ncoord.f90 Source File


Source Code

! This file is part of dftd4.
! SPDX-Identifier: LGPL-3.0-or-later
!
! dftd4 is free software: you can redistribute it and/or modify it under
! the terms of the Lesser GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! dftd4 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
! Lesser GNU General Public License for more details.
!
! You should have received a copy of the Lesser GNU General Public License
! along with dftd4.  If not, see <https://www.gnu.org/licenses/>.

module dftd4_ncoord
   use mctc_env, only : wp
   use mctc_io, only : structure_type
   use mctc_io_constants, only : pi
   implicit none
   private

   public :: get_coordination_number, add_coordination_number_derivs


   !> Steepness of counting function
   real(wp), parameter :: kcn = 7.5_wp

   !> Parameter for electronegativity scaling
   real(wp), parameter :: k4 = 4.10451_wp

   !> Parameter for electronegativity scaling
   real(wp), parameter :: k5 = 19.08857_wp

   !> Parameter for electronegativity scaling
   real(wp), parameter :: k6 = 2*11.28174_wp**2


contains


!> Geometric fractional coordination number, supports error function counting.
subroutine get_coordination_number(mol, trans, cutoff, rcov, en, cn, dcndr, dcndL)
   !DEC$ ATTRIBUTES DLLEXPORT :: get_coordination_number

   !> Molecular structure data
   type(structure_type), intent(in) :: mol

   !> Lattice points
   real(wp), intent(in) :: trans(:, :)

   !> Real space cutoff
   real(wp), intent(in) :: cutoff

   !> Covalent radius
   real(wp), intent(in) :: rcov(:)

   !> Electronegativity
   real(wp), intent(in) :: en(:)

   !> Error function coordination number.
   real(wp), intent(out) :: cn(:)

   !> Derivative of the CN with respect to the Cartesian coordinates.
   real(wp), intent(out), optional :: dcndr(:, :, :)

   !> Derivative of the CN with respect to strain deformations.
   real(wp), intent(out), optional :: dcndL(:, :, :)

   if (present(dcndr) .and. present(dcndL)) then
      call ncoord_derf(mol, trans, cutoff, rcov, en, cn, dcndr, dcndL)
   else
      call ncoord_erf(mol, trans, cutoff, rcov, en, cn)
   end if

end subroutine get_coordination_number


subroutine ncoord_erf(mol, trans, cutoff, rcov, en, cn)

   !> Molecular structure data
   type(structure_type), intent(in) :: mol

   !> Lattice points
   real(wp), intent(in) :: trans(:, :)

   !> Real space cutoff
   real(wp), intent(in) :: cutoff

   !> Covalent radius
   real(wp), intent(in) :: rcov(:)

   !> Electronegativity
   real(wp), intent(in) :: en(:)

   !> Error function coordination number.
   real(wp), intent(out) :: cn(:)

   integer :: iat, jat, izp, jzp, itr
   real(wp) :: r2, r1, rc, rij(3), countf, cutoff2, den

   cn(:) = 0.0_wp
   cutoff2 = cutoff**2

   !$omp parallel do default(none) reduction(+:cn) &
   !$omp shared(mol, trans, cutoff2, rcov, en) &
   !$omp private(jat, itr, izp, jzp, r2, rij, r1, rc, countf, den)
   do iat = 1, mol%nat
      izp = mol%id(iat)
      do jat = 1, iat
         jzp = mol%id(jat)
         den = k4*exp(-(abs(en(izp)-en(jzp)) + k5)**2/k6)

         do itr = 1, size(trans, dim=2)
            rij = mol%xyz(:, iat) - (mol%xyz(:, jat) + trans(:, itr))
            r2 = sum(rij**2)
            if (r2 > cutoff2 .or. r2 < 1.0e-12_wp) cycle
            r1 = sqrt(r2)

            rc = rcov(izp) + rcov(jzp)

            countf = den*erf_count(kcn, r1, rc)

            cn(iat) = cn(iat) + countf
            if (iat /= jat) then
               cn(jat) = cn(jat) + countf
            end if

         end do
      end do
   end do

end subroutine ncoord_erf


subroutine ncoord_derf(mol, trans, cutoff, rcov, en, cn, dcndr, dcndL)

   !> Molecular structure data
   type(structure_type), intent(in) :: mol

   !> Lattice points
   real(wp), intent(in) :: trans(:, :)

   !> Real space cutoff
   real(wp), intent(in) :: cutoff

   !> Covalent radius
   real(wp), intent(in) :: rcov(:)

   !> Electronegativity
   real(wp), intent(in) :: en(:)

   !> Error function coordination number.
   real(wp), intent(out) :: cn(:)

   !> Derivative of the CN with respect to the Cartesian coordinates.
   real(wp), intent(out) :: dcndr(:, :, :)

   !> Derivative of the CN with respect to strain deformations.
   real(wp), intent(out) :: dcndL(:, :, :)

   integer :: iat, jat, izp, jzp, itr
   real(wp) :: r2, r1, rc, rij(3), countf, countd(3), sigma(3, 3), cutoff2, den

   cn(:) = 0.0_wp
   dcndr(:, :, :) = 0.0_wp
   dcndL(:, :, :) = 0.0_wp
   cutoff2 = cutoff**2

   !$omp parallel do schedule(runtime) default(none) &
   !$omp reduction(+:cn, dcndr, dcndL) &
   !$omp shared(mol, trans, cutoff2, rcov, en) &
   !$omp private(jat, itr, izp, jzp, r2, rij, r1, rc, countf, countd, sigma, den)
   do iat = 1, mol%nat
      izp = mol%id(iat)
      do jat = 1, iat
         jzp = mol%id(jat)

         den = k4*exp(-(abs(en(izp)-en(jzp)) + k5)**2/k6)

         do itr = 1, size(trans, dim=2)
            rij = mol%xyz(:, iat) - (mol%xyz(:, jat) + trans(:, itr))
            r2 = sum(rij**2)
            if (r2 > cutoff2 .or. r2 < 1.0e-12_wp) cycle
            r1 = sqrt(r2)

            rc = rcov(izp) + rcov(jzp)

            countf = den*erf_count(kcn, r1, rc)
            countd = den*derf_count(kcn, r1, rc) * rij/r1

            cn(iat) = cn(iat) + countf
            if (iat /= jat) then
               cn(jat) = cn(jat) + countf
            end if

            dcndr(:, iat, iat) = dcndr(:, iat, iat) + countd
            dcndr(:, jat, jat) = dcndr(:, jat, jat) - countd
            dcndr(:, iat, jat) = dcndr(:, iat, jat) + countd
            dcndr(:, jat, iat) = dcndr(:, jat, iat) - countd

            sigma = spread(countd, 1, 3) * spread(rij, 2, 3)

            dcndL(:, :, iat) = dcndL(:, :, iat) + sigma
            if (iat /= jat) then
               dcndL(:, :, jat) = dcndL(:, :, jat) + sigma
            end if

         end do
      end do
   end do

end subroutine ncoord_derf


subroutine add_coordination_number_derivs(mol, trans, cutoff, rcov, en, dEdcn, gradient, sigma)

   !> Molecular structure data
   type(structure_type), intent(in) :: mol

   !> Lattice points
   real(wp), intent(in) :: trans(:, :)

   !> Real space cutoff
   real(wp), intent(in) :: cutoff

   !> Covalent radius
   real(wp), intent(in) :: rcov(:)

   !> Electronegativity
   real(wp), intent(in) :: en(:)

   !> Derivative of expression with respect to the coordination number
   real(wp), intent(in) :: dEdcn(:)

   !> Derivative of the CN with respect to the Cartesian coordinates
   real(wp), intent(inout) :: gradient(:, :)

   !> Derivative of the CN with respect to strain deformations
   real(wp), intent(inout) :: sigma(:, :)

   integer :: iat, jat, izp, jzp, itr
   real(wp) :: r2, r1, rc, rij(3), countf, countd(3), ds(3, 3), cutoff2, den

   cutoff2 = cutoff**2

   !$omp parallel do schedule(runtime) default(none) &
   !$omp reduction(+:gradient, sigma) &
   !$omp shared(mol, trans, cutoff2, rcov, en, dEdcn) &
   !$omp private(iat, jat, itr, izp, jzp, r2, rij, r1, rc, countd, ds, den)
   do iat = 1, mol%nat
      izp = mol%id(iat)
      do jat = 1, iat
         jzp = mol%id(jat)

         den = k4*exp(-(abs(en(izp)-en(jzp)) + k5)**2/k6)

         do itr = 1, size(trans, dim=2)
            rij = mol%xyz(:, iat) - (mol%xyz(:, jat) + trans(:, itr))
            r2 = sum(rij**2)
            if (r2 > cutoff2 .or. r2 < 1.0e-12_wp) cycle
            r1 = sqrt(r2)

            rc = rcov(izp) + rcov(jzp)

            countd = den*derf_count(kcn, r1, rc) * rij/r1

            gradient(:, iat) = gradient(:, iat) + countd * (dEdcn(iat) + dEdcn(jat))
            gradient(:, jat) = gradient(:, jat) - countd * (dEdcn(iat) + dEdcn(jat))

            ds = spread(countd, 1, 3) * spread(rij, 2, 3)

            sigma(:, :) = sigma(:, :) &
               & + ds * (dEdcn(iat) + merge(dEdcn(jat), 0.0_wp, jat /= iat))
         end do
      end do
   end do

end subroutine add_coordination_number_derivs


!> Error function counting function for coordination number contributions.
pure function erf_count(k, r, r0) result(count)

   !> Steepness of the counting function.
   real(wp), intent(in) :: k

   !> Current distance.
   real(wp), intent(in) :: r

   !> Cutoff radius.
   real(wp), intent(in) :: r0

   real(wp) :: count

   count = 0.5_wp * (1.0_wp + erf(-k*(r-r0)/r0))

end function erf_count


!> Derivative of the counting function w.r.t. the distance.
pure function derf_count(k, r, r0) result(count)

   !> Steepness of the counting function.
   real(wp), intent(in) :: k

   !> Current distance.
   real(wp), intent(in) :: r

   !> Cutoff radius.
   real(wp), intent(in) :: r0

   real(wp), parameter :: sqrtpi = sqrt(pi)

   real(wp) :: count

   count = -k/sqrtpi/r0*exp(-k**2*(r-r0)**2/r0**2)

end function derf_count


end module dftd4_ncoord