Simple Molecular Dynamics Program

Consider the problem of advancing the phase space trajectory from an initial phase x. Because particle trajectories are straight between collisions, we need only find the first collision. For each pair ij, consider the time of collision hj, ignoring the presence of other particles. Introduce relative coordinates and velocities 

For particles that are approaching, require that they lie in the collision cylinder, viz., 

For periodic boundary conditions, collisions between a particle i in the primary cell and image particles can also occur. Provided a jL, a simultaneous collision of i with j and its image is impossible—we always assume this condition. Under this same condition, collisions are possible only with an image particle in a neighbor of the primary cell, i.e., for particles j at ij+vL where v has components -1, 0, or +1. We label such collision times 

Finally each particle has a time at which, in the absence of other particles, it would cross a boundary of the primary cell 

Thus a simple MD program could consist of the following steps. Given phase 

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M. Schoen, Comput. Phys. Commun., 52, 175 (1989). Structure of a Simple Molecular Dynamics Fortran Program Optimized for Cray Vector Processing Computers. 

The basis for the determination of solution conformation from NMR data lies in the determination of cross relaxation rates between pairs of protons from cross peak intensities in two-dimensional nuclear Overhauser effect (NOE) experiments. In the event that pairs of protons may be assumed to be rigidly fixed in an isotopically tumbling sphere, a simple inverse sixth power relationship between interproton distances and cross relaxation rates permits the accurate determination of distances. Determination of a sufficient number of interproton distance constraints can lead to the unambiguous determination of solution conformation, as illustrated in the early work of Kuntz, et al. (25). While distance geometry algorithms remain the basis of much structural work done today (1-4), other approaches exist. For instance, those we intend to apply here represent NMR constraints as pseudoenergies for use in molecular dynamics or molecular mechanics programs (5-9). 

The credit load for die computational chemistry laboratory course requires that the average student should be able to complete almost all of the work required for the course within die time constraint of one four-hour laboratory period per week. This constraint limits the material covered in the course. Four principal computational methods have been identified as being of primary importance in the practice of chemistry and thus in the education of chemistry students (1) Monte Carlo Methods, (2) Molecular Mechanics Methods, (3) Molecular Dynamics Simulations, and (4) Quantum Chemical Calculations. Clearly, other important topics could be added when time permits. These four methods are developed as separate units, in each case beginning with die fundamental principles including simple programming and visualization, and building to the sophisticated application of the technique to a chemical problem. 

DPD codes are usually simple modifications of molecular dynamics (MD) programs, and since this latter correlation is inconvenient for algorithms with a finite time step h, the actual random number to be used in the nth step becomes ,>( ) = Gy(t)dt. Clearly, y(n)) =0 and f (n)) =h, while... 

In the next few chapters, we present computer simulations as a natural extension of statistical mechanical theories. We detail the methodological steps and provide a clear sequence of numerical steps, algorithms and computer codes to implement Monte Carlo and molecular dynamics simulations of simple systems. The reader will also benefit from numerous program codes made freely available on this book s sourceforge project at http //sourceforge.net/projects/statthermo. In this chapter we discuss prereqvusite steps in all computer simulations. 

Here is the FORTRAN code that implements the periodic boundary conditions. This is only part of the larger programs for molecular dynamics and Monte Carlo simulations of simple monoatomic fluids with N particles. These larger programs are presented in the next two chapters. 

The molecular mechanics force helds available are AMBER95 and CFIARMM. The molecular mechanics and dynamics portion of the code is capable of performing very sophisticated calculations. This is implemented through a large number of data hies used to hold different types of information along with keywords to create, use, process, and preprocess this information. This results in having a very hexible program, but it makes the input for simple calculations unnecessarily complex. QM/MM minimization and dynamics calculations are also possible. 

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