SC 98-38 Christof Schütte, Peter Nettesheim: Non-Adiabatic Effects in Quantum-Classical Molecular
Dynamics Appeared in: F. Keil, W. Mackens et al. Scientific Computing
in Chemical Engineering II, Computational Fluid Dynamics,
Reaction Engineering and Molecular Properties. Springer
(1999) pp. 42-56
Abstract: In molecular dynamics applications there is a growing
interest in mixed quantum-classical models. The article is concerned
with the so-called QCMD model. This model describes most atoms of the
molecular system by the means of classical mechanics but an important,
small portion of the system by the means of a wavefunction. We review the conditions
under
which the QCMD model is
known to approximate the full quantum dynamical evolution of the
system.
In most quantum-classical simulations the Born-Oppenheimer model
(BO) is used. In this model, the wavefunction is adiabatically coupled
to the classical motion which leads to serious approximation
deficiencies with respect to non-adiabatic effects in the fully
quantum dynamical description of the system. In contrast to the BO
model, the QCMD model does include non-adiabatic processes, e.g.,
transitions between the energy levels of the quantum system. It is demonstrated
that, in
mildly non-adiabatic scenarios, so-called surface hopping
extensions of QCMD simulations yield good approximations of the
non-adiabatic effects in full quantum dynamics. The algorithmic
strategy of such extensions of QCMD is explained and the crucial steps
of its realization are discussed with special emphasis on the
numerical problems caused by highly oscillatory phase effects.
Keywords: quantum-classical molecular dynamics,
non-adiabatic processes,
Schrödinger equation,
highly oscillatory phase,
adiabatic limit,
quantum adiabatic theorem,
Born-Oppenheimer model,
energy level crossings,
transition zone,
QCMD-based surface hopping,
QCMD trajectory bundle,
long-stepsize integration schemes,
averaging
MSC: 81Q20, 81Q15, 81S25, 81V55, 92E10