! 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 Axilrod-Teller-Muto triple dipole dispersion !> contribution with a modified zero (Chai--Head-Gordon) damping together !> with the critical radii from the rational (Becke--Johnson) damping. module dftd4_damping_atm use mctc_env, only : wp use mctc_io, only : structure_type implicit none public :: get_atm_dispersion contains !> Evaluation of the dispersion energy expression subroutine get_atm_dispersion(mol, trans, cutoff, s9, a1, a2, alp, r4r2, & & c6, dc6dcn, dc6dq, energy, dEdcn, dEdq, gradient, sigma) !> Molecular structure data class(structure_type), intent(in) :: mol !> Lattice points real(wp), intent(in) :: trans(:, :) !> Real space cutoff real(wp), intent(in) :: cutoff !> Scaling for dispersion coefficients real(wp), intent(in) :: s9 !> Scaling parameter for critical radius real(wp), intent(in) :: a1 !> Offset parameter for critical radius real(wp), intent(in) :: a2 !> Exponent of zero damping function real(wp), intent(in) :: alp !> 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(s9) < 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_atm_dispersion_derivs(mol, trans, cutoff, s9, a1, a2, alp, r4r2, & & c6, dc6dcn, dc6dq, energy, dEdcn, dEdq, gradient, sigma) else call get_atm_dispersion_energy(mol, trans, cutoff, s9, a1, a2, alp, r4r2, & & c6, energy) end if end subroutine get_atm_dispersion !> Evaluation of the dispersion energy expression subroutine get_atm_dispersion_energy(mol, trans, cutoff, s9, a1, a2, alp, r4r2, & & c6, energy) !> Molecular structure data class(structure_type), intent(in) :: mol !> Lattice points real(wp), intent(in) :: trans(:, :) !> Real space cutoff real(wp), intent(in) :: cutoff !> Scaling for dispersion coefficients real(wp), intent(in) :: s9 !> Scaling parameter for critical radius real(wp), intent(in) :: a1 !> Offset parameter for critical radius real(wp), intent(in) :: a2 !> Exponent of zero damping function real(wp), intent(in) :: alp !> 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 cutoff2 = cutoff*cutoff !$omp parallel do schedule(runtime) default(none) reduction(+:energy) & !$omp shared(mol, trans, c6, s9, a1, a2, alp, r4r2, cutoff2) & !$omp private(iat, jat, kat, izp, jzp, kzp, jtr, ktr, vij, vjk, vik, & !$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 = a1 * sqrt(3*r4r2(jzp)*r4r2(izp)) + 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 = -s9 * sqrt(abs(c6ij*c6ik*c6jk)) r0ik = a1 * sqrt(3*r4r2(kzp)*r4r2(izp)) + a2 r0jk = a1 * sqrt(3*r4r2(kzp)*r4r2(jzp)) + 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)**(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 energy(iat) = energy(iat) - dE/3 energy(jat) = energy(jat) - dE/3 energy(kat) = energy(kat) - dE/3 end do end do end do end do end do end subroutine get_atm_dispersion_energy !> Evaluation of the dispersion energy expression subroutine get_atm_dispersion_derivs(mol, trans, cutoff, s9, a1, a2, alp, r4r2, & & c6, dc6dcn, dc6dq, energy, dEdcn, dEdq, gradient, sigma) !> Molecular structure data class(structure_type), intent(in) :: mol !> Lattice points real(wp), intent(in) :: trans(:, :) !> Real space cutoff real(wp), intent(in) :: cutoff !> Scaling for dispersion coefficients real(wp), intent(in) :: s9 !> Scaling parameter for critical radius real(wp), intent(in) :: a1 !> Offset parameter for critical radius real(wp), intent(in) :: a2 !> Exponent of zero damping function real(wp), intent(in) :: alp !> 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, 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, dfdmp, ang, dang real(wp) :: cutoff2, c9, dE, dGij(3), dGjk(3), dGik(3), dS(3, 3) cutoff2 = cutoff*cutoff !$omp parallel do schedule(runtime) default(none) & !$omp reduction(+:energy, gradient, sigma, dEdcn, dEdq) & !$omp shared(mol, trans, c6, s9, a1, a2, alp, r4r2, cutoff2, dc6dcn, dc6dq) & !$omp private(iat, jat, kat, izp, jzp, kzp, jtr, ktr, vij, vjk, vik, & !$omp& r2ij, r2jk, r2ik, c6ij, c6jk, c6ik, triple, r0ij, r0jk, r0ik, r0, & !$omp& r1, r2, r3, r5, rr, fdmp, dfdmp, ang, dang, c9, dE, dGij, dGjk, & !$omp& dGik, dS) do iat = 1, mol%nat izp = mol%id(iat) do jat = 1, iat jzp = mol%id(jat) c6ij = c6(jat, iat) r0ij = a1 * sqrt(3*r4r2(jzp)*r4r2(izp)) + 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 = -s9 * sqrt(abs(c6ij*c6ik*c6jk)) r0ik = a1 * sqrt(3*r4r2(kzp)*r4r2(izp)) + a2 r0jk = a1 * sqrt(3*r4r2(kzp)*r4r2(jzp)) + 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)**(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 dfdmp = -2.0_wp * alp * (r0 / r1)**(alp / 3.0_wp) * fdmp**2 ! d/drij dang = -0.375_wp * (r2ij**3 + r2ij**2 * (r2jk + r2ik)& & + r2ij * (3.0_wp * r2jk**2 + 2.0_wp * r2jk*r2ik& & + 3.0_wp * r2ik**2)& & - 5.0_wp * (r2jk - r2ik)**2 * (r2jk + r2ik)) / r5 dGij(:) = c9 * (-dang*fdmp + ang*dfdmp) / r2ij * vij ! d/drik dang = -0.375_wp * (r2ik**3 + r2ik**2 * (r2jk + r2ij)& & + r2ik * (3.0_wp * r2jk**2 + 2.0_wp * r2jk * r2ij& & + 3.0_wp * r2ij**2)& & - 5.0_wp * (r2jk - r2ij)**2 * (r2jk + r2ij)) / r5 dGik(:) = c9 * (-dang * fdmp + ang * dfdmp) / r2ik * vik ! d/drjk dang = -0.375_wp * (r2jk**3 + r2jk**2*(r2ik + r2ij)& & + r2jk * (3.0_wp * r2ik**2 + 2.0_wp * r2ik * r2ij& & + 3.0_wp * r2ij**2)& & - 5.0_wp * (r2ik - r2ij)**2 * (r2ik + r2ij)) / r5 dGjk(:) = c9 * (-dang * fdmp + ang * dfdmp) / r2jk * vjk dE = rr * c9 * triple energy(iat) = energy(iat) - dE/3 energy(jat) = energy(jat) - dE/3 energy(kat) = energy(kat) - dE/3 gradient(:, iat) = gradient(:, iat) - dGij - dGik gradient(:, jat) = gradient(:, jat) + dGij - dGjk gradient(:, kat) = gradient(:, kat) + dGik + dGjk dS(:, :) = spread(dGij, 1, 3) * spread(vij, 2, 3)& & + spread(dGik, 1, 3) * spread(vik, 2, 3)& & + spread(dGjk, 1, 3) * spread(vjk, 2, 3) sigma(:, :) = sigma + dS * triple dEdcn(iat) = dEdcn(iat) - dE * 0.5_wp & & * (dc6dcn(iat, jat) / c6ij + dc6dcn(iat, kat) / c6ik) dEdcn(jat) = dEdcn(jat) - dE * 0.5_wp & & * (dc6dcn(jat, iat) / c6ij + dc6dcn(jat, kat) / c6jk) dEdcn(kat) = dEdcn(kat) - dE * 0.5_wp & & * (dc6dcn(kat, iat) / c6ik + dc6dcn(kat, jat) / c6jk) dEdq(iat) = dEdq(iat) - dE * 0.5_wp & & * (dc6dq(iat, jat) / c6ij + dc6dq(iat, kat) / c6ik) dEdq(jat) = dEdq(jat) - dE * 0.5_wp & & * (dc6dq(jat, iat) / c6ij + dc6dq(jat, kat) / c6jk) dEdq(kat) = dEdq(kat) - dE * 0.5_wp & & * (dc6dq(kat, iat) / c6ik + dc6dq(kat, jat) / c6jk) end do end do end do end do end do end subroutine get_atm_dispersion_derivs !> 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_atm