Optimal control of classical molecular systems

Starting with the harmonic potential approximation. A closed form solution for the optimal optical field is derived for a quadratic cost criterion and an asymptotic form for this field is obtained for large target times. The dynamics of a molecule are shown to be controllable if no normal mode has zero optical absorption intensity. The optimal control formalism is extended further to yield optimal fields exhibiting minimal sensitivity of the desired molecular objectives with respect to molecular parameters. In addition, examples are shown of optimal control of several molecules whose parameters are taken from experiment: vinylidene fluoride, fluorobenzene and the methylene halide chemical series. Aspects of molecule orientation relative to electric field polarization are addressed. The optimal control theory method is then extended to treat nonlinear classical systems. Control of selective unimolecular bond dissociation is demonstrated on a model linear triatomic molecule with spreading of the ensemble of trajectories held to a minimum for closer agreement between quantum and classical mechanics. We employ optimal control theory to design an external driving field which reduces the difference between certain quantum observables and their classical counterparts in addition to achieving some dynamical objective. Several examples are shown using a one dimensional model system which is highly nonclassical in the absence of a driving field. Similarly, we use optimal control theory to modify time-independent potentials such that chosen classical observables, with a corresponding resultant classically equivalent potential, match their quantum counterparts propagated on the true potential. We develop a method to graphically display the flow of energy within molecules. This method provides a means to display energy flow in still frames and as a tool to visualize hitherto undiscovered dynamical pathways in molecules