Surface hopping, asymptotic

Dissociation at High Bath Densities Asymptotic Surface Hopping Near Dissociation Photodissociation Dynamics... 

These simple conservation laws are nevertheless not assmed, in fact they are sometimes even severely violated, in many of existing calculation methods including mean-field methods like the semiclassical Ehrenfest theory (SET). The surface hopping method circumvents the problem by adjusting the linear momenta of nuclei so as to satisfy the asymptotic energy conservation law. 

Both the hopping and nonhopping trajectories are then further integrated on the appropriate adiabatic surface until they either hop again or reach the asymptotic region. 

Yet, some theoretical problems are left to be discussed to seek for the ultimate and idealistic features as a nonadiabatic-transition theory Although a trajectory thus hopping plural times converges to run on an adiabatic potential surface asymptotically, the off-diagonal density matrix element Pij t) does not vanish practically, as in the original SET. This is ascribed to an incomplete treatment of the nuclear-electronic entanglement. This issue, often referred to as the problem of decoherence, is originated from the nuclear wavepacket bifurcation due to different slopes of potential surfaces, which will be discussed more precisely below. 

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