Corrections to the quasiharmonic approximation for evaluating molecular entropies

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Abstract
Molecular dynamics and Monte Carlo simulations are now being used to analyze thermodynamic problems in chemical and biochemical systems. The evaluation of entropies requires, in principle, the calculation of partition functions which are difficult to compute accurately from simulations. One approach involves the approximation of the partition function by a multivariate Gaussian with coefficients evaluted from the simulation—the so-called quasiharmonic approximation. In this paper we show that the quasiharmonic approximation is the leading term in a series expansion of the configurational distribution function in its moments. We derive the formula for the cubic correction to the quasiharmonic entropy and apply it to two model systems. The exact entropies are calculated for comparison with the approximate results. We also show how the quasiharmonic model can be used as a reference system for the evaluation of molecular entropies using importance sampling methods. Importance sampling with the quasiharmonic reference appears to be a very promising approach for evaluating the entropy of macromolecules from computer simulations.