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The energy spacing distribution and the transition moment distribution of highly excited vibrational states are studied by numerical solution for a model of coupled Morse oscillators with typical molecular parameters. The results show the following: (a) The transition moment distribution differs considerably from the statistical (gaussian) Porter Model, even in the régime of strong coupling. Agreement of the numerical results with the statistical model improves for states that increasingly approach the dissociation limit (b) A much improved statistical model for the transition moment distribution can be constructed, using certain empirical statistical properties of the wavefunctions involved. (c) For states differing substantially in energy, the relevant transition moment distribution exhibits an energy gap dependence. (d) The energy spacing distribution for states in a small range of energies obeys the Brody form g(ω)∞ωβ exp [ - αω1+β]. β increases systematically with the energy of the states, with the distribution increasingly approaching the Wigner model. A significant difference between the two distributions persists even near dissociation.

The dynamics of vibrational relaxation in polyatomic van der Waals clusters is investigated theoretically, using as an example a one-dimensional model of I2(Ne)N with excited I2 vibration. The method employed is classical dynamics simplified by the time-dependent self-consistent-field (TDSCF) approximation. The dependence of the relaxation on cluster size is examined, with calculations for N = 4, 8, 16 and with extrapolation to N → ∞ representing I2 in a solid Ne matrix. Also studied is the variation of the relaxation mechanism with initial vibrational state v, in the range v = 25-60. The main results are: (i) Relaxation can be interpreted best as affected by collisions between I2 and neighbouring Ne atoms. Collective modes do not, in most cases, play a significant role in the relaxation. (ii) The I2 centre-of-mass vibration plays a less significant role than the Ne atoms in the redistribution of the released vibrational energy in the cluster. (iii) The initial relaxation rate decreases with cluster size, the lifetime of v = 28 being τ = 3·6 ps for N = 4 and τ = 51 ps for N = 8. This is due to decreasing frequency of impulsive I2-Ne 'collisions' in the larger clusters. (iv) Initial relaxation behaviour and rates for the N = 16 cluster appear converged to those of the corresponding solid matrix. (v) relaxation dynamics switches from weak to strong coupling-type behaviour as v increases from 35 to 60.

The extension to polyatomic molecules of the RKR procedure for inversion of ro-vibrational spectra to deduce the intramolecular potential surface depends on solving the semiclassical quantization problem for coupled modes. The semiclassical self-consistent field theory (SC-SCF) proposed recently provides an approximate method for solving the coupled mode problem, and thereby provides a means to extend RKR. We derive a closed-form, convenient expression for the inversion transform that constructs directly the potential surface from the spectral data. The inversion should be valid in the region (well below the quasi-continuum) for which SC-SCF holds. We test the method for a model problem of two coupled modes, and find that it works very well. For practical inversions, difficulties in assignment or in obtaining the requisite number of frequencies might occur; nevertheless, the extended RKR is direct, non-iterative, and potentially useful.

A semiclassical approximation is given for off-shell T-matrix elements for collisions between systems with internal degrees of freedom. The derivation is based on the approaches of Miller and Marcus to semiclassical dynamics and the result generalizes an expression given by Korsch for off-shell T-elements for potential scattering, obtained from the WKB approximation. The approximation proposed provides a simple physical interpretation for the off-shell quantities and can be calculated by practical methods. The result has potential applications to various multiple collision problems and especially to calculations of collision-induced dissociation of polyatomic molecules.

A two-step direct inversion method is described for the determination of non-adiabatic interactions from the corresponding inelastic atom-atom scattering data. In the first step the S-matrix elements are extracted as a function of the angular momentum from the measured inelastic differential cross-section. The second step recovers the interaction function from the S-matrix. The two steps are tested independently for a two-state model of He+/Ne, using numerically simulated data calculated from an assumed interaction potential. Both steps are found to be of very good accuracy, and the interaction function is reproduced to within a few per cent.

A study is made of phonon-assisted transitions between closely spaced librational levels of an impurity molecule in a host crystal. The contributions to librational relaxation of direct, of Orbach-type and of Raman processes are evaluated as a function of temperature. It is found for a model case of NH(3π) in solid Ar, that below T = 16 K, the direct process dominates, while for T > 20 K relaxation takes place mainly by the Raman mechanisms. The calculation predicts a nanosecond time scale for the relaxation at 4 K, and a picosecond time-scale for the relaxation at T = 24 K.

Structural instabilities in molecular clusters have been observed in several recent classical simulations. They arise from changes in the dynamical interactions among the vibrational modes as energy increases and are entirely unrelated to vibrationally-induced instabilities of Jahn-Teller type. We show that the self-consistent field (SCF) approximation for vibrations provides a simple predictive model for such instabilities, in which the onset of instability is shown to arise from changes in the effective (mean) potential acting on each mode, as the total energy changes. Exact classical dynamics was used to test the SCF prediction for a simple two-mode model, with the result that the instability onset is correctly predicted by the SCF approximation. We comment on the relevance of these mean potentials for characterizing related phase transitions in clusters.

The lifetimes of rotationally-mediated resonances in the scattering of HD from a flat Ag surface are calculated by the quantum-mechanical complex rotation method and by classical trajectories. Qualitatively, considerable similarity is found between the quantum and the classical descriptions of the nature of the trapped states and of the mechanism of their decay. Quantitatively, quantum lifetimes are shorter than the corresponding classical values by as much as a factor of 4 to 7. Several interesting properties of the resonance states and trends associated with the lifetimes are observed, and simple physical interpretations offered.

The optical-potential method (OPM) developed in the previous paper is applied to the calculation of a large manifold of transitions of the type v = 1, j, mj → v' = 0, j', mj in Li + N2 collisions. Trends related to the dependence of the cross section σv,j,mj→v',j',mj on the states j, j' and mj are observed and analysed in terms of the physical effects involved. An information-theoretic model of the cross sections is tested as a means for a simple parametric representation of the results.

An optical-potential method is developed for the calculation of cross sections for vib-rotational transitions in atom-molecule collisions. In this framework the multi-channel scattering equations are replaced by a pair of coupled equations for each vib-rotational transition. The effect of the large manifold of open rotational channels is introduced through an optical potential in each of the coupled equations. Both a phenomenological (trial function) procedure and a theoretical approximate method for obtaining the optical potentials are given. The method remains computationally feasible even in systems with very many open channels.To test the method, the cross section for the 10→00 transition in He + H2, He + D2, He + T2 was calculated over a wide range of energies and compared with results in the literature. An interesting scaling property is observed to hold with respect to the energy dependence of the above cross sections.

In molecular encounters, the total energy of the system may not be sufficient to enable any but the ground-state electronic surface to determine nuclear motions adiabatically. When this happens, non-adiabatic transitions are energetically forbidden.It is shown that for such collisions the phase shifts computed in the adiabatic approximation are lower bounds to the exact phase shifts.The proof derives from a study of the non-local potential which arises when the exact collision problem is transformed so as to involve only nuclear motion explicitly. Use is made of a well-known relation between magnitudes of effective potentials and of phase shifts associated with two respective hamiltonians [1, 2 (b)].This result is related to a theorem by Hahn et al. [2 (a]. The similarities and differences between the two are discussed.