqm) >= basis%nbas(l))
DO i = 1, basis%nbas(l)
basis%ns(i, l) = nqm(i)
END DO
END IF
END DO
END IF
! initialize basis function on a radial grid
nr = basis%grid%nr
m = MAXVAL(basis%nbas)
ALLOCATE (basis%bf(nr, m, 0:lmat))
ALLOCATE (basis%dbf(nr, m, 0:lmat))
ALLOCATE (basis%ddbf(nr, m, 0:lmat))
basis%bf = 0._dp
basis%dbf = 0._dp
basis%ddbf = 0._dp
DO l = 0, lmat
DO i = 1, basis%nbas(l)
al = basis%as(i, l)
nl = basis%ns(i, l)
pf = (2._dp*al)**nl*SQRT(2._dp*al/fac(2*nl))
DO k = 1, nr
rk = basis%grid%rad(k)
ear = rk**(nl - 1)*EXP(-al*rk)
basis%bf(k, i, l) = pf*ear
basis%dbf(k, i, l) = pf*(REAL(nl - 1, dp)/rk - al)*ear
basis%ddbf(k, i, l) = pf*(REAL((nl - 2)*(nl - 1), dp)/rk/rk &
- al*REAL(2*(nl - 1), dp)/rk + al*al)*ear
END DO
END DO
END DO
CASE (numerical)
basis%basis_type = NUM_BASIS
CPABORT("")
END SELECT
END SUBROUTINE init_atom_basis
! **************************************************************************************************
!> \brief ...
!> \param basis ...
! **************************************************************************************************
SUBROUTINE init_atom_basis_default_pp(basis)
TYPE(atom_basis_type), INTENT(INOUT) :: basis
INTEGER, PARAMETER :: nua = 40, nup = 20
REAL(KIND=dp), DIMENSION(nua), PARAMETER :: ugbs = (/0.007299_dp, 0.013705_dp, 0.025733_dp, &
0.048316_dp, 0.090718_dp, 0.170333_dp, 0.319819_dp, 0.600496_dp, 1.127497_dp, 2.117000_dp,&
3.974902_dp, 7.463317_dp, 14.013204_dp, 26.311339_dp, 49.402449_dp, 92.758561_dp, &
174.164456_dp, 327.013024_dp, 614.003114_dp, 1152.858743_dp, 2164.619772_dp, &
4064.312984_dp, 7631.197056_dp, 14328.416324_dp, 26903.186074_dp, 50513.706789_dp, &
94845.070265_dp, 178082.107320_dp, 334368.848683_dp, 627814.487663_dp, 1178791.123851_dp, &
2213310.684886_dp, 4155735.557141_dp, 7802853.046713_dp, 14650719.428954_dp, &
27508345.793637_dp, 51649961.080194_dp, 96978513.342764_dp, 182087882.613702_dp, &
341890134.751331_dp/)
INTEGER :: i, k, l, m, ngp, nr, nu, quadtype
REAL(KIND=dp) :: al, ear, rk
NULLIFY (basis%am, basis%cm, basis%as, basis%ns, basis%bf, basis%dbf, basis%ddbf)
! allocate and initialize the atomic grid
NULLIFY (basis%grid)
CALL allocate_grid_atom(basis%grid)
quadtype = do_gapw_log
ngp = 500
CALL create_grid_atom(basis%grid, ngp, 1, 1, 0, quadtype)
basis%grid%nr = ngp
basis%geometrical = .FALSE.
basis%aval = 0._dp
basis%cval = 0._dp
basis%start = 0
basis%eps_eig = 1.e-12_dp
basis%basis_type = GTO_BASIS
nu = nup
basis%nbas = nu
basis%nprim = nu
ALLOCATE (basis%am(nu, 0:lmat))
DO i = 0, lmat
basis%am(1:nu, i) = ugbs(1:nu)
END DO
! initialize basis function on a radial grid
nr = basis%grid%nr
m = MAXVAL(basis%nbas)
ALLOCATE (basis%bf(nr, m, 0:lmat))
ALLOCATE (basis%dbf(nr, m, 0:lmat))
ALLOCATE (basis%ddbf(nr, m, 0:lmat))
basis%bf = 0._dp
basis%dbf = 0._dp
basis%ddbf = 0._dp
DO l = 0, lmat
DO i = 1, basis%nbas(l)
al = basis%am(i, l)
DO k = 1, nr
rk = basis%grid%rad(k)
ear = EXP(-al*basis%grid%rad(k)**2)
basis%bf(k, i, l) = rk**l*ear
basis%dbf(k, i, l) = (REAL(l, dp)*rk**(l - 1) - 2._dp*al*rk**(l + 1))*ear
basis%ddbf(k, i, l) = (REAL(l*(l - 1), dp)*rk**(l - 2) - &
2._dp*al*REAL(2*l + 1, dp)*rk**(l) + 4._dp*al*rk**(l + 2))*ear
END DO
END DO
END DO
END SUBROUTINE init_atom_basis_default_pp
! **************************************************************************************************
!> \brief ...
!> \param basis ...
!> \param gbasis ...
!> \param r ...
!> \param rab ...
! **************************************************************************************************
SUBROUTINE atom_basis_gridrep(basis, gbasis, r, rab)
TYPE(atom_basis_type), INTENT(IN) :: basis
TYPE(atom_basis_type), INTENT(INOUT) :: gbasis
REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: r, rab
INTEGER :: i, j, k, l, m, n1, n2, n3, ngp, nl, nr, &
quadtype
REAL(KIND=dp) :: al, ear, pf, rk
NULLIFY (gbasis%am, gbasis%cm, gbasis%as, gbasis%ns, gbasis%bf, gbasis%dbf, gbasis%ddbf)
! copy basis info
gbasis%basis_type = basis%basis_type
gbasis%nbas(0:lmat) = basis%nbas(0:lmat)
gbasis%nprim(0:lmat) = basis%nprim(0:lmat)
IF (ASSOCIATED(basis%am)) THEN
n1 = SIZE(basis%am, 1)
n2 = SIZE(basis%am, 2)
ALLOCATE (gbasis%am(n1, 0:n2 - 1))
gbasis%am = basis%am
END IF
IF (ASSOCIATED(basis%cm)) THEN
n1 = SIZE(basis%cm, 1)
n2 = SIZE(basis%cm, 2)
n3 = SIZE(basis%cm, 3)
ALLOCATE (gbasis%cm(n1, n2, 0:n3 - 1))
gbasis%cm = basis%cm
END IF
IF (ASSOCIATED(basis%as)) THEN
n1 = SIZE(basis%as, 1)
n2 = SIZE(basis%as, 2)
ALLOCATE (gbasis%as(n1, 0:n2 - 1))
gbasis%as = basis%as
END IF
IF (ASSOCIATED(basis%ns)) THEN
n1 = SIZE(basis%ns, 1)
n2 = SIZE(basis%ns, 2)
ALLOCATE (gbasis%ns(n1, 0:n2 - 1))
gbasis%ns = basis%ns
END IF
gbasis%eps_eig = basis%eps_eig
gbasis%geometrical = basis%geometrical
gbasis%aval = basis%aval
gbasis%cval = basis%cval
gbasis%start(0:lmat) = basis%start(0:lmat)
! get information on quadrature type and number of grid points
! allocate and initialize the atomic grid
NULLIFY (gbasis%grid)
CALL allocate_grid_atom(gbasis%grid)
ngp = SIZE(r)
quadtype = do_gapw_log
IF (ngp <= 0) &
CPABORT("# point radial grid < 0")
CALL create_grid_atom(gbasis%grid, ngp, 1, 1, 0, quadtype)
gbasis%grid%nr = ngp
gbasis%grid%rad(:) = r(:)
gbasis%grid%rad2(:) = r(:)*r(:)
gbasis%grid%wr(:) = rab(:)*gbasis%grid%rad2(:)
! initialize basis function on a radial grid
nr = gbasis%grid%nr
m = MAXVAL(gbasis%nbas)
ALLOCATE (gbasis%bf(nr, m, 0:lmat))
ALLOCATE (gbasis%dbf(nr, m, 0:lmat))
ALLOCATE (gbasis%ddbf(nr, m, 0:lmat))
gbasis%bf = 0._dp
gbasis%dbf = 0._dp
gbasis%ddbf = 0._dp
SELECT CASE (gbasis%basis_type)
CASE DEFAULT
CPABORT("")
CASE (GTO_BASIS)
DO l = 0, lmat
DO i = 1, gbasis%nbas(l)
al = gbasis%am(i, l)
DO k = 1, nr
rk = gbasis%grid%rad(k)
ear = EXP(-al*gbasis%grid%rad(k)**2)
gbasis%bf(k, i, l) = rk**l*ear
gbasis%dbf(k, i, l) = (REAL(l, dp)*rk**(l - 1) - 2._dp*al*rk**(l + 1))*ear
gbasis%ddbf(k, i, l) = (REAL(l*(l - 1), dp)*rk**(l - 2) - &
2._dp*al*REAL(2*l + 1, dp)*rk**(l) + 4._dp*al*rk**(l + 2))*ear
END DO
END DO
END DO
CASE (CGTO_BASIS)
DO l = 0, lmat
DO i = 1, gbasis%nprim(l)
al = gbasis%am(i, l)
DO k = 1, nr
rk = gbasis%grid%rad(k)
ear = EXP(-al*gbasis%grid%rad(k)**2)
DO j = 1, gbasis%nbas(l)
gbasis%bf(k, j, l) = gbasis%bf(k, j, l) + rk**l*ear*gbasis%cm(i, j, l)
gbasis%dbf(k, j, l) = gbasis%dbf(k, j, l) &
+ (REAL(l, dp)*rk**(l - 1) - 2._dp*al*rk**(l + 1))*ear*gbasis%cm(i, j, l)
gbasis%ddbf(k, j, l) = gbasis%ddbf(k, j, l) + &
(REAL(l*(l - 1), dp)*rk**(l - 2) - 2._dp*al*REAL(2*l + 1, dp)*rk**(l) + 4._dp*al*rk**(l + 2))* &
ear*gbasis%cm(i, j, l)
END DO
END DO
END DO
END DO
CASE (STO_BASIS)
DO l = 0, lmat
DO i = 1, gbasis%nbas(l)
al = gbasis%as(i, l)
nl = gbasis%ns(i, l)
pf = (2._dp*al)**nl*SQRT(2._dp*al/fac(2*nl))
DO k = 1, nr
rk = gbasis%grid%rad(k)
ear = rk**(nl - 1)*EXP(-al*rk)
gbasis%bf(k, i, l) = pf*ear
gbasis%dbf(k, i, l) = pf*(REAL(nl - 1, dp)/rk - al)*ear
gbasis%ddbf(k, i, l) = pf*(REAL((nl - 2)*(nl - 1), dp)/rk/rk &
- al*REAL(2*(nl - 1), dp)/rk + al*al)*ear
END DO
END DO
END DO
CASE (NUM_BASIS)
gbasis%basis_type = NUM_BASIS
CPABORT("")
END SELECT
END SUBROUTINE atom_basis_gridrep
! **************************************************************************************************
!> \brief ...
!> \param basis ...
! **************************************************************************************************
SUBROUTINE release_atom_basis(basis)
TYPE(atom_basis_type), INTENT(INOUT) :: basis
IF (ASSOCIATED(basis%am)) THEN
DEALLOCATE (basis%am)
END IF
IF (ASSOCIATED(basis%cm)) THEN
DEALLOCATE (basis%cm)
END IF
IF (ASSOCIATED(basis%as)) THEN
DEALLOCATE (basis%as)
END IF
IF (ASSOCIATED(basis%ns)) THEN
DEALLOCATE (basis%ns)
END IF
IF (ASSOCIATED(basis%bf)) THEN
DEALLOCATE (basis%bf)
END IF
IF (ASSOCIATED(basis%dbf)) THEN
DEALLOCATE (basis%dbf)
END IF
IF (ASSOCIATED(basis%ddbf)) THEN
DEALLOCATE (basis%ddbf)
END IF
CALL deallocate_grid_atom(basis%grid)
END SUBROUTINE release_atom_basis
! **************************************************************************************************
! **************************************************************************************************
!> \brief ...
!> \param atom ...
! **************************************************************************************************
SUBROUTINE create_atom_type(atom)
TYPE(atom_type), POINTER :: atom
CPASSERT(.NOT. ASSOCIATED(atom))
ALLOCATE (atom)
NULLIFY (atom%zmp_section)
NULLIFY (atom%xc_section)
NULLIFY (atom%fmat)
atom%do_zmp = .FALSE.
atom%doread = .FALSE.
atom%read_vxc = .FALSE.
atom%dm = .FALSE.
atom%hfx_pot%scale_coulomb = 0.0_dp
atom%hfx_pot%scale_longrange = 0.0_dp
atom%hfx_pot%omega = 0.0_dp
END SUBROUTINE create_atom_type
! **************************************************************************************************
!> \brief ...
!> \param atom ...
! **************************************************************************************************
SUBROUTINE release_atom_type(atom)
TYPE(atom_type), POINTER :: atom
CPASSERT(ASSOCIATED(atom))
NULLIFY (atom%basis)
NULLIFY (atom%integrals)
IF (ASSOCIATED(atom%state)) THEN
DEALLOCATE (atom%state)
END IF
IF (ASSOCIATED(atom%orbitals)) THEN
CALL release_atom_orbs(atom%orbitals)
END IF
IF (ASSOCIATED(atom%fmat)) CALL release_opmat(atom%fmat)
DEALLOCATE (atom)
END SUBROUTINE release_atom_type
! ZMP adding input variables in subroutine do_zmp,doread,read_vxc,method_type
! **************************************************************************************************
!> \brief ...
!> \param atom ...
!> \param basis ...
!> \param state ...
!> \param integrals ...
!> \param orbitals ...
!> \param potential ...
!> \param zcore ...
!> \param pp_calc ...
!> \param do_zmp ...
!> \param doread ...
!> \param read_vxc ...