  The ultrafast quantum dynamics of photophysical processes in complex
molecules is an extremely challenging computational problem with a wide variety
of fascinating applications in quantum chemistry and biology. Inspired by
recent developments in open quantum systems, we introduce a pure-state
unraveled hybrid-bath method that describes a continuous environment via a set
of discrete, effective bosonic degrees of freedom using a Markovian embedding.
Our method is capable of describing both, a continuous spectral density and
sharp peaks embedded into it. Thereby, we overcome the limitations of previous
methods, which either capture long-time memory effects using the unitary
dynamics of a set of discrete vibrational modes or use memoryless Markovian
environments employing a Lindblad or Redfield master equation. We benchmark our
method against two paradigmatic problems from quantum chemistry and biology. We
demonstrate that compared to unitary descriptions, a significantly smaller
number of bosonic modes suffices to describe the excitonic dynamics accurately,
yielding a computational speed-up of nearly an order of magnitude. Furthermore,
we take into account explicitly the effect of a $\delta$-peak in the spectral
density of a light-harvesting complex, demonstrating the strong impact of the
long-time memory of the environment on the dynamics.
