A simple random-walk method for obtaining ab initio solutions of the Schrodinger equation is examined in its application to the case of the molecular ion "+3 in the equilateral triangle configuration with side length R = 1.66 bohr. The method, which is based on the similarity of the Schrodinger equation and the diffusion equation, involves the random movement of imaginary particles (psips) in electron configuration space subject to a variable chance of multiplication or disappearance. The computation requirements for high accuracy in determining energies of "+3 are greater than those of existing LCAO-MO-SCF-CI methods. For more complex molecular systems the method may be competitive. The Schrodinger equation in imaginary time has solution at large l' of the type (5)

There has been dramatic progress in the development of electron correlation techniques for the accurate treatment of the structures and energies of molecules. In this review, we give brief and somewhat qualitative descriptions of the different methods that have been developed in recent years. We also discuss the range of applicability as well as the limitations of the methods with a few selected examples. We focus particular attention on electron correlation methods which start from a Hartree-Fock wave function since such singleconfiguration-based approaches are most easily extended to larger molecules. Multiconfiguration-based correlation techniques are considered briefly. We also present a fairly thorough account of the recent developments and applications using novel quantum Monte Carlo approaches.

Anticrossings and microwave transitions between the k (4p) 3Π u , v = 1, N = 3 and the p (4d) 3Σ+ g , v = 1, N = 5 levels of H2The random-walk method of solving the Schrodinger equation for molecular wavefunctions is extended to incorporate the effects of electron spin in several one-to four-electron systems. Improved calculation procedures reduce computation requirements for high accuracy by a factor of about 10. Results are given for the systems H 2p, Hj D3h IA'I' H2 3~:, linear equidistant H4 I~;, and Be IS.In Ref.(2) we have provided a full description of computation procedures: details of the generalization to multidimensional systems, choice of step size, control of the total number of psips by varying Vrer, evaluation of E, and so forth. For the calculations re-

The velocity distributions in molecular beams of argon produced by the Kantrowitz-Grey supersonic nozzle technique have been investigated using a time-of-flight method. It is shown that the transition from continuum to free molecular flow in free jet expansion limits the minimum width of the velocity distribution which may be obtained. The Mach number corresponding to the axial velocity distribution of the expanding gas approaches a limit which varies inversely with the two-fifths power of the Knudsen number at the nozzle. With argon at room temperature the narrowest velocity distribution obtained corresponds to a Mach number of 23 (90% of the molecules within 5.4% of the most probable velocity).

The distribution of states in the transition region is considered for chemical reactions occurring with reactants in thermal equilibrium. It is argued that when products are absent the distribution in the transition region is identical to an equilibrium distribution except that states originating from products are missing. The phenomenon is illustrated with classical trajectory calculations for three collinear systems with widely different potential energy surfaces: (a) intersecting rectangular channels of different elevation, (b) a smooth curve of parabolic cross section, and (c) a surface for the endothermic reaction H, + J---'H + HI. For purely classical reactants in an equilibrium distribution a "bobsled noneffect" is found. The use of a conversion coefficient ~ in place of the usual transmission coefficient K in transition state theory is shown to correct for the nonequilibrium distribution in the transition region. The equivalence of the combined phase space/trajectory method and the conventional trajectory method is demonstrated for the three examples.