Bridging semiempirical and ab initio QM/MM potentials by Gaussian process regression and its sparse variants for free energy simulation

Abstract

Free energy simulations that employ combined quantum mechanical and molecular mechanical (QM/MM) potentials at ab initio QM (AI) levels are computationally highly demanding. Here, we present a machine-learning-facilitated approach for obtaining AI/MM-quality free energy profiles at the cost of efficient semiempirical QM/MM (SE/MM) methods. Specifically, we use Gaussian process regression (GPR) to learn the potential energy corrections needed for an SE/MM level to match an AI/MM target along the minimum free energy path (MFEP). Force modification using gradients of the GPR potential allows us to improve configurational sampling and update the MFEP. To adaptively train our model, we further employ the sparse variational GP (SVGP) and streaming sparse GPR (SSGPR) methods, which efficiently incorporate previous sample information without significantly increasing the training data size. We applied the QM-(SS)GPR/MM method to the solution-phase SN2 Menshutkin reaction, NH3+CH3Cl→CH3NH3++Cl−, using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. For 4000 configurations sampled along the MFEP, the iteratively optimized AM1-SSGPR-4/MM model reduces the energy error in AM1/MM from 18.2 to 4.4 kcal/mol. Although not explicitly fitting forces, our method also reduces the key internal force errors from 25.5 to 11.1 kcal/mol/Å and from 30.2 to 10.3 kcal/mol/Å for the N–C and C–Cl bonds, respectively. Compared to the uncorrected simulations, the AM1-SSGPR-4/MM method lowers the predicted free energy barrier from 28.7 to 11.7 kcal/mol and decreases the reaction free energy from −12.4 to −41.9 kcal/mol, bringing these results into closer agreement with their AI/MM and experimental benchmarks.

Training machine learning potentials for reactive systems: A Colab tutorial on basic models

“…Gaussian process regression (GPR) offers an alternative approach to modeling the relationship between molecular descriptors and the potential energy surface (PES) 46–55 . The developments and applications of GPR for materials and molecules have recently been reviewed by Deringer et al 40 Below, we will provide only a brief review of the GPR formalism that is relevant to this tutorial.…”

“…In addition to being trained based on energy‐only observations y , 54 the GPR model can be influenced by including force observations in training, as demonstrated in our recent QM/MM work 55 . Because the derivatives of Gaussian processes, , are also Gaussian processes, the observation set can be extended to include a set of derivative observations 56 .…”

Perspectives on Computational Enzyme Modeling: From Mechanisms to Design and Drug Development

“…In recent years, methods such as metadynamics, − string methods, , and their variants − have emerged as valuable tools for determining the minimum free energy paths (MFEP) and the corresponding PMF values along these paths. Nonetheless, these simulation techniques must be combined with hybrid quantum mechanical and molecular mechanical (QM/MM) potentials, using both semiempirical (SE) and ab initio/density functional theory (AI/DFT) methods as QM methods, to enable bond breaking and formation. − Recent studies have also explored machine learning potentials (MLPs) employing deep learning techniques, which show great promise in speeding up calculations by using potentials that are surrogates for time-consuming QM methods, − as well as approaches that use low-level QM theories to drive the QM/MM molecular dynamics (MD) simulations while high-level QM theories are used to provide corrections to the energy on the fly , or as a posterior correction. − Alternatively, the low-level QM potentials are reparameterized to reproduce results at high-level QM theories. ,− While each approach has its own strengths and weaknessese.g., speed versus transferability in MLPs and reparameterized SE-QM modelsthe ultimate goal may be to incorporate high-level QM energies and forces directly into the simulations, e.g., by applying multiple time step approaches, to overcome the limitations of MLPs and SE-QM/MM methods without significantly increasing the overall computational cost. ,,, …”

Surface-Accelerated String Method for Locating Minimum Free Energy Paths

“…The ability to model chemical reactions in the condensed phase using molecular simulations has far-reaching implications for the study of catalysis in biological systems. , Advances in fast, accurate quantum mechanical force fields , and machine learning models − have greatly extended the scope of applications that can be routinely addressed. Nonetheless, simulations of complex reaction pathways remain computationally intensive, and the ongoing development of new methods to improve the robustness and computational cost are important.…”