  Optimal control of molecular dynamics is commonly expressed from a quantum
mechanical perspective. However, in most contexts the preponderance of
molecular dynamics studies utilize classical mechanical models. This paper
treats laser-driven optimal control of molecular dynamics in a classical
framework. We consider the objective of steering a molecular system from an
initial point in phase space to a target point, subject to the dynamic
constraint of Hamilton's equations. The classical control landscape
corresponding to this objective is a functional of the control field, and the
topology of the landscape is analyzed through its gradient and Hessian with
respect to the control. Under specific assumptions on the regularity of the
control fields, the classical control landscape is found to be free of traps
that could hinder reaching the objective. The Hessian associated with an
optimal control field is shown to have finite rank, indicating the presence of
an inherent degree of robustness to control noise. Extensive numerical
simulations are performed to illustrate the theoretical principles on a) a
model diatomic molecule, b) two coupled Morse oscillators, and c) a chaotic
system with a coupled quartic oscillator, confirming the absence of traps in
the classical control landscape. We compare the classical formulation with the
mathematically analogous state-to-state transition probability control
landscape of N-level quantum systems. The absence of traps in both
circumstances provides a broader basis to understand the growing number of
successful control experiments with complex molecules, which can have dynamics
that transcend the classical and quantum regimes.
