  Simulating vibrationally resolved electronic spectra of anharmonic systems,
especially those involving double-well potential energy surfaces, often
requires expensive quantum dynamics methods. Here, we explore the applicability
and limitations of the recently proposed single-Hessian thawed Gaussian
approximation for the simulation of spectra of systems with double-well
potentials, including 1,2,4,5-tetrafluorobenzene, ammonia, phosphine, and
arsine. This semiclassical wavepacket approach is shown to be more robust and
to provide more accurate spectra than the conventional harmonic approximation.
Specifically, we identify two cases in which the Gaussian wavepacket method is
especially useful due to the breakdown of the harmonic approximation: (i) when
the nuclear wavepacket is initially at the top of the potential barrier but
delocalized over both wells, e.g., along a low-frequency mode, and (ii) when
the wavepacket has enough energy to classically go over the low potential
energy barrier connecting the two wells. The method is efficient and requires
only a single classical ab initio molecular dynamics trajectory, in addition to
the data required to compute the harmonic spectra. We also present an improved
algorithm for computing the wavepacket autocorrelation function, which
guarantees that the evaluated correlation function is continuous for arbitrary
size of the time step.
