Classical description of photodissociation

The classical picture of photodissociation closely resembles the time-dependent view. The electronic transition from the ground to the excited electronic state is assumed to take place instantaneously so that the internal coordinates and corresponding momenta of the parent molecule remain unchanged during the excitation step (vertical transition). After the molecule is promoted to the potential energy surface (PES) of the upper electronic state it starts to move subject to the classical equations 

The classical approach consists of three parts the solution of the equations of motion (5.1) in the excited electronic state with initial values Qo and Po the weighting of each set of initial values according to the distributions of coordinates and momenta in the electronic ground state before the photon is absorbed and finally the calculation of photodissociation cross sections by averaging over the phase-space. These three points will be discussed in Sections 5.1-5.3. Examples which demonstrate the usefulness and reliability of classical mechanics are presented in Section 5.4. 

---

The final application of classical S-matrix theory to be discussed is the description of photodissociation of a complex (e.g. triatomic) molecule. The completely classical description, essentially the half-collision model of Holdy, Klutz and Wilson,54 is discussed first, and then the semiclassical version of the theory is presented. A completely quantum mechanical description of the process has been developed in detail recently by Shapiro,55 The quantity of interest is the transition dipole,... 

In contrast to the subsystem representation, the adiabatic basis depends on the environmental coordinates. As such, one obtains a physically intuitive description in terms of classical trajectories along Born-Oppenheimer surfaces. A variety of systems have been studied using QCL dynamics in this basis. These include the reaction rate and the kinetic isotope effect of proton transfer in a polar condensed phase solvent and a cluster [29-33], vibrational energy relaxation of a hydrogen bonded complex in a polar liquid [34], photodissociation of F2 [35], dynamical analysis of vibrational frequency shifts in a Xe fluid [36], and the spin-boson model [37,38], which is of particular importance as exact quantum results are available for comparison. 

---