Quantum and semiclassical description of a triply degenerate anharmonic oscillatorThe propagation of an initially highly excited localized wave packet in an anharmonic oscillator potenti~ is stu~ied within th~ frozen Gaussian approximation. Comparison is made to quantum mec.h~lcal basIS set ~alc~lat1ons. The frozen Gaussian approximation involves the expansion of the ID1t1al wave function 10 terms of an overcomplete Gaussian basis set. The wave function evolution is ~v.aluated by allowing eac~ Gaussian to travel along a classical trajectory with its shape held n81d. A Monte Carlo algonthm is employed in the selection of the initial Gaussian basis functions. The frozen Gaussian results are very good for times on the order of a few vibrational periods of the oscillator and remain qualitatively correct for the entire length of the calculations which is 12 vibrational periods. The dependence of the calculations on the width of the Gaussian basis functions is investigated and the effect of a simplifying approximation for the prefactor of the Gaussians is tested.

Microcanonical simulations have shown that Ar 13 clusters have sharp but unequal melting and freezing energies. Between these energies, a hot solid-like form and a cooler, liquid-like form coexist in dynamic equilibrium. Monte Carlo and isothermal molecular dynamics simulations confirm that this coexistence behavior persists under canonical conditions as well. Many properties demonstrate the solid and liquid character of the two coexisting "phases." One previous result seemed to contradict this: Quirke and Sheng evaluated nearest neighbor angular distribution function P(B); its nonzero value for B = 1T/2 at 33 K was interpreted as that of a hot solid in a "premeIting expansion." Actually, that result is the average of a bimodal distribution, one mode for the solid and the other for the liquid. The average shifts smoothly with T, and each form's P(B) changes slightly with temperature. The solid has tiny nonzero probability for 1T/2. The liquid has a minimum probability there, but far above zero. Meansquare displacements and power spectra calculated at 33 K from the Nose constant temperature molecular dynamics method exhibit properties which are clearly distinguishable and identifiable with two distinct phases, as they are under isoergic conditions. Hence our results can be added to the evidence supporting the picture for finite systems of two phases coexisting over a finite temperature and energy range.6456

Means are presented for using stationary points in two ways. One, for well-understood potentials, elucidates relations between the form of the surface and the dynamics that it supports, including the determination of the effective molecular symmetry group. The other, for potentials of uncertain quality, provides a test for unphysical characteristics and suggests how the surface might be improved if it is found to be unsatisfactory in some respect. Our approach involves comparison of transition state calculations using the slowest slide and Cerjan–Miller algorithms for two example systems: the Lennard-Jones Ar7 cluster and the Handy–Carter many-body-expansion potential for the ground state of formaldehyde.

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