LCOV - code coverage report
Current view: top level - src - atom_energy.F (source / functions) Hit Total Coverage
Test: CP2K Regtests (git:b279b6b) Lines: 477 506 94.3 %
Date: 2024-04-24 07:13:09 Functions: 4 4 100.0 %

          Line data    Source code
       1             : !--------------------------------------------------------------------------------------------------!
       2             : !   CP2K: A general program to perform molecular dynamics simulations                              !
       3             : !   Copyright 2000-2024 CP2K developers group <https://cp2k.org>                                   !
       4             : !                                                                                                  !
       5             : !   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
       6             : !--------------------------------------------------------------------------------------------------!
       7             : 
       8             : MODULE atom_energy
       9             :    USE atom_admm_methods,               ONLY: atom_admm
      10             :    USE atom_electronic_structure,       ONLY: calculate_atom
      11             :    USE atom_fit,                        ONLY: atom_fit_density,&
      12             :                                               atom_fit_kgpot
      13             :    USE atom_grb,                        ONLY: atom_grb_construction
      14             :    USE atom_operators,                  ONLY: atom_int_release,&
      15             :                                               atom_int_setup,&
      16             :                                               atom_ppint_release,&
      17             :                                               atom_ppint_setup,&
      18             :                                               atom_relint_release,&
      19             :                                               atom_relint_setup
      20             :    USE atom_output,                     ONLY: atom_print_basis,&
      21             :                                               atom_print_info,&
      22             :                                               atom_print_method,&
      23             :                                               atom_print_orbitals,&
      24             :                                               atom_print_potential,&
      25             :                                               atom_write_pseudo_param
      26             :    USE atom_sgp,                        ONLY: atom_sgp_construction
      27             :    USE atom_types,                      ONLY: &
      28             :         atom_basis_type, atom_gthpot_type, atom_integrals, atom_optimization_type, atom_orbitals, &
      29             :         atom_p_type, atom_potential_type, atom_state, atom_type, create_atom_orbs, &
      30             :         create_atom_type, gth_pseudo, init_atom_basis, init_atom_potential, lmat, &
      31             :         read_atom_opt_section, release_atom_basis, release_atom_potential, release_atom_type, &
      32             :         set_atom
      33             :    USE atom_utils,                      ONLY: &
      34             :         atom_completeness, atom_condnumber, atom_consistent_method, atom_core_density, &
      35             :         atom_density, atom_local_potential, atom_read_external_density, atom_read_external_vxc, &
      36             :         atom_set_occupation, atom_write_zmp_restart, get_maxl_occ, get_maxn_occ
      37             :    USE atom_xc,                         ONLY: calculate_atom_ext_vxc,&
      38             :                                               calculate_atom_zmp
      39             :    USE cp_log_handling,                 ONLY: cp_get_default_logger,&
      40             :                                               cp_logger_type
      41             :    USE cp_output_handling,              ONLY: cp_print_key_finished_output,&
      42             :                                               cp_print_key_unit_nr
      43             :    USE input_constants,                 ONLY: do_analytic
      44             :    USE input_section_types,             ONLY: section_vals_get,&
      45             :                                               section_vals_get_subs_vals,&
      46             :                                               section_vals_type,&
      47             :                                               section_vals_val_get
      48             :    USE kinds,                           ONLY: default_string_length,&
      49             :                                               dp
      50             :    USE mathconstants,                   ONLY: dfac,&
      51             :                                               gamma1,&
      52             :                                               pi,&
      53             :                                               rootpi
      54             :    USE periodic_table,                  ONLY: nelem,&
      55             :                                               ptable
      56             :    USE physcon,                         ONLY: bohr
      57             : #include "./base/base_uses.f90"
      58             : 
      59             :    IMPLICIT NONE
      60             :    PRIVATE
      61             :    PUBLIC  :: atom_energy_opt
      62             : 
      63             :    CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'atom_energy'
      64             : 
      65             : CONTAINS
      66             : 
      67             : ! **************************************************************************************************
      68             : !> \brief Compute the atomic energy.
      69             : !> \param atom_section  ATOM input section
      70             : !> \par History
      71             : !>    * 11.2016 geometrical response basis set [Juerg Hutter]
      72             : !>    * 07.2016 ADMM analysis [Juerg Hutter]
      73             : !>    * 02.2014 non-additive kinetic energy term [Juerg Hutter]
      74             : !>    * 11.2013 Zhao, Morrison, and Parr (ZMP) potential [Daniele Varsano]
      75             : !>    * 02.2010 unrestricted KS and HF methods [Juerg Hutter]
      76             : !>    * 05.2009 electronic density fit [Juerg Hutter]
      77             : !>    * 04.2009 refactored and renamed to atom_energy_opt() [Juerg Hutter]
      78             : !>    * 08.2008 created as atom_energy() [Juerg Hutter]
      79             : ! **************************************************************************************************
      80         324 :    SUBROUTINE atom_energy_opt(atom_section)
      81             :       TYPE(section_vals_type), POINTER                   :: atom_section
      82             : 
      83             :       CHARACTER(len=*), PARAMETER                        :: routineN = 'atom_energy_opt'
      84             : 
      85             :       CHARACTER(LEN=2)                                   :: elem
      86             :       CHARACTER(LEN=default_string_length)               :: filename
      87             :       CHARACTER(LEN=default_string_length), &
      88         324 :          DIMENSION(:), POINTER                           :: tmpstringlist
      89             :       INTEGER :: do_eric, do_erie, handle, i, im, in, iw, k, maxl, mb, method, mo, n_meth, n_rep, &
      90             :          nder, nr_gh, num_gau, num_gto, num_pol, reltyp, zcore, zval, zz
      91             :       INTEGER, DIMENSION(0:lmat)                         :: maxn
      92         324 :       INTEGER, DIMENSION(:), POINTER                     :: cn
      93             :       LOGICAL                                            :: dm, do_gh, do_zmp, doread, eri_c, eri_e, &
      94             :                                                             had_ae, had_pp, lcomp, lcond, pp_calc, &
      95             :                                                             read_vxc
      96             :       REAL(KIND=dp)                                      :: crad, delta, lambda
      97         324 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: ext_density, ext_vxc
      98             :       REAL(KIND=dp), DIMENSION(0:lmat, 10)               :: pocc
      99             :       TYPE(atom_basis_type), POINTER                     :: ae_basis, pp_basis
     100             :       TYPE(atom_integrals), POINTER                      :: ae_int, pp_int
     101             :       TYPE(atom_optimization_type)                       :: optimization
     102             :       TYPE(atom_orbitals), POINTER                       :: orbitals
     103         324 :       TYPE(atom_p_type), DIMENSION(:, :), POINTER        :: atom_info
     104             :       TYPE(atom_potential_type), POINTER                 :: ae_pot, p_pot
     105             :       TYPE(atom_state), POINTER                          :: state
     106             :       TYPE(cp_logger_type), POINTER                      :: logger
     107             :       TYPE(section_vals_type), POINTER :: admm_section, basis_section, external_vxc_section, &
     108             :          method_section, opt_section, potential_section, powell_section, sgp_section, xc_section, &
     109             :          zmp_restart_section, zmp_section
     110             : 
     111         324 :       CALL timeset(routineN, handle)
     112             : 
     113             :       ! What atom do we calculate
     114         324 :       CALL section_vals_val_get(atom_section, "ATOMIC_NUMBER", i_val=zval)
     115         324 :       CALL section_vals_val_get(atom_section, "ELEMENT", c_val=elem)
     116         324 :       zz = 0
     117       11574 :       DO i = 1, nelem
     118       11574 :          IF (ptable(i)%symbol == elem) THEN
     119             :             zz = i
     120             :             EXIT
     121             :          END IF
     122             :       END DO
     123         324 :       IF (zz /= 1) zval = zz
     124             : 
     125             :       ! read and set up inofrmation on the basis sets
     126       11988 :       ALLOCATE (ae_basis, pp_basis)
     127         324 :       basis_section => section_vals_get_subs_vals(atom_section, "AE_BASIS")
     128         324 :       NULLIFY (ae_basis%grid)
     129         324 :       CALL init_atom_basis(ae_basis, basis_section, zval, "AE")
     130         324 :       NULLIFY (pp_basis%grid)
     131         324 :       basis_section => section_vals_get_subs_vals(atom_section, "PP_BASIS")
     132         324 :       CALL init_atom_basis(pp_basis, basis_section, zval, "PP")
     133             : 
     134             :       ! print general and basis set information
     135         324 :       logger => cp_get_default_logger()
     136         324 :       iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%PROGRAM_BANNER", extension=".log")
     137         324 :       IF (iw > 0) CALL atom_print_info(zval, "Atomic Energy Calculation", iw)
     138         324 :       CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%PROGRAM_BANNER")
     139         324 :       iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%BASIS_SET", extension=".log")
     140         324 :       IF (iw > 0) THEN
     141           0 :          CALL atom_print_basis(ae_basis, iw, " All Electron Basis")
     142           0 :          CALL atom_print_basis(pp_basis, iw, " Pseudopotential Basis")
     143             :       END IF
     144         324 :       CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%BASIS_SET")
     145             : 
     146             :       ! read and setup information on the pseudopotential
     147         324 :       NULLIFY (potential_section)
     148         324 :       potential_section => section_vals_get_subs_vals(atom_section, "POTENTIAL")
     149     3403620 :       ALLOCATE (ae_pot, p_pot)
     150         324 :       CALL init_atom_potential(p_pot, potential_section, zval)
     151         324 :       CALL init_atom_potential(ae_pot, potential_section, -1)
     152             : 
     153             :       ! if the ERI's are calculated analytically, we have to precalculate them
     154         324 :       eri_c = .FALSE.
     155         324 :       CALL section_vals_val_get(atom_section, "COULOMB_INTEGRALS", i_val=do_eric)
     156         324 :       IF (do_eric == do_analytic) eri_c = .TRUE.
     157         324 :       eri_e = .FALSE.
     158         324 :       CALL section_vals_val_get(atom_section, "EXCHANGE_INTEGRALS", i_val=do_erie)
     159         324 :       IF (do_erie == do_analytic) eri_e = .TRUE.
     160         324 :       CALL section_vals_val_get(atom_section, "USE_GAUSS_HERMITE", l_val=do_gh)
     161         324 :       CALL section_vals_val_get(atom_section, "GRID_POINTS_GH", i_val=nr_gh)
     162             : 
     163             :       ! information on the states to be calculated
     164         324 :       CALL section_vals_val_get(atom_section, "MAX_ANGULAR_MOMENTUM", i_val=maxl)
     165         324 :       maxn = 0
     166         324 :       CALL section_vals_val_get(atom_section, "CALCULATE_STATES", i_vals=cn)
     167         684 :       DO in = 1, MIN(SIZE(cn), 4)
     168         684 :          maxn(in - 1) = cn(in)
     169             :       END DO
     170        2268 :       DO in = 0, lmat
     171        1944 :          maxn(in) = MIN(maxn(in), ae_basis%nbas(in))
     172        2268 :          maxn(in) = MIN(maxn(in), pp_basis%nbas(in))
     173             :       END DO
     174             : 
     175             :       ! read optimization section
     176         324 :       opt_section => section_vals_get_subs_vals(atom_section, "OPTIMIZATION")
     177         324 :       CALL read_atom_opt_section(optimization, opt_section)
     178             : 
     179         324 :       had_ae = .FALSE.
     180         324 :       had_pp = .FALSE.
     181             : 
     182             :       ! Check for the total number of electron configurations to be calculated
     183         324 :       CALL section_vals_val_get(atom_section, "ELECTRON_CONFIGURATION", n_rep_val=n_rep)
     184             :       ! Check for the total number of method types to be calculated
     185         324 :       method_section => section_vals_get_subs_vals(atom_section, "METHOD")
     186         324 :       CALL section_vals_get(method_section, n_repetition=n_meth)
     187             : 
     188             :       ! integrals
     189      137700 :       ALLOCATE (ae_int, pp_int)
     190             : 
     191        1950 :       ALLOCATE (atom_info(n_rep, n_meth))
     192             : 
     193         654 :       DO in = 1, n_rep
     194         984 :          DO im = 1, n_meth
     195             : 
     196         330 :             NULLIFY (atom_info(in, im)%atom)
     197         330 :             CALL create_atom_type(atom_info(in, im)%atom)
     198             : 
     199         330 :             atom_info(in, im)%atom%optimization = optimization
     200             : 
     201         330 :             atom_info(in, im)%atom%z = zval
     202         330 :             xc_section => section_vals_get_subs_vals(method_section, "XC", i_rep_section=im)
     203         330 :             atom_info(in, im)%atom%xc_section => xc_section
     204             : 
     205             :             ! ZMP Reading input sections if they are found initialize everything
     206             :             do_zmp = .FALSE.
     207             :             doread = .FALSE.
     208             :             read_vxc = .FALSE.
     209             : 
     210         330 :             zmp_section => section_vals_get_subs_vals(method_section, "ZMP")
     211         330 :             CALL section_vals_get(zmp_section, explicit=do_zmp)
     212         330 :             atom_info(in, im)%atom%do_zmp = do_zmp
     213         330 :             CALL section_vals_val_get(zmp_section, "FILE_DENSITY", c_val=filename)
     214         330 :             atom_info(in, im)%atom%ext_file = filename
     215             :             CALL section_vals_val_get(zmp_section, "GRID_TOL", &
     216         330 :                                       r_val=atom_info(in, im)%atom%zmpgrid_tol)
     217         330 :             CALL section_vals_val_get(zmp_section, "LAMBDA", r_val=lambda)
     218         330 :             atom_info(in, im)%atom%lambda = lambda
     219         330 :             CALL section_vals_val_get(zmp_section, "DM", l_val=dm)
     220         330 :             atom_info(in, im)%atom%dm = dm
     221             : 
     222         330 :             zmp_restart_section => section_vals_get_subs_vals(zmp_section, "RESTART")
     223         330 :             CALL section_vals_get(zmp_restart_section, explicit=doread)
     224         330 :             atom_info(in, im)%atom%doread = doread
     225         330 :             CALL section_vals_val_get(zmp_restart_section, "FILE_RESTART", c_val=filename)
     226         330 :             atom_info(in, im)%atom%zmp_restart_file = filename
     227             : 
     228             :             ! ZMP Reading external vxc section, if found initialize
     229         330 :             external_vxc_section => section_vals_get_subs_vals(method_section, "EXTERNAL_VXC")
     230         330 :             CALL section_vals_get(external_vxc_section, explicit=read_vxc)
     231         330 :             atom_info(in, im)%atom%read_vxc = read_vxc
     232         330 :             CALL section_vals_val_get(external_vxc_section, "FILE_VXC", c_val=filename)
     233         330 :             atom_info(in, im)%atom%ext_vxc_file = filename
     234             :             CALL section_vals_val_get(external_vxc_section, "GRID_TOL", &
     235         330 :                                       r_val=atom_info(in, im)%atom%zmpvxcgrid_tol)
     236             : 
     237      119790 :             ALLOCATE (state)
     238             : 
     239             :             ! get the electronic configuration
     240             :             CALL section_vals_val_get(atom_section, "ELECTRON_CONFIGURATION", i_rep_val=in, &
     241         330 :                                       c_vals=tmpstringlist)
     242             : 
     243             :             ! set occupations
     244         330 :             CALL atom_set_occupation(tmpstringlist, state%occ, state%occupation, state%multiplicity)
     245         330 :             state%maxl_occ = get_maxl_occ(state%occ)
     246        2310 :             state%maxn_occ = get_maxn_occ(state%occ)
     247             : 
     248             :             ! set number of states to be calculated
     249         330 :             state%maxl_calc = MAX(maxl, state%maxl_occ)
     250         330 :             state%maxl_calc = MIN(lmat, state%maxl_calc)
     251        2310 :             state%maxn_calc = 0
     252        1524 :             DO k = 0, state%maxl_calc
     253        1524 :                state%maxn_calc(k) = MAX(maxn(k), state%maxn_occ(k))
     254             :             END DO
     255             : 
     256             :             ! is there a pseudo potential
     257        1104 :             pp_calc = ANY(INDEX(tmpstringlist(1:), "CORE") /= 0)
     258         330 :             IF (pp_calc) THEN
     259             :                ! get and set the core occupations
     260          72 :                CALL section_vals_val_get(atom_section, "CORE", c_vals=tmpstringlist)
     261          72 :                CALL atom_set_occupation(tmpstringlist, state%core, pocc)
     262        5112 :                zcore = zval - NINT(SUM(state%core))
     263          72 :                CALL set_atom(atom_info(in, im)%atom, zcore=zcore, pp_calc=.TRUE.)
     264             :             ELSE
     265       18318 :                state%core = 0._dp
     266         258 :                CALL set_atom(atom_info(in, im)%atom, zcore=zval, pp_calc=.FALSE.)
     267             :             END IF
     268             : 
     269         330 :             CALL section_vals_val_get(method_section, "METHOD_TYPE", i_val=method, i_rep_section=im)
     270         330 :             CALL section_vals_val_get(method_section, "RELATIVISTIC", i_val=reltyp, i_rep_section=im)
     271         330 :             CALL set_atom(atom_info(in, im)%atom, method_type=method, relativistic=reltyp)
     272             : 
     273         330 :             IF (atom_consistent_method(method, state%multiplicity)) THEN
     274         330 :                iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%METHOD_INFO", extension=".log")
     275         330 :                CALL atom_print_method(atom_info(in, im)%atom, iw)
     276         330 :                CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%METHOD_INFO")
     277             : 
     278         330 :                iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%POTENTIAL", extension=".log")
     279         330 :                IF (pp_calc) THEN
     280          72 :                   IF (iw > 0) CALL atom_print_potential(p_pot, iw)
     281             :                ELSE
     282         258 :                   IF (iw > 0) CALL atom_print_potential(ae_pot, iw)
     283             :                END IF
     284         330 :                CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%POTENTIAL")
     285             :             END IF
     286             : 
     287             :             ! calculate integrals
     288         330 :             IF (pp_calc) THEN
     289             :                ! general integrals
     290             :                CALL atom_int_setup(pp_int, pp_basis, &
     291          72 :                                    potential=p_pot, eri_coulomb=eri_c, eri_exchange=eri_e)
     292             :                ! potential
     293          72 :                CALL atom_ppint_setup(pp_int, pp_basis, potential=p_pot)
     294             :                !
     295          72 :                NULLIFY (pp_int%tzora, pp_int%hdkh)
     296             :                !
     297          72 :                CALL set_atom(atom_info(in, im)%atom, basis=pp_basis, integrals=pp_int, potential=p_pot)
     298         936 :                state%maxn_calc(:) = MIN(state%maxn_calc(:), pp_basis%nbas(:))
     299         504 :                CPASSERT(ALL(state%maxn_calc(:) >= state%maxn_occ))
     300             :                had_pp = .TRUE.
     301             :             ELSE
     302             :                ! general integrals
     303             :                CALL atom_int_setup(ae_int, ae_basis, potential=ae_pot, &
     304         258 :                                    eri_coulomb=eri_c, eri_exchange=eri_e)
     305             :                ! potential
     306         258 :                CALL atom_ppint_setup(ae_int, ae_basis, potential=ae_pot)
     307             :                ! relativistic correction terms
     308         258 :                CALL atom_relint_setup(ae_int, ae_basis, reltyp, zcore=REAL(zval, dp))
     309             :                !
     310         258 :                CALL set_atom(atom_info(in, im)%atom, basis=ae_basis, integrals=ae_int, potential=ae_pot)
     311        3354 :                state%maxn_calc(:) = MIN(state%maxn_calc(:), ae_basis%nbas(:))
     312        1806 :                CPASSERT(ALL(state%maxn_calc(:) >= state%maxn_occ))
     313             :                had_ae = .TRUE.
     314             :             END IF
     315             : 
     316         330 :             CALL set_atom(atom_info(in, im)%atom, state=state)
     317             : 
     318             :             CALL set_atom(atom_info(in, im)%atom, coulomb_integral_type=do_eric, &
     319         330 :                           exchange_integral_type=do_erie)
     320         330 :             atom_info(in, im)%atom%hfx_pot%do_gh = do_gh
     321         330 :             atom_info(in, im)%atom%hfx_pot%nr_gh = nr_gh
     322             : 
     323         330 :             NULLIFY (orbitals)
     324        2310 :             mo = MAXVAL(state%maxn_calc)
     325        2310 :             mb = MAXVAL(atom_info(in, im)%atom%basis%nbas)
     326         330 :             CALL create_atom_orbs(orbitals, mb, mo)
     327         330 :             CALL set_atom(atom_info(in, im)%atom, orbitals=orbitals)
     328             : 
     329        2310 :             IF (atom_consistent_method(method, state%multiplicity)) THEN
     330             :                !Calculate the electronic structure
     331         330 :                iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%SCF_INFO", extension=".log")
     332         330 :                CALL calculate_atom(atom_info(in, im)%atom, iw)
     333         330 :                CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%SCF_INFO")
     334             : 
     335             :                ! ZMP If we have the external density do zmp
     336         330 :                IF (atom_info(in, im)%atom%do_zmp) THEN
     337           0 :                   CALL atom_write_zmp_restart(atom_info(in, im)%atom)
     338             : 
     339           0 :                   ALLOCATE (ext_density(atom_info(in, im)%atom%basis%grid%nr))
     340           0 :                   ext_density = 0._dp
     341           0 :                   CALL atom_read_external_density(ext_density, atom_info(in, im)%atom, iw)
     342             :                   CALL calculate_atom_zmp(ext_density=ext_density, &
     343             :                                           atom=atom_info(in, im)%atom, &
     344           0 :                                           lprint=.TRUE.)
     345           0 :                   DEALLOCATE (ext_density)
     346             :                END IF
     347             :                ! ZMP If we have the external v_xc calculate KS quantities
     348         330 :                IF (atom_info(in, im)%atom%read_vxc) THEN
     349           0 :                   ALLOCATE (ext_vxc(atom_info(in, im)%atom%basis%grid%nr))
     350           0 :                   ext_vxc = 0._dp
     351           0 :                   CALL atom_read_external_vxc(ext_vxc, atom_info(in, im)%atom, iw)
     352             :                   CALL calculate_atom_ext_vxc(vxc=ext_vxc, &
     353             :                                               atom=atom_info(in, im)%atom, &
     354           0 :                                               lprint=.TRUE.)
     355           0 :                   DEALLOCATE (ext_vxc)
     356             :                END IF
     357             : 
     358             :                ! Print out the orbitals if requested
     359         330 :                iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%ORBITALS", extension=".log")
     360         330 :                IF (iw > 0) THEN
     361           0 :                   CALL atom_print_orbitals(atom_info(in, im)%atom, iw)
     362             :                END IF
     363         330 :                CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%ORBITALS")
     364             : 
     365             :                ! perform a fit of the total electronic density
     366         330 :                iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%FIT_DENSITY", extension=".log")
     367         330 :                IF (iw > 0) THEN
     368           0 :                   CALL section_vals_val_get(atom_section, "PRINT%FIT_DENSITY%NUM_GTO", i_val=num_gto)
     369           0 :                   powell_section => section_vals_get_subs_vals(atom_section, "POWELL")
     370           0 :                   CALL atom_fit_density(atom_info(in, im)%atom, num_gto, 0, iw, powell_section=powell_section)
     371             :                END IF
     372         330 :                CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%FIT_DENSITY")
     373             : 
     374             :                ! Optimize a local potential for the non-additive kinetic energy term in KG
     375         330 :                iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%FIT_KGPOT", extension=".log")
     376         330 :                IF (iw > 0) THEN
     377           1 :                   CALL section_vals_val_get(atom_section, "PRINT%FIT_KGPOT%NUM_GAUSSIAN", i_val=num_gau)
     378           1 :                   CALL section_vals_val_get(atom_section, "PRINT%FIT_KGPOT%NUM_POLYNOM", i_val=num_pol)
     379           1 :                   powell_section => section_vals_get_subs_vals(atom_section, "POWELL")
     380           1 :                   CALL atom_fit_kgpot(atom_info(in, im)%atom, num_gau, num_pol, iw, powell_section=powell_section)
     381             :                END IF
     382         330 :                CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%FIT_KGPOT")
     383             : 
     384             :                ! generate a response basis
     385         330 :                iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%RESPONSE_BASIS", extension=".log")
     386         330 :                IF (iw > 0) THEN
     387           1 :                   CALL section_vals_val_get(atom_section, "PRINT%RESPONSE_BASIS%DELTA_CHARGE", r_val=delta)
     388           1 :                   CALL section_vals_val_get(atom_section, "PRINT%RESPONSE_BASIS%DERIVATIVES", i_val=nder)
     389           1 :                   CALL atom_response_basis(atom_info(in, im)%atom, delta, nder, iw)
     390             :                END IF
     391         330 :                CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%RESPONSE_BASIS")
     392             : 
     393             :                ! generate a UPF file
     394             :                iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%UPF_FILE", extension=".upf", &
     395         330 :                                          file_position="REWIND")
     396         330 :                IF (iw > 0) THEN
     397           2 :                   CALL atom_write_upf(atom_info(in, im)%atom, iw)
     398             :                END IF
     399         330 :                CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%UPF_FILE")
     400             :             END IF
     401             : 
     402             :          END DO
     403             :       END DO
     404             : 
     405             :       ! generate a geometrical response basis (GRB)
     406         324 :       iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%GEOMETRICAL_RESPONSE_BASIS", extension=".log")
     407         324 :       IF (iw > 0) THEN
     408           2 :          CALL atom_grb_construction(atom_info, atom_section, iw)
     409             :       END IF
     410         324 :       CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%GEOMETRICAL_RESPONSE_BASIS")
     411             : 
     412             :       ! Analyze basis sets
     413         324 :       iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%ANALYZE_BASIS", extension=".log")
     414         324 :       IF (iw > 0) THEN
     415           3 :          CALL section_vals_val_get(atom_section, "PRINT%ANALYZE_BASIS%OVERLAP_CONDITION_NUMBER", l_val=lcond)
     416           3 :          CALL section_vals_val_get(atom_section, "PRINT%ANALYZE_BASIS%COMPLETENESS", l_val=lcomp)
     417           3 :          crad = ptable(zval)%covalent_radius*bohr
     418           3 :          IF (had_ae) THEN
     419           2 :             IF (lcond) CALL atom_condnumber(ae_basis, crad, iw)
     420           2 :             IF (lcomp) CALL atom_completeness(ae_basis, zval, iw)
     421             :          END IF
     422           3 :          IF (had_pp) THEN
     423           1 :             IF (lcond) CALL atom_condnumber(pp_basis, crad, iw)
     424           1 :             IF (lcomp) CALL atom_completeness(pp_basis, zval, iw)
     425             :          END IF
     426             :       END IF
     427         324 :       CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%ANALYZE_BASIS")
     428             : 
     429             :       ! Analyse ADMM approximation
     430         324 :       iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%ADMM", extension=".log")
     431         324 :       admm_section => section_vals_get_subs_vals(atom_section, "PRINT%ADMM")
     432         324 :       IF (iw > 0) THEN
     433           1 :          CALL atom_admm(atom_info, admm_section, iw)
     434             :       END IF
     435         324 :       CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%ADMM")
     436             : 
     437             :       ! Generate a separable form of the pseudopotential using Gaussian functions
     438         324 :       iw = cp_print_key_unit_nr(logger, atom_section, "PRINT%SEPARABLE_GAUSSIAN_PSEUDO", extension=".log")
     439         324 :       sgp_section => section_vals_get_subs_vals(atom_section, "PRINT%SEPARABLE_GAUSSIAN_PSEUDO")
     440         324 :       IF (iw > 0) THEN
     441           5 :          CALL atom_sgp_construction(atom_info, sgp_section, iw)
     442             :       END IF
     443         324 :       CALL cp_print_key_finished_output(iw, logger, atom_section, "PRINT%SEPARABLE_GAUSSIAN_PSEUDO")
     444             : 
     445             :       ! clean up
     446         324 :       IF (had_ae) THEN
     447         256 :          CALL atom_int_release(ae_int)
     448         256 :          CALL atom_ppint_release(ae_int)
     449         256 :          CALL atom_relint_release(ae_int)
     450             :       END IF
     451         324 :       IF (had_pp) THEN
     452          70 :          CALL atom_int_release(pp_int)
     453          70 :          CALL atom_ppint_release(pp_int)
     454          70 :          CALL atom_relint_release(pp_int)
     455             :       END IF
     456         324 :       CALL release_atom_basis(ae_basis)
     457         324 :       CALL release_atom_basis(pp_basis)
     458             : 
     459         324 :       CALL release_atom_potential(p_pot)
     460         324 :       CALL release_atom_potential(ae_pot)
     461             : 
     462         654 :       DO in = 1, n_rep
     463         984 :          DO im = 1, n_meth
     464         660 :             CALL release_atom_type(atom_info(in, im)%atom)
     465             :          END DO
     466             :       END DO
     467         324 :       DEALLOCATE (atom_info)
     468             : 
     469         324 :       DEALLOCATE (ae_pot, p_pot, ae_basis, pp_basis, ae_int, pp_int)
     470             : 
     471         324 :       CALL timestop(handle)
     472             : 
     473        2268 :    END SUBROUTINE atom_energy_opt
     474             : 
     475             : ! **************************************************************************************************
     476             : !> \brief Calculate response basis contraction coefficients.
     477             : !> \param atom   information about the atomic kind
     478             : !> \param delta  variation of charge used in finite difference derivative calculation
     479             : !> \param nder   number of wavefunction derivatives to calculate
     480             : !> \param iw     output file unit
     481             : !> \par History
     482             : !>    * 10.2011 Gram-Schmidt orthogonalization [Joost VandeVondele]
     483             : !>    * 05.2009 created [Juerg Hutter]
     484             : ! **************************************************************************************************
     485           1 :    SUBROUTINE atom_response_basis(atom, delta, nder, iw)
     486             : 
     487             :       TYPE(atom_type), POINTER                           :: atom
     488             :       REAL(KIND=dp), INTENT(IN)                          :: delta
     489             :       INTEGER, INTENT(IN)                                :: nder, iw
     490             : 
     491             :       INTEGER                                            :: i, ider, j, k, l, lhomo, m, n, nhomo, &
     492             :                                                             s1, s2
     493             :       REAL(KIND=dp)                                      :: dene, emax, expzet, fhomo, o, prefac, &
     494             :                                                             zeta
     495           1 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: amat
     496           1 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :)     :: rbasis
     497           1 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :, :)  :: wfn
     498           1 :       REAL(KIND=dp), DIMENSION(:, :, :), POINTER         :: ovlp
     499             :       TYPE(atom_state), POINTER                          :: state
     500             : 
     501           1 :       WRITE (iw, '(/," ",79("*"),/,T30,A,A/," ",79("*"))') "RESPONSE BASIS for ", ptable(atom%z)%symbol
     502             : 
     503           1 :       state => atom%state
     504           1 :       ovlp => atom%integrals%ovlp
     505             : 
     506             :       ! find HOMO
     507           1 :       lhomo = -1
     508           1 :       nhomo = -1
     509           1 :       emax = -HUGE(1._dp)
     510           4 :       DO l = 0, state%maxl_occ
     511           6 :          DO i = 1, state%maxn_occ(l)
     512           5 :             IF (atom%orbitals%ener(i, l) > emax) THEN
     513           1 :                lhomo = l
     514           1 :                nhomo = i
     515           1 :                emax = atom%orbitals%ener(i, l)
     516           1 :                fhomo = state%occupation(l, i)
     517             :             END IF
     518             :          END DO
     519             :       END DO
     520             : 
     521           1 :       s1 = SIZE(atom%orbitals%wfn, 1)
     522           1 :       s2 = SIZE(atom%orbitals%wfn, 2)
     523           6 :       ALLOCATE (wfn(s1, s2, 0:lmat, -nder:nder))
     524           7 :       s2 = MAXVAL(state%maxn_occ) + nder
     525           5 :       ALLOCATE (rbasis(s1, s2, 0:lmat))
     526          91 :       rbasis = 0._dp
     527             : 
     528           4 :       DO ider = -nder, nder
     529           3 :          dene = REAL(ider, KIND=dp)*delta
     530           3 :          CPASSERT(fhomo > ABS(dene))
     531           3 :          state%occupation(lhomo, nhomo) = fhomo + dene
     532           3 :          CALL calculate_atom(atom, iw=0, noguess=.TRUE.)
     533         147 :          wfn(:, :, :, ider) = atom%orbitals%wfn
     534           4 :          state%occupation(lhomo, nhomo) = fhomo
     535             :       END DO
     536             : 
     537           4 :       DO l = 0, state%maxl_occ
     538             :          ! occupied states
     539           6 :          DO i = 1, MAX(state%maxn_occ(l), 1)
     540          24 :             rbasis(:, i, l) = wfn(:, i, l, 0)
     541             :          END DO
     542             :          ! differentiation
     543           6 :          DO ider = 1, nder
     544           3 :             i = MAX(state%maxn_occ(l), 1)
     545           3 :             SELECT CASE (ider)
     546             :             CASE (1)
     547          21 :                rbasis(:, i + 1, l) = 0.5_dp*(wfn(:, i, l, 1) - wfn(:, i, l, -1))/delta
     548             :             CASE (2)
     549           0 :                rbasis(:, i + 2, l) = 0.25_dp*(wfn(:, i, l, 2) - 2._dp*wfn(:, i, l, 0) + wfn(:, i, l, -2))/delta**2
     550             :             CASE (3)
     551             :                rbasis(:, i + 3, l) = 0.125_dp*(wfn(:, i, l, 3) - 3._dp*wfn(:, i, l, 1) &
     552           0 :                                                + 3._dp*wfn(:, i, l, -1) - wfn(:, i, l, -3))/delta**3
     553             :             CASE DEFAULT
     554           3 :                CPABORT("")
     555             :             END SELECT
     556             :          END DO
     557             : 
     558             :          ! orthogonalization, use gram-schmidt in order to keep the natural order (semi-core, valence, response) of the wfn.
     559           3 :          n = state%maxn_occ(l) + nder
     560           3 :          m = atom%basis%nbas(l)
     561           8 :          DO i = 1, n
     562           7 :             DO j = 1, i - 1
     563         192 :                o = DOT_PRODUCT(rbasis(1:m, j, l), RESHAPE(MATMUL(ovlp(1:m, 1:m, l), rbasis(1:m, i:i, l)), (/m/)))
     564          19 :                rbasis(1:m, i, l) = rbasis(1:m, i, l) - o*rbasis(1:m, j, l)
     565             :             END DO
     566         480 :             o = DOT_PRODUCT(rbasis(1:m, i, l), RESHAPE(MATMUL(ovlp(1:m, 1:m, l), rbasis(1:m, i:i, l)), (/m/)))
     567          38 :             rbasis(1:m, i, l) = rbasis(1:m, i, l)/SQRT(o)
     568             :          END DO
     569             : 
     570             :          ! check
     571          12 :          ALLOCATE (amat(n, n))
     572         578 :          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)))
     573           8 :          DO i = 1, n
     574           8 :             amat(i, i) = amat(i, i) - 1._dp
     575             :          END DO
     576          17 :          IF (MAXVAL(ABS(amat)) > 1.e-12) THEN
     577           0 :             WRITE (iw, '(/,A,G20.10)') " Orthogonality error  ", MAXVAL(ABS(amat))
     578             :          END IF
     579           3 :          DEALLOCATE (amat)
     580             : 
     581             :          ! Quickstep normalization
     582           3 :          WRITE (iw, '(/,A,T30,I3)') " Angular momentum :", l
     583             : 
     584           3 :          WRITE (iw, '(/,A,I0,A,I0,A)') "             Exponent     Coef.(Quickstep Normalization), first ", &
     585           6 :             n - nder, " valence ", nder, " response"
     586           3 :          expzet = 0.25_dp*REAL(2*l + 3, dp)
     587           3 :          prefac = SQRT(rootpi/2._dp**(l + 2)*dfac(2*l + 1))
     588          22 :          DO i = 1, m
     589          18 :             zeta = (2._dp*atom%basis%am(i, l))**expzet
     590          51 :             WRITE (iw, '(4X,F20.10,4X,15ES20.6)') atom%basis%am(i, l), ((prefac*rbasis(i, k, l)/zeta), k=1, n)
     591             :          END DO
     592             : 
     593             :       END DO
     594             : 
     595           1 :       DEALLOCATE (wfn, rbasis)
     596             : 
     597           1 :       WRITE (iw, '(" ",79("*"))')
     598             : 
     599           2 :    END SUBROUTINE atom_response_basis
     600             : 
     601             : ! **************************************************************************************************
     602             : !> \brief Write pseudo-potential in Quantum Espresso UPF format.
     603             : !> \param atom  information about the atomic kind
     604             : !> \param iw    output file unit
     605             : !> \par History
     606             : !>    * 09.2012 created [Juerg Hutter]
     607             : ! **************************************************************************************************
     608           2 :    SUBROUTINE atom_write_upf(atom, iw)
     609             : 
     610             :       TYPE(atom_type), POINTER                           :: atom
     611             :       INTEGER, INTENT(IN)                                :: iw
     612             : 
     613             :       CHARACTER(LEN=default_string_length)               :: string
     614             :       INTEGER                                            :: i, ibeta, j, k, l, lmax, nbeta, nr, &
     615             :                                                             nwfc, nwfn
     616             :       LOGICAL                                            :: up
     617             :       REAL(KIND=dp)                                      :: pf, rl, rmax
     618           2 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: beta, corden, dens, ef, locpot, rp
     619           2 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: dij
     620             :       TYPE(atom_gthpot_type), POINTER                    :: pot
     621             : 
     622           2 :       IF (.NOT. atom%pp_calc) RETURN
     623           2 :       IF (atom%potential%ppot_type /= gth_pseudo) RETURN
     624           2 :       pot => atom%potential%gth_pot
     625           2 :       CPASSERT(.NOT. pot%lsdpot)
     626             : 
     627           2 :       WRITE (iw, '(A)') '<UPF version="2.0.1">'
     628             : 
     629           2 :       WRITE (iw, '(T4,A)') '<PP_INFO>'
     630           2 :       WRITE (iw, '(T8,A)') 'Converted from CP2K GTH format'
     631           2 :       WRITE (iw, '(T8,A)') '<PP_INPUTFILE>'
     632           2 :       CALL atom_write_pseudo_param(pot, iw)
     633           2 :       WRITE (iw, '(T8,A)') '</PP_INPUTFILE>'
     634           2 :       WRITE (iw, '(T4,A)') '</PP_INFO>'
     635           2 :       WRITE (iw, '(T4,A)') '<PP_HEADER'
     636           2 :       WRITE (iw, '(T8,A)') 'generated="Generated in analytical, separable form"'
     637           2 :       WRITE (iw, '(T8,A)') 'author="Goedecker/Hartwigsen/Hutter/Teter"'
     638           2 :       WRITE (iw, '(T8,A)') 'date="Phys.Rev.B58, 3641 (1998); B54, 1703 (1996)"'
     639           2 :       WRITE (iw, '(T8,A)') 'comment="This file generated by CP2K ATOM code"'
     640           2 :       CALL compose(string, "element", cval=pot%symbol)
     641           2 :       WRITE (iw, '(T8,A)') TRIM(string)
     642           2 :       WRITE (iw, '(T8,A)') 'pseudo_type="NC"'
     643           2 :       WRITE (iw, '(T8,A)') 'relativistic="no"'
     644           2 :       WRITE (iw, '(T8,A)') 'is_ultrasoft="F"'
     645           2 :       WRITE (iw, '(T8,A)') 'is_paw="F"'
     646           2 :       WRITE (iw, '(T8,A)') 'is_coulomb="F"'
     647           2 :       WRITE (iw, '(T8,A)') 'has_so="F"'
     648           2 :       WRITE (iw, '(T8,A)') 'has_wfc="F"'
     649           2 :       WRITE (iw, '(T8,A)') 'has_gipaw="F"'
     650           2 :       WRITE (iw, '(T8,A)') 'paw_as_gipaw="F"'
     651           2 :       IF (pot%nlcc) THEN
     652           1 :          WRITE (iw, '(T8,A)') 'core_correction="T"'
     653             :       ELSE
     654           1 :          WRITE (iw, '(T8,A)') 'core_correction="F"'
     655             :       END IF
     656           2 :       WRITE (iw, '(T8,A)') 'functional="DFT"'
     657           2 :       CALL compose(string, "z_valence", rval=pot%zion)
     658           2 :       WRITE (iw, '(T8,A)') TRIM(string)
     659           2 :       CALL compose(string, "total_psenergy", rval=2._dp*atom%energy%etot)
     660           2 :       WRITE (iw, '(T8,A)') TRIM(string)
     661           2 :       WRITE (iw, '(T8,A)') 'wfc_cutoff="0.0E+00"'
     662           2 :       WRITE (iw, '(T8,A)') 'rho_cutoff="0.0E+00"'
     663           2 :       lmax = -1
     664          14 :       DO l = 0, lmat
     665          14 :          IF (pot%nl(l) > 0) lmax = l
     666             :       END DO
     667           2 :       CALL compose(string, "l_max", ival=lmax)
     668           2 :       WRITE (iw, '(T8,A)') TRIM(string)
     669           2 :       WRITE (iw, '(T8,A)') 'l_max_rho="0"'
     670           2 :       WRITE (iw, '(T8,A)') 'l_local="-3"'
     671           2 :       nr = atom%basis%grid%nr
     672           2 :       CALL compose(string, "mesh_size", ival=nr)
     673           2 :       WRITE (iw, '(T8,A)') TRIM(string)
     674          14 :       nwfc = SUM(atom%state%maxn_occ)
     675           2 :       CALL compose(string, "number_of_wfc", ival=nwfc)
     676           2 :       WRITE (iw, '(T8,A)') TRIM(string)
     677          14 :       nbeta = SUM(pot%nl)
     678           2 :       CALL compose(string, "number_of_proj", ival=nbeta)
     679           2 :       WRITE (iw, '(T8,A)') TRIM(string)//'/>'
     680             : 
     681             :       ! Mesh
     682           2 :       up = atom%basis%grid%rad(1) < atom%basis%grid%rad(nr)
     683           2 :       WRITE (iw, '(T4,A)') '<PP_MESH'
     684           2 :       WRITE (iw, '(T8,A)') 'dx="1.E+00"'
     685           2 :       CALL compose(string, "mesh", ival=nr)
     686           2 :       WRITE (iw, '(T8,A)') TRIM(string)
     687           2 :       WRITE (iw, '(T8,A)') 'xmin="1.E+00"'
     688         804 :       rmax = MAXVAL(atom%basis%grid%rad)
     689           2 :       CALL compose(string, "rmax", rval=rmax)
     690           2 :       WRITE (iw, '(T8,A)') TRIM(string)
     691           2 :       WRITE (iw, '(T8,A)') 'zmesh="1.E+00">'
     692           2 :       WRITE (iw, '(T8,A)') '<PP_R type="real"'
     693           2 :       CALL compose(string, "size", ival=nr)
     694           2 :       WRITE (iw, '(T12,A)') TRIM(string)
     695           2 :       WRITE (iw, '(T12,A)') 'columns="4">'
     696           2 :       IF (up) THEN
     697           0 :          WRITE (iw, '(T12,4ES25.12E3)') (atom%basis%grid%rad(i), i=1, nr)
     698             :       ELSE
     699         802 :          WRITE (iw, '(T12,4ES25.12E3)') (atom%basis%grid%rad(i), i=nr, 1, -1)
     700             :       END IF
     701           2 :       WRITE (iw, '(T8,A)') '</PP_R>'
     702           2 :       WRITE (iw, '(T8,A)') '<PP_RAB type="real"'
     703           2 :       CALL compose(string, "size", ival=nr)
     704           2 :       WRITE (iw, '(T12,A)') TRIM(string)
     705           2 :       WRITE (iw, '(T12,A)') 'columns="4">'
     706           2 :       IF (up) THEN
     707           0 :          WRITE (iw, '(T12,4ES25.12E3)') (atom%basis%grid%wr(i)/atom%basis%grid%rad2(i), i=1, nr)
     708             :       ELSE
     709         802 :          WRITE (iw, '(T12,4ES25.12E3)') (atom%basis%grid%wr(i)/atom%basis%grid%rad2(i), i=nr, 1, -1)
     710             :       END IF
     711           2 :       WRITE (iw, '(T8,A)') '</PP_RAB>'
     712           2 :       WRITE (iw, '(T4,A)') '</PP_MESH>'
     713             : 
     714             :       ! NLCC
     715           2 :       IF (pot%nlcc) THEN
     716           1 :          WRITE (iw, '(T4,A)') '<PP_NLCC type="real"'
     717           1 :          CALL compose(string, "size", ival=nr)
     718           1 :          WRITE (iw, '(T8,A)') TRIM(string)
     719           1 :          WRITE (iw, '(T8,A)') 'columns="4">'
     720           3 :          ALLOCATE (corden(nr))
     721         401 :          corden(:) = 0.0_dp
     722           1 :          CALL atom_core_density(corden, atom%potential, "RHO", atom%basis%grid%rad)
     723           1 :          IF (up) THEN
     724           0 :             WRITE (iw, '(T8,4ES25.12E3)') (corden(i), i=1, nr)
     725             :          ELSE
     726           1 :             WRITE (iw, '(T8,4ES25.12E3)') (corden(i), i=nr, 1, -1)
     727             :          END IF
     728           1 :          DEALLOCATE (corden)
     729           1 :          WRITE (iw, '(T4,A)') '</PP_NLCC>'
     730             :       END IF
     731             : 
     732             :       ! local PP
     733           2 :       WRITE (iw, '(T4,A)') '<PP_LOCAL type="real"'
     734           2 :       CALL compose(string, "size", ival=nr)
     735           2 :       WRITE (iw, '(T8,A)') TRIM(string)
     736           2 :       WRITE (iw, '(T8,A)') 'columns="4">'
     737           6 :       ALLOCATE (locpot(nr))
     738         802 :       locpot(:) = 0.0_dp
     739           2 :       CALL atom_local_potential(locpot, pot, atom%basis%grid%rad)
     740           2 :       IF (up) THEN
     741           0 :          WRITE (iw, '(T8,4ES25.12E3)') (2.0_dp*locpot(i), i=1, nr)
     742             :       ELSE
     743         802 :          WRITE (iw, '(T8,4ES25.12E3)') (2.0_dp*locpot(i), i=nr, 1, -1)
     744             :       END IF
     745           2 :       DEALLOCATE (locpot)
     746           2 :       WRITE (iw, '(T4,A)') '</PP_LOCAL>'
     747             : 
     748             :       ! nonlocal PP
     749           2 :       WRITE (iw, '(T4,A)') '<PP_NONLOCAL>'
     750          14 :       ALLOCATE (rp(nr), ef(nr), beta(nr))
     751           2 :       ibeta = 0
     752          14 :       DO l = 0, lmat
     753          12 :          IF (pot%nl(l) == 0) CYCLE
     754           3 :          rl = pot%rcnl(l)
     755        1203 :          rp(:) = atom%basis%grid%rad
     756        1203 :          ef(:) = EXP(-0.5_dp*rp*rp/(rl*rl))
     757           8 :          DO i = 1, pot%nl(l)
     758           3 :             pf = rl**(l + 0.5_dp*(4._dp*i - 1._dp))
     759           3 :             j = l + 2*i - 1
     760           3 :             pf = SQRT(2._dp)/(pf*SQRT(gamma1(j)))
     761        1203 :             beta(:) = pf*rp**(l + 2*i - 2)*ef
     762           3 :             ibeta = ibeta + 1
     763           3 :             CALL compose(string, "<PP_BETA", counter=ibeta)
     764           3 :             WRITE (iw, '(T8,A)') TRIM(string)
     765           3 :             CALL compose(string, "angular_momentum", ival=l)
     766           3 :             WRITE (iw, '(T12,A)') TRIM(string)
     767           3 :             WRITE (iw, '(T12,A)') 'type="real"'
     768           3 :             CALL compose(string, "size", ival=nr)
     769           3 :             WRITE (iw, '(T12,A)') TRIM(string)
     770           3 :             WRITE (iw, '(T12,A)') 'columns="4">'
     771        1203 :             beta(:) = beta*rp
     772           3 :             IF (up) THEN
     773           0 :                WRITE (iw, '(T12,4ES25.12E3)') (2._dp*beta(j), j=1, nr)
     774             :             ELSE
     775        1203 :                WRITE (iw, '(T12,4ES25.12E3)') (2._dp*beta(j), j=nr, 1, -1)
     776             :             END IF
     777           3 :             CALL compose(string, "</PP_BETA", counter=ibeta, isfinal=.TRUE.)
     778          15 :             WRITE (iw, '(T8,A)') TRIM(string)
     779             :          END DO
     780             :       END DO
     781           2 :       DEALLOCATE (rp, ef, beta)
     782             :       ! nonlocal PP matrix elements
     783           8 :       ALLOCATE (dij(nbeta, nbeta))
     784          10 :       dij = 0._dp
     785          14 :       DO l = 0, lmat
     786          12 :          IF (pot%nl(l) == 0) CYCLE
     787           4 :          ibeta = SUM(pot%nl(0:l - 1)) + 1
     788           3 :          i = ibeta + pot%nl(l) - 1
     789          11 :          dij(ibeta:i, ibeta:i) = pot%hnl(1:pot%nl(l), 1:pot%nl(l), l)
     790             :       END DO
     791           2 :       WRITE (iw, '(T8,A)') '<PP_DIJ type="real"'
     792           2 :       WRITE (iw, '(T12,A)') 'columns="4">'
     793          10 :       WRITE (iw, '(T12,4ES25.12E3)') ((0.5_dp*dij(i, j), j=1, nbeta), i=1, nbeta)
     794           2 :       WRITE (iw, '(T8,A)') '</PP_DIJ>'
     795           2 :       DEALLOCATE (dij)
     796           2 :       WRITE (iw, '(T4,A)') '</PP_NONLOCAL>'
     797             : 
     798             :       ! atomic wavefunctions
     799           6 :       ALLOCATE (beta(nr))
     800           2 :       WRITE (iw, '(T4,A)') '<PP_PSWFC>'
     801           2 :       nwfn = 0
     802          14 :       DO l = 0, lmat
     803         134 :          DO i = 1, 10
     804         120 :             IF (ABS(atom%state%occupation(l, i)) == 0._dp) CYCLE
     805           4 :             nwfn = nwfn + 1
     806           4 :             CALL compose(string, "<PP_CHI", counter=nwfn)
     807           4 :             WRITE (iw, '(T8,A)') TRIM(string)
     808           4 :             CALL compose(string, "l", ival=l)
     809           4 :             WRITE (iw, '(T12,A)') TRIM(string)
     810           4 :             CALL compose(string, "occupation", rval=atom%state%occupation(l, i))
     811           4 :             WRITE (iw, '(T12,A)') TRIM(string)
     812           4 :             CALL compose(string, "pseudo_energy", rval=2._dp*atom%orbitals%ener(i, l))
     813           4 :             WRITE (iw, '(T12,A)') TRIM(string)
     814           4 :             WRITE (iw, '(T12,A)') 'columns="4">'
     815        1604 :             beta = 0._dp
     816          75 :             DO k = 1, atom%basis%nbas(l)
     817       28475 :                beta(:) = beta(:) + atom%orbitals%wfn(k, i, l)*atom%basis%bf(:, k, l)
     818             :             END DO
     819        1604 :             beta(:) = beta*atom%basis%grid%rad
     820           4 :             IF (up) THEN
     821           0 :                WRITE (iw, '(T12,4ES25.12E3)') (beta(j)*atom%basis%grid%rad(j), j=1, nr)
     822             :             ELSE
     823        1604 :                WRITE (iw, '(T12,4ES25.12E3)') (beta(j)*atom%basis%grid%rad(j), j=nr, 1, -1)
     824             :             END IF
     825           4 :             CALL compose(string, "</PP_CHI", counter=nwfn, isfinal=.TRUE.)
     826         132 :             WRITE (iw, '(T8,A)') TRIM(string)
     827             :          END DO
     828             :       END DO
     829           2 :       WRITE (iw, '(T4,A)') '</PP_PSWFC>'
     830           2 :       DEALLOCATE (beta)
     831             : 
     832             :       ! atomic charge
     833           6 :       ALLOCATE (dens(nr))
     834           2 :       WRITE (iw, '(T4,A)') '<PP_RHOATOM type="real"'
     835           2 :       CALL compose(string, "size", ival=nr)
     836           2 :       WRITE (iw, '(T8,A)') TRIM(string)
     837           2 :       WRITE (iw, '(T8,A)') 'columns="4">'
     838             :       CALL atom_density(dens, atom%orbitals%pmat, atom%basis, atom%state%maxl_occ, &
     839           2 :                         "RHO", atom%basis%grid%rad)
     840           2 :       IF (up) THEN
     841           0 :          WRITE (iw, '(T8,4ES25.12E3)') (4._dp*pi*dens(j)*atom%basis%grid%rad2(j), j=1, nr)
     842             :       ELSE
     843         802 :          WRITE (iw, '(T8,4ES25.12E3)') (4._dp*pi*dens(j)*atom%basis%grid%rad2(j), j=nr, 1, -1)
     844             :       END IF
     845           2 :       WRITE (iw, '(T4,A)') '</PP_RHOATOM>'
     846           2 :       DEALLOCATE (dens)
     847             : 
     848           2 :       WRITE (iw, '(A)') '</UPF>'
     849             : 
     850           2 :    END SUBROUTINE atom_write_upf
     851             : 
     852             : ! **************************************************************************************************
     853             : !> \brief Produce an XML attribute string 'tag="counter/rval/ival/cval"'
     854             : !> \param string   composed string
     855             : !> \param tag      attribute tag
     856             : !> \param counter  counter
     857             : !> \param rval     real variable
     858             : !> \param ival     integer variable
     859             : !> \param cval     string variable
     860             : !> \param isfinal  close the current XML element if this is the last attribute
     861             : !> \par History
     862             : !>    * 09.2012 created [Juerg Hutter]
     863             : ! **************************************************************************************************
     864          59 :    SUBROUTINE compose(string, tag, counter, rval, ival, cval, isfinal)
     865             :       CHARACTER(len=*), INTENT(OUT)                      :: string
     866             :       CHARACTER(len=*), INTENT(IN)                       :: tag
     867             :       INTEGER, INTENT(IN), OPTIONAL                      :: counter
     868             :       REAL(KIND=dp), INTENT(IN), OPTIONAL                :: rval
     869             :       INTEGER, INTENT(IN), OPTIONAL                      :: ival
     870             :       CHARACTER(len=*), INTENT(IN), OPTIONAL             :: cval
     871             :       LOGICAL, INTENT(IN), OPTIONAL                      :: isfinal
     872             : 
     873             :       CHARACTER(LEN=default_string_length)               :: str
     874             :       LOGICAL                                            :: fin
     875             : 
     876          59 :       IF (PRESENT(counter)) THEN
     877          14 :          WRITE (str, "(I12)") counter
     878          45 :       ELSEIF (PRESENT(rval)) THEN
     879          14 :          WRITE (str, "(G18.8)") rval
     880          31 :       ELSEIF (PRESENT(ival)) THEN
     881          29 :          WRITE (str, "(I12)") ival
     882           2 :       ELSEIF (PRESENT(cval)) THEN
     883           2 :          WRITE (str, "(A)") TRIM(ADJUSTL(cval))
     884             :       ELSE
     885           0 :          WRITE (str, "(A)") ""
     886             :       END IF
     887          59 :       fin = .FALSE.
     888          59 :       IF (PRESENT(isfinal)) fin = isfinal
     889          59 :       IF (PRESENT(counter)) THEN
     890          14 :          IF (fin) THEN
     891           7 :             WRITE (string, "(A,A1,A,A1)") TRIM(ADJUSTL(tag)), '.', TRIM(ADJUSTL(str)), '>'
     892             :          ELSE
     893           7 :             WRITE (string, "(A,A1,A)") TRIM(ADJUSTL(tag)), '.', TRIM(ADJUSTL(str))
     894             :          END IF
     895             :       ELSE
     896          45 :          IF (fin) THEN
     897           0 :             WRITE (string, "(A,A2,A,A2)") TRIM(ADJUSTL(tag)), '="', TRIM(ADJUSTL(str)), '>"'
     898             :          ELSE
     899          45 :             WRITE (string, "(A,A2,A,A1)") TRIM(ADJUSTL(tag)), '="', TRIM(ADJUSTL(str)), '"'
     900             :          END IF
     901             :       END IF
     902          59 :    END SUBROUTINE compose
     903             : 
     904          10 : END MODULE atom_energy

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