The demand for exploring thermodynamic and structural properties of complex fluids and their mixtures using molecular simulation methods sparks the need for efficient computational techniques. One such method is the fine-lattice discretization technique, for which these calculations can run up to two orders of magnitude faster than the off-lattice calculations. Generally, a major obstacle to simulating real systemsis the computational time required for evaluating the potential energy. In fine-lattice discretization techniques, the potentials of intermolecular interactions are calculated once at the beginning of thesimulation and are used repeatedly during the simulation. In this thesis, this technique is used along with grand canonical histogram reweighting Monte Carlo calculations to obtain the coexistence properties of various non-polar and polar real and model fluids. Moreover, mixed-field finite size scaling methods have been used to determine critical parameters of the systems studied.

New intermolecular potential models have been developed for diatomic molecules using off-lattice calculations to reproduce experimentally observed coexistence densities, vapor pressures, and critical parameters. The goal was to investigate an important problem in fine-lattice discretization technique, namely, how to build fine-lattice models reproducing properties of diatomic molecules and other systems of interest. The results reported indicate that it is possible to obtain a good description of the phase behavior of models of real systems such as nitrogen, carbon dioxide, and water over a broad range of temperatures. It has been observed that the structural properties of lattice models depend heavily on the lattice discretization parameter, which controls how closely the lattice system approaches the continuum behavior.

We have found that deviations of the critical temperatures are stronger by a factor of 5 for dipolar dumbbell model, compared to non-polar fluid models, monomers'' and dimers'' with one and two Buckingham exponential-6 sites, respectively. For the trimer model with quadrupolar interactions, the critical temperatures are less sensitive to the lattice discretization parameter.

The observed effect of the lattice discretization parameter on estimates for the thermodynamic and structural properties of fluids raises the need for a theoretical investigation. We have studied the subject analytically in one-dimensional space for a hard-core potential model and numerically for a hard-core with a square-well and a variety of logarithmic repulsive potentials. We have found that the smoothness of the repulsive part of the function is largely responsible for the speed of convergence of critical parameters to their continuum counterparts. A numerical study of the two- and three-dimensional cases is presented and the dependence of the lattice discretization parameter on the number of lattice points contained within a hard-core sphere has been investigated. The distribution of the lattice points oscillates around a limiting form for the lattice discretization parameter.