A canonical transformation method for use in molecular structure calculations is given whereby the original coordinates and momenta of the N-body system are expressed in closed form in terms of the transformed coordinates and momenta. The method is illustrated for a general N-dimensional (i) linear transformation and (ii) point transformation, in phase space. The difficulties in the generalization of this method to arbitrary canonical quantum mechanical transformations are discussed. This method is compared with that of using unitary operators, and its advantages over that method are described.

A method is developed for explicitely including the quasicontinuum, or the continuum, in N-level molecule model computations of laser-induced dissociation and chemical processes. The quasicontinuum levels are summed over, or the true continuum levels are integrated over, before the computation is performed.

A laser-driven molecular species A, represented as a two-level system, is taken to react forming a finite-level molecular species B. Criteria are developed that, when satisfied, enable this model to be approximated by a two-level molecular A system reacting to form a single-level molecular species B. Further criteria are then developed that, when satisfied, enable this model to be approximated by a two-level molecular species A with irreversible population loss.

A four-level model is solved analytically and used to show that laser induced excitation can result in population trapping in excited states under quasi-steady state conditions, even when chemical reactivity and/or dissociation occurs from higher states.

The temperature dependence of the cross section for intermolecular vibration–vibration (V–V) energy transfer processes is calculated in the distorted-wave Born approximation with a thermal average over relative velocities. The molecular elastic scattering is assumed to be dominated by a hard core from which the distorted wave functions are calculated. Different forms of the potential (Vin) responsible for the V–V energy transfer have been used in the calculation. For near resonance a positive temperature dependence of the V–V cross section is found regardless of whether Vin is an exponential function (’’short range’’) or an inverse power function 1/r5 (’’long range’’). It is demonstrated numerically that the temperature dependence is very sensitive to the magnitude of energy defect ΔE. In general, the positive temperature dependence becomes negative when ΔE becomes sufficiently large. The accuracy of various numerical approximations used in the literature is also investigated.

A model is developed for laser-induced selective low-level excitation of a molecular species which phenomenologically incorporates coherent resonant energy transfer and collision damping. The molecules are represented as harmonic oscillators, perturbed by resonant and non-resonant collisions and driven by an external monochromatic electromagnetic field (laser). The non-resonant collisions are treated as a thermal bath. The laser field is shown to be able to drive the molecules far from thermal equilibrium, even in the presence of collisions. The resonant exchange rate Omega R renormalizes the resonant condition, whereas the non-resonant collision rate Omega D causes damping.

The problem of constructing an orthogonal curvilinear coordinate system which retains the intuitive clarity of the reaction path concept is treated by canonical point transformation. The Hamiltonian describing the collision process is transformed rigorously onto the reaction-coordinate net; no linearization or approximation is employed. Difficulties inherent in earlier work (e.g., triple-valued regions, restriction to regions very close to the reaction path, etc.) do not occur. The transformed momenta and Hamiltonian are obtained in general. A simple, yet useful, example transformation is worked out in detail and applied to a realistic problem, the LEPS potential surface for H+Cl2→HCl+Cl. The example transformation is also used in a comparison of our method with that of Marcus. The canonical mapping of Connor and Marcus is shown to be a special case of the present method. Applications of the procedure to polydimensional surfaces, dissociative reactions, and actual dynamical calculations are discussed.

For a fixed nonzero energy mismatch an adiabaticity factor of the order of one is shown to be necessary for large transfer probabilities to be predicted by a previously proposed semiclassical model for V—V transfer induced by short-range forces. For zero energy mismatches, the predicted contribution can dominate traditional predictions for strongly interacting systems. A calculations purporting to invalidate this model is shown not, in fact, to do so.

V–T and V–V intermolecular potentials have been calculated within the CNDO approximation for the CO2 (asymmetric mode) –N2 system. The procedure followed was to compute the total energy of the CO2–N2 system for a variety of intermolecular separations, orientations, and normal mode displacements, and subtract the relevant isolated CO2 and isolated N2 total energies. The V–T and V–V intermolecular potentials were then obtained by fitting a second-order polynomial expansion in the normal mode displacements of both molecules to the total intermolecular energy for each intermolecular orientation and displacement. The resulting elastic potentials are much too deep. The inelastic potentials are highly orientation dependent, generally not well represented by a P2(ϑ) expansion in the relative angular orientation, and different for each specific V–T or V–V process.

V-T and V-V intermolecular potentials have been calculated in the CNDO approximation for the CO2 (asymmetric mode)-N2 system. Our procedure is to compute the CO2-N2 intermolecular potential for a variety of intermolecular separations, orientations, and normal mode displacements. For each intermolecular displacement and orientation, the elastic, V-T, and V-V intermolecular potentials are obtained by fitting a second-order polynomial expansion, in the normal mode displacement of both molecules, to the total intermolecular energy. Two specific orientations are considered: collinear and N2 perpendicular to CO2. The elastic potential is much too deep. The inelastic potentials are highly orientation dependent and different for each specific V-T or V-V process.

The self-consistent harmonic theory of lattice dynamics for a crystal whose interatomic potential includes a hard core is developed in systematic fashion by application of point-transformation methods. In order to show the essential structure of the theory without undue complication, the many-body point transform is truncated by the assumption of pairwise additivity. A flexible class of healing functions is introduced. The variational energy in terms of the harmonic-pair-density distribution is then derived, followed by the development of the self-consistent dynamical matrix. The latter is found to be of much more complicated structure than that met in the usual self-consistent harmonic theory, and a discussion of that structure is given. A comparison of the present theory with some aspects of various other methods of handling hard-core quantum crystals is given.

The contribution of an exponential and a gaussian short range force to vibration-to-vibration energy exchange is calculated in the impact parameter approximation. For near-resonant conditions, an inverse temperature dependence of the exchange probability is predicted. Estimates of selected exchange probabilities predicted by this theory are made for CoCo, HClHCl and HBrHBr. These results are in all cases greater than the predictions of SSH theory and are close to the experimental values for HCl-HCl and HBr-HBr.