Isotropic Periodic Sum for Polarizable Gaussian Multipole Model.

The isotropic periodic sum (IPS) method provides an efficient approach for computing long-range interactions by approximating distant molecular structures through isotropic periodic images of a local region. Here, we present a novel integration of IPS with the polarizable Gaussian multipole (pGM) model, extending its applicability to systems with Gaussian-distributed charges and dipoles. By developing and implementing the IPS multipole tensor theorem within the Gaussian multipole framework, we derive analytical expressions for IPS potentials that efficiently handle both permanent and induced multipole interactions. Our comprehensive validation includes energy conservation tests in the NVE ensemble, potential energy distributions in the NVT ensemble, structural analysis through radial distribution functions, diffusion coefficients, induced dipole calculations across various molecular systems, and ionic charging free energies. The results demonstrate that the pGM-IPS approach successfully reproduces energetic, structural, and dynamic properties of molecular systems with accuracy comparable to the traditional particle mesh Ewald method. Our work establishes pGM-IPS as a promising method for simulations of polarizable molecular systems, achieving a balance between computational efficiency and accuracy.