  We present a framework for simulating relaxation dynamics through a conical
intersection of an open quantum system that combines methods to approximate the
motion of degrees of freedom with disparate time and energy scales. In the
vicinity of a conical intersection, a few degrees of freedom render the nuclear
dynamics nonadiabatic with respect to the electronic degrees of freedom. We
treat these strongly coupled modes by evolving their wavepacket dynamics in the
absence of additional coupling exactly. The remaining weakly coupled nuclear
degrees of freedom are partitioned into modes that are fast relative to the
nonadiabatic coupling and those that are slow. The fast degrees of freedom can
be traced out and treated with second-order perturbation theory in the form of
the time-convolutionless master equation. The slow degrees of freedom are
assumed to be frozen over the ultrafast relaxation, and treated as sources of
static disorder. In this way, we adopt the recently developed frozen-mode
extension to second-order quantum master equations. We benchmark this approach
to numerically exact results in models of pyrazine internal conversion and
rhodopsin photoisomerization. We use this framework to study the dependence of
the quantum yield on the reorganization energy and the characteristic timescale
of the bath, in a two-mode model of photoisomerization. We find that the yield
is monotonically increasing with reorganization energy for a Markovian bath,
but monotonically decreasing with reorganization energy for a non-Markovian
bath. This reflects the subtle interplay between dissipation and decoherence in
conical intersection dynamics in the condensed phase.
