Abstract

The sampling problem lies at the heart of atomistic simulations and over the years many different enhanced sampling methods have been suggested towards its solution. These methods are often grouped into two broad families. On the one hand methods such as umbrella sampling and metadynamics that build a bias potential based on few order parameters or collective variables. On the other hand, tempering methods such as replica exchange that combine different thermodynamic ensembles in one single expanded ensemble. We instead adopt a unifying perspective, focusing on the target probability distribution sampled by the different methods. This allows us to introduce a new class of collective-variables-based bias potentials that can be used to sample any of the expanded ensembles normally sampled via replica exchange. We also provide a practical implementation, by properly adapting the iterative scheme of the recently developed on-the-fly probability enhanced sampling method [Invernizzi and Parrinello, J. Phys. Chem. Lett. 11.7 (2020)], which was originally introduced for metadynamics-like sampling. The resulting method is very general and can be used to achieve different types of enhanced sampling. It is also reliable and simple to use, since it presents only few and robust external parameters and has a straightforward reweighting scheme. Furthermore, it can be used with any number of parallel replicas. We show the versatility of our approach with applications to multicanonical and multithermal-multibaric simulations, thermodynamic integration, umbrella sampling, and combinations thereof.

Highlights

  • Sampling is one of the main challenges in atomistic simulations

  • The sampling problem lies at the heart of atomistic simulations and over the years many different enhanced sampling methods have been suggested toward its solution

  • We provide a practical implementation by properly adapting the iterative scheme of the recently developed on-the-fly probability enhanced sampling method [M

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Summary

INTRODUCTION

Sampling is one of the main challenges in atomistic simulations. even the most accurate models cannot produce high-quality results if the phase space is not properly sampled. The sampling issue is due to the large gap between the physical macroscopic timescales and the actual time that can be explored in standard atomistic simulations This results in an ergodicity problem that can be encountered in fields as varied as materials science, chemistry, and biology. Instead of extracting configurations from the relevant physical ensemble, these methods create an ad hoc modified ensemble in which the probability of sampling rare events is greatly enhanced One kind of such target ensembles is obtained by combining multiple subensembles that differ only by the temperature or some other quantity, a typical example being parallel tempering [1]. Can provide the same type of enhanced sampling, but presents in most cases a faster convergence and has only few and robust adjustable parameters These properties of OPES are retained when it is applied to sample expanded ensembles. VI) enhanced sampling based on an order parameter, both alone and in combination with the previous ensembles

UNIFIED APPROACH
ON-THE-FLY PROBABILITY ENHANCED SAMPLING
TARGETING EXPANDED ENSEMBLES
PλðxÞ: λ ð3Þ
Iterative OPES scheme
Reweighting
LINEARLY EXPANDED ENSEMBLES
Multicanonical ensemble
Multithermal-multibaric ensemble
Thermodynamic integration
BEYOND LINEARITY
Combining thermodynamic and order parameter expansions
ABOUT THE OPTIMAL TARGET DISTRIBUTION
VIII. CONCLUSION
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