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atom_fit.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 routines that fit parameters for /from atomic calculations
! **************************************************************************************************
MODULE atom_fit
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_output, ONLY: atom_print_basis,&
atom_print_basis_file,&
atom_write_pseudo_param
USE atom_types, ONLY: &
GTO_BASIS, STO_BASIS, atom_basis_type, atom_gthpot_type, atom_integrals, atom_p_type, &
atom_potential_type, atom_type, create_opgrid, create_opmat, lmat, opgrid_type, &
opmat_type, release_opgrid, release_opmat, set_atom
USE atom_utils, ONLY: &
atom_completeness, atom_condnumber, atom_consistent_method, atom_core_density, &
atom_denmat, atom_density, atom_orbital_charge, atom_orbital_max, atom_orbital_nodes, &
atom_wfnr0, get_maxn_occ, integrate_grid
USE cp_files, ONLY: close_file,&
open_file
USE input_constants, ONLY: do_analytic,&
do_rhf_atom,&
do_rks_atom,&
do_rohf_atom,&
do_uhf_atom,&
do_uks_atom
USE input_section_types, ONLY: section_vals_type,&
section_vals_val_get
USE kinds, ONLY: dp
USE mathconstants, ONLY: fac,&
fourpi,&
pi
USE periodic_table, ONLY: ptable
USE physcon, ONLY: bohr,&
evolt
USE powell, ONLY: opt_state_type,&
powell_optimize
USE qs_grid_atom, ONLY: grid_atom_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'atom_fit'
PUBLIC :: atom_fit_density, atom_fit_basis, atom_fit_pseudo, atom_fit_kgpot
TYPE wfn_init
REAL(KIND=dp), DIMENSION(:, :, :), POINTER :: wfn => NULL()
END TYPE wfn_init
CONTAINS
! **************************************************************************************************
!> \brief Fit the atomic electron density using a geometrical Gaussian basis set.
!> \param atom information about the atomic kind
!> \param num_gto number of Gaussian basis functions
!> \param norder ...
!> \param iunit output file unit
!> \param agto Gaussian exponents
!> \param powell_section POWELL input section
!> \param results (output) array of num_gto+2 real numbers in the following format:
!> starting exponent, factor of geometrical series, expansion coefficients(1:num_gto)
! **************************************************************************************************
SUBROUTINE atom_fit_density(atom, num_gto, norder, iunit, agto, powell_section, results)
TYPE(atom_type), POINTER :: atom
INTEGER, INTENT(IN) :: num_gto, norder, iunit
REAL(KIND=dp), DIMENSION(:), OPTIONAL :: agto
TYPE(section_vals_type), OPTIONAL, POINTER :: powell_section
REAL(KIND=dp), DIMENSION(:), OPTIONAL :: results
INTEGER :: i, n10
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: co, pe
REAL(KIND=dp), DIMENSION(2) :: x
TYPE(opgrid_type), POINTER :: density
TYPE(opt_state_type) :: ostate
ALLOCATE (co(num_gto), pe(num_gto))
co = 0._dp
pe = 0._dp
NULLIFY (density)
CALL create_opgrid(density, atom%basis%grid)
CALL atom_denmat(atom%orbitals%pmat, atom%orbitals%wfn, atom%basis%nbas, atom%state%occupation, &
atom%state%maxl_occ, atom%state%maxn_occ)
CALL atom_density(density%op, atom%orbitals%pmat, atom%basis, atom%state%maxl_occ, &
typ="RHO")
density%op = fourpi*density%op
IF (norder /= 0) THEN
density%op = density%op*atom%basis%grid%rad**norder
END IF
IF (PRESENT(agto)) THEN
CPASSERT(num_gto <= SIZE(agto))
pe(1:num_gto) = agto(1:num_gto)
ELSE
ostate%nf = 0
ostate%nvar = 2
x(1) = 0.10_dp !starting point of geometric series
x(2) = 2.00_dp !factor of series
IF (PRESENT(powell_section)) THEN
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)
ELSE
ostate%rhoend = 1.e-8_dp
ostate%rhobeg = 5.e-2_dp
ostate%maxfun = 1000
END IF
ostate%iprint = 1
ostate%unit = iunit
ostate%state = 0
IF (iunit > 0) THEN
WRITE (iunit, '(/," POWELL| Start optimization procedure")')
END IF
n10 = ostate%maxfun/10
DO
IF (ostate%state == 2) THEN
pe(1:num_gto) = [(x(1)*x(2)**i, i=1, num_gto)]
CALL density_fit(density%op, density%grid, num_gto, pe, co, ostate%f)
END IF
IF (ostate%state == -1) EXIT
CALL powell_optimize(ostate%nvar, x, ostate)
IF (MOD(ostate%nf, n10) == 0 .AND. iunit > 0) THEN
WRITE (iunit, '(" POWELL| Reached",i4,"% of maximal function calls")') &
INT(REAL(ostate%nf, dp)/REAL(ostate%maxfun, dp)*100._dp)
END IF
END DO
ostate%state = 8
CALL powell_optimize(ostate%nvar, x, ostate)
pe(1:num_gto) = [(x(1)*x(2)**i, i=1, num_gto)]
END IF
CALL density_fit(density%op, density%grid, num_gto, pe, co, ostate%f)
CALL release_opgrid(density)
IF (iunit > 0 .AND. .NOT. PRESENT(agto)) THEN
WRITE (iunit, '(" POWELL| Number of function evaluations",T71,I10)') ostate%nf
WRITE (iunit, '(" POWELL| Final value of function",T61,G20.10)') ostate%fopt
WRITE (iunit, '(" Optimized representation of density using a Geometrical Gaussian basis")')
WRITE (iunit, '(A,I3,/,T10,A,F10.6,T48,A,F10.6)') " Number of Gaussians:", num_gto, &
"Starting exponent:", x(1), "Proportionality factor:", x(2)
WRITE (iunit, '(A)') " Expansion coefficients"
WRITE (iunit, '(4F20.10)') co(1:num_gto)
END IF
IF (PRESENT(results)) THEN
IF (PRESENT(agto)) THEN
CPASSERT(SIZE(results) >= num_gto)
results(1:num_gto) = co(1:num_gto)
ELSE
CPASSERT(SIZE(results) >= num_gto + 2)
results(1) = x(1)
results(2) = x(2)
results(3:2 + num_gto) = co(1:num_gto)
END IF
END IF
DEALLOCATE (co, pe)
END SUBROUTINE atom_fit_density
! **************************************************************************************************
!> \brief ...
!> \param atom_info ...
!> \param basis ...
!> \param pptype ...
!> \param iunit output file unit
!> \param powell_section POWELL input section
! **************************************************************************************************
SUBROUTINE atom_fit_basis(atom_info, basis, pptype, iunit, powell_section)
TYPE(atom_p_type), DIMENSION(:, :), POINTER :: atom_info
TYPE(atom_basis_type), POINTER :: basis
LOGICAL, INTENT(IN) :: pptype
INTEGER, INTENT(IN) :: iunit
TYPE(section_vals_type), POINTER :: powell_section
INTEGER :: i, j, k, l, ll, m, n, n10, nl, nr, zval
INTEGER, ALLOCATABLE, DIMENSION(:, :) :: xtob
LOGICAL :: explicit, mult, penalty
REAL(KIND=dp) :: al, crad, ear, fopt, pf, rk
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: x
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: wem
REAL(KIND=dp), DIMENSION(:), POINTER :: w
TYPE(opt_state_type) :: ostate
penalty = .FALSE.
SELECT CASE (basis%basis_type)
CASE DEFAULT
CPABORT("")
CASE (GTO_BASIS)
IF (basis%geometrical) THEN
ostate%nvar = 2
ALLOCATE (x(2))
x(1) = SQRT(basis%aval)
x(2) = SQRT(basis%cval)
ELSE
ll = MAXVAL(basis%nprim(:))
ALLOCATE (xtob(ll, 0:lmat))
xtob = 0
ll = SUM(basis%nprim(:))
ALLOCATE (x(ll))
x = 0._dp
ll = 0
DO l = 0, lmat
DO i = 1, basis%nprim(l)
mult = .FALSE.
DO k = 1, ll
IF (ABS(basis%am(i, l) - x(k)) < 1.e-6_dp) THEN
mult = .TRUE.
xtob(i, l) = k
END IF
END DO
IF (.NOT. mult) THEN
ll = ll + 1
x(ll) = basis%am(i, l)
xtob(i, l) = ll
END IF
END DO
END DO
ostate%nvar = ll
DO i = 1, ostate%nvar
x(i) = SQRT(LOG(1._dp + x(i)))
END DO
penalty = .TRUE.
END IF
CASE (STO_BASIS)
ll = MAXVAL(basis%nbas(:))
ALLOCATE (xtob(ll, 0:lmat))
xtob = 0
ll = SUM(basis%nbas(:))
ALLOCATE (x(ll))
x = 0._dp
ll = 0
DO l = 0, lmat
DO i = 1, basis%nbas(l)
ll = ll + 1
x(ll) = basis%as(i, l)
xtob(i, l) = ll
END DO
END DO
ostate%nvar = ll
DO i = 1, ostate%nvar
x(i) = SQRT(LOG(1._dp + x(i)))
END DO
END SELECT
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)
n = SIZE(atom_info, 1)
m = SIZE(atom_info, 2)
ALLOCATE (wem(n, m))
wem = 1._dp
CALL section_vals_val_get(powell_section, "WEIGHT_ELECTRON_CONFIGURATION", explicit=explicit)
IF (explicit) THEN
CALL section_vals_val_get(powell_section, "WEIGHT_ELECTRON_CONFIGURATION", r_vals=w)
DO i = 1, MIN(SIZE(w), n)
wem(i, :) = w(i)*wem(i, :)
END DO
END IF
CALL section_vals_val_get(powell_section, "WEIGHT_METHOD", explicit=explicit)
IF (explicit) THEN
CALL section_vals_val_get(powell_section, "WEIGHT_METHOD", r_vals=w)
DO i = 1, MIN(SIZE(w), m)
wem(:, i) = w(i)*wem(:, i)
END DO
END IF
DO i = 1, SIZE(atom_info, 1)
DO j = 1, SIZE(atom_info, 2)
atom_info(i, j)%atom%weight = wem(i, j)
END DO
END DO
DEALLOCATE (wem)
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
SELECT CASE (basis%basis_type)
CASE DEFAULT
CPABORT("")
CASE (GTO_BASIS)
IF (basis%geometrical) 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)
ELSE
DO l = 0, lmat
DO i = 1, basis%nprim(l)
al = x(xtob(i, l))**2
basis%am(i, l) = EXP(al) - 1._dp
END DO
END DO
END IF
basis%bf = 0._dp
basis%dbf = 0._dp
basis%ddbf = 0._dp
nr = basis%grid%nr
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 (STO_BASIS)
DO l = 0, lmat
DO i = 1, basis%nbas(l)
al = x(xtob(i, l))**2
basis%as(i, l) = EXP(al) - 1._dp
END DO
END DO
basis%bf = 0._dp
basis%dbf = 0._dp
basis%ddbf = 0._dp
nr = basis%grid%nr
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
END SELECT
CALL basis_fit(atom_info, basis, pptype, ostate%f, 0, penalty)
fopt = MIN(fopt, ostate%f)
END IF
IF (ostate%state == -1) EXIT
CALL powell_optimize(ostate%nvar, x, ostate)
IF (ostate%nf == 2 .AND. iunit > 0) THEN
WRITE (iunit, '(" POWELL| Initial value of function",T61,F20.10)') ostate%f
END IF
IF (MOD(ostate%nf, n10) == 0 .AND. iunit > 0) THEN
WRITE (iunit, '(" POWELL| Reached",i4,"% of maximal function calls",T61,F20.10)') &
INT(REAL(ostate%nf, dp)/REAL(ostate%maxfun, dp)*100._dp), fopt
END IF
END DO
ostate%state = 8
CALL powell_optimize(ostate%nvar, x, ostate)
IF (iunit > 0) THEN
WRITE (iunit, '(" POWELL| Number of function evaluations",T71,I10)') ostate%nf
WRITE (iunit, '(" POWELL| Final value of function",T61,F20.10)') ostate%fopt
! x->basis
SELECT CASE (basis%basis_type)
CASE DEFAULT
CPABORT("")
CASE (GTO_BASIS)
IF (basis%geometrical) 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)
ELSE
DO l = 0, lmat
DO i = 1, basis%nprim(l)
al = x(xtob(i, l))**2
basis%am(i, l) = EXP(al) - 1._dp
END DO
END DO
END IF
basis%bf = 0._dp
basis%dbf = 0._dp
basis%ddbf = 0._dp
nr = basis%grid%nr
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 (STO_BASIS)
DO l = 0, lmat
DO i = 1, basis%nprim(l)
al = x(xtob(i, l))**2
basis%as(i, l) = EXP(al) - 1._dp
END DO
END DO
basis%bf = 0._dp
basis%dbf = 0._dp
basis%ddbf = 0._dp
nr = basis%grid%nr
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
END SELECT
CALL atom_print_basis(basis, iunit, " Optimized Basis")
CALL atom_print_basis_file(basis, atom_info(1, 1)%atom%orbitals%wfn)
END IF
DEALLOCATE (x)
IF (ALLOCATED(xtob)) THEN
DEALLOCATE (xtob)
END IF
SELECT CASE (basis%basis_type)
CASE DEFAULT
CPABORT("")
CASE (GTO_BASIS)
zval = atom_info(1, 1)%atom%z
crad = ptable(zval)%covalent_radius*bohr
IF (iunit > 0) THEN
CALL atom_condnumber(basis, crad, iunit)
CALL atom_completeness(basis, zval, iunit)
END IF
CASE (STO_BASIS)
! no basis test available
END SELECT
END SUBROUTINE atom_fit_basis
! **************************************************************************************************
!> \brief ...
!> \param atom_info ...
!> \param atom_refs ...
!> \param ppot ...
!> \param iunit output file unit
!> \param powell_section POWELL input section
! **************************************************************************************************
SUBROUTINE atom_fit_pseudo(atom_info, atom_refs, ppot, iunit, powell_section)
TYPE(atom_p_type), DIMENSION(:, :), POINTER :: atom_info, atom_refs
TYPE(atom_potential_type), POINTER :: ppot
INTEGER, INTENT(IN) :: iunit
TYPE(section_vals_type), POINTER :: powell_section
LOGICAL, PARAMETER :: debug = .FALSE.
CHARACTER(len=2) :: pc1, pc2, pct
INTEGER :: i, i1, i2, iw, j, j1, j2, k, l, m, n, &
n10, np, nre, nreinit, ntarget
INTEGER, ALLOCATABLE, DIMENSION(:, :) :: xtob
INTEGER, DIMENSION(0:lmat) :: ncore
LOGICAL :: explicit, noopt_nlcc, preopt_nlcc
REAL(KIND=dp) :: afun, charge, de, deig, drho, dx, eig, fopt, oc, pchg, peig, pv, rcm, rcov, &
rmax, semicore_level, step_size_scaling, t_ener, t_psir0, t_semi, t_valence, t_virt, &
w_ener, w_node, w_psir0, w_semi, w_valence, w_virt, wtot
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: x, xi
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: wem
REAL(KIND=dp), ALLOCATABLE, &
DIMENSION(:, :, :, :, :) :: dener, pval
REAL(KIND=dp), DIMENSION(:), POINTER :: w
TYPE(atom_type), POINTER :: atom
TYPE(opt_state_type) :: ostate
TYPE(wfn_init), DIMENSION(:, :), POINTER :: wfn_guess
! weights for the optimization
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)
CALL section_vals_val_get(powell_section, "MAX_INIT", i_val=nreinit)
CALL section_vals_val_get(powell_section, "STEP_SIZE_SCALING", r_val=step_size_scaling)
CALL section_vals_val_get(powell_section, "WEIGHT_POT_VALENCE", r_val=w_valence)
CALL section_vals_val_get(powell_section, "WEIGHT_POT_VIRTUAL", r_val=w_virt)
CALL section_vals_val_get(powell_section, "WEIGHT_POT_SEMICORE", r_val=w_semi)
CALL section_vals_val_get(powell_section, "WEIGHT_POT_NODE", r_val=w_node)
CALL section_vals_val_get(powell_section, "WEIGHT_DELTA_ENERGY", r_val=w_ener)
CALL section_vals_val_get(powell_section, "TARGET_PSIR0", r_val=t_psir0)
CALL section_vals_val_get(powell_section, "WEIGHT_PSIR0", r_val=w_psir0)
CALL section_vals_val_get(powell_section, "RCOV_MULTIPLICATION", r_val=rcm)
CALL section_vals_val_get(powell_section, "TARGET_POT_VALENCE", r_val=t_valence)
CALL section_vals_val_get(powell_section, "TARGET_POT_VIRTUAL", r_val=t_virt)
CALL section_vals_val_get(powell_section, "TARGET_POT_SEMICORE", r_val=t_semi)
CALL section_vals_val_get(powell_section, "TARGET_DELTA_ENERGY", r_val=t_ener)
CALL section_vals_val_get(powell_section, "SEMICORE_LEVEL", r_val=semicore_level)
CALL section_vals_val_get(powell_section, "NOOPT_NLCC", l_val=noopt_nlcc)
CALL section_vals_val_get(powell_section, "PREOPT_NLCC", l_val=preopt_nlcc)
n = SIZE(atom_info, 1)
m = SIZE(atom_info, 2)
ALLOCATE (wem(n, m))
wem = 1._dp
ALLOCATE (pval(8, 10, 0:lmat, m, n))
ALLOCATE (dener(2, m, m, n, n))
dener = 0.0_dp
ALLOCATE (wfn_guess(n, m))
DO i = 1, n
DO j = 1, m
atom => atom_info(i, j)%atom
NULLIFY (wfn_guess(i, j)%wfn)
IF (atom_consistent_method(atom%method_type, atom%state%multiplicity)) THEN
i1 = SIZE(atom%orbitals%wfn, 1)
i2 = SIZE(atom%orbitals%wfn, 2)
ALLOCATE (wfn_guess(i, j)%wfn(i1, i2, 0:lmat))
END IF
END DO
END DO
CALL section_vals_val_get(powell_section, "WEIGHT_ELECTRON_CONFIGURATION", explicit=explicit)
IF (explicit) THEN
CALL section_vals_val_get(powell_section, "WEIGHT_ELECTRON_CONFIGURATION", r_vals=w)
DO i = 1, MIN(SIZE(w), n)
wem(i, :) = w(i)*wem(i, :)
END DO
END IF
CALL section_vals_val_get(powell_section, "WEIGHT_METHOD", explicit=explicit)
IF (explicit) THEN
CALL section_vals_val_get(powell_section, "WEIGHT_METHOD", r_vals=w)
DO i = 1, MIN(SIZE(w), m)
wem(:, i) = w(i)*wem(:, i)
END DO
END IF
IF (debug) THEN
CALL open_file(file_name="POWELL_RESULT", file_status="UNKNOWN", file_action="WRITE", unit_number=iw)
END IF
IF (ppot%gth_pot%nlcc) THEN
CALL opt_nlcc_param(atom_info, atom_refs, ppot%gth_pot, iunit, preopt_nlcc)
ELSE
noopt_nlcc = .TRUE.
preopt_nlcc = .FALSE.
END IF
ALLOCATE (xi(200))
!decide here what to optimize
CALL get_pseudo_param(xi, ostate%nvar, ppot%gth_pot, noopt_nlcc)
ALLOCATE (x(ostate%nvar))
x(1:ostate%nvar) = xi(1:ostate%nvar)
DEALLOCATE (xi)
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)
rcov = ptable(atom_refs(1, 1)%atom%z)%covalent_radius*bohr*rcm
!set all reference values
ntarget = 0
wtot = 0.0_dp
DO i = 1, SIZE(atom_info, 1)
DO j = 1, SIZE(atom_info, 2)
atom => atom_info(i, j)%atom
IF (atom_consistent_method(atom%method_type, atom%state%multiplicity)) THEN
dener(2, j, j, i, i) = atom_refs(i, j)%atom%energy%etot
IF (atom%state%multiplicity == -1) THEN
! no spin polarization
atom%weight = wem(i, j)
ncore = get_maxn_occ(atom%state%core)
DO l = 0, lmat
np = atom%state%maxn_calc(l)
DO k = 1, np
CALL atom_orbital_max(rmax, atom_refs(i, j)%atom%orbitals%wfn(:, ncore(l) + k, l), &
rcov, l, atom_refs(i, j)%atom%basis)
atom%orbitals%rcmax(k, l, 1) = MAX(rcov, rmax)
CALL atom_orbital_charge(charge, atom_refs(i, j)%atom%orbitals%wfn(:, ncore(l) + k, l), &
atom%orbitals%rcmax(k, l, 1), l, atom_refs(i, j)%atom%basis)
atom%orbitals%refene(k, l, 1) = atom_refs(i, j)%atom%orbitals%ener(ncore(l) + k, l)
atom%orbitals%refchg(k, l, 1) = charge
IF (k > atom%state%maxn_occ(l)) THEN
IF (k <= atom%state%maxn_occ(l) + 1) THEN
atom%orbitals%wrefene(k, l, 1) = w_virt
atom%orbitals%wrefchg(k, l, 1) = w_virt/100._dp
atom%orbitals%crefene(k, l, 1) = t_virt
atom%orbitals%reftype(k, l, 1) = "U1"
ntarget = ntarget + 2
wtot = wtot + atom%weight*(w_virt + w_virt/100._dp)
ELSE
atom%orbitals%wrefene(k, l, 1) = w_virt/100._dp
atom%orbitals%wrefchg(k, l, 1) = 0._dp
atom%orbitals%crefene(k, l, 1) = t_virt*10._dp
atom%orbitals%reftype(k, l, 1) = "U2"
ntarget = ntarget + 1
wtot = wtot + atom%weight*w_virt/100._dp
END IF
ELSEIF (k < atom%state%maxn_occ(l)) THEN
atom%orbitals%wrefene(k, l, 1) = w_semi
atom%orbitals%wrefchg(k, l, 1) = w_semi/100._dp
atom%orbitals%crefene(k, l, 1) = t_semi
atom%orbitals%reftype(k, l, 1) = "SC"
ntarget = ntarget + 2
wtot = wtot + atom%weight*(w_semi + w_semi/100._dp)
ELSE
IF (ABS(atom%state%occupation(l, k) - REAL(4*l + 2, KIND=dp)) < 0.01_dp .AND. &
ABS(atom%orbitals%refene(k, l, 1)) > semicore_level) THEN
! full shell semicore
atom%orbitals%wrefene(k, l, 1) = w_semi
atom%orbitals%wrefchg(k, l, 1) = w_semi/100._dp
atom%orbitals%crefene(k, l, 1) = t_semi
atom%orbitals%reftype(k, l, 1) = "SC"
wtot = wtot + atom%weight*(w_semi + w_semi/100._dp)
ELSE
atom%orbitals%wrefene(k, l, 1) = w_valence
atom%orbitals%wrefchg(k, l, 1) = w_valence/100._dp
atom%orbitals%crefene(k, l, 1) = t_valence
atom%orbitals%reftype(k, l, 1) = "VA"
wtot = wtot + atom%weight*(w_valence + w_valence/100._dp)
END IF
IF (l == 0) THEN
atom%orbitals%tpsir0(k, 1) = t_psir0
atom%orbitals%wpsir0(k, 1) = w_psir0
wtot = wtot + atom%weight*w_psir0
END IF
ntarget = ntarget + 2
END IF
END DO
DO k = 1, np
atom%orbitals%refnod(k, l, 1) = REAL(k - 1, KIND=dp)
! we only enforce 0-nodes for the first state
IF (k == 1 .AND. atom%state%occupation(l, k) /= 0._dp) THEN
atom%orbitals%wrefnod(k, l, 1) = w_node
wtot = wtot + atom%weight*w_node
END IF
END DO
END DO
ELSE
! spin polarization
atom%weight = wem(i, j)
ncore = get_maxn_occ(atom_info(i, j)%atom%state%core)
DO l = 0, lmat
np = atom%state%maxn_calc(l)
DO k = 1, np
CALL atom_orbital_max(rmax, atom_refs(i, j)%atom%orbitals%wfna(:, ncore(l) + k, l), &
rcov, l, atom_refs(i, j)%atom%basis)
atom%orbitals%rcmax(k, l, 1) = MAX(rcov, rmax)
CALL atom_orbital_max(rmax, atom_refs(i, j)%atom%orbitals%wfnb(:, ncore(l) + k, l), &
rcov, l, atom_refs(i, j)%atom%basis)
atom%orbitals%rcmax(k, l, 2) = MAX(rcov, rmax)
CALL atom_orbital_charge(charge, atom_refs(i, j)%atom%orbitals%wfna(:, ncore(l) + k, l), &
atom%orbitals%rcmax(k, l, 1), l, atom_refs(i, j)%atom%basis)
atom%orbitals%refene(k, l, 1) = atom_refs(i, j)%atom%orbitals%enera(ncore(l) + k, l)
atom%orbitals%refchg(k, l, 1) = charge
CALL atom_orbital_charge(charge, atom_refs(i, j)%atom%orbitals%wfnb(:, ncore(l) + k, l), &
atom%orbitals%rcmax(k, l, 1), l, atom_refs(i, j)%atom%basis)
atom%orbitals%refene(k, l, 2) = atom_refs(i, j)%atom%orbitals%enerb(ncore(l) + k, l)
atom%orbitals%refchg(k, l, 2) = charge
! the following assignments could be further specialized
IF (k > atom%state%maxn_occ(l)) THEN
IF (k <= atom%state%maxn_occ(l) + 1) THEN
atom%orbitals%wrefene(k, l, 1:2) = w_virt
atom%orbitals%wrefchg(k, l, 1:2) = w_virt/100._dp
atom%orbitals%crefene(k, l, 1:2) = t_virt
atom%orbitals%reftype(k, l, 1:2) = "U1"
ntarget = ntarget + 4
wtot = wtot + atom%weight*2._dp*(w_virt + w_virt/100._dp)
ELSE
atom%orbitals%wrefene(k, l, 1:2) = w_virt/100._dp
atom%orbitals%wrefchg(k, l, 1:2) = 0._dp
atom%orbitals%crefene(k, l, 1:2) = t_virt*10.0_dp
atom%orbitals%reftype(k, l, 1:2) = "U2"
wtot = wtot + atom%weight*2._dp*w_virt/100._dp
ntarget = ntarget + 2
END IF
ELSEIF (k < atom%state%maxn_occ(l)) THEN
atom%orbitals%wrefene(k, l, 1:2) = w_semi
atom%orbitals%wrefchg(k, l, 1:2) = w_semi/100._dp
atom%orbitals%crefene(k, l, 1:2) = t_semi
atom%orbitals%reftype(k, l, 1:2) = "SC"
ntarget = ntarget + 4
wtot = wtot + atom%weight*2._dp*(w_semi + w_semi/100._dp)
ELSE
IF (ABS(atom%state%occupation(l, k) - REAL(2*l + 1, KIND=dp)) < 0.01_dp .AND. &
ABS(atom%orbitals%refene(k, l, 1)) > semicore_level) THEN
atom%orbitals%wrefene(k, l, 1:2) = w_semi
atom%orbitals%wrefchg(k, l, 1:2) = w_semi/100._dp
atom%orbitals%crefene(k, l, 1:2) = t_semi
atom%orbitals%reftype(k, l, 1:2) = "SC"
wtot = wtot + atom%weight*2._dp*(w_semi + w_semi/100._dp)
ELSE
atom%orbitals%wrefene(k, l, 1:2) = w_valence
atom%orbitals%wrefchg(k, l, 1:2) = w_valence/100._dp
atom%orbitals%crefene(k, l, 1:2) = t_valence
atom%orbitals%reftype(k, l, 1:2) = "VA"
wtot = wtot + atom%weight*2._dp*(w_valence + w_valence/100._dp)
END IF
ntarget = ntarget + 4
IF (l == 0) THEN
atom%orbitals%tpsir0(k, 1:2) = t_psir0
atom%orbitals%wpsir0(k, 1:2) = w_psir0
wtot = wtot + atom%weight*2._dp*w_psir0
END IF
END IF
END DO
DO k = 1, np
atom%orbitals%refnod(k, l, 1:2) = REAL(k - 1, KIND=dp)
! we only enforce 0-nodes for the first state
IF (k == 1 .AND. atom%state%occa(l, k) /= 0._dp) THEN
atom%orbitals%wrefnod(k, l, 1) = w_node
wtot = wtot + atom%weight*w_node
END IF
IF (k == 1 .AND. atom%state%occb(l, k) /= 0._dp) THEN
atom%orbitals%wrefnod(k, l, 2) = w_node
wtot = wtot + atom%weight*w_node
END IF
END DO
END DO
END IF
CALL calculate_atom(atom, 0)
END IF
END DO
END DO
! energy differences
DO j1 = 1, SIZE(atom_info, 2)
DO j2 = 1, SIZE(atom_info, 2)
DO i1 = 1, SIZE(atom_info, 1)
DO i2 = 1, SIZE(atom_info, 1)
IF ((j1 > j2) .OR. (j1 == j2 .AND. i1 >= i2)) CYCLE
dener(2, j1, j2, i1, i2) = dener(2, j1, j1, i1, i1) - dener(2, j2, j2, i2, i2)
wtot = wtot + w_ener
END DO
END DO
END DO
END DO
DEALLOCATE (wem)
ALLOCATE (xi(ostate%nvar))
DO nre = 1, nreinit
xi(:) = x(:)
CALL put_pseudo_param(x, ppot%gth_pot, noopt_nlcc)
CALL pseudo_fit(atom_info, wfn_guess, ppot, ostate%f, wtot, pval, dener, w_ener, t_ener, .TRUE.)
IF (nre == 1) THEN
WRITE (iunit, '(/," POWELL| Initial errors of target values")')
afun = ostate%f*wtot
DO i = 1, SIZE(atom_info, 1)
DO j = 1, SIZE(atom_info, 2)
atom => atom_info(i, j)%atom
IF (atom_consistent_method(atom%method_type, atom%state%multiplicity)) THEN
! start orbitals
wfn_guess(i, j)%wfn = atom%orbitals%wfn
!
WRITE (iunit, '(/," Reference configuration ",T31,i5,T50," Method number ",T76,i5)') i, j
IF (atom%state%multiplicity == -1) THEN
! no spin polarization
WRITE (iunit, '(" L N Occupation Eigenvalue [eV] dE [eV] dCharge ")')
DO l = 0, lmat
np = atom%state%maxn_calc(l)
IF (np > 0) THEN
DO k = 1, np
oc = atom%state%occupation(l, k)
eig = atom%orbitals%ener(k, l)
deig = eig - atom%orbitals%refene(k, l, 1)
peig = pval(1, k, l, j, i)/afun*100._dp
IF (pval(5, k, l, j, i) > 0.5_dp) THEN
pc1 = " X"
ELSE
WRITE (pc1, "(I2)") NINT(peig)
END IF
CALL atom_orbital_charge(charge, atom%orbitals%wfn(:, k, l), &
atom%orbitals%rcmax(k, l, 1), l, atom%basis)
drho = charge - atom%orbitals%refchg(k, l, 1)
pchg = pval(2, k, l, j, i)/afun*100._dp
IF (pval(6, k, l, j, i) > 0.5_dp) THEN
pc2 = " X"
ELSE
WRITE (pc2, "(I2)") MIN(NINT(pchg), 99)
END IF
pct = atom%orbitals%reftype(k, l, 1)
WRITE (iunit, '(I5,I5,F14.2,F21.10,A3,F11.6,"[",A2,"]",F13.6,"[",A2,"]")') &
l, k, oc, eig*evolt, pct, deig*evolt, pc1, drho, pc2
END DO
END IF
END DO
ELSE
! spin polarization
WRITE (iunit, '(" L N Spin Occupation Eigenvalue [eV] dE [eV] dCharge ")')
DO l = 0, lmat
np = atom%state%maxn_calc(l)
IF (np > 0) THEN
DO k = 1, np
oc = atom%state%occa(l, k)
eig = atom%orbitals%enera(k, l)
deig = eig - atom%orbitals%refene(k, l, 1)
peig = pval(1, k, l, j, i)/afun*100._dp
IF (pval(5, k, l, j, i) > 0.5_dp) THEN
pc1 = " X"
ELSE
WRITE (pc1, "(I2)") NINT(peig)
END IF
CALL atom_orbital_charge( &
charge, atom%orbitals%wfna(:, k, l), atom%orbitals%rcmax(k, l, 1), l, atom%basis)
drho = charge - atom%orbitals%refchg(k, l, 1)
pchg = pval(2, k, l, j, i)/afun*100._dp
IF (pval(6, k, l, j, i) > 0.5_dp) THEN
pc2 = " X"
ELSE
WRITE (pc2, "(I2)") MIN(NINT(pchg), 99)
END IF
pct = atom%orbitals%reftype(k, l, 1)
WRITE (iunit, '(I5,I5,2X,A5,F11.2,F19.10,A3,F10.6,"[",A2,"]",F12.6,"[",A2,"]")') &
l, k, "alpha", oc, eig*evolt, pct, deig*evolt, pc1, drho, pc2
oc = atom%state%occb(l, k)
eig = atom%orbitals%enerb(k, l)
deig = eig - atom%orbitals%refene(k, l, 2)
peig = pval(3, k, l, j, i)/afun*100._dp
IF (pval(7, k, l, j, i) > 0.5_dp) THEN
pc1 = " X"
ELSE
WRITE (pc1, "(I2)") NINT(peig)
END IF
CALL atom_orbital_charge( &
charge, atom%orbitals%wfnb(:, k, l), atom%orbitals%rcmax(k, l, 2), l, atom%basis)
drho = charge - atom%orbitals%refchg(k, l, 2)
pchg = pval(4, k, l, j, i)/afun*100._dp
IF (pval(8, k, l, j, i) > 0.5_dp) THEN
pc2 = " X"
ELSE
WRITE (pc2, "(I2)") MIN(NINT(pchg), 99)
END IF
pct = atom%orbitals%reftype(k, l, 2)
WRITE (iunit, '(I5,I5,2X,A5,F11.2,F19.10,A3,F10.6,"[",A2,"]",F12.6,"[",A2,"]")') &
l, k, " beta", oc, eig*evolt, pct, deig*evolt, pc1, drho, pc2
END DO
END IF
END DO
END IF
END IF
END DO
WRITE (iunit, *)
END DO
! energy differences
IF (n*m > 1) THEN
WRITE (iunit, '(" Method/Econf 1 "," Method/Econf 2"," Delta Energy "," Error Energy "," Target")')
DO j1 = 1, SIZE(atom_info, 2)
DO j2 = 1, SIZE(atom_info, 2)
DO i1 = 1, SIZE(atom_info, 1)
DO i2 = 1, SIZE(atom_info, 1)
IF ((j1 > j2) .OR. (j1 == j2 .AND. i1 >= i2)) CYCLE
IF (ABS(dener(1, j1, j1, i1, i1)) < 0.000001_dp) CYCLE
IF (ABS(dener(2, j1, j1, i1, i1)) < 0.000001_dp) CYCLE
IF (ABS(dener(1, j2, j2, i2, i2)) < 0.000001_dp) CYCLE
IF (ABS(dener(2, j2, j2, i2, i2)) < 0.000001_dp) CYCLE
de = dener(2, j1, j2, i1, i2) - dener(1, j1, j2, i1, i2)
WRITE (iunit, '(i6,i6,i10,i6,5X,F16.6,F19.6,F12.6)') &
j1, i1, j2, i2, dener(2, j1, j2, i1, i2), de, t_ener
END DO
END DO
END DO
END DO
WRITE (iunit, *)
END IF
WRITE (iunit, '(" Number of target values reached: ",T69,i5," of ",i3)') &
INT(SUM(pval(5:8, :, :, :, :))), ntarget
WRITE (iunit, *)
END IF
WRITE (iunit, '(" POWELL| Start optimization",I4," of total",I4,T60,"rhobeg = ",F12.8)') &
nre, nreinit, ostate%rhobeg
fopt = HUGE(0._dp)
ostate%state = 0
CALL powell_optimize(ostate%nvar, x, ostate)
DO
IF (ostate%state == 2) THEN
CALL put_pseudo_param(x, ppot%gth_pot, noopt_nlcc)
CALL pseudo_fit(atom_info, wfn_guess, ppot, ostate%f, wtot, pval, dener, w_ener, t_ener, .FALSE.)
fopt = MIN(fopt, ostate%f)
END IF
IF (ostate%state == -1) EXIT
CALL powell_optimize(ostate%nvar, x, ostate)
IF (ostate%nf == 2 .AND. iunit > 0) THEN
WRITE (iunit, '(" POWELL| Initial value of function",T61,F20.10)') ostate%f
END IF
IF (MOD(ostate%nf, n10) == 0 .AND. iunit > 0 .AND. ostate%nf > 2) THEN
WRITE (iunit, '(" POWELL| Reached",i4,"% of maximal function calls",T61,F20.10)') &
INT(REAL(ostate%nf, dp)/REAL(ostate%maxfun, dp)*100._dp), fopt
CALL put_pseudo_param(ostate%xopt, ppot%gth_pot, noopt_nlcc)
CALL atom_write_pseudo_param(ppot%gth_pot)
END IF
IF (fopt < 1.e-12_dp) EXIT
IF (debug) THEN
WRITE (iw, *) ostate%nf, ostate%f, x(1:ostate%nvar)
END IF
END DO
dx = SQRT(SUM((ostate%xopt(:) - xi(:))**2)/REAL(ostate%nvar, KIND=dp))
IF (iunit > 0) THEN
WRITE (iunit, '(" POWELL| RMS average of variables",T69,F12.10)') dx
END IF
ostate%state = 8
CALL powell_optimize(ostate%nvar, x, ostate)
CALL put_pseudo_param(x, ppot%gth_pot, noopt_nlcc)
CALL atom_write_pseudo_param(ppot%gth_pot)
! dx < SQRT(ostate%rhoend)
IF ((dx*dx) < ostate%rhoend) EXIT
ostate%rhobeg = step_size_scaling*ostate%rhobeg
END DO
DEALLOCATE (xi)
IF (iunit > 0) THEN
WRITE (iunit, '(" POWELL| Number of function evaluations",T71,I10)') ostate%nf
WRITE (iunit, '(" POWELL| Final value of function",T61,F20.10)') ostate%fopt
CALL put_pseudo_param(x, ppot%gth_pot, noopt_nlcc)
CALL pseudo_fit(atom_info, wfn_guess, ppot, ostate%f, wtot, pval, dener, w_ener, t_ener, .FALSE.)
afun = wtot*ostate%f
WRITE (iunit, '(/," POWELL| Final errors of target values")')
DO i = 1, SIZE(atom_info, 1)
DO j = 1, SIZE(atom_info, 2)
atom => atom_info(i, j)%atom
IF (atom_consistent_method(atom%method_type, atom%state%multiplicity)) THEN
WRITE (iunit, '(/," Reference configuration ",T31,i5,T50," Method number ",T76,i5)') i, j
IF (atom%state%multiplicity == -1) THEN
!no spin polarization
WRITE (iunit, '(" L N Occupation Eigenvalue [eV] dE [eV] dCharge ")')
DO l = 0, lmat
np = atom%state%maxn_calc(l)