Development and application of phase-space overlap measures for free-energy calculations
We present intuitive concepts and develop methods to improve free-energy calculations performed in molecular simulations. Accuracy of the calculations is emphasized, and bias-detection heuristics are proposed to enable identification of inaccuracies in free-energy calculations. The concept of phase-space overlap plays a central role in the analysis and methods. The important phase space of a system is the set of configurations that are relevant to its properties, and the overlap of the important regions of two systems relates to the difficulty of calculating free energy differences between them. The difficulties originate from two barriers: an energetic barrier that arises when the phase spaces exhibit a partial - or non-overlap relation, and an entropic barrier that arises when they exhibit a subset relation. We propose metrics to quantify the overlap, and provide a basis for predicting the likelihood of bias in free-energy calculations of a specified length. The quantification metrics, total energy distribution , overlap integral and relative entropy , categorize systems into different types that need to be treated with different free-energy methods. This leads to development of a very effective fail-safe bias-detection scheme which identifies the presence of bias for any work-based free-energy calculation. With the guidance of the overlap measures, staging methods are formulated appropriately for each type of overlap relation. The strategy for effective staging is to construct a phase-space subset between each pair of intermediate stages, and direct the perturbation from superset to subset for reliable and accurate results. Another aspect to understand free-energy calculation is through work distributions, upon which we develop a neglected-tail bias model that accurately predicts the bias for both small and large sampling cases. The developments stem from free-energy perturbation calculations and have been extended to more generalized work-based methods. Applications given in this work are restricted to simple model systems ( harmonic multi-oscillator and discrete two-state models ) and simple real fluids (Lennard-Jones fluid, water model and an ion-charging system). However, we expect that the value of this work is not restricted by these limitations and can be further extended to density-of-state free-energy methods and more complicated applications.