Semiclassical Theory of Electronically Non-Adiabatic Dynamics

William Miller
University of California, Berkeley (UC Berkeley)

The focus of my research over the last decade has been on developing semiclassical (SC) theory into a practical way for adding quantum effects to classical molecular dynamics (MD) simulations of large, complex molecular systems. A particularly interesting and important aspect of this is the ability to describe electronically non-adiabatic processes in a fashion that treats nuclear and electronic degrees of freedom (DOF) in an equivalent dynamical framework. This is accomplished by using a model developed by Meyer and Miller (MM) [J. Chem. Phys. 70, 3214 (1979)] for replacing a finite set of electronic states of a molecular system (i.e., the various potential energy surfaces and their couplings) by a classical Hamiltonian involving the nuclear and (collective) electronic DOF. Much later Stock and Thoss (ST) [Phys. Rev. Lett. 78, 578 (1997)] showed that the MM model is actually not a ‘model’, but rather a ‘representation’ of the nuclear-electronic system; i.e., were the MM nuclear-electronic Hamiltonian taken as a Hamiltonian operator and used in the Schrödinger equation, the exact (quantum) nuclear-electronic dynamics would be obtained. In recent years various initial value representations (IVRs) of SC theory have been used with the MM Hamiltonian to describe electronically non-adiabatic processes. Of special interest is the fact that although the classical trajectories generated by the MM Hamiltonian (and which are the ‘input’ for an SC-IVR treatment) are ‘Ehrenfest trajectories’, when they are used within the SC-IVR framework the nuclear motion emerges from regions of non-adiabaticity on one potential energy surface (PES) or another, and not on an average PES as in the traditional Ehrenfest model. Very recently an even more ambitious SC description of electronic DOF—one which replaces the fermionic creation and annihilation operators in the general second-quantized many-electron Hamiltonian by functions of classical action-angle variables—has been seen to provide an excellent description of transmission of electrons through a molecular junction. This opens up the possibility of being able to use classical MD simulations (of electronic and nuclear DOF) to model the many aspects of current interest in ‘molecular electronics’.

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