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Surface hopping
Surface hopping is a semi-classical technique that incorporates quantum mechanical effects into molecular dynamics simulations.〔〔〔〔 Traditional approaches propagate the dynamics only on one surface. However, quantum mechanics predicts that the dynamics happen on all the surfaces simultaneously. Surface hopping incorporates the effect of other surfaces by allowing for 'hops' between the surfaces, subject to certain criteria. This method is particularly useful when the Born-Oppenheimer approximation breaks down in certain regions, particularly conical intersections and avoided crossings.
== Motivation ==
Molecular dynamics simulations numerically solve the classical equations of motion. These simulations, though, ignore the effects of zero-point energy, quantum interference, and quantum tunneling.〔 Solving the time-dependent Schrödinger equation numerically incorporates all these effects, but is computationally unfeasible when the system has many degrees of freedom.
To tackle this issue, one approach is the mean field or Ehrenfest method, where the molecular dynamics is run on the average potential energy surface given by a linear combination of the adiabatic states. This was applied successfully for some applications, but has some important limitations. When the difference between the adiabatic states is large, then the dynamics must be primarily driven by only one surface, and not an average potential. In addition, this method also violates the principle of microscopic reversibility.〔
Surface hopping accounts for these limitations by propagating an ensemble of trajectories, each one of them on a single adiabatic surface at any given time. The trajectories are allowed to 'hop' between various adiabatic states at certain times such that the quantum amplitudes for the adiabatic states follow the time dependent Schrödinger equation. The probability of these hops are dependent on the coupling between the states, and is generally significant only in the regions where the difference between adiabatic energies is small.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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