Breakthrough accuracy in semi-empirical quantum chemistry via deep learning

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In the HIPNN+SEQM model, the hierarchical interacting-particle neural network passes molecular configuration input features through on-site layers (red blocks) and then shares this information through continuous message-passing layers (green blocks) to generate Hamiltonian parameters based on a molecular configuration. These parameters are used in a semi-empirical Hamiltonian to solve the Schrödinger equation and predict atomic properties.

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Semi-empirical electronic Hamiltonians have nearly 30 years of successful history modeling chemistry processes such as photon absorption and chemical reactivity. However, they have always suffered from limited accuracy and generalizability due to the use of static parameters fit to limited datasets. New research from Los Alamos National Laboratory published in the Proceedings of the National Academy of Sciences uses a machine learning model to dynamically reparametrize semi-empirical Hamiltonians. Allowing physically interpretable model parameters to be adjusted according to the local chemical environment both significantly increases the model accuracy and enables new ways of interpreting results produced by machine learning models. This new paradigm of physics-informed machine learning seeks to revolutionize the way machine learning models are applied to physics problems.

The hierarchical interacting-particle neural network, or HIPNN architecture, is a message-passing neural network for use on atomistic systems. HIPNN takes the molecular configuration as input, where each molecule is represented as a set of atom types and positions. The input features are passed through on-site layers, which are applied to the local features for each individual atom. Then this information is shared through continuous message-passing layers, which pass information between nearby atoms and allow atoms to see their chemical environments. An inference layer is applied to the output from each of the last on-site layers to obtain zero- to higher-order corrections of Parametric Method 3 Hamiltonian parameters.

The Hamiltonian parameters are fed into the semi-empirical quantum mechanics (SEQM) module, which uses the self-consistent field procedure to solve the motion of electrons in the current molecular configuration. The solution of this problem provides full quantum information including wavefunctions, charge distributions, molecular energy and atomic forces. The properties predicted by the combined HIPNN+SEQM model generally outperform both traditional SEQM and neural network results. This new type of machine learning model will facilitate the accurate solution of complex electronic structure problems, such as excited state and open shell systems.

This work represents a significant development in both machine learning models and semi-empirical quantum mechanics. While most machine learning models are “black box” methods, the HIPNN+SEQM model provides additional physical insight through the parameters predicted by the neural network. Interestingly, the neural network assigns different values to atomic Hamiltonian parameters based on traditional views of atomic bonding. If an atom forms a triple bond with a neighbor, it has a significantly different p-orbital energy parameter than if it forms a double or only single bonds.

This new class of machine learning enhanced semi-empirical quantum mechanics models will enable increasingly accurate theoretical studies of chemical reactivity, photo-absorption, excited state dynamics, polaritonics and other related phenomena. These applications are critical to the Los Alamos National Laboratory mission, either through the simulation of reactive molecules or simulating future organic photovoltaic systems critical to national energy security.

Funding and mission

This work was funded by the Laboratory Directed Research and Development program and supports the Energy Security mission area and the Materials for the Future capability pillar.

Reference

“Deep learning of dynamically responsive chemical Hamiltonians with semiempirical quantum mechanics,” Proceedings of the National Academy of Sciences, 119, 27, e2120333119 (2022); DOI: 10.1073/pnas.2120333119. Authors: Guoqing Zhou, Nicholas Lubbers, Kipton Barros, Sergei Tretiak and Benjamin Nebgen (Los Alamos National Laboratory).

Technical Contacts: Benjamin Nebgen, Kipton Barros, Sergei Tretiak (T-1)

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The combined HIPNN+SEQM model (d) makes significantly more accurate predictions than either the pure neural network (c) or SEQM (a, b) models.