  For complex molecules, nuclear degrees of freedom can act as an environment
for the electronic `system' variables, allowing the theory and concepts of open
quantum systems to be applied. However, when molecular system-environment
interactions are non-perturbative and non-Markovian, numerical simulations of
the complete system-environment wave function become necessary. These many body
dynamics can be very expensive to simulate, and extracting finite-temperature
results - which require running and averaging over many such simulations -
becomes especially challenging. Here, we present numerical simulations that
exploit a recent theoretical result that allows dissipative environmental
effects at finite temperature to be extracted efficiently from a single,
zero-temperature wave function simulation. Using numerically exact
time-dependent variational matrix product states, we verify that this approach
can be applied to vibronic tunneling systems and provide insight into the
practical problems lurking behind the elegance of the theory, such as the
rapidly growing numerical demands that can appear for high temperatures over
the length of computations.
