Machine Learning Facilitated Quantum Mechanic/Molecular Mechanic Free Energy Simulations

Abstract

Bridging the accuracy of ab initio (AI) QM/MM with the efficiency of semi-empirical (SE) QM/MM methods has long been a goal in computational chemistry. This dissertation presents four ∆-Machine learning schemes aimed at achieving this objective. Firstly, the incorporation of negative force observations into the Gaussian process regression (GPR) model, resulting in GPR with derivative observations, demonstrates the remarkable capability to attain high-quality potential energy surfaces, accurate Cartesian force descriptions, and reliable free energy profiles using a training set of just 80 points. Secondly, the adaptation of the sparse streaming GPR algorithm showcases the potential of memory retention from previous phasespace, enabling energy-only models to converge using simple descriptors while faithfully reproducing high-quality potential energy surfaces and accurate free energy profiles. Thirdly, the utilization of GPR with atomic environmental vectors as input features proves effective in enhancing both potential energy surface and free energy description. Furthermore, incorporating derivative information on solute atoms further improves the accuracy of force predictions on molecular mechanical (MM) atoms, addressing discrepancies arising from QM/MM interaction energies between the target and base levels of theory. Finally, a comprehensive comparison of three distinct GPR schemes, namely GAP, GPR with an average kernel, and GPR with a system-specific sum kernel, is conducted to evaluate the impact of permutational invariance and atomistic learning on the model’s quality. Additionally, this dissertation introduces the adaptation of the GAP method to be compatible with the sparse variational Gaussian processes scheme and the streaming sparse GPR scheme, enhancing their efficiency and applicability. Through these four ∆-Machine learning schemes, this dissertation makes significant contributions to the field of computational chemistry, advancing the quest for accurate potential energy surfaces, reliable force descriptions, and informative free energy profiles in QM/MM simulations.