Perturbation theory semiclassical method

Purely quantum studies of the fully coupled anharmonic (and sometimes nonrigid) rovibrational state densities have also been obtained with a variety of methods. The simplest to implement are spectroscopic perturbation theory based studies [121, 122, 124]. Related semiclassical perturbation treatments have been described by Miller and coworkers [172-174]. Vibrational self-consistent field (SCF) plus configuration interaction (Cl) calculations [175, 176] provide another useful alternative, for which interesting illustrative results have been presented by Christoffel and Bowman for the H + CO2 reaction [123] and by Isaacson for the H2 + OH reaction [121]. The MULTIMODE code provides a general procedure for implementing such SCF-CI calculations [177]. Numerous studies of the state densities for triatomic molecules have also been presented. 

The models for the control processes start with the Schrodinger equation for the molecule in interaction with a laser field that is treated either as a classical or as a quantized electromagnetic field. In Section II we describe the Floquet formalism, and we show how it can be used to establish the relation between the semiclassical model and a quantized representation that allows us to describe explicitly the exchange of photons. The molecule in interaction with the photon field is described by a time-independent Floquet Hamiltonian, which is essentially equivalent to the time-dependent semiclassical Hamiltonian. The analysis of the effect of the coupling with the field can thus be done by methods of stationary perturbation theory, instead of the time-dependent one used in the semiclassical description. In Section III we describe an approach to perturbation theory that is based on applying unitary transformations that simplify the problem. The method is an iterative construction of unitary transformations that reduce the size of the coupling terms. This procedure allows us to detect in a simple way dynamical or field induced resonances—that is, resonances that... 

To determine the H2O semiclassical vibrational eigenstates using the vibrational part of the molecular Hamiltonian, a second order classical perturbation theory method was used. This relates the vibrational energy to the three good constants of the motion Jjj2> the vibrational good actions. These actions... 

The most accurate method for multilevel curve crossing problems is, of course, to solve the close-coupling differential equations numerically. This is not the subject here, however instead, we discuss the applications of the two-state semiclassical theory and the diagrammatic technique. With these tools we can deal with various problems such as inelastic scattering, elastic scattering with resonance, photon impact process, and perturbed bound state in a unified way. The overall scattering matrix 5, for instance, can be defined as... 

The second method follows the semiclassical perturbation approach to dispersion theory. However, it recognizes from the outset that the polarizabilities must be complex quantities and that electronic absorption bands are not shaped like 6 functions. This second approach has been carried through with an attempt at making allowances for the fact that E =t= E. However, as might be anticipated, the most general form of the expressions achieved by this method cannot be utilized until some specific assumption is made about E. ... 

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