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Accelerated Computation of Free Energy Profile at Ab Initio QM/MM Accuracy via a Semi-Empirical Reference-Potential. III. Gaussian Smoothing on Density-of-States

preprint
submitted on 20.07.2020 and posted on 29.07.2020 by Wenxin Hu, Pengfei Li, Jia-Ning Wang, Yuanfei Xue, Yan Mo, Jun Zheng, Xiaoliang Pan, Yihan Shao, Ye Mei
Calculations of free energy profile, aka potential of mean force (PMF), along a chosen collective variable (CV) are now routinely applied to the studies of chemical processes, such as enzymatic reactions and chemical reactions in condensed phases. However, if the ab initio QM/MM level of accuracy is required for the PMF, it can be formidably expensive even with the most advanced enhanced sampling methods, such as umbrella sampling. To ameliorate this difficulty, we developed a novel method for the computation of free energy profile based on the reference-potential method recently, in which a low-level reference Hamiltonian is employed for phase space sampling and the free energy profile can be corrected to the level of interest (the target Hamiltonian) by energy reweighting in a nonparametric way. However, when the reference Hamiltonian is very different from the target Hamiltonian, the calculated ensemble averages, including the PMF, often suffer from numerical instability, which mainly comes from the overestimation of the density-of-states (DoS) in the low-energy region. Stochastic samplings of these low-energy configurations are rare events. If a low-energy configuration has been sampled with a small sample size N, the probability of visiting this energy region is ~ 1/N (shall be exactly 1/N for a single ensemble), which can be orders-of-magnitude larger than the actual DoS. In this work, an assumption of Gaussian distribution is applied to the DoS in each CV bin, and the weight of each configuration is rescaled according to the accumulated DoS. The results show that this smoothing process can remarkably reduce the ruggedness of the PMF and increase the reliability of the reference-potential method.

Funding

National Natural Science Foundation of China No. 21773066

Fundamental Research Funds for the Central Universities

National Natural Science Foundation of China No. 21973030

National Institutes of Health No. R01GM135392

History

Email Address of Submitting Author

ymei@phy.ecnu.edu.cn

Institution

State Key Laboratory of Precision Spectroscopy, East China Normal University

Country

China

ORCID For Submitting Author

0000-0002-3953-8508

Declaration of Conflict of Interest

no conflict of interests

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