Characterization of anharmonicities on complex potential energy surfaces: Perturbation theory and simulation

We have systematically investigated the effect of anharmonicity on the equilibrium properties of systems with a complex potential energy surface. Anharmonicities are modeled by the temperature dependence of the harmonic frequencies {nu (i)} near a stationary point of the PES. The low-temperature behavior is described by a simple thermal expansion nu ((i))(beta)=nu ((i))(0)[1-alpha ((i))(1)/beta+alpha ((i))(2)/2 beta (2)+.], where the coefficients {alpha ((i))(j)} are obtained from perturbation theory. Using a simple diagrammatic representation, we give the complete expressions for the first two coefficients alpha (1) and alpha (2) in terms of derivatives of the potential. This approach is illustrated for the example of a bulk Lennard-Jones system of 32 particles, in both the solid and the liquid states. We also determine the anharmonic frequencies from reversible-scaling Monte Carlo simulations, which appear particularly well suited to this problem. As an example, we have studied a model biopolymer that exhibits significant first and second order anharmonicities. To show the importance of treating anharmonicities properly, we have calculated the caloric curve (heat capacity) of the quantum Ne-13 cluster in both the classical and quantum regimes. For this calculation we have used a superposition approximation and exact anharmonic classical corrections to second order in perturbation theory. When every vibrational mode of each inherent structure is treated separately, we find good agreement between our results and previous quantum Monte Carlo calculations. (C) 2001 American Institute of Physics.