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atom_grb.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 !
!--------------------------------------------------------------------------------------------------!
MODULE atom_grb
USE ai_onecenter, ONLY: sg_conf,&
sg_kinetic,&
sg_nuclear,&
sg_overlap
USE atom_electronic_structure, ONLY: calculate_atom
USE atom_operators, ONLY: atom_int_release,&
atom_int_setup,&
atom_ppint_release,&
atom_ppint_setup,&
atom_relint_release,&
atom_relint_setup
USE atom_types, ONLY: &
CGTO_BASIS, GTO_BASIS, atom_basis_type, atom_integrals, atom_orbitals, atom_p_type, &
atom_potential_type, atom_state, atom_type, create_atom_orbs, create_atom_type, lmat, &
release_atom_basis, release_atom_type, set_atom
USE atom_utils, ONLY: atom_basis_condnum,&
atom_density
USE cp_files, ONLY: close_file,&
open_file
USE input_constants, ONLY: barrier_conf,&
do_analytic,&
do_rhf_atom,&
do_rks_atom,&
do_rohf_atom,&
do_uhf_atom,&
do_uks_atom
USE input_section_types, ONLY: section_vals_get_subs_vals,&
section_vals_type,&
section_vals_val_get
USE kinds, ONLY: default_string_length,&
dp
USE mathconstants, ONLY: dfac,&
rootpi
USE orbital_pointers, ONLY: deallocate_orbital_pointers,&
init_orbital_pointers
USE orbital_transformation_matrices, ONLY: deallocate_spherical_harmonics,&
init_spherical_harmonics
USE periodic_table, ONLY: ptable
USE physcon, ONLY: bohr
USE powell, ONLY: opt_state_type,&
powell_optimize
USE qs_grid_atom, ONLY: allocate_grid_atom,&
create_grid_atom
#include "./base/base_uses.f90"
IMPLICIT NONE
TYPE basis_p_type
TYPE(atom_basis_type), POINTER :: basis => NULL()
END TYPE basis_p_type
PRIVATE
PUBLIC :: atom_grb_construction
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'atom_grb'
CONTAINS
! **************************************************************************************************
!> \brief Construct geometrical response basis set.
!> \param atom_info information about the atomic kind. Two-dimensional array of size
!> (electronic-configuration, electronic-structure-method)
!> \param atom_section ATOM input section
!> \param iw output file unit
!> \par History
!> * 11.2016 created [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE atom_grb_construction(atom_info, atom_section, iw)
TYPE(atom_p_type), DIMENSION(:, :), POINTER :: atom_info
TYPE(section_vals_type), POINTER :: atom_section
INTEGER, INTENT(IN) :: iw
CHARACTER(len=default_string_length) :: abas, basname
CHARACTER(len=default_string_length), DIMENSION(1) :: basline
CHARACTER(len=default_string_length), DIMENSION(3) :: headline
INTEGER :: i, ider, is, iunit, j, k, l, lhomo, ll, &
lval, m, maxl, mb, method, mo, n, &
nder, ngp, nhomo, nr, num_gto, &
num_pol, quadtype, s1, s2
INTEGER, DIMENSION(0:7) :: nbas
INTEGER, DIMENSION(0:lmat) :: next_bas, next_prim
INTEGER, DIMENSION(:), POINTER :: num_bas
REAL(KIND=dp) :: al, amin, aval, cnum, crad, cradx, cval, delta, dene, ear, emax, &
energy_ex(0:lmat), energy_ref, energy_vb(0:lmat), expzet, fhomo, o, prefac, rconf, rk, &
rmax, scon, zeta, zval
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: ale, alp, rho
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: amat
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: ebasis, pbasis, qbasis, rbasis
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :, :) :: wfn
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: ovlp
TYPE(atom_basis_type), POINTER :: basis, basis_grb, basis_ref, basis_vrb
TYPE(atom_integrals), POINTER :: atint
TYPE(atom_orbitals), POINTER :: orbitals
TYPE(atom_state), POINTER :: state
TYPE(atom_type), POINTER :: atom, atom_ref, atom_test
TYPE(basis_p_type), DIMENSION(0:10) :: vbasis
TYPE(section_vals_type), POINTER :: grb_section, powell_section
IF (iw > 0) WRITE (iw, '(/," ",79("*"),/,T28,A,/," ",79("*"))') "GEOMETRICAL RESPONSE BASIS"
DO i = 0, 10
NULLIFY (vbasis(i)%basis)
END DO
! make some basic checks
is = SIZE(atom_info)
IF (iw > 0 .AND. is > 1) THEN
WRITE (iw, '(/,A,/)') " WARNING: Only use first electronic structure/method for basis set generation"
END IF
atom_ref => atom_info(1, 1)%atom
! check method
method = atom_ref%method_type
SELECT CASE (method)
CASE (do_rks_atom, do_rhf_atom)
! restricted methods are okay
CASE (do_uks_atom, do_uhf_atom, do_rohf_atom)
CPABORT("Unrestricted methods not allowed for GRB generation")
CASE DEFAULT
CPABORT("")
END SELECT
! input for basis optimization
grb_section => section_vals_get_subs_vals(atom_section, "PRINT%GEOMETRICAL_RESPONSE_BASIS")
! generate an atom type
NULLIFY (atom)
CALL create_atom_type(atom)
CALL copy_atom_basics(atom_ref, atom, state=.TRUE., potential=.TRUE., optimization=.TRUE., xc=.TRUE.)
! set confinement potential
atom%potential%confinement = .TRUE.
atom%potential%conf_type = barrier_conf
atom%potential%acon = 200._dp
atom%potential%rcon = 4._dp
CALL section_vals_val_get(grb_section, "CONFINEMENT", r_val=scon)
atom%potential%scon = scon
! generate main block geometrical exponents
basis_ref => atom_ref%basis
ALLOCATE (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
NULLIFY (basis%grid)
CALL allocate_grid_atom(basis%grid)
CALL section_vals_val_get(grb_section, "QUADRATURE", i_val=quadtype)
CALL section_vals_val_get(grb_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
!
maxl = atom%state%maxl_occ
basis%basis_type = GTO_BASIS
CALL section_vals_val_get(grb_section, "NUM_GTO_CORE", i_val=num_gto)
basis%nbas = 0
basis%nbas(0:maxl) = num_gto
basis%nprim = basis%nbas
CALL section_vals_val_get(grb_section, "GEOMETRICAL_FACTOR", r_val=cval)
CALL section_vals_val_get(grb_section, "GEO_START_VALUE", r_val=aval)
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
basis%am(i, l) = aval*cval**(ll)
END DO
END DO
basis%eps_eig = basis_ref%eps_eig
basis%geometrical = .TRUE.
basis%aval = aval
basis%cval = cval
basis%start = 0
! 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
NULLIFY (orbitals)
mo = MAXVAL(atom%state%maxn_calc)
mb = MAXVAL(basis%nbas)
CALL create_atom_orbs(orbitals, mb, mo)
CALL set_atom(atom, orbitals=orbitals)
powell_section => section_vals_get_subs_vals(atom_section, "POWELL")
CALL atom_fit_grb(atom, basis, iw, powell_section)
CALL set_atom(atom, basis=basis)
! generate response contractions
CALL section_vals_val_get(grb_section, "DELTA_CHARGE", r_val=delta)
CALL section_vals_val_get(grb_section, "DERIVATIVES", i_val=nder)
IF (iw > 0) THEN
WRITE (iw, '(/,A,T76,I5)') " Generate Response Basis Sets with Order ", nder
END IF
state => atom%state
! find HOMO
lhomo = -1
nhomo = -1
emax = -HUGE(1._dp)
DO l = 0, state%maxl_occ
DO i = 1, state%maxn_occ(l)
IF (atom%orbitals%ener(i, l) > emax) THEN
lhomo = l
nhomo = i
emax = atom%orbitals%ener(i, l)
fhomo = state%occupation(l, i)
END IF
END DO
END DO
s1 = SIZE(atom%orbitals%wfn, 1)
s2 = SIZE(atom%orbitals%wfn, 2)
ALLOCATE (wfn(s1, s2, 0:lmat, -nder:nder))
s2 = MAXVAL(state%maxn_occ) + nder
ALLOCATE (rbasis(s1, s2, 0:lmat), qbasis(s1, s2, 0:lmat))
rbasis = 0._dp
qbasis = 0._dp
! calculate integrals
ALLOCATE (atint)
CALL atom_int_setup(atint, basis, potential=atom%potential, eri_coulomb=.FALSE., eri_exchange=.FALSE.)
CALL atom_ppint_setup(atint, basis, potential=atom%potential)
IF (atom%pp_calc) THEN
NULLIFY (atint%tzora, atint%hdkh)
ELSE
! relativistic correction terms
CALL atom_relint_setup(atint, basis, atom%relativistic, zcore=REAL(atom%z, dp))
END IF
CALL set_atom(atom, integrals=atint)
CALL calculate_atom(atom, iw=0)
DO ider = -nder, nder
dene = REAL(ider, KIND=dp)*delta
CPASSERT(fhomo > ABS(dene))
state%occupation(lhomo, nhomo) = fhomo + dene
CALL calculate_atom(atom, iw=0, noguess=.TRUE.)
wfn(:, :, :, ider) = atom%orbitals%wfn
state%occupation(lhomo, nhomo) = fhomo
END DO
IF (iw > 0) THEN
WRITE (iw, '(A,T76,I5)') " Total number of electronic structure calculations ", 2*nder + 1
END IF
ovlp => atom%integrals%ovlp
DO l = 0, state%maxl_occ
IF (iw > 0) THEN
WRITE (iw, '(A,T76,I5)') " Response derivatives for l quantum number ", l
END IF
! occupied states
DO i = 1, MAX(state%maxn_occ(l), 1)
rbasis(:, i, l) = wfn(:, i, l, 0)
END DO
! differentiation
DO ider = 1, nder
i = MAX(state%maxn_occ(l), 1)
SELECT CASE (ider)
CASE (1)
rbasis(:, i + 1, l) = 0.5_dp*(wfn(:, i, l, 1) - wfn(:, i, l, -1))/delta
CASE (2)
rbasis(:, i + 2, l) = 0.25_dp*(wfn(:, i, l, 2) - 2._dp*wfn(:, i, l, 0) + wfn(:, i, l, -2))/delta**2
CASE (3)
rbasis(:, i + 3, l) = 0.125_dp*(wfn(:, i, l, 3) - 3._dp*wfn(:, i, l, 1) &
+ 3._dp*wfn(:, i, l, -1) - wfn(:, i, l, -3))/delta**3
CASE DEFAULT
CPABORT("")
END SELECT
END DO
! orthogonalization, use gram-schmidt in order to keep the natural order (semi-core, valence, response) of the wfn.
n = state%maxn_occ(l) + nder
m = atom%basis%nbas(l)
DO i = 1, n
DO j = 1, i - 1
o = DOT_PRODUCT(rbasis(1:m, j, l), RESHAPE(MATMUL(ovlp(1:m, 1:m, l), rbasis(1:m, i:i, l)), (/m/)))
rbasis(1:m, i, l) = rbasis(1:m, i, l) - o*rbasis(1:m, j, l)
END DO
o = DOT_PRODUCT(rbasis(1:m, i, l), RESHAPE(MATMUL(ovlp(1:m, 1:m, l), rbasis(1:m, i:i, l)), (/m/)))
rbasis(1:m, i, l) = rbasis(1:m, i, l)/SQRT(o)
END DO
! check
ALLOCATE (amat(n, n))
amat(1:n, 1:n) = MATMUL(TRANSPOSE(rbasis(1:m, 1:n, l)), MATMUL(ovlp(1:m, 1:m, l), rbasis(1:m, 1:n, l)))
DO i = 1, n
amat(i, i) = amat(i, i) - 1._dp
END DO
IF (MAXVAL(ABS(amat)) > 1.e-12) THEN
IF (iw > 0) WRITE (iw, '(A,G20.10)') " Orthogonality error ", MAXVAL(ABS(amat))
END IF
DEALLOCATE (amat)
! Quickstep normalization
expzet = 0.25_dp*REAL(2*l + 3, dp)
prefac = SQRT(rootpi/2._dp**(l + 2)*dfac(2*l + 1))
DO i = 1, m
zeta = (2._dp*atom%basis%am(i, l))**expzet
qbasis(i, 1:n, l) = rbasis(i, 1:n, l)*prefac/zeta
END DO
END DO
! check for condition numbers
IF (iw > 0) WRITE (iw, '(/,A)') " Condition Number of Valence Response Basis Sets"
CALL init_orbital_pointers(lmat)
CALL init_spherical_harmonics(lmat, 0)
DO ider = 0, nder
NULLIFY (basis_vrb)
ALLOCATE (basis_vrb)
NULLIFY (basis_vrb%am, basis_vrb%cm, basis_vrb%as, basis_vrb%ns, basis_vrb%bf, &
basis_vrb%dbf, basis_vrb%ddbf)
! allocate and initialize the atomic grid
NULLIFY (basis_vrb%grid)
CALL allocate_grid_atom(basis_vrb%grid)
CALL create_grid_atom(basis_vrb%grid, ngp, 1, 1, 0, quadtype)
basis_vrb%grid%nr = ngp
!
basis_vrb%eps_eig = basis_ref%eps_eig
basis_vrb%geometrical = .FALSE.
basis_vrb%basis_type = CGTO_BASIS
basis_vrb%nprim = basis%nprim
basis_vrb%nbas = 0
DO l = 0, state%maxl_occ
basis_vrb%nbas(l) = state%maxn_occ(l) + ider
END DO
m = MAXVAL(basis_vrb%nprim)
n = MAXVAL(basis_vrb%nbas)
ALLOCATE (basis_vrb%am(m, 0:lmat))
basis_vrb%am = basis%am
! contractions
ALLOCATE (basis_vrb%cm(m, n, 0:lmat))
DO l = 0, state%maxl_occ
m = basis_vrb%nprim(l)
n = basis_vrb%nbas(l)
basis_vrb%cm(1:m, 1:n, l) = rbasis(1:m, 1:n, l)
END DO
! initialize basis function on a radial grid
nr = basis_vrb%grid%nr
m = MAXVAL(basis_vrb%nbas)
ALLOCATE (basis_vrb%bf(nr, m, 0:lmat))
ALLOCATE (basis_vrb%dbf(nr, m, 0:lmat))
ALLOCATE (basis_vrb%ddbf(nr, m, 0:lmat))
basis_vrb%bf = 0._dp
basis_vrb%dbf = 0._dp
basis_vrb%ddbf = 0._dp
DO l = 0, lmat
DO i = 1, basis_vrb%nprim(l)
al = basis_vrb%am(i, l)
DO k = 1, nr
rk = basis_vrb%grid%rad(k)
ear = EXP(-al*basis_vrb%grid%rad(k)**2)
DO j = 1, basis_vrb%nbas(l)
basis_vrb%bf(k, j, l) = basis_vrb%bf(k, j, l) + rk**l*ear*basis_vrb%cm(i, j, l)
basis_vrb%dbf(k, j, l) = basis_vrb%dbf(k, j, l) &
+ (REAL(l, dp)*rk**(l - 1) - 2._dp*al*rk**(l + 1))*ear*basis_vrb%cm(i, j, l)
basis_vrb%ddbf(k, j, l) = basis_vrb%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_vrb%cm(i, j, l)
END DO
END DO
END DO
END DO
IF (iw > 0) THEN
CALL basis_label(abas, basis_vrb%nprim, basis_vrb%nbas)
WRITE (iw, '(A,A)') " Basis set ", TRIM(abas)
END IF
crad = 2.0_dp*ptable(atom%z)%covalent_radius*bohr
cradx = crad*1.00_dp
CALL atom_basis_condnum(basis_vrb, cradx, cnum)
IF (iw > 0) WRITE (iw, '(T5,A,F15.3,T50,A,F14.4)') " Lattice constant:", cradx, "Condition number:", cnum
cradx = crad*1.10_dp
CALL atom_basis_condnum(basis_vrb, cradx, cnum)
IF (iw > 0) WRITE (iw, '(T5,A,F15.3,T50,A,F14.4)') " Lattice constant:", cradx, "Condition number:", cnum
cradx = crad*1.20_dp
CALL atom_basis_condnum(basis_vrb, cradx, cnum)
IF (iw > 0) WRITE (iw, '(T5,A,F15.3,T50,A,F14.4)') " Lattice constant:", cradx, "Condition number:", cnum
vbasis(ider)%basis => basis_vrb
END DO
CALL deallocate_orbital_pointers
CALL deallocate_spherical_harmonics
! get density maximum
ALLOCATE (rho(basis%grid%nr))
CALL calculate_atom(atom, iw=0, noguess=.TRUE.)
CALL atom_density(rho(:), atom%orbitals%pmat, atom%basis, maxl, typ="RHO")
n = SUM(MAXLOC(rho(:)))
rmax = basis%grid%rad(n)
IF (rmax < 0.1_dp) rmax = 1.0_dp
DEALLOCATE (rho)
! generate polarization sets
maxl = atom%state%maxl_occ
CALL section_vals_val_get(grb_section, "NUM_GTO_POLARIZATION", i_val=num_gto)
num_pol = num_gto
IF (num_gto > 0) THEN
IF (iw > 0) THEN
WRITE (iw, '(/,A)') " Polarization basis set "
END IF
ALLOCATE (pbasis(num_gto, num_gto, 0:7), alp(num_gto))
pbasis = 0.0_dp
! optimize exponents
lval = maxl + 1
zval = SQRT(REAL(2*lval + 2, dp))*REAL(lval + 1, dp)/(2._dp*rmax)
aval = atom%basis%am(1, 0)
cval = 2.5_dp
rconf = atom%potential%scon
CALL atom_fit_pol(zval, rconf, lval, aval, cval, num_gto, iw, powell_section)
! calculate contractions
DO i = 1, num_gto
alp(i) = aval*cval**(i - 1)
END DO
ALLOCATE (rho(num_gto))
DO l = maxl + 1, MIN(maxl + num_gto, 7)
zval = SQRT(REAL(2*l + 2, dp))*REAL(l + 1, dp)/(2._dp*rmax)
CALL hydrogenic(zval, rconf, l, alp, num_gto, rho, pbasis(:, :, l))
IF (iw > 0) WRITE (iw, '(T5,A,i5,T66,A,F10.4)') &
" Polarization basis set contraction for lval=", l, "zval=", zval
END DO
DEALLOCATE (rho)
END IF
! generate valence expansion sets
maxl = atom%state%maxl_occ
CALL section_vals_val_get(grb_section, "NUM_GTO_EXTENDED", i_val=num_gto)
CALL section_vals_val_get(grb_section, "EXTENSION_BASIS", i_vals=num_bas)
next_bas(0:lmat) = 0
IF (num_bas(1) == -1) THEN
DO l = 0, maxl
next_bas(l) = maxl - l + 1
END DO
ELSE
n = MIN(SIZE(num_bas, 1), 4)
next_bas(0:n - 1) = num_bas(1:n)
END IF
next_prim = 0
DO l = 0, lmat
IF (next_bas(l) > 0) next_prim(l) = num_gto
END DO
IF (iw > 0) THEN
CALL basis_label(abas, next_prim, next_bas)
WRITE (iw, '(/,A,A)') " Extension basis set ", TRIM(abas)
END IF
n = MAXVAL(next_prim)
m = MAXVAL(next_bas)
ALLOCATE (ebasis(n, n, 0:lmat), ale(n))
basis_vrb => vbasis(0)%basis
amin = atom%basis%aval/atom%basis%cval**1.5_dp
DO i = 1, n
ale(i) = amin*atom%basis%cval**(i - 1)
END DO
ebasis = 0._dp
ALLOCATE (rho(n))
rconf = 2.0_dp*atom%potential%scon
DO l = 0, lmat
IF (next_bas(l) < 1) CYCLE
zval = SQRT(REAL(2*l + 2, dp))*REAL(l + 1, dp)/(2._dp*rmax)
CALL hydrogenic(zval, rconf, l, ale, n, rho, ebasis(:, :, l))
IF (iw > 0) WRITE (iw, '(T5,A,i5,T66,A,F10.4)') &
" Extension basis set contraction for lval=", l, "zval=", zval
END DO
DEALLOCATE (rho)
! check for condition numbers
IF (iw > 0) WRITE (iw, '(/,A)') " Condition Number of Extended Basis Sets"
CALL init_orbital_pointers(lmat)
CALL init_spherical_harmonics(lmat, 0)
DO ider = 0, nder
NULLIFY (basis_vrb)
ALLOCATE (basis_vrb)
NULLIFY (basis_vrb%am, basis_vrb%cm, basis_vrb%as, basis_vrb%ns, basis_vrb%bf, &
basis_vrb%dbf, basis_vrb%ddbf)
! allocate and initialize the atomic grid
NULLIFY (basis_vrb%grid)
CALL allocate_grid_atom(basis_vrb%grid)
CALL create_grid_atom(basis_vrb%grid, ngp, 1, 1, 0, quadtype)
basis_vrb%grid%nr = ngp
!
basis_vrb%eps_eig = basis_ref%eps_eig
basis_vrb%geometrical = .FALSE.
basis_vrb%basis_type = CGTO_BASIS
basis_vrb%nprim = basis%nprim + next_prim
basis_vrb%nbas = 0
DO l = 0, state%maxl_occ
basis_vrb%nbas(l) = state%maxn_occ(l) + ider + next_bas(l)
END DO
m = MAXVAL(basis_vrb%nprim)
ALLOCATE (basis_vrb%am(m, 0:lmat))
! exponents
m = SIZE(basis%am, 1)
basis_vrb%am(1:m, :) = basis%am(1:m, :)
n = SIZE(ale, 1)
DO l = 0, state%maxl_occ
basis_vrb%am(m + 1:m + n, l) = ale(1:n)
END DO
! contractions
m = MAXVAL(basis_vrb%nprim)
n = MAXVAL(basis_vrb%nbas)
ALLOCATE (basis_vrb%cm(m, n, 0:lmat))
basis_vrb%cm = 0.0_dp
DO l = 0, state%maxl_occ
m = basis%nprim(l)
n = state%maxn_occ(l) + ider
basis_vrb%cm(1:m, 1:n, l) = rbasis(1:m, 1:n, l)
basis_vrb%cm(m + 1:m + next_prim(l), n + 1:n + next_bas(l), l) = ebasis(1:next_prim(l), 1:next_bas(l), l)
END DO
! initialize basis function on a radial grid
nr = basis_vrb%grid%nr
m = MAXVAL(basis_vrb%nbas)
ALLOCATE (basis_vrb%bf(nr, m, 0:lmat))
ALLOCATE (basis_vrb%dbf(nr, m, 0:lmat))
ALLOCATE (basis_vrb%ddbf(nr, m, 0:lmat))
basis_vrb%bf = 0._dp
basis_vrb%dbf = 0._dp
basis_vrb%ddbf = 0._dp
DO l = 0, lmat
DO i = 1, basis_vrb%nprim(l)
al = basis_vrb%am(i, l)
DO k = 1, nr
rk = basis_vrb%grid%rad(k)
ear = EXP(-al*basis_vrb%grid%rad(k)**2)
DO j = 1, basis_vrb%nbas(l)
basis_vrb%bf(k, j, l) = basis_vrb%bf(k, j, l) + rk**l*ear*basis_vrb%cm(i, j, l)
basis_vrb%dbf(k, j, l) = basis_vrb%dbf(k, j, l) &
+ (REAL(l, dp)*rk**(l - 1) - 2._dp*al*rk**(l + 1))*ear*basis_vrb%cm(i, j, l)
basis_vrb%ddbf(k, j, l) = basis_vrb%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_vrb%cm(i, j, l)
END DO
END DO
END DO
END DO
IF (iw > 0) THEN
CALL basis_label(abas, basis_vrb%nprim, basis_vrb%nbas)
WRITE (iw, '(A,A)') " Basis set ", TRIM(abas)
END IF
crad = 2.0_dp*ptable(atom%z)%covalent_radius*bohr
cradx = crad*1.00_dp
CALL atom_basis_condnum(basis_vrb, cradx, cnum)
IF (iw > 0) WRITE (iw, '(T5,A,F15.3,T50,A,F14.4)') " Lattice constant:", cradx, "Condition number:", cnum
cradx = crad*1.10_dp
CALL atom_basis_condnum(basis_vrb, cradx, cnum)
IF (iw > 0) WRITE (iw, '(T5,A,F15.3,T50,A,F14.4)') " Lattice constant:", cradx, "Condition number:", cnum
cradx = crad*1.20_dp
CALL atom_basis_condnum(basis_vrb, cradx, cnum)
IF (iw > 0) WRITE (iw, '(T5,A,F15.3,T50,A,F14.4)') " Lattice constant:", cradx, "Condition number:", cnum
vbasis(nder + 1 + ider)%basis => basis_vrb
END DO
CALL deallocate_orbital_pointers
CALL deallocate_spherical_harmonics
! Tests for energy
energy_ref = atom_ref%energy%etot
IF (iw > 0) WRITE (iw, '(/,A,A)') " Basis set tests "
IF (iw > 0) WRITE (iw, '(T10,A,T59,F22.9)') " Reference Energy [a.u.] ", energy_ref
DO ider = 0, 2*nder + 1
! generate an atom type
NULLIFY (atom_test)
CALL create_atom_type(atom_test)
CALL copy_atom_basics(atom_ref, atom_test, state=.TRUE., potential=.TRUE., &
optimization=.TRUE., xc=.TRUE.)
basis_grb => vbasis(ider)%basis
NULLIFY (orbitals)
mo = MAXVAL(atom_test%state%maxn_calc)
mb = MAXVAL(basis_grb%nbas)
CALL create_atom_orbs(orbitals, mb, mo)
CALL set_atom(atom_test, orbitals=orbitals, basis=basis_grb)
! calculate integrals
ALLOCATE (atint)
CALL atom_int_setup(atint, basis_grb, potential=atom_test%potential, eri_coulomb=.FALSE., eri_exchange=.FALSE.)
CALL atom_ppint_setup(atint, basis_grb, potential=atom_test%potential)
IF (atom_test%pp_calc) THEN
NULLIFY (atint%tzora, atint%hdkh)
ELSE
! relativistic correction terms
CALL atom_relint_setup(atint, basis_grb, atom_test%relativistic, zcore=REAL(atom_test%z, dp))
END IF
CALL set_atom(atom_test, integrals=atint)
!
CALL calculate_atom(atom_test, iw=0)
IF (ider <= nder) THEN
energy_vb(ider) = atom_test%energy%etot
IF (iw > 0) WRITE (iw, '(T10,A,i1,A,T40,F13.9,T59,F22.9)') " GRB (VB)", ider, " Energy [a.u.] ", &
energy_ref - energy_vb(ider), energy_vb(ider)
ELSE
i = ider - nder - 1
energy_ex(i) = atom_test%energy%etot
IF (iw > 0) WRITE (iw, '(T10,A,i1,A,T40,F13.9,T59,F22.9)') " GRB (EX)", i, " Energy [a.u.] ", &
energy_ref - energy_ex(i), energy_ex(i)
END IF
CALL atom_int_release(atint)
CALL atom_ppint_release(atint)
CALL atom_relint_release(atint)
DEALLOCATE (atom_test%state, atom_test%potential, atint)
CALL release_atom_type(atom_test)
END DO
! Quickstep normalization polarization basis
DO l = 0, 7
expzet = 0.25_dp*REAL(2*l + 3, dp)
prefac = SQRT(rootpi/2._dp**(l + 2)*dfac(2*l + 1))
DO i = 1, num_pol
zeta = (2._dp*alp(i))**expzet
pbasis(i, 1:num_pol, l) = pbasis(i, 1:num_pol, l)*prefac/zeta
END DO
END DO
! Quickstep normalization extended basis
DO l = 0, lmat
expzet = 0.25_dp*REAL(2*l + 3, dp)
prefac = SQRT(rootpi/2._dp**(l + 2)*dfac(2*l + 1))
DO i = 1, next_prim(l)
zeta = (2._dp*ale(i))**expzet
ebasis(i, 1:next_bas(l), l) = ebasis(i, 1:next_bas(l), l)*prefac/zeta
END DO
END DO
! Print basis sets
CALL section_vals_val_get(grb_section, "NAME_BODY", c_val=basname)
CALL open_file(file_name="GRB_BASIS", file_status="UNKNOWN", file_action="WRITE", unit_number=iunit)
! header info
headline = ""
headline(1) = "#"
headline(2) = "# Generated with CP2K Atom Code"
headline(3) = "#"
CALL grb_print_basis(header=headline, iunit=iunit)
! valence basis
basline(1) = ""
WRITE (basline(1), "(T2,A)") ADJUSTL(ptable(atom_ref%z)%symbol)
DO ider = 0, nder
basline(1) = ""
WRITE (basline(1), "(T2,A,T5,A,I1)") ADJUSTL(ptable(atom_ref%z)%symbol), TRIM(ADJUSTL(basname))//"-VAL-", ider
CALL grb_print_basis(header=basline, nprim=vbasis(ider)%basis%nprim(0), nbas=vbasis(ider)%basis%nbas, &
al=vbasis(ider)%basis%am(:, 0), gcc=qbasis, iunit=iunit)
END DO
! polarization basis
maxl = atom_ref%state%maxl_occ
DO l = maxl + 1, MIN(maxl + num_pol, 7)
nbas = 0
DO i = maxl + 1, l
nbas(i) = l - i + 1
END DO
i = l - maxl
basline(1) = ""
WRITE (basline(1), "(T2,A,T5,A,I1)") ADJUSTL(ptable(atom_ref%z)%symbol), TRIM(ADJUSTL(basname))//"-POL-", i
CALL grb_print_basis(header=basline, nprim=num_pol, nbas=nbas, al=alp, gcc=pbasis, iunit=iunit)
END DO
! extension set
IF (SUM(next_bas) > 0) THEN
basline(1) = ""
WRITE (basline(1), "(T2,A,T5,A)") ADJUSTL(ptable(atom_ref%z)%symbol), TRIM(ADJUSTL(basname))//"-EXT"
CALL grb_print_basis(header=basline, nprim=next_prim(0), nbas=next_bas, al=ale, gcc=ebasis, iunit=iunit)
END IF
!
CALL close_file(unit_number=iunit)
! clean up
IF (ALLOCATED(pbasis)) DEALLOCATE (pbasis)
IF (ALLOCATED(alp)) DEALLOCATE (alp)
IF (ALLOCATED(ebasis)) DEALLOCATE (ebasis)
DEALLOCATE (wfn, rbasis, qbasis, ale)
DO ider = 0, 10
IF (ASSOCIATED(vbasis(ider)%basis)) THEN
CALL release_atom_basis(vbasis(ider)%basis)
DEALLOCATE (vbasis(ider)%basis)
END IF
END DO
CALL atom_int_release(atom%integrals)
CALL atom_ppint_release(atom%integrals)
CALL atom_relint_release(atom%integrals)
CALL release_atom_basis(basis)
DEALLOCATE (atom%potential, atom%state, atom%integrals, basis)
CALL release_atom_type(atom)
IF (iw > 0) WRITE (iw, '(" ",79("*"))')
END SUBROUTINE atom_grb_construction
! **************************************************************************************************
!> \brief Print geometrical response basis set.
!> \param header banner to print on top of the basis set
!> \param nprim number of primitive exponents
!> \param nbas number of basis functions for the given angular momentum
!> \param al list of the primitive exponents
!> \param gcc array of contraction coefficients of size
!> (index-of-the-primitive-exponent, index-of-the-contraction-set, angular-momentum)
!> \param iunit output file unit
!> \par History
!> * 11.2016 created [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE grb_print_basis(header, nprim, nbas, al, gcc, iunit)
CHARACTER(len=*), DIMENSION(:), INTENT(IN), &
OPTIONAL :: header
INTEGER, INTENT(IN), OPTIONAL :: nprim
INTEGER, DIMENSION(0:), INTENT(IN), OPTIONAL :: nbas
REAL(KIND=dp), DIMENSION(:), INTENT(IN), OPTIONAL :: al
REAL(KIND=dp), DIMENSION(:, :, 0:), INTENT(IN), &
OPTIONAL :: gcc
INTEGER, INTENT(IN) :: iunit
INTEGER :: i, j, l, lmax, lmin, nval
IF (PRESENT(header)) THEN
DO i = 1, SIZE(header, 1)
IF (header(i) .NE. "") THEN
WRITE (iunit, "(A)") TRIM(header(i))
END IF
END DO
END IF
IF (PRESENT(nprim)) THEN
IF (nprim > 0) THEN
CPASSERT(PRESENT(nbas))
CPASSERT(PRESENT(al))
CPASSERT(PRESENT(gcc))
DO i = LBOUND(nbas, 1), UBOUND(nbas, 1)
IF (nbas(i) > 0) THEN
lmin = i
EXIT
END IF
END DO
DO i = UBOUND(nbas, 1), LBOUND(nbas, 1), -1
IF (nbas(i) > 0) THEN
lmax = i
EXIT
END IF
END DO
nval = lmax
WRITE (iunit, *) " 1"
WRITE (iunit, "(40I3)") nval, lmin, lmax, nprim, (nbas(l), l=lmin, lmax)
DO i = nprim, 1, -1
WRITE (iunit, "(G20.12)", advance="no") al(i)
DO l = lmin, lmax
DO j = 1, nbas(l)
WRITE (iunit, "(F16.10)", advance="no") gcc(i, j, l)
END DO
END DO
WRITE (iunit, *)
END DO
WRITE (iunit, *)
END IF
END IF
END SUBROUTINE grb_print_basis
! **************************************************************************************************
!> \brief Compose the basis set label:
!> (np(0)'s'np(1)'p'...) -> [nb(0)'s'nb(1)'p'...] .
!> \param label basis set label
!> \param np number of primitive basis functions per angular momentum
!> \param nb number of contracted basis functions per angular momentum
!> \par History
!> * 11.2016 created [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE basis_label(label, np, nb)
CHARACTER(len=*), INTENT(out) :: label
INTEGER, DIMENSION(0:), INTENT(in) :: np, nb
INTEGER :: i, l, lmax
CHARACTER(len=1), DIMENSION(0:7), PARAMETER :: &
lq = (/"s", "p", "d", "f", "g", "h", "i", "k"/)
label = ""
lmax = MIN(UBOUND(np, 1), UBOUND(nb, 1), 7)
i = 1
label(i:i) = "("
DO l = 0, lmax
IF (np(l) > 0) THEN
i = i + 1
IF (np(l) > 9) THEN
WRITE (label(i:i + 1), "(I2)") np(l)
i = i + 2
ELSE
WRITE (label(i:i), "(I1)") np(l)
i = i + 1
END IF
label(i:i) = lq(l)
END IF
END DO
i = i + 1
label(i:i + 6) = ") --> ["
i = i + 6
DO l = 0, lmax
IF (nb(l) > 0) THEN
i = i + 1
IF (nb(l) > 9) THEN
WRITE (label(i:i + 1), "(I2)") nb(l)
i = i + 2
ELSE
WRITE (label(i:i), "(I1)") nb(l)
i = i + 1
END IF
label(i:i) = lq(l)
END IF
END DO
i = i + 1
label(i:i) = "]"
END SUBROUTINE basis_label
! **************************************************************************************************
!> \brief Compute the total energy for the given atomic kind and basis set.
!> \param atom information about the atomic kind
!> \param basis basis set to fit
!> \param afun (output) atomic total energy
!> \param iw output file unit
!> \par History
!> * 11.2016 created [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE grb_fit(atom, basis, afun, iw)
TYPE(atom_type), POINTER :: atom
TYPE(atom_basis_type), POINTER :: basis
REAL(dp), INTENT(OUT) :: afun
INTEGER, INTENT(IN) :: iw
INTEGER :: do_eric, do_erie, reltyp, zval
LOGICAL :: eri_c, eri_e
TYPE(atom_integrals), POINTER :: atint
TYPE(atom_potential_type), POINTER :: pot
ALLOCATE (atint)
! calculate integrals
NULLIFY (pot)
eri_c = .FALSE.
eri_e = .FALSE.
pot => atom%potential
zval = atom%z
reltyp = atom%relativistic
do_eric = atom%coulomb_integral_type
do_erie = atom%exchange_integral_type
IF (do_eric == do_analytic) eri_c = .TRUE.
IF (do_erie == do_analytic) eri_e = .TRUE.
! general integrals
CALL atom_int_setup(atint, basis, potential=pot, eri_coulomb=eri_c, eri_exchange=eri_e)
! potential
CALL atom_ppint_setup(atint, basis, potential=pot)
IF (atom%pp_calc) THEN
NULLIFY (atint%tzora, atint%hdkh)
ELSE
! relativistic correction terms
CALL atom_relint_setup(atint, basis, reltyp, zcore=REAL(zval, dp))
END IF
CALL set_atom(atom, basis=basis)
CALL set_atom(atom, integrals=atint)
CALL calculate_atom(atom, iw)
afun = atom%energy%etot
CALL atom_int_release(atint)
CALL atom_ppint_release(atint)
CALL atom_relint_release(atint)
DEALLOCATE (atint)
END SUBROUTINE grb_fit
! **************************************************************************************************
!> \brief Copy basic information about the atomic kind.
!> \param atom_ref atom to copy
!> \param atom new atom to create
!> \param state also copy electronic state and occupation numbers
!> \param potential also copy pseudo-potential
!> \param optimization also copy optimization procedure
!> \param xc also copy the XC input section
!> \par History
!> * 11.2016 created [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE copy_atom_basics(atom_ref, atom, state, potential, optimization, xc)
TYPE(atom_type), POINTER :: atom_ref, atom
LOGICAL, INTENT(IN), OPTIONAL :: state, potential, optimization, xc
atom%z = atom_ref%z
atom%zcore = atom_ref%zcore
atom%pp_calc = atom_ref%pp_calc
atom%method_type = atom_ref%method_type
atom%relativistic = atom_ref%relativistic
atom%coulomb_integral_type = atom_ref%coulomb_integral_type
atom%exchange_integral_type = atom_ref%exchange_integral_type
NULLIFY (atom%potential, atom%state, atom%xc_section)
NULLIFY (atom%basis, atom%integrals, atom%orbitals, atom%fmat)
IF (PRESENT(state)) THEN
IF (state) THEN
ALLOCATE (atom%state)
atom%state = atom_ref%state
END IF
END IF
IF (PRESENT(potential)) THEN
IF (potential) THEN
ALLOCATE (atom%potential)
atom%potential = atom_ref%potential
END IF
END IF
IF (PRESENT(optimization)) THEN
IF (optimization) THEN
atom%optimization = atom_ref%optimization
END IF
END IF
IF (PRESENT(xc)) THEN
IF (xc) THEN
atom%xc_section => atom_ref%xc_section
END IF
END IF
END SUBROUTINE copy_atom_basics
! **************************************************************************************************
!> \brief Optimise a geometrical response basis set.
!> \param atom information about the atomic kind
!> \param basis basis set to fit
!> \param iunit output file unit
!> \param powell_section POWELL input section
!> \par History
!> * 11.2016 created [Juerg Hutter]
! **************************************************************************************************
SUBROUTINE atom_fit_grb(atom, basis, iunit, powell_section)
TYPE(atom_type), POINTER :: atom
TYPE(atom_basis_type), POINTER :: basis
INTEGER, INTENT(IN) :: iunit
TYPE(section_vals_type), POINTER :: powell_section
INTEGER :: i, k, l, ll, n10, nr
REAL(KIND=dp) :: al, cnum, crad, cradx, ear, fopt, rk
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: x
TYPE(opt_state_type) :: ostate
CPASSERT(basis%geometrical)
CALL section_vals_val_get(powell_section, "ACCURACY", r_val=ostate%rhoend)
CALL section_vals_val_get(powell_section, "STEP_SIZE", r_val=ostate%rhobeg)
CALL section_vals_val_get(powell_section, "MAX_FUN", i_val=ostate%maxfun)
ostate%nvar = 2
ALLOCATE (x(2))
x(1) = SQRT(basis%aval)
x(2) = SQRT(basis%cval)
ostate%nf = 0
ostate%iprint = 1
ostate%unit = iunit
ostate%state = 0
IF (iunit > 0) THEN
WRITE (iunit, '(/," POWELL| Start optimization procedure")')
WRITE (iunit, '(" POWELL| Total number of parameters in optimization",T71,I10)') ostate%nvar
END IF
n10 = MAX(ostate%maxfun/100, 1)
fopt = HUGE(0._dp)
DO
IF (ostate%state == 2) THEN
basis%am = 0._dp
DO l = 0, lmat
DO i = 1, basis%nbas(l)
ll = i - 1 + basis%start(l)
basis%am(i, l) = x(1)*x(1)*(x(2)*x(2))**(ll)
END DO
END DO
basis%aval = x(1)*x(1)
basis%cval = x(2)*x(2)
basis%bf = 0._dp
basis%dbf = 0._dp
basis%ddbf = 0._dp
nr = basis%grid%nr