Electrostatics#

Examples demonstrating GPU-accelerated computation of long-range electrostatic interactions in periodic systems using Coulomb, Ewald summation, and Particle Mesh Ewald (PME).

These examples show how to:

Compute direct Coulomb interactions (damped and undamped)
Use Ewald summation for periodic systems with automatic parameter estimation
Apply two-dimensional slab corrections for Ewald and PME interfacial systems
Apply Particle Mesh Ewald (PME) for O(N log N) scaling
Work with neighbor list and neighbor matrix formats
Perform batch evaluation for multiple systems
Leverage autograd for computing forces and gradients
Compute multipole Ewald and PME totals with charges, dipoles, and quadrupoles (l_max = 0 / 1 / 2), including stress tensors via the cell gradient and force-loss-style training via the second-order backward Warp kernel
Extract atom-centered multipole features by projecting the periodic potential onto receiver GTOs
Amortize the position-independent reciprocal-space state with the multipole SCF cache and reuse it across many step evaluations
Train on forces, stress, and charge gradients via the energy-derivative contract (the recommended replacement for the deprecated direct-output flags)

The full Torch Ewald/PME APIs support first- and second-order energy-derived training workflows. The full JAX Ewald/PME APIs support first-order energy-derived gradients for positions, charges, and row-vector displacement virials. Higher-order JAX support is limited to tested position and charge scalar losses; PME cell/stress/strain higher-order derivatives are unsupported. Electrostatics does not expose public Hessian or Jacobian APIs.

Point-charge Ewald/PME examples use float64 for accuracy-sensitive reciprocal-space calculations and gradient checks. The APIs also support float32 when throughput is the priority; keep all floating inputs and precomputed metadata in a call on a consistent dtype.