Tullys fewest switch surface hopping method and its variants

3 Tully s fewest switch surface hopping method and its variants 

As explained above, the naive surface hopping model lets a classical trajectory running on an adiabatic potential siu face jumps to another at a specific point with a transition probability borrowed from other theories. Although 

The basic idea of the algorithm is to allow a path to jump with the prob-abihty estimated internally (in a self-contained maimer) with the electronic-state mixing as in the semiclassical Ehrenfest theory but the number of transitions (hops) should be minimized. Suppose we have an electronic wavepacket (t)) = X]/C /(t) /) as in the SET, the dynamics of the corresponding density matrix, pij t) = Cj t)Cj t), is written as 

A main interest exists in its diagonal part, which is compactly expressed as 

With this representation, one can estimate a transition probability from state K to I during one time step, t t + dr, as 

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