Hamiltonian dynamical systems model components

Molecular level computer simulations based on molecular dynamics and Monte Carlo methods have become widely used techniques in the study and modeling of aqueous systems. These simulations of water involve a few hundred to a few thousand water molecules at liquid density. Because one can form statistical mechanical averages with arbitrary precision from the generated coordinates, it is possible to calculate an exact answer. The value of a given simulation depends on the potential functions contained in the Hamiltonian for the model. The potential describing the interaction between water molecules is thus an essential component of all molecular level models of aqueous systems. 

Most microscopic theories of adsorption and desorption are based on the lattice gas model. One assumes that the surface of a sohd can be divided into two-dimensional cells, labelled i, for which one introduces microscopic variables Hi = 1 or 0, depending on whether cell i is occupied by an adsorbed gas particle or not. (The connection with magnetic systems is made by a transformation to spin variables cr, = 2n, — 1.) In its simplest form a lattice gas model is restricted to the submonolayer regime and to gas-solid systems in which the surface structure and the adsorption sites do not change as a function of coverage. To introduce the dynamics of the system one writes down a model Hamiltonian which, for the simplest system of a one-component adsorbate with one adsorption site per unit cell, is... 

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