OPES (On-the-fly Probability Enhanced Sampling)

## Overview

The OPES module contains the implementation of the on-the-fly probability enhanced sampling mehtod (OPES) [66] [67].

The OPES method aims at sampling a given target distribution over the configuration space, $$p^{\text{tg}}(\mathbf{x})$$, different from the equilibrium Boltzmann distribution, $$P(\mathbf{x})\propto e^{-\beta U(\mathbf{x})}$$. To do so, it incrementally builds a bias potential $$V(\mathbf{x})$$, by estimating on-the-fly the needed probability distributions:

$V(\mathbf{x}) = -\frac{1}{\beta}\log\frac{p^{\text{tg}}(\mathbf{x})}{P(\mathbf{x})}\, .$

The bias quickly becomes quasi-static and the desired properties, such as the free energy, can be calculated with a simple reweighting REWEIGHT_BIAS.

Depending on the kind of target distribution one wishes to sample, different OPES biases can be used.

## Installation

This module is not installed by default. Add '--enable-modules=opes' to your './configure' command when building PLUMED to enable these features. See also List of modules.

## Usage

The OPES module contains three bias actions, OPES_METAD and OPES_METAD_EXPLORE that sample metadynamics-like target distributions (e.g. the well-tempered one), and OPES_EXPANDED that samples expanded ensembles target distributions (replica-exchange-like). It also contains various expansion collective variables (ECVs) to define such expanded targets.