  We present systematic comparison of three quantum mechanical approaches
describing excitation dynamics in molecular complexes using the Time-Dependent
variational principle (TDVP) with three increasing sophistication trial
wavefunctions (ansatze): Davydov D2 , squeezed D2 (sqD2) and a numerically
exact multiple D2 (mD2) ansatz in order to characterize validity of the sqD2
ansatze. Numerical simulation of molecular aggregate absorption and
fluorescence spectra with intra- and intermolecular vibrational modes,
including quadratic electron-vibrational (vibronic) coupling term, which is due
to vibrational frequency shift upon pigment excitation is presented. Simulated
absorption and fluorescence spectra of J type molecular dimer with high
frequency intramolecular vibrational modes obtained with D2 and sqD2 ansatze
matches spectra of mD2 ansatz only in the single pigment model without
quadratic vibronic coupling. In general, the use of mD2 ansatz is required to
model accurate dimer and larger aggregate's spectra. For a J dimer aggregate
coupled to a low frequency intermolecular phonon bath, absorption and
fluorescence spectra are qualitatively similar using all three ansatze. The
quadratic vibronic coupling term in both absorption and fluorescence spectra
manifests itself as a lineshape peak amplitude redistribution, static frequency
shift and an additional shift, which is temperature dependent. Overall, the
squeezed D2 model does not result in considerable improvement of simulation
results compared to the simplest Davydov D2 approach.
