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Fix per-atom error in the Laplacian meta-GGA nuclear gradient #228

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Fix per-atom error in the Laplacian meta-GGA nuclear gradient #228

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28 changes: 24 additions & 4 deletions src/xc_integrator/replicated/host/reference_replicated_xc_host_integrator_exc_grad.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -203,6 +203,9 @@ void ReferenceReplicatedXCHostIntegrator<ValueType>::
host_data.tau .resize( spin_dim_scal * npts );
host_data.vtau.resize( spin_dim_scal * npts );
if ( needs_laplacian ) {
// One more block holds 2 P lapl(B), which the nuclear derivative
// of lapl(rho) contracts against; see the assembly below.
host_data.zmat .resize( 5 * spin_dim_scal * npts * nbe );
host_data.basis_eval.resize( 24 * npts * nbe ); // 11 + lapl_grad(3) + der3(10)
host_data.lapl .resize( spin_dim_scal * npts );
host_data.vlapl.resize( spin_dim_scal * npts );
Expand All @@ -222,6 +225,7 @@ void ReferenceReplicatedXCHostIntegrator<ValueType>::
double* xZmat_x = nullptr;
double* xZmat_y = nullptr;
double* xZmat_z = nullptr;
double* xLmat = nullptr; // 2 P lapl(B), laplacian mGGAs only

auto* eps = host_data.eps.data();
auto* gamma = host_data.gamma.data();
Expand Down Expand Up @@ -358,6 +362,13 @@ void ReferenceReplicatedXCHostIntegrator<ValueType>::
blas::lacpy( 'A', nbe, npts, d3basis_xxz_eval, nbe, dlgradbasis_z_eval, nbe );
blas::axpy( nbe * npts, 1., d3basis_yyz_eval, 1, dlgradbasis_z_eval, 1);
blas::axpy( nbe * npts, 1., d3basis_zzz_eval, 1, dlgradbasis_z_eval, 1);

// lapl(rho) = 2 X . lapl(B) + 2 sum_c X_c . d_c B, so one term of
// its nuclear derivative contracts the BARE d_x B against
// 2 P lapl(B). That matrix is not otherwise formed, so build it.
xLmat = host_data.zmat.data() + 4 * spin_dim_scal * npts * nbe;
lwd->eval_xmat( npts, nbf, nbe, submat_map, xmat_fac, Ps, ldps,
lbasis_eval, nbe, xLmat, nbe, nbe_scr );
}
if(is_rks)
lwd->eval_uvvar_mgga_rks( npts, nbe, basis_eval, dbasis_x_eval, dbasis_y_eval,
Expand Down Expand Up @@ -557,13 +568,22 @@ void ReferenceReplicatedXCHostIntegrator<ValueType>::

if( needs_laplacian ) {
const double vlapl_ipt = weights[ipt] * vlapl[ipt];
const double lbf = lbasis_eval[mu_i];
const double dlbx = dlgradbasis_x_eval[mu_i];
const double dlby = dlgradbasis_y_eval[mu_i];
const double dlbz = dlgradbasis_z_eval[mu_i];
d2_term_x = xN * dlbx + xNx * lbf + 2.0*d2_term_x;
d2_term_y = xN * dlby + xNy * lbf + 2.0*d2_term_y;
d2_term_z = xN * dlbz + xNz * lbf + 2.0*d2_term_z;
const double xL = xLmat[mu_i];

// d/dA lapl(rho) = -2 [ X d_x lapl(B) + d_x B (2P lapl(B))
// + 2 sum_c (hess B)_xc X_c ].
// The middle term pairs the bare gradient with the
// density-matrix-contracted laplacian. Pairing them the
// other way round -- (2P d_x B) against lapl(B) -- is equal
// only after summing over EVERY basis function, so it left
// the total gradient and translational invariance intact
// while putting the wrong force on each individual atom.
d2_term_x = xN * dlbx + dbx * xL + 2.0*d2_term_x;
d2_term_y = xN * dlby + dby * xL + 2.0*d2_term_y;
d2_term_z = xN * dlbz + dbz * xL + 2.0*d2_term_z;

g_acc_x += vlapl_ipt * d2_term_x;
g_acc_y += vlapl_ipt * d2_term_y;
Expand Down