A unified theoretical framework for fluctuating-charge models in atom-space and in bond-space

TL;DR

This paper presents a unified theoretical framework for fluctuating-charge models, specifically reformulating the QTPIE model in terms of atomic charges to reduce computational complexity and connect it to electrical circuit theory.

Contribution

It introduces an exact reformulation of QTPIE from bond-space to atom-space, simplifying calculations and revealing a topological framework linking charge models to circuit theory.

Findings

Reformulation reduces computational complexity of QTPIE.

Uncovers a topological framework relating charge models to electrical circuits.

Enables application of the framework to arbitrary fluctuating charge models.

Abstract

Our previously introduced QTPIE (charge transfer with polarization current equilibration) model (J. Chen and T. J. Martinez, Chem. Phys. Lett. 438, 315 (2007)) is a fluctuating-charge model with correct asymptotic behavior. Unlike most other fluctuating-charge models, QTPIE is formulated in terms of charge-transfer variables and pairwise electronegativities, not atomic charge variables and electronegativities. The pairwise character of the electronegativities in QTPIE avoids spurious charge transfer when bonds are broken. However, the increased number of variables leads to considerable computational expense and a rank-deficient set of working equations, which is numerically inconvenient. Here, we show that QTPIE can be exactly reformulated in terms of atomic charge variables, leading to a considerable reduction in computational complexity. The transformation between atomic and bond variables is generally applicable to arbitrary fluctuating charge models, and uncovers an underlying topological framework that can be used to understand the relation between fluctuating-charge models and the classical theory of electrical circuits.