Monomeric machine learning potential for general covalent molecules: linear alkanes as an example

TL;DR

This paper extends the MB-PIPNet framework to covalently bonded molecular systems by employing a fragmentation-based, monomer-level energy decomposition in combination with permutationally invariant polynomial descriptors. The total energy is expressed as $E_{ ext{total}} = \sum_i E_i$, where each monomer energy $E_i$ is predicted from descriptors that encode both intramonomer structure and inter-monomer environment, enabling efficient two-body interactions within a fragmentation scheme. Through a proof-of-concept on linear alkanes (C$_{14}$H$_{30}$), MB-PIPNet achieves competitive accuracy with MB-PES while delivering substantial computational efficiency, outperforming DeePMD in combined energy and force evaluations. The results include torsional profiles, harmonic frequencies, and vibrational spectra from MD, demonstrating robust transferability and potential applicability to larger covalent systems and condensed phases, with future work aimed at refining PIP bases and incorporating equivariant architectures.

Abstract

Machine-learning potentials (MLPs) have become important tools for modern molecular simulations. However, developing models that simultaneously achieve high accuracy and high computational efficiency remains a significant challenge. In this work, we extend the recently proposed MB-PIPNet framework to general covalently bonded molecular systems by combining monomer-based energy decomposition, permutationally invariant polynomial (PIP) descriptors, and neural networks within a fragmentation-based strategy. Within this framework, the total potential energy is represented as a sum of effective monomeric contributions, where PIPs provide compact and chemically motivated descriptions of both monomer internal structures and their local chemical environments. As a proof-of-concept application, we apply the MB-PIPNet framework to linear alkanes, using n-Tetradecane as a representative system, and benchmark its performance against established atomistic machine-learning models. The resulting MB-PIPNet potential accurately reproduces reference ab initio electronic energies and reliably captures key molecular properties, including torsional potential energy profiles, harmonic vibrational frequencies, and vibrational power spectra obtained from molecular dynamics simulations. Importantly, MB-PIPNet demonstrates a substantial advantage in computational efficiency over other MLP models for combined energy and force evaluations. These results establish MB-PIPNet as a scalable and efficient framework for constructing MLPs, providing an additional route for large-scale quantum and classical simulations of complex molecular systems.

Figures (8)

• Figure 1: a) Global minimum structure of the alkane C14H30, with carbon atoms numbered. b) Schematic of the MB-PIPNet architecture with the example of linear alkane.
• Figure 2: Distribution of potential energies relative to the global minimum of C14H30, the end-to-end carbon distance ($R_{\text{ee}}$), and the root-mean-square deviation (RMSD) with respect to the global-minimum structure for both the training (a-c) and test sets (d-f) respectively.
• Figure 3: Correlation plots of the energies for C14H30 from the MB-PIPNet PES and direct DFT B3LYP calculations.
• Figure 4: Four selected structures from the data set
• Figure 5: Torsional potential energy curves for (a) methyl rotation about the C13–C14 bond and (b) ethyl rotation about the C12–C13 bond of the global-minimum structure of C14H30. Carbon atoms are labeled sequentially as C1–C14 along the alkane chain, starting from one terminal end.