Meishan Zhao

On the classical theory of the rate of isomerization of HCN

We report the results of calculations, using classical mechanics, of the rate of the isomerization reaction HCN↔CNH. The three purposes of the calculations are (i) to test whether or not the Zhao–Rice approximate version of the Davis–Gray theory provides an accurate description of the rate of isomerization when there is a large scale atomic rearrangement; (ii) to determine if the quasi‐two‐dimensional reaction path representation of dynamical evolution on a multidimensional potential energy surface preserves the major features of the phase space mappings in two dimensions that are the key features of the Davis–Gray formulation of unimolecular reaction rate theory; and (iii) to determine if the reaction path representation is useful when the energy of the system is considerably greater than that along the minimum energy path. We find that both the Zhao–Rice (ZR) and the reaction path calculations of the isomerization rate constant are in reasonable agreement with the rate constant estimated from trajectory...

Structure of the liquid-vapor interface of a metal from a simple model potential: Corresponding states of the alkali metals

We present the results of self-consistent quantum Monte Carlo simulations of the structures of the liquid-vapor interfaces of alkali metals (Na, K, Rb, Cs) using a modified semiempirical empty-core model potential. The purpose of this investigation is to simplify the analysis of inhomogeneous metals sufficiently to permit qualitative inferences to be drawn about the properties of families of metals. Both electronic and ion density profiles along the normal to the surface show oscillations in the liquid–vapor transition zone. These oscillations closely resemble those found in previous simulation studies of the liquid–vapor interfaces of alkalis, based on sophisticated nonlocal model potentials. Because of its semianalytical representation, the model potential used in this paper allows considerable simplification in the computational scheme relative to the effort involved in the previously published simulations. We find liquid Na, K, Rb, and Cs to exhibit similar surface layering. Moreover, our results sugg...

An approximate classical unimolecular reaction rate theory

We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration–rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is cal...

QUANTUM MONTE CARLO SIMULATIONS OF THE STRUCTURE IN THE LIQUID-VAPOR INTERFACE OF BIGA BINARY ALLOYS

We report the results of self-consistent quantum Monte Carlo simulations of the structure of the liquid–vapor interface of a dilute alloy of Bi in Ga. The results of the simulations are shown to be in good agreement with the results of experimental studies of the structure of the liquid–vapor interface of such an alloy reported by Lei, Huang, and Rice [J. Chem. Phys. 104, 4802 (1996), who determined the longitudinal density distribution] and by Flom et al. [Science 260, 332 (1993), who determined the transverse pair structure function].

Unimolecular fragmentation rate theory revisited: An improved classical theory

We propose a modification of the approximate classical theory of unimolecular fragmentation developed by Gray, Rice, and Davis; the important difference is the use a vibrational state dependent separatrix as the bottleneck to reaction. This version of the theory is well adapted to the description of the predissociation of van der Waals molecules, the rates of fragmentation of which are poorly described by the conventional statistical theory of unimolecular reaction. A test of the modified theory against molecular dynamics simulations of the predissociation of HeI2 reveals considerable improvement relative to the predictions of the Gray–Rice–Davis treatment. For large vibrational excitation, when intramolecular energy transfer is fast enough to not influence the predissociation rate, there is also very good agreement with the experimental data of Johnson, Wharton, and Levy. For small vibrational excitation it is necessary to explicitly account for the slow intramolecular transfer of energy in order to repr...

Comment on the rate of isomerization in molecules with a symmetric triple well potential

The classical theory of the rate of unimolecular isomerization developed by Gray and Rice, and extended by Zhao and Rice, is applied to the calculation of the rate of isomerization in model systems which have linear symmetric triple well potentials. Two of these wells define equally stable isomers A and A’; the third well, which defines a less stable intermediate B, is positioned along the reaction coordinate between A and A’. The model system also has a state C which corresponds to conformations with energies greater than the barrier energy between A and B. Both ‘‘direct’’ conversion A→C→A’ and ‘‘indirect’’ conversion A→C→B→C→A’ are allowed by the dynamics of the system. Then the rate of isomerization A→A’ depends on the extent to which the intermediate state B modifies the flow of points in the system phase space, and it is the dynamics associated with that modification which is the major point of interest in our study. We find a straightforward relationship between the areas in the Poincare surface of ...

Comment concerning the optimum control of transformations in an unbounded quantum system

We discuss the achievability of optimal control of the evolution of an unbounded quantum system by the action of external fields. Previous work has established that the evolution of a quantum system with a nondegenerate discrete and bounded spectrum of states can, in principle, be fully controlled, i.e., that the system wave function can be guided by external fields to approach arbitrarily closely a selected target state wave function. The optimal control of the evolution of a quantum system with a discrete and bounded spectrum of states has also been studied, using a method of analysis that depends on the localized character of bound state wave functions and the fact that the spectrum of states is bounded. In this paper, we examine whether it is possible to control, partially or fully, the evolution of an unbounded quantum system. We show that optimal control of the evolution of an unbounded quantum system is possible, in the sense that it is possible to minimize the difference between the product functi...

Comment on the classical theory of the rate of isomerization

The classical theory of the rate of unimolecular isomerization developed by Gray and Rice is extended in two ways. First, an improved state dependent approximation to the system separatrix is introduced. Second, a systematic approximation for the rate of intramolecular energy transfer in one isomer is introduced. These new approximations considerably improve the accuracy of the prediction of the rate of isomerization. Indeed, using the analysis described in this paper, the calculated rates of isomerization as a function of energy for the model system studied by Gray and Rice are in excellent agreement with the exact rates obtained from trajectory calculations.

Comparison of the structures of the liquid-vapor interfaces of Al, Ga, In, and Tl

We report the results of self-consistent quantum Monte Carlo simulations of the liquid-vapor interfaces of the members of the family of trivalent metals Al, Ga, In, and Tl. In each case the single particle density distribution along the normal to the liquid-vapor interface is stratified and the pair correlation function in the plane of the interface is essentially the same as that in the bulk liquid. We have examined the results of the calculations for structural similarities that hint at the existence of a corresponding states representation valid for a family of metals, such as has been shown for the family of alkali metals. The effective pair potentials of Al, Ga, In, and Tl are rather different from each other. Consequently, characterization of the interface structure using a corresponding states representation in two variables (reduced density and reduced diameter) is not accurate, unlike the case of the alkali metals for which such a characterization is accurate. Experimental data concerning the str...

The structure of the liquid-vapor interface of a gallium-tin binary alloy

We report the results of self-consistent quantum Monte Carlo simulations of the structure of the liquid-vapor interface of the alloy Sn0.09Ga0.81. Our calculations are in very good agreement with the experimental results reported by Lei, Huang and Rice [J. Chem. Phys. 107, 4051 (1997)]. In particular, our calculations confirm the experimentally inferred existence of a partial second layer of Sn below the complete outermost layer of Sn in the stratified liquid-vapor interface of this alloy.