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Electronically non-adiabatic dynamics via semiclassical initial value methods

Wednesday, March 4, 2009 - 8:30am - 9:00am
EE/CS 3-180
William Miller (University of California, Berkeley)
In the late 1970’s Meyer and Miller (MM) [J. Chem.
Phys
.
70,
3214 (1979)] presented a classical Hamiltonian corresponding to
a finite set of electronic states of a molecular system (i.e.,
the various potential energy surfaces and their couplings), so
that classical trajectory simulations could be carried out
treating the nuclear and electronic degrees of freedom (DOF) in
an equivalent dynamical framework (i.e., by classical
mechanics), thereby describing non-adiabatic dynamics in a more
unified manner. 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 MMST
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 semiclassical
(SC) theory have been used with the MMST Hamiltonian to
describe electronically non-adiabatic processes. Of special
interest is the fact that though the classical trajectories
generated by the MMST 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. Examples are presented to
illustrate and (hopefully) illuminate this behavior.
MSC Code: 
34A12