I. Harold Zimmerman

Quantum mechanical study of electronic transitions in collinear atom—diatom collisions☆

Abstract Quantum mechanical calculations are reported for model, nonreactive, collinear collision systems composed of the H 2 diatom and the halogen atom X = F, Cl, Br or I. The model involves two electronic potential energy surfaces, obtained in a diatomics-in-molecules formulation, that correspond asymptotically to the two spin-orbit states of X. On each surface the calculations include as many vibrational states of H 2 as are asymptotically allowed, up to a limiting number of five. The first two collision systems, FH 2 and ClH 2 , are characterized by electronic splittings much smaller than any vibrational spacing included in the diatom spectrum, and as a result they show a high degree of vibrational elasticity with essentially all transition activity testricted to spin—orbit switching in the halogen. This pattern is broken for BrH 2 collisions, where the near-equality between electronic and vibrational quanta apparently leads to a resonant exchange of energy between the two modes. The greater spinorbit splitting in iodine (∼ 2 vibrational quanta) results in largely elastic behavior in IH 2 collisions for both vibrational and electronic transitions. A modified Massey criterion is exhibited for some of the FH 2 and BrH 2 transitions.

Quantum mechanical theory of molecular collisions in a laser field

The effect of a radiation field on (ion)atom–(di)atom collision systems is considered. A detailed derivation is presented for the modified coupled equations that result from adding the field to the coupled channel formalism for nonreactive collisions. A discussion of the coherent state in this context concludes that the number state representation of the field offers a more convenient basis for defining probability channels in the combined system, but that further research on the applicability of the coherent state in more approximate treatments of the system should be carried out. An example of the general formalism is worked out for collinear Br+H2 collisions in the presence of the field, and calculated results are presented. Comparison is made with the results obtained from a vibronic (resonance) model.

The vibronic representation for collinear atom–diatom collisions: Two‐state semiclassical model

A unique semiclassical description of atom–diatom collisions is presented in which the vibrational as well as the electronic motion is treated quantum mechanically. The electronic Hamiltonian and the vibrational nuclear kinetic energy operator are diagonalized to yield vibronic potential energy curves, each correlating asymptotically to a specific electronic and vibrational state of the colliding species. The vibronic curves are used in Stueckelberg‐like calculations to yield individual S‐matrix elements. This theory is applied to a collinear nonreactive model of X+H2 collisions in which X is either F or Br. S‐matrix elements are calculated for transitions between the 2P3/2 and 2P1/2 spin–orbit states of the halogen and vibrational states of H2. The results are in very good agreement with rigorous quantum results.

Semiclassical theory of electronic transitions in molecular collisions: Combined effects of tunneling and energetically inaccessible electronic states

The semiclassical theory of collision‐induced electronic transitions is extended to describe tunneling and the effect of energetically inaccessible states. The powerful technique of analytic continuation is utilized to yield very good agreement with exact quantum mechanical results on some model systems. The inaccessible states have a significant effect on transmission coefficients and thus can be important in semiclassical studies of molecular reactions.

Numerical comparison between electronically adiabatic and diabatic representations for collinear atom--diatom collisions

Within the framework of quantum coupled‐channel calculations on nonreactive atom–diatom collision systems involving two electronic potential surfaces, we test the electronically adiabatic representation obtained within the diatomics‐in‐molecules approximation against a similarly derived diabatic representation. The testing is numerical, with a view toward establishing computational advantages of one representation over the other with regard to (a) convergence of computed probability as the diatomic molecular basis is expanded; (b) convergence with respect to the starting position of the numerical integration; (c) convergence with respect to the distance between stabilizations; and (d) convergence with respect to the integration steplength. The adiabatic representation shows definite advantages in tests (a) and (b), but they are not sufficient to offset the much more rapid execution time possible with the diabatic basis. The significance of these results is discussed.

Optical potential calculations for molecular collisions

Abstract The Feshbach optical formalism is applied to elastic, nonreactive atom-diatom scattering on a single potential energy surface. The optical potential depends on GQ, the resolvent of E-QHQ, where Q projects onto open as well as closed channels. A method for generating GQ is developed which goes beyond the free-space approximation by partitioning the radial part of the intermolecular separation into a set of intervals, on each of which the projected interaction QVQ is represented by a constant diagonal form. The resulting GQ is used in calculations on a model collinear system. The calculations are carried out with various approximations on the full nonlocal optical potential equation for Pψ Emphasis is placed on two of these, one of which is characterized by a local homogeneous equation for Pψ, and the other by a local inhomogeneous equation for Pψ.

Semiclassical approach to collision-induced emission in the presence of intense laser radiation: An aspect in the study of cooperative chemical and optical pumping☆

Abstract Collion-induced emission in molecular systems in an intense laser field is studied using the semiclassical approach, with a view towards cooperative chemical and optical pumping in laser production. The formalism is developed with the electronic-field representation, which treats collision and radiative interaction on the same footing. Electronic-field surfaces can be regarded as forming spectra for spontaneous emission; and particular emission events can be accounted for by propagating classical trajectories on emission electronic-field surfaces. Pre-emission loss from the excited state is dealt with by propagating classical trajectories on a loss surface along a complex contour of emission branch points. This loss surface is derived on the basis of localized radiative couplings between electronic-field states and provides a framework to treat the general problem of discrete state-continuum interactions. The formalism is applied to a two-state, collinear exponential model to compute S -matrix elements and transition probabilities between asymptotic states.

Radiative transitions for molecular collisions in an intense laser field

Quantum mechanical and semiclassical approaches are discussed for the study of molecular collisions in an intense laser field. Both a coherent state and Fock state representation of the photon field are investigated. The collision dynamics is described in terms of transitions between two electronic-field potential energy surfaces, where each surface depends on the field-free adiabatic surfaces and electric dipole transition matrix elements as functions of nuclear coordinates. The electronic-field surfaces exhibit avoided crossings (on the real axis) due to the radiative coupling at the resonance nuclear configurations, and other parts of these surfaces are similar to the field-free adiabatic surfaces with one of them shifted by ħω for single photon processes. Metastable states, formed at some collision energies, are conjectured to occur in the field, although absent from the field-free case. From a spectroscopic point of view, changes in energy spectra are expected from those of the individual collision-free species. Numerical results are presented for the collinear collision process Br(2P3/2)+ H2(v= 0)+ħω→ Br(2P1/2)+ H2(v= 0).

A quantum-mechanical method for calculating level widths and shifts, applicable to type I unimolecular predissociation

A quantum mechanical approach to type I unimolecular predissociation is developed in terms of Feshbachs optical potential. The resulting method is formally applicable to many cases of molecular breakup caused by the crossing of coupled bound and dissociative electronic surfaces. These include cases in which multiple bound and/or dissociative channels are accessible. There are two restrictions : (1) coupling among dissociative channels should be negligible, and (2) only two product fragments are allowed, of fixed atomic composition regardless of internal state. A harmonic oscillator coupled to a dissociative infinite-step or hard-sphere potential is used in comparing the usual perturbation theory results to the present approach.

Generalized semiclassical optical model and velocity-dependent potentials

A procedure is developed for the construction of a complex potential in a generalized semiclassical optical model for molecular collisions involving internal nuclear degrees of freedom. The procedure involves a local approximation on the exact quantum optical potential, which is an integral operator over an energy-dependent, non-local kernel. The resulting potential for the model is velocity-dependent. The classical limit of transition amplitudes is obtained from complex-valued classical trajectories whose equations of motion are derived with this potential. The potential contains coordinate integrals over the kernel, and various approximations for the kernel are discussed. Sample calculations are carried out for collinear atom-diatom collisions.