Computing free energies using nested sampling-based approaches

Nested sampling (NS) has emerged as a powerful statistical mechanical sampling technique to compute the partition function of atomic and molecular systems. From the partition function all thermodynamic quantities can be calculated in absolute terms, including absolute free energies and entropies. In this article, we provide a brief overview of NS within a Bayesian context, as well as overviews of how NS is used to compute the partition functions and thermodynamic quantities in the canonical and isothermal-isobaric ensembles. Then we introduce a new scheme, Coupling Parameter Path Nested Sampling, to estimate the free energy difference between two systems with different potential energy functions. The method uses a NS simulation to traverse the same path through phase space as would be covered in traditional coupling parameter-based methods such as thermodynamic integration and perturbation approaches. We demonstrate the new method with two case studies and confirm its accuracy by comparison to conventional methods, including Widom test particle insertion and thermodynamic integration. The proposed method provides a powerful alternative to traditional coupling parameter-based free energy simulation methods.