sternheimer.F90

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!! Copyright (C) 2004-2012 Xavier Andrade, Eugene S. Kadantsev (ekadants@mjs1.phy.queensu.ca), David Strubbe
!! Copyright (C) 2021 Davis Welakuh
!!
!! This program is free software; you can redistribute it and/or modify
!! it under the terms of the GNU General Public License as published by
!! the Free Software Foundation; either version 2, or (at your option)
!! any later version.
!!
!! This program is distributed in the hope that it will be useful,
!! but WITHOUT ANY WARRANTY; without even the implied warranty of
!! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
!! GNU General Public License for more details.
!!
!! You should have received a copy of the GNU General Public License
!! along with this program; if not, write to the Free Software
!! Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
!! 02110-1301, USA.
!!
 
#include "global.h"
 
module sternheimer_oct_m
  use batch_oct_m
  use batch_ops_oct_m
  use comm_oct_m
  use debug_oct_m
  use density_oct_m
  use electron_space_oct_m
  use global_oct_m
  use grid_oct_m
  use hamiltonian_elec_oct_m
  use hamiltonian_elec_base_oct_m
  use io_oct_m
  use, intrinsic :: iso_fortran_env
  use kpoints_oct_m
  use ks_potential_oct_m
  use lalg_basic_oct_m
  use lda_u_oct_m
  use linear_response_oct_m
  use linear_solver_oct_m
  use math_oct_m
  use mesh_oct_m
  use mesh_function_oct_m
  use messages_oct_m
  use mix_oct_m
  use mpi_oct_m
  use multicomm_oct_m
  use namespace_oct_m
  use parser_oct_m
  use perturbation_oct_m
  use photon_mode_oct_m
  use poisson_oct_m
  use profiling_oct_m
  use restart_oct_m
  use scf_tol_oct_m
  use smear_oct_m
  use space_oct_m
  use states_abst_oct_m
  use states_elec_oct_m
  use states_elec_restart_oct_m
  use unit_oct_m
  use unit_system_oct_m
  use types_oct_m
  use v_ks_oct_m
  use wfs_elec_oct_m
  use xc_oct_m
  use xc_sic_oct_m
  use xc_f03_lib_m
  use xc_kernel_oct_m
  use walltimer_oct_m
 
  implicit none
 
  private
  public ::                    &
    sternheimer_t,             &
    sternheimer_init,          &
    sternheimer_end,           &
    dsternheimer_solve,        &
    zsternheimer_solve,        &
    dsternheimer_solve_order2, &
    zsternheimer_solve_order2, &
    sternheimer_build_kxc,     &
    dsternheimer_calc_hvar,    &
    zsternheimer_calc_hvar,    &
    dsternheimer_set_rhs,      &
    zsternheimer_set_rhs,      &
    sternheimer_have_rhs,      &
    sternheimer_unset_rhs,     &
    dsternheimer_set_inhomog,  &
    zsternheimer_set_inhomog,  &
    sternheimer_have_inhomog,  &
    sternheimer_unset_inhomog, &
    sternheimer_unset_kxc,     &
    sternheimer_has_converged, &
    swap_sigma,                &
    wfs_tag_sigma,             &
    sternheimer_obsolete_variables, &
    dcalc_hvar,                &
    zcalc_hvar,                &
    dcalc_kvar,                &
    zcalc_kvar
 
  character(len=*), public, parameter :: EM_RESP_PHOTONS_DIR = "em_resp_photons/"
 
  type sternheimer_t
    private
    type(linear_solver_t)       :: solver
    type(mix_t)                 :: mixer
    type(mixfield_t), pointer   :: mixfield
    type(scf_tol_t)             :: scf_tol
    real(real64), allocatable          :: fxc(:,:,:)
    real(real64), allocatable          :: kxc(:,:,:,:)
    real(real64), pointer, contiguous  :: drhs(:, :, :, :) => null() 
    complex(real64), pointer, contiguous  :: zrhs(:, :, :, :) => null()
    real(real64), pointer, contiguous  :: dinhomog(:, :, :, :, :) => null() 
    complex(real64), pointer, contiguous  :: zinhomog(:, :, :, :, :) => null()
    logical                     :: add_fxc_kernel
    logical                     :: ok
    logical                     :: occ_response
    logical                     :: last_occ_response
    logical                     :: occ_response_by_sternheimer
    logical                     :: preorthogonalization
    logical, public             :: has_photons
    real(real64)                :: domega
    complex(real64)             :: zomega
    real(real64), allocatable, public  :: dphoton_coord_q(:, :)
    complex(real64), allocatable, public  :: zphoton_coord_q(:, :)
    real(real64)                :: pt_eta
    type(photon_mode_t)         :: pt_modes
 
    real(real64)                :: coeff_hartree
  contains
    procedure :: add_fxc => sternheimer_add_fxc
    procedure :: add_hartree => sternheimer_add_hartree
  end type sternheimer_t
 
 
contains
 
  !-----------------------------------------------------------
  subroutine sternheimer_init(this, namespace, space, gr, st, hm, ks, mc, wfs_are_cplx, set_ham_var, set_occ_response, &
    set_last_occ_response, occ_response_by_sternheimer)
    type(sternheimer_t),      intent(out)   :: this
    type(namespace_t),        intent(in)    :: namespace
    class(space_t),           intent(in)    :: space
    type(grid_t),             intent(inout) :: gr
    type(states_elec_t),      intent(in)    :: st
    type(hamiltonian_elec_t), intent(in)    :: hm
    type(v_ks_t),             intent(in)    :: ks
    type(multicomm_t),        intent(in)    :: mc
    logical,                  intent(in)    :: wfs_are_cplx
    integer,        optional, intent(in)    :: set_ham_var
    logical,        optional, intent(in)    :: set_occ_response
    logical,        optional, intent(in)    :: set_last_occ_response
    logical,        optional, intent(in)    :: occ_response_by_sternheimer
 
    logical :: add_hartree
    integer :: ham_var, iunit
    logical :: default_preorthog
 
    push_sub(sternheimer_init)
 
    if (family_is_mgga(ks%xc%family)) then
      call messages_not_implemented("MGGA functionals with Sternheimer calculation")
    end if
    if (family_is_hybrid(ks%xc)) then
      call messages_not_implemented("Hybrid functionals with Sternheimer calculation")
    end if
 
    if (ks%sic%level /= sic_none) then
      call messages_not_implemented("SIC with Sternheimer calculation")
    end if
 
    if (hm%lda_u_level /= dft_u_none) then
      call messages_not_implemented("DFT+U with Sterheimer calculation")
    end if
 
    if (st%smear%method == smear_fixed_occ) then
      call messages_experimental("Sternheimer equation for arbitrary occupations", namespace=namespace)
    end if
    if (st%smear%method == smear_semiconductor .and. &
      (abs(st%smear%ef_occ) > m_epsilon) .and. abs(st%smear%ef_occ - m_one) > m_epsilon) then
      write(message(1),'(a,f12.6)') 'Partial occupation at the Fermi level: ', st%smear%ef_occ
      message(2) = 'Semiconducting smearing cannot be used for Sternheimer in this situation.'
      call messages_fatal(2, namespace=namespace)
    end if
 
    if (wfs_are_cplx) then
      call mix_init(this%mixer, namespace, space, gr%der, gr%np, st%d%nspin, func_type_= type_cmplx)
    else
      call mix_init(this%mixer, namespace, space, gr%der, gr%np, st%d%nspin, func_type_= type_float)
    end if
    call mix_get_field(this%mixer, this%mixfield)
 
    this%occ_response = optional_default(set_occ_response, .false.)
    this%occ_response_by_sternheimer = optional_default(occ_response_by_sternheimer, .false.)
    this%last_occ_response = optional_default(set_last_occ_response, .false.)
 
    !%Variable Preorthogonalization
    !%Type logical
    !%Section Linear Response::Sternheimer
    !%Description
    !% Whether initial linear-response wavefunctions should be orthogonalized
    !% or not against the occupied states, at the start of each SCF cycle.
    !% Default is true only if <tt>SmearingFunction = semiconducting</tt>,
    !% or if the <tt>Occupations</tt> block specifies all full or empty states,
    !% and we are not solving for linear response in the occupied subspace too.
    !%End
    default_preorthog = (st%smear%method == smear_semiconductor .or. &
      (st%smear%method == smear_fixed_occ .and. st%smear%integral_occs)) &
      .and. .not. this%occ_response
    call parse_variable(namespace, 'Preorthogonalization', default_preorthog, this%preorthogonalization)
 
    !%Variable HamiltonianVariation
    !%Type integer
    !%Default hartree+fxc
    !%Section Linear Response::Sternheimer
    !%Description
    !% The terms to be considered in the variation of the
    !% Hamiltonian. The external potential (V_ext) is always considered. The default is to include
    !% also the exchange-correlation and Hartree terms, which fully
    !% takes into account local fields.
    !% Just <tt>hartree</tt> gives you the random-phase approximation (RPA).
    !% If you want to choose the exchange-correlation kernel, use the variable
    !% <tt>XCKernel</tt>. For <tt>kdotp</tt> and magnetic <tt>em_resp</tt> modes,
    !% or if <tt>TheoryLevel = independent_particles</tt>,
    !% the value <tt>V_ext_only</tt> is used and this variable is ignored.
    !%Option V_ext_only 0
    !% Neither Hartree nor XC potentials included.
    !%Option hartree 1
    !% The variation of the Hartree potential only.
    !%Option fxc 2
    !% The exchange-correlation kernel (the variation of the
    !% exchange-correlation potential) only.
    !%End
    if (present(set_ham_var)) then
      ham_var = set_ham_var
    else if (hm%theory_level /= independent_particles) then
      call parse_variable(namespace, 'HamiltonianVariation', 3, ham_var)
    else
      ham_var = 0
    end if
 
    if (hm%theory_level /= independent_particles) then
      this%add_fxc_kernel = ((ham_var / 2) == 1)
      add_hartree = (mod(ham_var, 2) == 1)
    else
      this%add_fxc_kernel = .false.
      add_hartree = .false.
    end if
 
 
    message(1) = "Variation of the Hamiltonian in Sternheimer equation: V_ext"
    if (add_hartree) write(message(1), '(2a)') trim(message(1)), ' + hartree'
    if (this%add_fxc_kernel) write(message(1), '(2a)') trim(message(1)), ' + fxc'
 
    message(2) = "Solving Sternheimer equation for"
    if (this%occ_response) then
      write(message(2), '(2a)') trim(message(2)), ' full linear response.'
    else
      write(message(2), '(2a)') trim(message(2)), ' linear response in unoccupied subspace only.'
    end if
 
    message(3) = "Sternheimer preorthogonalization:"
    if (this%preorthogonalization) then
      write(message(3), '(2a)') trim(message(3)), ' yes'
    else
      write(message(3), '(2a)') trim(message(3)), ' no'
    end if
    call messages_info(3, namespace=namespace)
 
    call linear_solver_init(this%solver, namespace, gr, states_are_real(st), mc, space)
 
    ! will not converge for non-self-consistent calculation unless LRTolScheme = fixed
    if (ham_var == 0) then
      call scf_tol_init(this%scf_tol, namespace, st%qtot, tol_scheme = 0) ! fixed
    else
      call scf_tol_init(this%scf_tol, namespace, st%qtot)
    end if
 
    ! Build the fxc from the GS density
    this%coeff_hartree = m_zero
    if (this%add_fxc_kernel) then
      this%coeff_hartree = this%coeff_hartree - ks%xc%lrc%alpha / (m_four * m_pi)
    end if
    if (add_hartree) this%coeff_hartree = this%coeff_hartree + m_one
    if (this%add_fxc_kernel) then
      call sternheimer_build_fxc(this, namespace, gr, st, ks%xc)
 
      call messages_print_with_emphasis(msg="XC Kernel level", namespace=namespace)
      call xc_write_fxc_info(ks%xc, namespace=namespace)
      call xc_sic_write_info(ks%sic, namespace=namespace)
      call messages_print_with_emphasis(namespace=namespace)
    end if
 
 
    ! This variable is documented in xc_oep_init.
    call parse_variable(namespace, 'EnablePhotons', .false., this%has_photons)
    call messages_print_var_value('EnablePhotons', this%has_photons, namespace=namespace)
 
    if (this%has_photons) then
      call messages_experimental('EnablePhotons = yes', namespace=namespace)
      call photon_mode_init(this%pt_modes, namespace, space%dim)
      call photon_mode_set_n_electrons(this%pt_modes, m_zero)
      call photon_mode_compute_dipoles(this%pt_modes, gr)
      call io_mkdir(em_resp_photons_dir, namespace)
      iunit = io_open(em_resp_photons_dir // 'photon_modes', namespace, action='write')
      call photon_mode_write_info(this%pt_modes, iunit=iunit)
      safe_allocate(this%zphoton_coord_q(1:this%pt_modes%nmodes, 1:space%dim))
      call io_close(iunit)
    end if
 
    !%Variable PhotonEta
    !%Type float
    !%Default 0.0000367
    !%Section Linear Response::Sternheimer
    !%Description
    !% This variable provides the value for the broadening of the photonic spectra
    !% when the coupling of electrons to photons is enabled in the frequency-dependent Sternheimer equation
    !%End
    call parse_variable(namespace, 'PhotonEta', 0.0000367_real64, this%pt_eta, units_inp%energy)
    call messages_print_var_value('PhotonEta', this%pt_eta, units_inp%energy, namespace=namespace)
 
 
    pop_sub(sternheimer_init)
  end subroutine sternheimer_init
 
  !-----------------------------------------------------------
  subroutine sternheimer_end(this)
    type(sternheimer_t), intent(inout) :: this
 
    push_sub(sternheimer_end)
 
    safe_deallocate_a(this%zphoton_coord_q)
 
    call linear_solver_end(this%solver)
    call scf_tol_end(this%scf_tol)
    call mix_end(this%mixer)
 
    nullify(this%mixfield)
 
    safe_deallocate_a(this%fxc)
 
    pop_sub(sternheimer_end)
  end subroutine sternheimer_end
 
 
  !-----------------------------------------------------------
  subroutine sternheimer_build_fxc(this, namespace, gr, st, xc)
    type(sternheimer_t), intent(inout) :: this
    type(namespace_t),   intent(in)    :: namespace
    type(grid_t),        intent(in)    :: gr
    type(states_elec_t), intent(in)    :: st
    type(xc_t),          intent(in)    :: xc
 
    real(real64), allocatable :: rho(:, :)
 
    push_sub(sternheimer_build_fxc)
 
    safe_allocate(this%fxc(1:gr%np, 1:st%d%nspin, 1:st%d%nspin))
    safe_allocate(rho(1:gr%np_part, 1:st%d%nspin))
    call states_elec_total_density(st, gr, rho)
    call xc_get_fxc(xc, gr, namespace, rho, st%d%ispin, this%fxc)
    safe_deallocate_a(rho)
 
    pop_sub(sternheimer_build_fxc)
  end subroutine sternheimer_build_fxc
 
 
  !-----------------------------------------------------------
  subroutine sternheimer_build_kxc(this, namespace, mesh, st, xc)
    type(sternheimer_t), intent(inout) :: this
    type(namespace_t),   intent(in)    :: namespace
    class(mesh_t),       intent(in)    :: mesh
    type(states_elec_t), intent(in)    :: st
    type(xc_t),          intent(in)    :: xc
 
    real(real64), allocatable :: rho(:, :)
 
    push_sub(sternheimer_build_kxc)
 
    if (this%add_fxc()) then
      safe_allocate(this%kxc(1:mesh%np, 1:st%d%nspin, 1:st%d%nspin, 1:st%d%nspin))
      this%kxc = m_zero
 
      safe_allocate(rho(1:mesh%np, 1:st%d%nspin))
      call states_elec_total_density(st, mesh, rho)
      call xc_get_kxc(xc, mesh, namespace, rho, st%d%ispin, this%kxc)
      safe_deallocate_a(rho)
    end if
 
    pop_sub(sternheimer_build_kxc)
 
  end subroutine sternheimer_build_kxc
 
  !---------------------------------------------
  subroutine sternheimer_unset_kxc(this)
    type(sternheimer_t), intent(inout) :: this
 
    push_sub(sternheimer_unset_kxc)
 
    safe_deallocate_a(this%kxc)
 
    pop_sub(sternheimer_unset_kxc)
  end subroutine sternheimer_unset_kxc
 
  !-----------------------------------------------------------
  pure logical function sternheimer_add_fxc(this) result(rr)
    class(sternheimer_t), intent(in) :: this
    rr = this%add_fxc_kernel
  end function sternheimer_add_fxc
 
 
  !-----------------------------------------------------------
  pure logical function sternheimer_add_hartree(this) result(rr)
    class(sternheimer_t), intent(in) :: this
    rr = abs(this%coeff_hartree) > m_epsilon
  end function sternheimer_add_hartree
 
 
  !-----------------------------------------------------------
  logical function sternheimer_has_converged(this) result(rr)
    type(sternheimer_t), intent(in) :: this
    rr = this%ok
  end function sternheimer_has_converged
 
  !-----------------------------------------------------------
  logical pure function sternheimer_have_rhs(this) result(have)
    type(sternheimer_t), intent(in) :: this
    have = associated(this%drhs) .or. associated(this%zrhs)
  end function sternheimer_have_rhs
 
  !-----------------------------------------------------------
  subroutine sternheimer_unset_rhs(this)
    type(sternheimer_t), intent(inout) :: this
 
    push_sub(sternheimer_unset_rhs)
 
    nullify(this%drhs)
    nullify(this%zrhs)
 
    pop_sub(sternheimer_unset_rhs)
  end subroutine sternheimer_unset_rhs
 
  !-----------------------------------------------------------
  logical pure function sternheimer_have_inhomog(this) result(have)
    type(sternheimer_t), intent(in) :: this
    have = associated(this%dinhomog) .or. associated(this%zinhomog)
  end function sternheimer_have_inhomog
 
  !-----------------------------------------------------------
  subroutine sternheimer_unset_inhomog(this)
    type(sternheimer_t), intent(inout) :: this
 
    push_sub(sternheimer_unset_inhomog)
 
    nullify(this%dinhomog)
    nullify(this%zinhomog)
 
    pop_sub(sternheimer_unset_inhomog)
  end subroutine sternheimer_unset_inhomog
 
  !-----------------------------------------------------------
  integer pure function swap_sigma(sigma)
    integer, intent(in) :: sigma
 
    if (sigma == 1) then
      swap_sigma = 2
    else
      swap_sigma = 1
    end if
 
  end function swap_sigma
 
! ---------------------------------------------------------
  character(len=100) function wfs_tag_sigma(namespace, base_name, isigma) result(str)
    type(namespace_t), intent(in) :: namespace
    character(len=*),  intent(in) :: base_name
    integer,           intent(in) :: isigma
 
    character :: sigma_char
 
    push_sub(wfs_tag_sigma)
 
    select case (isigma)
    case (1)
      sigma_char = '+'
    case (2)
      sigma_char = '-'
    case default
      write(message(1),'(a,i2)') "Illegal integer isigma passed to wfs_tag_sigma: ", isigma
      call messages_fatal(1, namespace=namespace)
    end select
 
    str = trim(base_name) // sigma_char
 
    pop_sub(wfs_tag_sigma)
 
  end function wfs_tag_sigma
 
  ! --------------------------------------------------------
 
  subroutine sternheimer_obsolete_variables(namespace, old_prefix, new_prefix)
    type(namespace_t),   intent(in)    :: namespace
    character(len=*),    intent(in)    :: old_prefix
    character(len=*),    intent(in)    :: new_prefix
 
    push_sub(sternheimer_obsolete_variables)
 
    call messages_obsolete_variable(namespace, trim(old_prefix)//'Preorthogonalization', trim(new_prefix)//'Preorthogonalization')
    call messages_obsolete_variable(namespace, trim(old_prefix)//'HamiltonianVariation', trim(new_prefix)//'HamiltonianVariation')
 
    call linear_solver_obsolete_variables(namespace, old_prefix, new_prefix)
    call scf_tol_obsolete_variables(namespace, old_prefix, new_prefix)
 
    pop_sub(sternheimer_obsolete_variables)
  end subroutine sternheimer_obsolete_variables
 
  !--------------------------------------------------------------
  subroutine calc_hvar_photons(this, mesh, nspin, lr_rho, nsigma, hvar, idir)
    type(sternheimer_t),    intent(inout) :: this
    class(mesh_t),          intent(in)    :: mesh
    integer,                intent(in)    :: nspin
    integer,                intent(in)    :: nsigma
    complex(real64),        intent(in)    :: lr_rho(:,:)
    complex(real64),        intent(inout) :: hvar(:,:,:)
    integer,                intent(in)    :: idir
 
    real(real64), allocatable :: lambda_dot_r(:)
    complex(real64), allocatable :: s_lr_rho(:), vp_dip_self_ener(:), vp_bilinear_el_pt(:)
    integer :: nm, is, ii
    complex(real64) :: first_moments
 
    push_sub(calc_hvar_photons)
    call profiling_in('CALC_HVAR_PHOTONS')
 
    nm = this%pt_modes%nmodes
 
    ! photonic terms
    safe_allocate(s_lr_rho(1:mesh%np))
    safe_allocate(lambda_dot_r(1:mesh%np))
    safe_allocate(vp_dip_self_ener(1:mesh%np))
    safe_allocate(vp_bilinear_el_pt(1:mesh%np))
 
    ! spin summed density
    s_lr_rho = m_zero
    do is = 1, nspin
      s_lr_rho = s_lr_rho + lr_rho(:, is)
    end do
 
    ! Compute electron-photon potentials
    vp_dip_self_ener = m_zero
    vp_bilinear_el_pt = m_zero
    do ii = 1, nm
      lambda_dot_r(1:mesh%np) = this%pt_modes%lambda(ii)*this%pt_modes%pol_dipole(1:mesh%np, ii)
      first_moments = zmf_integrate(mesh, lambda_dot_r(1:mesh%np)*s_lr_rho(1:mesh%np))
 
      ! Compute photon displacement coordinate q_{\alpha}s
      this%zphoton_coord_q(ii, idir) = -m_half * &
        ((m_one/(this%zomega - cmplx(this%pt_modes%omega(ii),-this%pt_eta, real64))) -  &
        (m_one/(this%zomega + cmplx(this%pt_modes%omega(ii), this%pt_eta, real64)))) *first_moments
 
      ! Compute potential for bilinear el-pt interaction
      vp_bilinear_el_pt = vp_bilinear_el_pt - &
        this%pt_modes%omega(ii)*lambda_dot_r(1:mesh%np)*this%zphoton_coord_q(ii, idir)
 
      ! Compute potential with dipole-self energy term
      vp_dip_self_ener = vp_dip_self_ener + first_moments*lambda_dot_r(1:mesh%np)
    end do
 
    hvar(1:mesh%np, 1, 1) = hvar(1:mesh%np, 1, 1) + vp_dip_self_ener(1:mesh%np) + vp_bilinear_el_pt(1:mesh%np)
    do ii = 2, nspin
      hvar(1:mesh%np, ii, 1) = hvar(1:mesh%np, 1, 1)
    end do
 
    safe_deallocate_a(s_lr_rho)
    safe_deallocate_a(lambda_dot_r)
    safe_deallocate_a(vp_dip_self_ener)
    safe_deallocate_a(vp_bilinear_el_pt)
 
    if (nsigma == 2) hvar(1:mesh%np, 1:nspin, 2) = conjg(hvar(1:mesh%np, 1:nspin, 1))
 
    call profiling_out('CALC_HVAR_PHOTONS')
    pop_sub(calc_hvar_photons)
  end subroutine calc_hvar_photons
 
 
#include "complex.F90"
#include "sternheimer_inc.F90"
 
#include "undef.F90"
 
#include "real.F90"
#include "sternheimer_inc.F90"
 
end module sternheimer_oct_m
 
!! Local Variables:
!! mode: f90
!! coding: utf-8
!! End: