Multi-center decomposition of molecular densities: A numerical perspective

TL;DR

This paper evaluates the numerical performance of the LISA method for molecular density partitioning, demonstrating its efficiency and accuracy advantages over other ISA variants across diverse molecules.

Contribution

It systematically derives iterative solvers for LISA and compares its performance with GISA and MBIS, highlighting LISA's improved efficiency and accuracy.

Findings

LISA methods are more numerically efficient than GISA and MBIS.

LISA avoids negative atomic charges in negatively charged molecules.

Elevated entropy in LISA can be mitigated with additional basis functions.

Abstract

In this study, we analyze various Iterative Stockholder Analysis (ISA) methods for molecular density partitioning, focusing on the numerical performance of the recently proposed Linear approximation of Iterative Stockholder Analysis model (LISA) [J. Chem. Phys. 156, 164107 (2022)]. We first provide a systematic derivation of various iterative solvers to find the unique LISA solution. In a subsequent systematic numerical study, we evaluate their performance on 48 organic and inorganic, neutral and charged molecules and also compare LISA to two other well-known ISA variants: the Gaussian Iterative Stockholder Analysis (GISA) and Minimum Basis Iterative Stockholder analysis (MBIS). The study reveals that LISA-family methods can offer a numerically more efficient approach with better accuracy compared to the two comparative methods. Moreover, the well-known issue with the MBIS method, where atomic charges obtained for negatively charged molecules are anomalously negative, is not observed in LISA-family methods. Despite the fact that LISA occasionally exhibits elevated entropy as a consequence of the absence of more diffuse basis functions, this issue can be readily mitigated by incorporating additional or integrating supplementary basis functions within the LISA framework. This research provides the foundation for future studies on the efficiency and chemical accuracy of molecular density partitioning schemes.