Spawning method of Martinez

The greatest advantage of the frozen Gaussian is its simplicity and therefore can be applied to many generalizations of the naive surface hopping 

On the other hand, the obvious concern about this method is inaccuracy arising from the frozen Gaussian exponents (see below in Sec. 4.3.5 though). It is desirable to seek for a theory more satisfactory to quantize non-classical path in the quality level similar to or better than that of the WKB theory. 

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To add non-adiabatic effects to semiclassical methods, it is necessary to allow the trajectories to sample the different surfaces in a way that simulates the population transfer between electronic states. This sampling is most commonly done by using surface hopping techniques or Ehrenfest dynamics. Recent reviews of these methods are found in [30-32]. Gaussian wavepacket methods have also been extended to include non-adiabatic effects [33,34]. Of particular interest here is the spawning method of Martinez, Ben-Nun, and Levine [35,36], which has been used already in a number of direct dynamics studies. 

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