Optical control of molecular dynamics: Liouville-space theory

We lay some theoretical foundations to deal with the experimental realities faced in controlling molecular dynamics with tailored light fields: the nonideality of the light, the mixed rather than pure quantum-state nature of matter, and environmental and solvent effects. The optimal control of molecular dynamics using light fields is formulated in terms of the density matrix in Liouville space, generalizing existing wave-function-based formulations. This formulation allows the inclusion of mixed states, so that thermal and other nonpure quantum states of matter can be treated, as well as reduced descriptions useful in studying dense gas and condensed phases. In addition, it allows for general constraints and arbitrary coherent and partially coherent radiation fields and provides a unified picture for quantum, semiclassical, and classical molecular dynamics. For weak fields, the calculation simplifies and is given in terms of a molecular response function which itself does not depend upon the field. The solution of an eigenequation then directly gives the globally optimal field and the yield with respect to the target. As a demonstration, we explicitly consider a two electronic surface displaced harmonic oscillator molecular system in a Brownian oscillator solvent at finite temperatures, including nuclear and electronic solvation effects. Numerical illustrations are presented for the quantum control of thermal samples using phase-locked and random-phase light fields in the presence of solvent. © 1993 American Chemical Society.