| Accurate quantum mechanical partition functions and absolute free energies are determined using realistic potential energy surfaces for temperatures ranging from 300 K to 2400 K by using Monte Carlo path integral calculations with a new, efficient polyatomic importance sampling method. This method will be used to calculate partition functions at a significantly lower computational cost than conventional Schrodinger-based methods. The systems studied include systems with low-frequency torsional modes (H2O2, HOOD, D2O2, H18OOH, H2 18O2, D18OOH, and H18OOD). The path centroids are sampled in Jacobi coordinates via a set of independent ziggurat schemes. The calculations employ enhanced-same-path extrapolation of trapezoidal Trotter Fourier path integrals, which are constructed using fast Fourier sine transforms. Importance sampling will also be used in Fourier coefficient space, and adaptively optimized stratified sampling is used in configuration space. The free energy values obtained from the path integral calculations are compared to separable-mode approximations, to the Pitzer-Gwinn approximation, to several hindered-rotor methods, and to available values in thermodynamic tables. Isotope effects are also considered.; Chapter 1 is an introduction to path integrals; it contains a brief discussion of their use in dynamics and a more extensive look at their use in statistical mechanics. This chapter also explores various path integral statistical mechanical methods for determining partition functions. Chapter 2 presents the first work on calculating an accurate vibrational-rotational partition function for a four-atom system, H2O2, based on a new Monte Carlo path integral technique. These results are compared to experiment and to the popular harmonic-oscillator and Pitzer-Gwinn methods as well as comparing the classical and quantum mechanical methods for the rotational partition function including the symmetric approximation. Chapter 3 explores the path integral partition function values of six of the isotopologs of H2O 2 (HOOD, D2O2, H18OOH, H 18O2, D18OOH, and H18OOD) and examines the harmonic-oscillator and Pitzer-Gwinn methods. The isotope effects are also presented. Chapter 4 examines various hindered rotor methods for determining the vibrational partition function when applied to H 2O2 and the six isotopologs and compares those results to the accurate Monte Carlo path integral results first presented in chapters 2 and 3. |
