Smooth Particle Mesh Ewald-integrated stochastic Lanczos Many-body Dispersion algorithm

TL;DR

This paper introduces a novel SPME-integrated stochastic Lanczos algorithm for efficient and accurate long-range interaction modeling in many-body dispersion calculations with periodic boundary conditions.

Contribution

It develops a new formulation of the stochastic Lanczos algorithm that leverages SPME for improved periodic boundary condition treatment in MBD models.

Findings

Outperforms the standard replica method in convergence speed.

Enables efficient parallel computation for periodic boundary conditions.

Provides a scalable approach for long-range dispersion interactions.

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.