Classical many particle simulator

While at the National Resource for Computation in Chemistry, I have developed a general classical simulation program, called, CLAMPS (for classical many particle simulator)(5) capable of performing MC and MD simulations of arbitrary mixtures of single atoms. The potential energy of a configuration of N atoms at positions R = (r, ..., r and with chemical species aj,..., o is assumed to be a pairwise sum of spherically symmetric functions. 

Molecular dynamics, in contrast to MC simulations, is a typical model in which hydrodynamic effects are incorporated in the behavior of polymer solutions and may be properly accounted for. In the so-called nonequilibrium molecular dynamics method [54], Newton s equations of a (classical) many-particle problem are iteratively solved whereby quantities of both macroscopic and microscopic interest are expressed in terms of the configurational quantities such as the space coordinates or velocities of all particles. In addition, shear flow may be imposed by the homogeneous shear flow algorithm of Evans [56]. 

Recent years have seen the extensive application of computer simulation techniques to the study of condensed phases of matter. The two techniques of major importance are the Monte Carlo method and the method of molecular dynamics. Monte Carlo methods are ways of evaluating the partition function of a many-particle system through sampling the multidimensional integral that defines it, and can be used only for the study of equilibrium quantities such as thermodynamic properties and average local structure. Molecular dynamics methods solve Newton s classical equations of motion for a system of particles placed in a box with periodic boundary conditions, and can be used to study both equilibrium and nonequilibrium properties such as time correlation functions. 

The crunch comes when trying to analyse non-classical many-electron systems by the same procedure. The mathematics to solve the many-body differential equation does not exist. The popular alternative is to consider each electron as an individual particle and to describe an n-electron system by a probability density in 3n-dimensional configuration space. The use of complex variables is tacitly avoided. The result is a procedure that pretends to simulate a non-classical problem by a classical model, with an unnecessary complicated structure, designed to resemble quantum formalism. In this case, the statistical model that works for an ideal gas fails to explain the behavior of a many-electron wave. 

The statistical analysis required for real systems is no different in conception from the treatment of the hypothetical two-state system. The elementary particles from which the properties of macroscopic aggregates may be derived by mechanical simulation, could be chemical atoms or molecules, or they may be electrons and atomic nuclei. Depending on the nature of the particles their behaviour could best be described in terms of either classical or quantum mechanics. The statistical mechanics of classical and quantum systems may have many features in common, but equally pronounced differences exist. The two schemes are therefore discussed separately here, starting with the simpler classical sytems. 

Computer simulations of many-body systems have nearly as long history as the modem computers. [1] Along with the rapid development in the computer technology, the molecular computer simulations and particularly the classical Molecular Dynamics (MD) methods, treating the atoms and the molecules as classical particles, have developed in the last three decades to an important discipline to obtain information about thermod)mamics, stmcture and dynamical properties in condensed matter from pure simple liquids to studies of complex biomolecular systems in solution. [2]... 

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