
Characterization of anharmonicities on complex potential energy surfaces:Perturbation theory and simulationFlorent Calvo, Jonathan P. K. Doye and David J. WalesJ. Chem. Phys. 115, 96279636 (2001)AbstractWe have systematically investigated the effect of anharmonicity on the equilibrium properties of systems with a complex potential energy surface (PES). Anharmonicities are modeled by the temperature dependence of the harmonic frequencies nu^{(i)} near a stationary point of the PES. The lowtemperature behavior is described by a simple thermal expansion nu^{(i)}_{beta}=nu^{(i)}_{0} [1alpha^{(i)}_{1}/beta+alpha^{(i)}_{2}/2beta^{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 LennardJones system of 32 particles, in both the solid and the liquid states. We also determine the anharmonic frequencies from reversiblescaling 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 pathintegral Monte Carlo calculations.The full paper is available from JCP Online. 