Centroid molecular dynamics functions

Abstract The theoretical basis for the quantum time evolution of path integral centroid variables is described, as weU as the motivation for using these variables to study condensed phase quantum dynamics. The equihbrium centroid distribution is shown to be a well-defined distribution function in the canonical ensemble. A quantum mechanical quasi-density operator (QDO) can then be associated with each value of the distribution so that, upon the application of rigorous quantum mechanics, it can be used to provide an exact definition of both static and dynamical centroid variables. Various properties of the dynamical centroid variables can thus be defined and explored. Importantly, this perspective shows that the centroid constraint on the imaginary time paths introduces a non-stationarity in the equihbrium ensemble. This, in turn, can be proven to yield information on the correlations of spontaneous dynamical fluctuations. This exact formalism also leads to a derivation of Centroid Molecular Dynamics, as well as the basis for systematic improvements of that theory. 

Following Fey nman s original work, several authors pmsued extensions of the effective potential idea to construct variational approximations for the quantum partition function (see, e g., Refs. 7,8). The importance of the path centroid variable in quantum activated rate processes was also explored and revealed, which gave rise to path integral quantum transition state theory and even more general approaches. The Centroid Molecular Dynamics (CMD) method for quantum dynamics simulation was also formulated. In the CMD method, the position centroid evolves classically on the efiective centroid potential. Various analysis and numerical tests for realistic systems have shown that CMD captures the main quantum effects for several processes in condensed matter such as transport phenomena. 

General Time Correlation Functions Centroid Molecular Dynamics Method... 

In a path-integral Monte Carlo (PIMC) calculation, the centroid force can readily be calculated from Eq. (3.64) by using the importance sampling function exp[-5p(q,. . . , qp) h] and pairwise MC moves to enforce the centroid constraint. For a path-integral molecular dynamics (PIMD) calculation [71], one defines fictitious momenta p, for each of the quasiparticles q and then runs an MD simulation with Hamilton s... 

Although the complete atomistic simulation of ensembles of mesogenic molecules is within reach of present computational facilities, the traditional treatment of liquid crystals in molecular dynamics or Monte Carlo simulations makes use of the Gay-Berne potential, an ingenious computational machine whose aspects deserve to be described here for their epistemological implications. An ordinary Lennard-Jones (LJ) potential, equation 4.38 or 4.40, can be written as a function of the distance between two particles, /Jy, the well depth e and the equilibrium separation a. An ellipsoidal object is identified by the position of its centroid and by an orientation unit vector u, and the Gay-Berne (GB) potential is a modified U that takes into account the anisotropy of the ellipsoid, both in energy and equilibrium separation ... 

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