Driven by the rapid development of experimental methods and technology, nano scale physics and chemistry has become more and more important and practicable to study. Monolayers of organic molecules have been studied a lot recently because of many potential applications, such as organic photovoltaic devices (OPV) or organic Liquid Electric Diodes (OLED). It is important to understand and interpret these new experimental advances. At molecular scales, Monte Carlo (MC) simulations and molecular dynamics (MD) are two important methods in computational chemistry and materials science. This dissertation will use these simulation methods along with statistical mechanical theory to study the behavior of single monolayers of organic molecules on solid surfaces.

First we give a brief introduction to two dimensional molecular systems. Different from bulk system or single molecules, 2D systems have many unique properties, and attract much experimental and theoretical research attention. Some common methods in experimental and theoretical studies are reviewed.

After introducing the properties and experimental results of ACA/Ag(111), we build a lattice gas model and run Monte Carlo simulations to help interpret the experiments.

The Pair approximation, a generalization of mean-field theory, is used to calculate the global phase diagrams and put our model into the more general class of spin-1 Ising models. The pair approximation can be used for modeling various monolayer organic molecular systems which correspond to different regions of the parameter space.

Then we studied the C60/ZnPc/Ag(111) system, using molecular dynamic simulations. The C60 molecules form unusual chain structures instead of the close packed islands seen on metal surfaces, and we try to provide a theoretical explanation.

Finally we use a density functional theory software to calculate the electronic structures of the C60/ZnPc/Ag(111) systems. This calculation predicts a 0.4e charge transfer from substrate to C60 molecule, which we believe is important for the C60 interactions on these surfaces.

In general this thesis studies the behavior of organic monolayers and bilayers on metal substrates. This basic work could help us to understand general 2-D system dynamics and electronic properties, and may help us to find new interesting systems with special properties and applications.