Articles you may be interested inA reaction-path Hamiltonian described with quasirectilinear vibrational coordinates constructed from a nonlinear combination of curvilinear internal coordinates: FormulationWe present equations for generalized-normal-mode vibrational frequencies in reaction-path calculations based on various sets of coordinates for describing the internal motions of the system in the vicinity of a reaction path. We consider two special cases in detail as examples, in particular three-dimensional atom-diatom collisions with collinear steepest descent paths and reactions of the form CX 3 + yz .... CX 3 Y + Zwith reaction paths having e 3v symmetry. We then present numerical comparisons of the differences in harmonic reaction-path frequencies for various coordinate choices for three such systems, namely, H + H2 .... H2 + H, 0+ H2 .... OH + H, and CH 3 + H2 .... CH 4 + H. We test the importance of the differences in the harmonic frequencies for dynamics calculations by using them to compute thermal rate constants using variational transition state theory with semiclassical ground-state tunneling corrections. We present a new coordinate system for the reaction CH 3 + H2 that should allow for more accurate calculations than the Cartesian system used for previous reaction-path calculations on this and other polyatomic systems.

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Approximate partition functions are constructed from approximate quantum mechanical models of near-rigid, solidlike and nonrigid, liquidlike clusters. The Helmholtz free energies are evaluated for these clusters as functions of temperature T and cluster size N. The thermodynamic temperatures of melting, at which the free energies of the two forms are equal, match well with the melting temperatures determined from classical simulations of Ar clusters. Moreover, the effective coexistence ranges of temperature for solid- and liquidlike forms are approximately the same as the range of ‘‘supercooling’’ and ‘‘superheating’’ found in molecular dynamics computations of Ar. The surface tension is determined from an expansion of the free energy in powers of N−1/3. The concept of melting in small clusters, as a transition from a near-rigid, small-amplitude vibrator to a nonrigid molecule capable of frequent passage from one local equilibrium geometry to another, is related to the recent proposal by Stillinger and Weber of the nature of the melting transition.