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An extension of the CCS-method [Chem. Phys. 2004, 304, p. 103-120] forsimulating non-adiabatic dynamics with quantum effects of the nuclei is putforward.  The time-dependent Schr\"{o}dinger equation for the motion of the nuclei issolved in a moving basis set. The basis set is guided by classicaltrajectories, which can hop stochastically between different electronicpotential energy surfaces. The non-adiabatic transitions are modelled by amodified version of Tully's fewest switches algorithm. The trajectories consistof Gaussians in the phase space of the nuclei (coherent states) combined withamplitudes for an electronic wave function. The time-dependent matrix elementsbetween different coherent states determine the amplitude of each trajectory inthe total multistate wave function; the diagonal matrix elements determine thehopping probabilities and gradients. In this way, both intereference effectsand non-adiabatic transitions can be described in a very compact fashion,leading to the exact solution if convergence with respect to the number oftrajectories 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 ofdegeneracy between two potential energy surfaces and intereferes with itself.These intereference effects are absent in classical trajectory-based moleculardynamics but can be fully incorporated if trajectories are replaced by surfacehopping coupled coherent states.

Non-Adiabatic Dynamics around a Conical Intersection with Surface-Hopping Coupled Coherent States