Toward Improving Multiple Time Step QM/MM Simulations with Δ‑Machine Learning

Semiempirical methods
are popular for QM/MM simulations of chemical
reactions in the condensed phase due to their immense speedup compared
to higher-level ab initio or density functional theory
(DFT) methods but can be much less accurate depending on the system
of interest. Multiple time step (MTS) methods can improve the accuracy
of semiempirical QM/MM simulations by using higher-level calculations
at less frequent outer time steps, yet accurate results and efficient
sampling require the low- and high-level methods to be sufficiently
similar. In this work, we show the limitations of standard semiempirical
methods (e.g., AM1) for MTS applications. In a condensed-phase reaction
of proton transfer from water to methyl phosphate, for which DFT (B3LYP)
is used as the high-level method, we can only reach an outer time
step of 4, even with the stochastic isokinetic thermostat. We then
explore the value of employing Δ-machine learning to enhance
the efficiency of MTS QM/MM simulations. As an initial step, we train
neural network potentials and Δ-learning corrections to the
AM1 method for the corresponding gas-phase reaction. We show that
Δ-corrections outperform ML potentials and that the amount of
training data has a major impact on the accuracy and transferability
of the learned correction. In a gas-phase MTS simulation with appropriate
machine-learned Δ-corrections, we can reach an outer integration
frequency of 25 for a nearly exact result compared to B3LYP and 30
if we accept an error of 0.3 kcal·mol–1 for
the free energy profile. The study validates and provides guidance
to Δ-learning based MTS simulations, setting the stage for future
development and realistic applications in the condensed phase.