#include <ewald.hpp>
Public Member Functions | |
| EwaldForceCalculator (const Crystal &crystal_structure, const PlanewaveBasis &planewave_basis) | |
| std::vector< Vector3D > | compute () const |
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inline |
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inline |
factor = 2 · exp(-G²/4α) / G², doubled again on a half sphere.
The 2 is not about the sphere, and it is not the Rydberg e² either — that is applied separately below. It is the factor from differentiating a modulus squared: ∂|ρ(G)|²/∂τ = 2 Re[ρ* ∂ρ/∂τ]. So it is correct for the full-sphere G list Q3 normally builds. Gamma-only stores only the positive half sphere (g_vectors_grid.hpp), and the summand here is even under G → −G (the imaginary part is odd and G_α is odd), so the missing half contributes exactly as much again.
Without this the Ewald force is exactly half at Gamma while the Ewald energy — which depends only on geometry — is unchanged: measured -0.02549078 against a −dE_ewald/dy of -0.05098040.
F_{G,α} = +(e²⋅2π/Ω) factor Z_i G_α Im[S(G) e^{-iGτ_i}] complex_product = S(G) × conj(e^{iGτ_i}) = S(G) × e^{-iGτ_i}. Im[S e^{-iGτ}] = -Im[e^{+iGτ} S*] (conjugate of correct formula), combined with the F = -∂E/∂τ sign, the result is +=.
The image loop is sized for a separation in the home cell, and positions outside [0, 1) are legal input; see Crystal::home_cell_separation().
Definition at line 34 of file ewald.hpp.
References q3::Crystal::cell_volume(), q3::PlanewaveBasis::charge_density_energy_cutoff(), q3::compute_phase_factor(), q3::Crystal::convert_from_crystal_to_cartesian(), q3::math::tolerances::ewald_convergence_threshold, q3::PlanewaveBasis::first_nonzero_g_index(), q3::PlanewaveBasis::g_vectors(), q3::Crystal::home_cell_separation(), q3::PlanewaveBasis::is_gamma_only(), q3::Crystal::lattice_parameter(), q3::Crystal::lattice_vectors(), q3::Vector3D::norm(), q3::Crystal::number_of_atoms(), q3::PlanewaveBasis::number_of_g_vectors(), q3::Crystal::species_type_index(), q3::Crystal::two_pi_over_lattice_parameter(), q3::Crystal::two_pi_over_lattice_parameter_squared(), q3::Crystal::valence_charge(), and q3::math::tolerances::zero_vector_magnitude_threshold.
Referenced by q3::ForceCalculator::compute_forces().
1.9.8 