Calculation of free energy landscapes: A Histogram Reweighted Metadynamics approach

We present an efficient method for the calculation of free energy landscapes. Our approach involves a history dependent bias potential which is evaluated on a grid. The corresponding free energy landscape is constructed via a histogram reweighting procedure a posteriori. Due to the presence of the bias potential, it can be also used to accelerate rare events. In addition, the calculated free energy landscape is not restricted to the actual choice of collective variables and can in principle be extended to auxiliary variables of interest without further numerical effort. The applicability is shown for several examples. We present numerical results for the alanine dipeptide and the Met-Enkephalin in explicit solution to illustrate our approach. Furthermore we derive an empirical formula that allows the prediction of the computational cost for the ordinary metadynamics variant in comparison to our approach which is validated by a dimensionless representation.

💡 Research Summary

The paper introduces a novel algorithm called Histogram Reweighted Metadynamics (HR‑MetaD) for efficiently constructing free‑energy landscapes. Traditional metadynamics adds Gaussian bias potentials on‑the‑fly to push the system over energy barriers, but the continuous accumulation of these Gaussians leads to high computational cost and potential over‑filling, especially in high‑dimensional collective variable (CV) spaces. HR‑MetaD addresses these issues by discretizing the bias potential onto a predefined grid and updating the grid weights through an adaptive histogram reweighting scheme.

In the HR‑MetaD framework the bias potential is expressed as
(V_{\text{bias}}(s,t)=\sum_{i\in\text{grid}} w_i(t),G(s-s_i)),
where (s) denotes the set of CVs, (G) is a Gaussian kernel, (s_i) are grid points, and (w_i(t)) are time‑dependent weights. The weights are adjusted to minimize the Kullback‑Leibler divergence between the instantaneous histogram (H(s)) and a chosen target distribution (P_{\text{target}}(s)). A simple update rule, (w_i(t+\Delta t)=w_i(t)+\eta\big