Smooth Particle Mesh Ewald-integrated stochastic Lanczos Many-body Dispersion algorithm
Abstract
We derive and implement an alternative formulation of the Stochastic Lanczos algorithm to be employed in connection with the Many-Body Dispersion model (MBD). Indeed, this formulation, which is only possible due to the Stochastic Lanczos' reliance on matrix-vector products, introduces generalized dipoles and fields. These key quantities allow for a state-of-the-art treatment of periodic boundary conditions via the O(Nlog(N)) Smooth Particle Mesh Ewald (SPME) approach which uses efficient fast Fourier transforms. This SPME-Lanczos algorithm drastically outperforms the standard replica method which is affected by a slow and conditionally convergence rate that limits an efficient and reliable inclusion of long-range periodic boundary conditions interactions in many-body dispersion modelling. The proposed algorithm inherits the embarrassingly parallelism of the original Stochastic Lanczos scheme, thus opening up for a fully converged and efficient periodic boundary condition treatment of MBD approaches.
Cite
@article{arxiv.2307.02278,
title = {Smooth Particle Mesh Ewald-integrated stochastic Lanczos Many-body Dispersion algorithm},
author = {Pier P. Poier and Louis Lagardère and Jean-Philip Piquemal},
journal= {arXiv preprint arXiv:2307.02278},
year = {2023}
}