[Paper Review] Molecular-orbital-based Machine Learning for Open-shell and Multi-reference Systems with Kernel Addition Gaussian Process Regression

Lixue Cheng, Jiace Sun+3 more|arXiv (Cornell University)|Jul 17, 2022

Machine Learning in Materials Science64 references4 citations

TL;DR

This paper introduces kernel addition Gaussian process regression (KA-GPR) within molecular-orbital-based machine learning (MOB-ML) to predict total correlation energies for both closed-shell and open-shell systems with multi-reference character, achieving chemical accuracy (1 kcal/mol) using only one training structure for small radicals and enabling accurate potential energy surfaces and large-scale benchmark predictions beyond DFT levels.

ABSTRACT

We introduce a novel machine learning strategy, kernel addition Gaussian process regression (KA-GPR), in molecular-orbital-based machine learning (MOB-ML) to learn the total correlation energies of general electronic structure theories for closed- and open-shell systems by introducing a machine learning strategy. The learning efficiency of MOB-ML (KA-GPR) is the same as the original MOB-ML method for the smallest criegee molecule, which is a closed-shell molecule with multi-reference characters. In addition, the prediction accuracies of different small free radicals could reach the chemical accuracy of 1 kcal/mol by training on one example structure. Accurate potential energy surfaces for the H10 chain (closed-shell) and water OH bond dissociation (open-shell) could also be generated by MOB-ML (KA-GPR). To explore the breadth of chemical systems that KA-GPR can describe, we further apply MOB-ML to accurately predict the large benchmark datasets for closed- (QM9, QM7b-T, GDB-13-T) and open-shell (QMSpin) molecules.

Motivation & Objective

• To extend molecular-orbital-based machine learning (MOB-ML) to open-shell and strongly-correlated systems with multi-reference character.
• To develop a machine learning framework capable of learning total correlation energies directly, without pair-wise decomposition.
• To achieve chemical accuracy (1 kcal/mol) for open-shell radicals and complex systems like the H10 chain and water bond dissociation.
• To enable accurate prediction of large benchmark datasets including QM9, QM7b-T, GDB-13-T, and QMSpin for both closed- and open-shell molecules.
• To demonstrate transferability and robustness of the method across diverse chemical systems, including challenging carbene and radical species.

Proposed method

• KA-GPR is introduced as a kernel addition strategy to enhance Gaussian process regression in MOB-ML, enabling direct learning of total correlation energies from molecular-orbital features.
• MOB-ML features are derived from Hartree-Fock orbitals and used to represent electron correlation contributions via spin-orbital pairs.
• The method uses Nesbet's theorem to express correlation energy as a sum over occupied spin-orbital pairs, with ML models trained on these contributions.
• Kernel addition in GPR allows for improved regression performance by incorporating structured prior knowledge into the covariance function.
• The approach is applied to MRCI-based correlation energies, enabling accurate learning of post-Hartree-Fock energies at Hartree-Fock computational cost.
• Multi-GPU implementation of the algorithm ensures scalability for large datasets like QMSpin and GDB-13-T.

Experimental results

Research questions

• RQ1 Can KA-GPR in MOB-ML achieve chemical accuracy (1 kcal/mol) for open-shell radicals with minimal training data, such as one example structure?
• RQ2 How well can MOB-ML (KA-GPR) predict potential energy surfaces for strongly correlated systems like the H10 chain and water bond dissociation?
• RQ3 Can the method generalize across different molecular datasets, including QM9, QM7b-T, GDB-13-T, and QMSpin, while maintaining high accuracy?
• RQ4 What is the performance of MOB-ML (KA-GPR) in predicting spin gap energies for open-shell systems, particularly in the QMSpin dataset?
• RQ5 Does the KA-GPR framework preserve transferability when applied to larger molecular spaces, such as predicting GDB-13-T energies from QM7b-T-trained models?

Key findings

• MOB-ML (KA-GPR) achieved chemical accuracy (1 kcal/mol) for nine small radicals using only one training structure, demonstrating high data efficiency.
• The method predicted the water OH bond dissociation curve with near-exact accuracy, matching high-level reference data.
• For the H10 chain, MOB-ML (KA-GPR) generated an accurate potential energy surface for the strongly correlated system.
• On the QMSpin dataset, the MAE for total singlet and triplet energies was 0.623 kcal/mol and 1.120 kcal/mol, respectively, with the spin gap predictions reaching chemical accuracy.
• The method outperformed SpookyNet on the QMSpin dataset, achieving an MAE of 0.872 kcal/mol compared to SpookyNet’s 1.57 kcal/mol with larger training data.
• Despite high accuracy, transferability of absolute total energies from QM7b-T to GDB-13-T was significantly reduced, indicating domain shift challenges.