! 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/>. !> Implementation of the rational (Becke--Johnson) damping function. module dftd4_damping_rational use dftd4_damping, only : damping_param use dftd4_damping_atm, only : get_atm_dispersion use dftd4_data, only : get_r4r2_val use mctc_env, only : wp use mctc_io, only : structure_type implicit none private public :: rational_damping_param !> Rational (Becke-Johnson) damping model type, extends(damping_param) :: rational_damping_param real(wp) :: s6 = 1.0_wp real(wp) :: s8 real(wp) :: s9 = 1.0_wp real(wp) :: a1 real(wp) :: a2 real(wp) :: alp = 16.0_wp contains !> Evaluate pairwise dispersion energy expression procedure :: get_dispersion2 !> Evaluate ATM three-body dispersion energy expression procedure :: get_dispersion3 !> Evaluate pairwise representation of additive dispersion energy procedure :: get_pairwise_dispersion2 !> Evaluate pairwise representation of non-additive dispersion energy procedure :: get_pairwise_dispersion3 end type rational_damping_param contains !> Evaluation of the dispersion energy expression subroutine get_dispersion2(self, mol, trans, cutoff, r4r2, c6, dc6dcn, dc6dq, & & energy, dEdcn, dEdq, gradient, sigma) !DEC$ ATTRIBUTES DLLEXPORT :: get_dispersion2 !> Damping parameters class(rational_damping_param), intent(in) :: self !> Molecular structure data class(structure_type), intent(in) :: mol !> Lattice points real(wp), intent(in) :: trans(:, :) !> Real space cutoff real(wp), intent(in) :: cutoff !> Expectation values for r4 over r2 operator real(wp), intent(in) :: r4r2(:) !> C6 coefficients for all atom pairs. real(wp), intent(in) :: c6(:, :) !> Derivative of the C6 w.r.t. the coordination number real(wp), intent(in), optional :: dc6dcn(:, :) !> Derivative of the C6 w.r.t. the partial charges real(wp), intent(in), optional :: dc6dq(:, :) !> Dispersion energy real(wp), intent(inout) :: energy(:) !> Derivative of the energy w.r.t. the coordination number real(wp), intent(inout), optional :: dEdcn(:) !> Derivative of the energy w.r.t. the partial charges real(wp), intent(inout), optional :: dEdq(:) !> Dispersion gradient real(wp), intent(inout), optional :: gradient(:, :) !> Dispersion virial real(wp), intent(inout), optional :: sigma(:, :) logical :: grad if (abs(self%s6) < epsilon(1.0_wp) .and. abs(self%s8) < epsilon(1.0_wp)) return grad = present(dc6dcn) .and. present(dEdcn) .and. present(dc6dq) & & .and. present(dEdq) .and. present(gradient) .and. present(sigma) if (grad) then call get_dispersion_derivs(self, mol, trans, cutoff, r4r2, c6, dc6dcn, dc6dq, & & energy, dEdcn, dEdq, gradient, sigma) else call get_dispersion_energy(self, mol, trans, cutoff, r4r2, c6, energy) end if end subroutine get_dispersion2 !> Evaluation of the dispersion energy expression subroutine get_dispersion_energy(self, mol, trans, cutoff, r4r2, c6, energy) !> Damping parameters class(rational_damping_param), intent(in) :: self !> Molecular structure data class(structure_type), intent(in) :: mol !> Lattice points real(wp), intent(in) :: trans(:, :) !> Real space cutoff real(wp), intent(in) :: cutoff !> Expectation values for r4 over r2 operator real(wp), intent(in) :: r4r2(:) !> C6 coefficients for all atom pairs. real(wp), intent(in) :: c6(:, :) !> Dispersion energy real(wp), intent(inout) :: energy(:) integer :: iat, jat, izp, jzp, jtr real(wp) :: vec(3), r2, cutoff2, r0ij, rrij, c6ij, t6, t8, edisp, dE cutoff2 = cutoff*cutoff !$omp parallel do schedule(runtime) default(none) reduction(+:energy) & !$omp shared(mol, self, c6, trans, cutoff2, r4r2) & !$omp private(iat, jat, izp, jzp, jtr, vec, r2, r0ij, rrij, c6ij, & !$omp& t6, t8, edisp, dE) do iat = 1, mol%nat izp = mol%id(iat) do jat = 1, iat jzp = mol%id(jat) rrij = 3*r4r2(izp)*r4r2(jzp) r0ij = self%a1 * sqrt(rrij) + self%a2 c6ij = c6(jat, iat) do jtr = 1, size(trans, 2) vec(:) = mol%xyz(:, iat) - (mol%xyz(:, jat) + trans(:, jtr)) r2 = vec(1)*vec(1) + vec(2)*vec(2) + vec(3)*vec(3) if (r2 > cutoff2 .or. r2 < epsilon(1.0_wp)) cycle t6 = 1.0_wp/(r2**3 + r0ij**6) t8 = 1.0_wp/(r2**4 + r0ij**8) edisp = self%s6*t6 + self%s8*rrij*t8 dE = -c6ij*edisp * 0.5_wp energy(iat) = energy(iat) + dE if (iat /= jat) then energy(jat) = energy(jat) + dE end if end do end do end do end subroutine get_dispersion_energy !> Evaluation of the dispersion energy expression subroutine get_dispersion_derivs(self, mol, trans, cutoff, r4r2, c6, dc6dcn, dc6dq, & & energy, dEdcn, dEdq, gradient, sigma) !> Damping parameters class(rational_damping_param), intent(in) :: self !> Molecular structure data class(structure_type), intent(in) :: mol !> Lattice points real(wp), intent(in) :: trans(:, :) !> Real space cutoff real(wp), intent(in) :: cutoff !> Expectation values for r4 over r2 operator real(wp), intent(in) :: r4r2(:) !> C6 coefficients for all atom pairs. real(wp), intent(in) :: c6(:, :) !> Derivative of the C6 w.r.t. the coordination number real(wp), intent(in) :: dc6dcn(:, :) !> Derivative of the C6 w.r.t. the partial charges real(wp), intent(in) :: dc6dq(:, :) !> Dispersion energy real(wp), intent(inout) :: energy(:) !> Derivative of the energy w.r.t. the coordination number real(wp), intent(inout) :: dEdcn(:) !> Derivative of the energy w.r.t. the partial charges real(wp), intent(inout) :: dEdq(:) !> Dispersion gradient real(wp), intent(inout) :: gradient(:, :) !> Dispersion virial real(wp), intent(inout) :: sigma(:, :) integer :: iat, jat, izp, jzp, jtr real(wp) :: vec(3), r2, cutoff2, r0ij, rrij, c6ij, t6, t8, d6, d8, edisp, gdisp real(wp) :: dE, dG(3), dS(3, 3) cutoff2 = cutoff*cutoff !$omp parallel do schedule(runtime) default(none) & !$omp reduction(+:energy, gradient, sigma, dEdcn, dEdq) & !$omp shared(mol, self, c6, dc6dcn, dc6dq, trans, cutoff2, r4r2) & !$omp private(iat, jat, izp, jzp, jtr, vec, r2, r0ij, rrij, c6ij, t6, t8, & !$omp& d6, d8, edisp, gdisp, dE, dG, dS) do iat = 1, mol%nat izp = mol%id(iat) do jat = 1, iat jzp = mol%id(jat) rrij = 3*r4r2(izp)*r4r2(jzp) r0ij = self%a1 * sqrt(rrij) + self%a2 c6ij = c6(jat, iat) do jtr = 1, size(trans, 2) vec(:) = mol%xyz(:, iat) - (mol%xyz(:, jat) + trans(:, jtr)) r2 = vec(1)*vec(1) + vec(2)*vec(2) + vec(3)*vec(3) if (r2 > cutoff2 .or. r2 < epsilon(1.0_wp)) cycle t6 = 1.0_wp/(r2**3 + r0ij**6) t8 = 1.0_wp/(r2**4 + r0ij**8) d6 = -6*r2**2*t6**2 d8 = -8*r2**3*t8**2 edisp = self%s6*t6 + self%s8*rrij*t8 gdisp = self%s6*d6 + self%s8*rrij*d8 dE = -c6ij*edisp * 0.5_wp dG(:) = -c6ij*gdisp*vec dS(:, :) = spread(dG, 1, 3) * spread(vec, 2, 3) * 0.5_wp energy(iat) = energy(iat) + dE dEdcn(iat) = dEdcn(iat) - dc6dcn(iat, jat) * edisp dEdq(iat) = dEdq(iat) - dc6dq(iat, jat) * edisp sigma(:, :) = sigma + dS if (iat /= jat) then energy(jat) = energy(jat) + dE dEdcn(jat) = dEdcn(jat) - dc6dcn(jat, iat) * edisp dEdq(jat) = dEdq(jat) - dc6dq(jat, iat) * edisp gradient(:, iat) = gradient(:, iat) + dG gradient(:, jat) = gradient(:, jat) - dG sigma(:, :) = sigma + dS end if end do end do end do end subroutine get_dispersion_derivs !> Evaluation of the dispersion energy expression subroutine get_dispersion3(self, mol, trans, cutoff, r4r2, c6, dc6dcn, dc6dq, & & energy, dEdcn, dEdq, gradient, sigma) !DEC$ ATTRIBUTES DLLEXPORT :: get_dispersion3 !> Damping parameters class(rational_damping_param), intent(in) :: self !> Molecular structure data class(structure_type), intent(in) :: mol !> Lattice points real(wp), intent(in) :: trans(:, :) !> Real space cutoff real(wp), intent(in) :: cutoff !> Expectation values for r4 over r2 operator real(wp), intent(in) :: r4r2(:) !> C6 coefficients for all atom pairs. real(wp), intent(in) :: c6(:, :) !> Derivative of the C6 w.r.t. the coordination number real(wp), intent(in), optional :: dc6dcn(:, :) !> Derivative of the C6 w.r.t. the partial charges real(wp), intent(in), optional :: dc6dq(:, :) !> Dispersion energy real(wp), intent(inout) :: energy(:) !> Derivative of the energy w.r.t. the coordination number real(wp), intent(inout), optional :: dEdcn(:) !> Derivative of the energy w.r.t. the partial charges real(wp), intent(inout), optional :: dEdq(:) !> Dispersion gradient real(wp), intent(inout), optional :: gradient(:, :) !> Dispersion virial real(wp), intent(inout), optional :: sigma(:, :) call get_atm_dispersion(mol, trans, cutoff, self%s9, self%a1, self%a2, & & self%alp, r4r2, c6, dc6dcn, dc6dq, energy, dEdcn, dEdq, & & gradient, sigma) end subroutine get_dispersion3 !> Evaluation of the dispersion energy expression projected on atomic pairs subroutine get_pairwise_dispersion2(self, mol, trans, cutoff, r4r2, c6, energy) !DEC$ ATTRIBUTES DLLEXPORT :: get_pairwise_dispersion2 !> Damping parameters class(rational_damping_param), intent(in) :: self !> Molecular structure data class(structure_type), intent(in) :: mol !> Lattice points real(wp), intent(in) :: trans(:, :) !> Real space cutoff real(wp), intent(in) :: cutoff !> Expectation values for r4 over r2 operator real(wp), intent(in) :: r4r2(:) !> C6 coefficients for all atom pairs. real(wp), intent(in) :: c6(:, :) !> Dispersion energy real(wp), intent(inout) :: energy(:, :) integer :: iat, jat, izp, jzp, jtr real(wp) :: vec(3), r2, cutoff2, r0ij, rrij, c6ij, t6, t8, edisp, dE if (abs(self%s6) < epsilon(1.0_wp) .and. abs(self%s8) < epsilon(1.0_wp)) return cutoff2 = cutoff*cutoff !$omp parallel do schedule(runtime) default(none) reduction(+:energy) & !$omp shared(mol, self, c6, trans, cutoff2, r4r2) & !$omp private(iat, jat, izp, jzp, jtr, vec, r2, r0ij, rrij, c6ij, & !$omp& t6, t8, edisp, dE) do iat = 1, mol%nat izp = mol%id(iat) do jat = 1, iat jzp = mol%id(jat) rrij = 3*r4r2(izp)*r4r2(jzp) r0ij = self%a1 * sqrt(rrij) + self%a2 c6ij = c6(jat, iat) do jtr = 1, size(trans, 2) vec(:) = mol%xyz(:, iat) - (mol%xyz(:, jat) + trans(:, jtr)) r2 = vec(1)*vec(1) + vec(2)*vec(2) + vec(3)*vec(3) if (r2 > cutoff2 .or. r2 < epsilon(1.0_wp)) cycle t6 = 1.0_wp/(r2**3 + r0ij**6) t8 = 1.0_wp/(r2**4 + r0ij**8) edisp = self%s6*t6 + self%s8*rrij*t8 dE = -c6ij*edisp * 0.5_wp energy(jat, iat) = energy(jat, iat) + dE if (iat /= jat) then energy(iat, jat) = energy(iat, jat) + dE end if end do end do end do end subroutine get_pairwise_dispersion2 !> Evaluation of the dispersion energy expression subroutine get_pairwise_dispersion3(self, mol, trans, cutoff, r4r2, c6, energy) !DEC$ ATTRIBUTES DLLEXPORT :: get_pairwise_dispersion3 !> Damping parameters class(rational_damping_param), intent(in) :: self !> Molecular structure data class(structure_type), intent(in) :: mol !> Lattice points real(wp), intent(in) :: trans(:, :) !> Real space cutoff real(wp), intent(in) :: cutoff !> Expectation values for r4 over r2 operator real(wp), intent(in) :: r4r2(:) !> C6 coefficients for all atom pairs. real(wp), intent(in) :: c6(:, :) !> Dispersion energy real(wp), intent(inout) :: energy(:, :) integer :: iat, jat, kat, izp, jzp, kzp, jtr, ktr real(wp) :: vij(3), vjk(3), vik(3), r2ij, r2jk, r2ik, c6ij, c6jk, c6ik, triple real(wp) :: r0ij, r0jk, r0ik, r0, r1, r2, r3, r5, rr, fdmp, ang real(wp) :: cutoff2, c9, dE if (abs(self%s9) < epsilon(1.0_wp)) return cutoff2 = cutoff*cutoff !$omp parallel do schedule(runtime) default(none) reduction(+:energy) & !$omp shared(mol, trans, c6, r4r2, cutoff2, self) & !$omp private(iat, jat, kat, izp, jzp, kzp, jtr, ktr, vij, vjk, vik, & !$omp& r2ij, r2jk, r2ik, c6ij, c6jk, c6ik, triple, r0ij, r0jk, r0ik, r0, & !$omp& r1, r2, r3, r5, rr, fdmp, ang, c9, dE) do iat = 1, mol%nat izp = mol%id(iat) do jat = 1, iat jzp = mol%id(jat) c6ij = c6(jat, iat) r0ij = self%a1 * sqrt(3*r4r2(jzp)*r4r2(izp)) + self%a2 do jtr = 1, size(trans, 2) vij(:) = mol%xyz(:, jat) + trans(:, jtr) - mol%xyz(:, iat) r2ij = vij(1)*vij(1) + vij(2)*vij(2) + vij(3)*vij(3) if (r2ij > cutoff2 .or. r2ij < epsilon(1.0_wp)) cycle do kat = 1, jat kzp = mol%id(kat) c6ik = c6(kat, iat) c6jk = c6(kat, jat) c9 = -self%s9 * sqrt(abs(c6ij*c6ik*c6jk)) r0ik = self%a1 * sqrt(3*r4r2(kzp)*r4r2(izp)) + self%a2 r0jk = self%a1 * sqrt(3*r4r2(kzp)*r4r2(jzp)) + self%a2 r0 = r0ij * r0ik * r0jk triple = triple_scale(iat, jat, kat) do ktr = 1, size(trans, 2) vik(:) = mol%xyz(:, kat) + trans(:, ktr) - mol%xyz(:, iat) r2ik = vik(1)*vik(1) + vik(2)*vik(2) + vik(3)*vik(3) if (r2ik > cutoff2 .or. r2ik < epsilon(1.0_wp)) cycle vjk(:) = mol%xyz(:, kat) + trans(:, ktr) - mol%xyz(:, jat) & & - trans(:, jtr) r2jk = vjk(1)*vjk(1) + vjk(2)*vjk(2) + vjk(3)*vjk(3) if (r2jk > cutoff2 .or. r2jk < epsilon(1.0_wp)) cycle r2 = r2ij*r2ik*r2jk r1 = sqrt(r2) r3 = r2 * r1 r5 = r3 * r2 fdmp = 1.0_wp / (1.0_wp + 6.0_wp * (r0 / r1)**(self%alp / 3.0_wp)) ang = 0.375_wp*(r2ij + r2jk - r2ik)*(r2ij - r2jk + r2ik)& & *(-r2ij + r2jk + r2ik) / r5 + 1.0_wp / r3 rr = ang*fdmp dE = rr * c9 * triple/6 energy(jat, iat) = energy(jat, iat) - dE energy(kat, iat) = energy(kat, iat) - dE energy(iat, jat) = energy(iat, jat) - dE energy(kat, jat) = energy(kat, jat) - dE energy(iat, kat) = energy(iat, kat) - dE energy(jat, kat) = energy(jat, kat) - dE end do end do end do end do end do end subroutine get_pairwise_dispersion3 !> Logic exercise to distribute a triple energy to atomwise energies. elemental function triple_scale(ii, jj, kk) result(triple) !> Atom indices integer, intent(in) :: ii, jj, kk !> Fraction of energy real(wp) :: triple if (ii == jj) then if (ii == kk) then ! ii'i" -> 1/6 triple = 1.0_wp/6.0_wp else ! ii'j -> 1/2 triple = 0.5_wp end if else if (ii /= kk .and. jj /= kk) then ! ijk -> 1 (full) triple = 1.0_wp else ! ijj' and iji' -> 1/2 triple = 0.5_wp end if end if end function triple_scale end module dftd4_damping_rational