Controlling quantum wavepacket motion in reduced-dimensional spaces: reaction path analysis in optimal control of HCN isomerization

Abstract

We report the results of a theoretical study of control of the dynamics of the reaction HCNCNH. We introduce the objectives of the theory of optimal control of molecular dynamics and argue that the calculation of the optimal field is very complicated for systems with more than a few degrees of freedom. To make this theory applicable to real systems, a control strategy using an alternative Hamiltonian is described. The reaction path Hamiltonian has the same dimensionality as does the actual system, but leads to a reduced dimensionality treatment that considers the steepest descent path on the potential energy surface as the most representative of the possible paths. The coupling of the reaction path to the other degrees of freedom may be incorporated as a perturbation. We calculate the optimal field required to maximize the populations of target eigenstates in the isomerization of HCN using the zero-curvature reaction path Hamiltonian. The intermediary dynamics are restricted to the ground state, by using infrared pulses. Using trial fields of two time-delayed Gaussian pulses, we separately optimized the field parameters consisted with the Gaussian paradigm and the field amplitude at each point in time. In both cases we find that the control field can generate complete isomerization using pulses that traverse the states of the system in single and multiple photon transitions.