# Determining Free Energy Differences Through Variational Morphing

## TL;DR

This paper introduces a generalized variational morphing approach for free energy calculations that improves sampling efficiency and accuracy, especially with small sample sizes, by optimizing Hamiltonian transformation sequences.

## Contribution

It develops a non-linear Hamiltonian transformation framework that enhances free energy estimation methods like BAR, extending their applicability and efficiency.

## Key findings

- Order of magnitude less sampling needed compared to traditional methods
- Sequences are optimal for both FEP and BAR methods
- Framework generalizes BAR to small samples and non-Gaussian errors

## Abstract

Free energy calculations based on atomistic Hamiltonians and sampling are key to a first principles understanding of biomolecular processes, material properties, and macromolecular chemistry. Here, we generalize the Free Energy Perturbation method and derive non-linear Hamiltonian transformation sequences for optimal sampling accuracy that differ markedly from established linear transformations. We show that our sequences are also optimal for the Bennett Acceptance Ratio (BAR) method, and our unifying framework generalizes BAR to small sampling sizes and non-Gaussian error distributions. Simulations on a Lennard-Jones gas show that an order of magnitude less sampling is required compared to established methods.