Nested sampling in the canonical ensemble: Direct calculation of the partition function from NVT trajectories
The Journal of Chemical Physics 139 (12): 124104 (September 2013)

Nested sampling has emerged as a powerful sampling technique to directly compute the partition function of a realistic molecular system. However, it does so with a non-standard sampling of phase space, which excludes the use of molecular dynamics simulations. Here we show how to use the standard canonical (NVT) sampling of phase space to directly compute the partition function. There are two components to the nested NVT sampling procedure. First, the temperatures at which the simulations should be run are chosen sequentially, from high to low, based on a histogram reweighting strategy. Second, a harmonic umbrella biasing potential is added, where necessary, to enhance the sampling. We also show how to evaluate the expectation value of an observable and compute the free energy as a function of an order parameter. NVT sampling procedures are common and readily available in conventional Monte Carlo and molecular dynamics codes. The proposed algorithm is easy to integrate into existing codes, which opens up the nested sampling technique to a wide audience.
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