add_coordination_number_derivs Subroutine

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