  Here we outline and test an extension of the energy grained master equation
(EGME) for treating nonadiabatic (NA) hopping between different potential
energy surfaces, which enables us to model the competition between stepwise
collisional relaxation and kinetic processes which transfer population between
different potential energy surfaces of the same spin symmetry. By incorporating
Zhu-Nakamura theory into the EGME, we are able to treat nonadiabatic passages
beyond the simple Landau-Zener approximation, along with corresponding
treatments of zero-point energy and tunnelling probability. To evaluate this
NA-EGME approach, we carried out detailed studies of the UV photodynamics of
the volatile organic compound C6-hydroperoxyaldehyde (C6-HPALD) using
on-the-fly ab initio molecular dynamics and trajectory surface hopping. For
this multi-chromophore molecule, we show that the EGME is able to
quantitatively capture important aspects of the dynamics, including kinetic
timescales, and diabatic trapping. Such an approach provides a promising and
efficient strategy for treating the long-time dynamics of photo-excited
molecules in regimes which are difficult to capture using atomistic on-the-fly
molecular dynamics.
