Photodissociation theory

The review is divided into two major parts. The first deals with photodissociation theory and the second, with reactive scattering methods. 

The first part of the review deals with aspects of photodissociation theory and the second, with reactive scattering theory. Three appendix sections are devoted to important technical details of photodissociation theory, namely, the detailed form of the parity-adapted body-fixed scattering wavefunction needed to analyze the asymptotic wavefunction in photodissociation theory, the definition of the initial wavepacket in photodissociation theory and its relationship to the initial bound-state wavepacket, and finally the theory of differential state-specific photo-fragmentation cross sections. Many of the details developed in these appendix sections are also relevant to the theory of reactive scattering. 

Photodissociation theory is in principle much simpler than reactive scattering theory. This is because only three values of the total angular momentum are involved in a photodissociation process while reactive scattering requires a summation over a very large number of total angular momentum quantum numbers. 

The first part of the chapter deals with aspects of photodissociation theory and the second with reactive scattering theory. Key topics covered in the chapter are the anal sis of the wavepacket in the exit channel to ield product (piantuin state distributions, photofragmentation T matrix elements, state-to-state S matrices and the real wavepacket method, which we have applied only to reactive scattering calculations. 

Detailed discussions of photodissociation theory " and its application to van der Waals molecules have been given elsewhere. Here we will concentrate on a brief presentation of the essential elements of the theory and on a discussion of the different approximations which are commonly invoked. 

Pack R T 1976 Simple theory of diffuse vibrational structure in continuous UV spectra of polyatomic molecules. I. Collinear photodissociation of symmetric triatomics J. Chem. Phys. 65 4765... 

Harris A L, Berg M and Harris C B 1986 Studies of chemical reactivity in the condensed phase. I. The dynamics of iodine photodissociation and recombination on a picosecond time scale and comparison to theories for chemical reactions in solution J. Chem. Phys. 84 788... 

For two Bom-Oppenlieimer surfaces (the ground state and a single electronic excited state), the total photodissociation cross section for the system to absorb a photon of energy ai, given that it is initially at a state x) with energy can be shown, by simple application of second-order perturbation theory, to be [89]... 

Detailed reaction dynamics not only require that reagents be simple but also that these remain isolated from random external perturbations. Theory can accommodate that condition easily. Experiments have used one of three strategies. (/) Molecules ia a gas at low pressure can be taken to be isolated for the short time between coUisions. Unimolecular reactions such as photodissociation or isomerization iaduced by photon absorption can sometimes be studied between coUisions. (2) Molecular beams can be produced so that motion is not random. Molecules have a nonzero velocity ia one direction and almost zero velocity ia perpendicular directions. Not only does this reduce coUisions, it also aUows bimolecular iateractions to be studied ia intersecting beams and iacreases the detail with which unimolecular processes that can be studied, because beams facUitate dozens of refined measurement techniques. (J) Means have been found to trap molecules, isolate them, and keep them motionless at a predetermined position ia space (11). Thus far, effort has been directed toward just manipulating the molecules, but the future is bright for exploiting the isolated molecules for kinetic and dynamic studies. 

The problem of controlling the outcome of photodissociation processes has been considered by many authors [63, 79-87]. The basic theory is derived in detail in Appendix B. Our set objective in this application is to maximize the flux of dissociation products in a chosen exit channel or final quantum state. The theory differs from that set out in Appendix A in that the final state is a continuum or dissociative state and that there is a continuous range of possible energies (i.e., quantum states) available to the system. The equations derived for this case are... 

This chapter has provided a brief overview of the application of optimal control theory to the control of molecular processes. It has addressed only the theoretical aspects and approaches to the topic and has not covered the many successful experimental applications [33, 37, 164-183], arising especially from the closed-loop approach of Rabitz [32]. The basic formulae have been presented and carefully derived in Section II and Appendix A, respectively. The theory required for application to photodissociation and unimolecular dissociation processes is also discussed in Section II, while the new equations needed in this connection are derived in Appendix B. An exciting related area of coherent control which has not been treated in this review is that of the control of bimolecular chemical reactions, in which both initial and final states are continuum scattering states [7, 14, 27-29, 184-188]. 

This chapter deals with the theory underlying the apphcation of wavepackets to molecular photodissociation and reactive scattering. The objective will be to derive and gather together the equations and theoretical methods needed in such calculations. No attempt will be made to reference aU calculations that have been undertaken in this very popular field. Several alternative related methods will be discussed, but it will not be possible to do full justice to all the different methods that have been proposed, many of which are being successfully used. 

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