Abstract
We introduce and explore an approach for constructing force fields for small molecules, which combines intuitive low body order empirical force field terms with the concepts of data driven statistical fits of recent machine learned potentials. We bring these two key ideas together to bridge the gap between established empirical force fields that have a high degree of transferability on the one hand, and the machine learned potentials that are systematically improvable and can converge to very high accuracy, on the other. Our framework extends the atomic permutationally invariant polynomials (aPIP) developed for elemental materials in (2019 Mach. Learn.: Sci. Technol. 1 015004) to molecular systems. The body order decomposition allows us to keep the dimensionality of each term low, while the use of an iterative fitting scheme as well as regularisation procedures improve the extrapolation outside the training set. We investigate aPIP force fields with up to generalised 4-body terms, and examine the performance on a set of small organic molecules. We achieve a high level of accuracy when fitting individual molecules, comparable to those of the many-body machine learned force fields. Fitted to a combined training set of short linear alkanes, the accuracy of the aPIP force field still significantly exceeds what can be expected from classical empirical force fields, while retaining reasonable transferability to both configurations far from the training set and to new molecules.
Highlights
Molecular mechanics (MM) with classical empirical force fields has been used to perform simulations of organic molecules for many decades [1, 2]
We introduce a way of making force fields for molecules that has the transferability and reasonable extrapolation property, due to limited body order, of empirical force fields, and the accuracy of the recent machine learning (ML) models, due to its systematic nature
Each term in the total energy expression (1) is expanded as a linear combination of the basis functions defined in (3) and we are left with the determination of the coefficients which will be described in Section II B
Summary
Molecular mechanics (MM) with classical empirical force fields has been used to perform simulations of organic molecules for many decades [1, 2]. One of the principle reasons why such force fields have been so successful is that the simplicity of their functional form results in both a low body order and relatively few fitting parameters. Improvements were made in the description of both the intermolecular interactions, through the construction of polarizable models [3], and the intramolecular interactions, mainly with the development of Class II force fields [4,5,6] that introduced new couplings between bond and angle terms. The aim of this paper is to bridge this formalism gap, and to seek answers to questions such as: what makes the ML models accurate, is it their high dimensionality (i.e. body order) or their flexible functional form? How much additional accuracy is gained by allowing a controlled increase in body order?
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