  An extension of the CCS-method [Chem. Phys. 2004, 304, p. 103-120] for
simulating non-adiabatic dynamics with quantum effects of the nuclei is put
forward.
  The time-dependent Schr\"{o}dinger equation for the motion of the nuclei is
solved in a moving basis set. The basis set is guided by classical
trajectories, which can hop stochastically between different electronic
potential energy surfaces. The non-adiabatic transitions are modelled by a
modified version of Tully's fewest switches algorithm. The trajectories consist
of Gaussians in the phase space of the nuclei (coherent states) combined with
amplitudes for an electronic wave function. The time-dependent matrix elements
between different coherent states determine the amplitude of each trajectory in
the total multistate wave function; the diagonal matrix elements determine the
hopping probabilities and gradients. In this way, both intereference effects
and non-adiabatic transitions can be described in a very compact fashion,
leading to the exact solution if convergence with respect to the number of
trajectories is achieved and the potential energy surfaces are known globally.
  The method is tested on a 2D model for a conical intersection [J. Chem.
Phys., 1996, 104, p. 5517], where a nuclear wavepacket encircles the point of
degeneracy between two potential energy surfaces and intereferes with itself.
These intereference effects are absent in classical trajectory-based molecular
dynamics but can be fully incorporated if trajectories are replaced by surface
hopping coupled coherent states.
