namespace rgpot_tersoff

Overview

Tersoff bond-order potential in gather form. More…

namespace rgpot_tersoff {
 
// global variables
 
real(wp), parameter zeta_floor = 1.0e-15_wp;
 
// global functions
 
subroutine, public tersoff_energy_forces(real(wp), dimension(:, :), intent(in), contiguous positions, real(wp), dimension(3, 3), intent(in) cell, type(tersoff_params_t), intent(in) par, type(neighbor_table_t), intent(inout) table, real(wp), intent(out) energy, real(wp), dimension(:, :), intent(out), contiguous forces, integer, intent(out) status, character(len=:), intent(out), allocatable errmsg);
 
} // namespace rgpot_tersoff

Detailed Documentation

Tersoff bond-order potential in gather form.

Every directed pair (i, j) carries a bond order b_ij set by a coordination sum zeta_ij over the neighbours k of i. The pair therefore couples to a whole shell of third atoms, and its gradient splits into terms landing on i, on j, and on each k. That is why a bond-order kernel resists the one-pass gather a pair potential allows: the k terms need dE_ij/dzeta_ij, which is not known until the whole shell has been summed.

Splitting the evaluation into three passes over the full neighbour table removes the obstacle:

  1. zeta for every directed pair, from the neighbours of the pair’s first atom;

  2. the per-pair scalars the gradient needs, dE_ij/dr_ij at fixed bond order and dE_ij/dzeta_ij;

  3. the gather, in which atom a collects every term that lands on it and writes only forces(:, a).

Pass 3 closes because pass 2 leaves dE_ij/dzeta_ij stored per pair. Atom a then plays three roles, all reachable from its own row of the table:

  • owner of the pairs (a, j), taking their radial term and dzeta_aj/dr_a;

  • far end of the pairs (m, a) for m in a ‘s row, reached through the reverse entry, taking their radial term and dzeta_ma/dr_a;

  • third atom of the pairs (m, j) for m in a ‘s row and j in m ‘s, taking dzeta_mj/dr_a.

The last two roles share one walk over m ‘s row and one cosine per step, so the gather costs O(natoms * nn^2) like the two passes before it. All three passes run under do concurrent; none of them scatters.

Global Variables

real(wp), parameter zeta_floor = 1.0e-15_wp

Below this coordination the bond order is its zeta -> 0 limit chi, and its derivative is dropped: zeta**(n - 1) has a negative exponent and diverges at the origin while the energy stays finite.

Global Functions

subroutine, public tersoff_energy_forces(real(wp), dimension(:, :), intent(in), contiguous positions, real(wp), dimension(3, 3), intent(in) cell, type(tersoff_params_t), intent(in) par, type(neighbor_table_t), intent(inout) table, real(wp), intent(out) energy, real(wp), dimension(:, :), intent(out), contiguous forces, integer, intent(out) status, character(len=:), intent(out), allocatable errmsg)

Energy and forces for positions (3 x natoms) in cell.