COHERENT CONTROL OF BIMOLECULAR PROCESSES

Here E, q, n ) denotes the incoming scattering solutions associated with the product in state E, q1, n 0), and Vq is the component of the total potential that vanishes as the A to B distance becomes arbitrarily large. The cross section for scattering into arrangement q, independent of the product internal state n, is then 

Note that Eqs. (7.2) to (7.4) describe motion in the center-of-mass coordinate system, that is, they arise in scattering theory after separating out the motion of the center of mass of A-B, a feature discussed in greater detail in Section 7.1. 

Control of bimolecular collisions is achieved by constructing an initial state E, q, am ) composed of a superposition of N energetically degenerate asymptotic states E, q, m 0)  

Note that Eq. (7.6), and hence Eq. (7.7), are of a standard coherent control form, is, direct contributions from each individual member of the superposition, prop. 

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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]. 

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