General Principles of Molecular Dynamics

An especially useful book on the topic of molecular dynamics is that by Haile.41 It does not cover polymers explicitly, but it contains a good introduction to dynamics. It is a good idea to understand the logic behind the source code that is presented. 

During a typical molecular dynamics (MD) simulation, one solves the equation of motion of all atoms in the system  

The potential energy function is the same as that employed in MM and uses the same assumptions and approximations. By employing analytical functions fit to empirical results, one obtains the total potential energy as a sum of contributing terms  

In practice, the differential equation (Equation [1]) is solved by transforming it into a difference equation employing a finite time step. The resulting time discretization error is dealt with in a number of publications.42-46 Simplification of Equation [3] is often required to expedite the calculation and therefore allow generation of longer trajectories. One approximation (for nonpolar species) is to write 

Molecular dynamics are time-consuming because the nonbonded interactions scale as n where n is the number of atoms. To save time, one may implement the united atom approach, substituting some atomistic detail with an imaginary entity that represents the essential features of what has been substituted. For example, it is common to substitute methylene groups with an imaginary spherical atom with mass 14. Therefore a polyethylene chain would look like a chain of spherical atoms, appropriately rescaled, terminated by similar entities with mass = 15 for the methyl groups. 

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