Some applications of centroid molecular dynamics

There has been extensive development of algorithms for carrying out CMD simulations in realistic systems,as well as a number ofnon-trivial applications of the methodology (see, e g.. Ref. 17). In this section, a few illustrative applications will be described. The interested reader is referred to the above citations for more details on CMD algorithms and applications. 

Tests of CMD on simple one-dimensional systems can be carried out by calculating the symmetrized position correlation function  

In the perspective of the centroid time evolution, this correlation fimction cannot be calculated directly but is obtained through the following relation between the Fourier transforms  

The centroid distribution function and the effective potential for the CMD simulation can be obtained through the path integral simulation method, but 

Natural units were used in these simulations, where m = = ku = 1. The sampling of the initial position and momentum centroids were made through the Nose-Hoover chain dynamics (NHC) on the effective potential of Van, More details of these calculations can again be found in Ref. 10. 

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