Hybrid Path Integral Monte Carlo/Molecular Dynamics Approach for the Simulation of Rigid Rotating and Translating Molecules

Abstract

The path integral formulation of quantum statistical mechanics [1] is widely used for formulating the partition function and diverse thermodynamic properties. The basic objective of this thesis is to present the benchmark calculations and develop new methods to study the quantum rotating and translating system. Prior to the development of a new method, we perform benchmark calculations on newly implemented Path Integral Monte Carlo code in the Molecular Modelling Toolkit software package [2] against exact diagonalization calculation on Hydrogen Fluoride in an electric field. An energy convergence study proved the validity of the new integrated Path Integral Monte Carlo code within statistical error. Then, we benchmark our PIMC code against the direct Classical Monte Carlo (dCMC) calculations to study the interacting quantum rotors at finite temperature. Then, the application of the direct Classical Monte Carlo code for a 1D water chain system at different temperature and various lattice spacing is performed. Two phase transitions and three specific phase regions have been observed from the calculations.

Then, we combine our well-established Path Integral Molecular Dynamics code [3, 4] with the Path Integral Monte Carlo code to develop a novel hybrid Path Integral Molecular Dynamics/Path Integral Monte Carlo program for quantum system simulation including rotation and translation. This proposed methodology is successfully benchmarked for CO 2 He system at a large tau region. The second Path Integral Monte Carlo methodology introduces a cluster-update algorithm applying on quantum rotational system. This methodology has been previously applied to lattice spin system [5, 6] and hard sphere continuum system [7]. This is the first time to discuss and develop a cluster-update method on quantum rotors. A primary cluster-update Path Integral Monte Carlo algorithm and related test is presented. The preliminary results for the test of Hydrogen Fluoride molecules with dipole-dipole interaction shows an existing problem within our code, and the problem is fully discussed in this thesis for future study. Overall, this thesis focuses on the development of new methodologies to study quantum molecules. Noted that all methodologies require more tests and benchmark calculations to prove its validity. In spite of that, this discussion of a novel methodology and application will lead to an exciting further study.