UC Irvine

The projects comprising my thesis lie in the area of quantum statistical mechanics, and are in line with the Mandelshtam group’s broad goals of developing new approaches for computing thermodynamic and dynamic properties of classical and quantum many-body systems, improving existing methods, and demonstrating their utility and efficiency on systems of chemical interest. My research has been particularly involved with the implementation and ongoing development of variational approaches which exploit the tractability of Gaussian functions and their well-known properties. In this thesis I describe what I believe to be my most important research accomplishments.

In my first project, I combined the variational Gaussian wavepacket (VGW) approximation with Gibbs ensemble Monte Carlo to compute the equation of state for a quantum Lennard-Jones liquid as a function of temperature and quantum-character, providing data which enables one to describe a large variety of real liquids that could be mapped to a Lennard-Jones model. After performing Lennard-Jones parameter optimization for neon, the results were found to be in excellent agreement with experimental data. With this work we demonstrated the efficiency of VGW, and highlighted its advantages over path integral-based approaches.

My subsequent projects have been based on the implementation, ongoing development, and evaluation of the self-consistent phonons (SCP) method. Based on the Gibbs-Bogoliubov inequality, SCP yields an effective, temperature-dependent harmonic Hamiltonian which minimizes the Helmholtz free energy. In the SCP framework, the best approximation for the effective temperature-dependent harmonic Hamiltonian is obtained by solving iteratively a system of coupled nonlinear equations in a self-consistent fashion. While the method itself is not new, I succeeded in reducing the overall computational cost of the method by several orders of magnitude by incorporating quasi-Monte Carlo integration in place of standard Monte Carlo integration, thereby making it practical for general many-body quantum systems. The newfound utility of this method has been demonstrated by computing a wide array of properties, such as vibrational frequencies and free energies, for polycyclic aromatic hydrocarbons, Lennard-Jones clusters, and water clusters.