The Calculation of Time Correlation Functions and Static Properties

The Calculation of Time Correlation Functions and Static Properties 

The preceding sections were devoted to the generation of the phase space trajectory. The goal of a molecular dynamics calculation is the evaluation of static and dynamical properties of statistical-mechanical interest. Because these evaluations often turn out to be formidable computations, we would like to make a few observations on this phase of molecular dynamics. 

In the study of dynamical properties, one usually wishes to evaluate a variety of time correlation functions. If A (t) is a real dynamical property of the system, then the time correlation function C t) is defined by an ensemble average  

For ergodic systems, the ensemble average may be replaced by an infinite-limit time integral over the phase space trajectory of a single system  

In molecular dynamics, one calculates C t) by a time average over discrete phase points  

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