Approximations of the Iterative Stockholder Analysis scheme using exponential basis functions

TL;DR

This paper introduces approximations of the Iterative Stockholder Analysis method using exponential basis functions, creating models that balance accuracy and efficiency for molecular electron density analysis.

Contribution

It develops new LISA variants and benchmarks their performance against existing methods on small molecules, highlighting improved computational robustness and efficiency.

Findings

LISA achieves a good balance of accuracy and efficiency.

LISA variants outperform some existing methods in robustness.

The proposed metrics effectively compare different ISA approaches.

Abstract

In this work, we introduce several approximations of the Iterative Stockholder Analysis (ISA) method based on exponential basis functions. These approximations are categorized into linear and non-linear models, referred to as LISA and NLIS, respectively. By particular choices of hyperparameters in the NLIS model, both LISA and the Minimal-Basis Iterative Stockholder (MBIS) method can be reproduced. Four LISA variants are constructed using systematically generated exponential basis functions derived from the NLIS model applied to atomic systems. The performance of these LISA variants and NLIS models is benchmarked on 15 small molecules, including neutral, anionic, and cationic species. To facilitate comparison, we propose several metrics designed to highlight differences between the methods. Our results demonstrate that LISA, employing Gaussian basis functions derived from the NLIS model on isolated atomic systems, achieves an optimal balance of computational accuracy, robustness, and efficiency, particularly in minimizing the objective function.