Treating geometric phase effects in nonadiabatic dynamics

We present an approach for eliminating the gauge freedom for derivative couplings, enabling nonadiabatic dynamics in the presence of geometric phase effects. This approach relies on a bottom-up construction of a parametric quantum Hamiltonian in terms of functions of a dynamical variable. These functions can be associated with real- and imaginary-valued contributions to the Hamiltonian in a given diabatic basis. By minimizing variable-dependent fluctuations of the imaginary functions we identify a set of diabatic bases that recover the real-valued gauge commonly used for topologically trivial systems. This minimization, however, also confines the gauge freedom in the topologically nontrivial case, opening a path towards finding gauge-invariant derivative couplings under geometric phase effects. Encouraging results are presented for fewest-switches surface-hopping calculations of a nuclear wave packet traversing an avoided-crossing region, for which fully gauge-invariant derivative couplings are found.