This thesis deals with the application of path integrals to statistical mechanics and the development of a molecular pseudopotential theory.

The first part, which is the core of this thesis, summarizes the implementation and application of path integrals to various model systems. After a brief introduction to path integrals, I present a double proton transfer study on DNA base pair models. The next chapter describes an ab initio path integral (AIPI) study of ambient water near the complete basis set limit using discrete variable representation (DVR) functions. The combined AIPI/DVR approach is expected to clarify a controversy surrounding one recent AIPI study that predicts overstructuring of liquid water when nuclear effects are included. Chapter 4 describes the implementation of free energy methods in path integral molecular dynamics to investigate the isotope effect and transformations in the potential. Chapter 5 presents a comparative study of the centroid and ring polymer molecular dynamics methods for approximating quantum time correlation functions.

The second part discusses our ongoing work of formulating a theory for molecular pseudopotentials. This new formalism aims to describe rigorously the interaction between the quantum-mechanical and molecular mechanics regions using First Principles.