  Nonadiabatic ring-polymer molecular dynamics employs the mapping approach to
describe nonadiabatic effects within the ring-polymer ansatz. In this paper, it
is generalized to allow for the nuclear and electronic degrees of freedom to be
described by different numbers of ring-polymer beads. Analysis of the resulting
method shows that as the number of electronic mapping variables increases,
certain problems associated with the approach are removed, such as the
non-unique choice of the mapping Hamiltonian and negative populations leading
to inverted potential-energy surfaces. Explicit integration over cyclic
variables reduces the sign problem for the initial distribution in the general
case. A new application for the simulation of vibronic spectra is described and
promising results are presented for a model system.
