Development and implementation of atomic/molecular simulation methods based on nested sampling

Atomic/molecular simulation continues to grow as a supplement to, and in some cases a replacement for, experimental studies. As such, there is an increasing need to develop new simulation methods that can overcome the deficiencies of existing methods, including an ever increasing demand for more robust and efficient simulation methods.;This dissertation focuses on developing and implementing new atomic/molecular simulation methods based on the Nested Sampling framework. The methods based on Nested Sampling perform well in the vicinity of phase transitions, and in many cases can outperform existing methods in both efficiency and robustness.;We begin by developing an isobaric Nested Sampling scheme. This athermal scheme makes a single top down sweep of the isobaric phase space, from which the isothermal-isobaric partition function can be computed for essentially any temperature. We show that the method effectively handles isobaric phase transitions and is more efficient than parallel tempering for the test cases examined. We then continue to explore the use of the Nested Sampling framework for free energy calculations. The Nested Sampling Monte Carlo method we have developed can be used to compute the relative free energy between systems governed by different Hamiltonian functions. We show that the method outperforms Widom's test particle insertion method at high density, while avoiding problems of the end point catastrophe on the reference side. We also show that this method effectively handles phase transitions, and can used to compute system properties as a function of a Hamiltonian-scaling factor. Lastly, we explore a Nested Sampling Monte Carlo framework for grand canonical ensemble calculations. We develop the theory for an athermal and a thermal approach. The athermal approach is similar to the isobaric Nested Sampling scheme, and can be used to compute the Grand Canonical partition function. However, we show that the athermal approach is theoretically flawed. Initial test cases demonstrate that the error may be small, and suggest that additional modifications may restore the validity of the approach. The thermal approach to Nested Sampling in the grand canonical case is based on our relative free energy Nested Sampling scheme, and could be used to compute the relative grand canonical free energy. The thermal approach could also be used to compute system properties as a function of chemical potential. Although we believe this approach is theoretically sound, we have yet to test the approach, and we suspect there may be some practical issues surrounding the sampling.