A test of the dependence of an optimal control field on the number of molecular degrees of freedom: HCN isomerization

This paper reports the results of a study of the robustness of the field re quired to generate the isomerization reaction HCN --> CNH as a function of number of degrees of freedom and the complexity of the description of the d ynamics. The particular reduced state representation of the control process that is tested in this paper is the reaction path method proposed by Zhao and Rice. We show that if the description of the system dynamics includes v ibrational motions perpendicular to the one-dimensional reaction path and b oth the interactions between those vibrations and between them and the reac tion path, the fields found by the conventional computational scheme repres ent local optima, and none of these correspond to generating a transfer of 100% of the population from the ground vibrational state of HCN to a mixtur e of vibrational states of CNH. Moreover, it is very difficult to find fiel ds that will efficiently transfer population from the ground vibrational st ate of HCN to particular vibrational states of CNH. Comparing the optimized control fields reported in this paper with those previously obtained using simplified versions of the reaction path reduction, one finds that the com plexity (measured by the power spectra) of optimal control fields increases as the dynamical description includes more degrees of freedom and then the interactions between all of the degrees of freedom. The optimal control fi eld generated using a simpler dynamical description is not a good guide to the optimal control field associated with a more complex dynamical descript ion. We conclude that the reaction path method of reduction of the complexi ty of calculation of the optimal field required to drive a particular react ion is not likely to be useful for the design of fields with which to activ ely control reactions of polyatomic molecules. (C) 2000 American Institute of Physics. [S0021-9606(00)02140-1].