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Adequate simulation of non-adiabatic dynamics through conical intersectionrequires account for a non-trivial geometric phase (GP) emerging in electronicand nuclear wave-functions in the adiabatic representation. Popular mixedquantum-classical (MQC) methods, surface hopping and Ehrenfest, do not carry anuclear wave-function to be able to incorporate the GP into nuclear dynamics.Surprisingly, the MQC methods reproduce ultra-fast interstate crossing dynamicsgenerated with the exact quantum propagation so well as if they containedinformation about the GP. Using two-dimensional linear vibronic coupling modelswe unravel how the MQC methods can effectively mimic the most significantdynamical GP effects: 1) compensation for repulsive diagonal second ordernon-adiabatic couplings and 2) transfer enhancement for a fully cylindricallysymmetric component of a nuclear distribution.

Why do mixed quantum-classical methods describe short-time dynamics through conical intersections so well? Analysis of geometric phase effects