  Effects of non-linear coupling between the system and the bath vibrational
modes on the system internal conversion dynamics are investigated using the
Dirac-Frenkel variational approach with the defined sD2 ansatz. It explicitly
accounts for the entangled system electron-vibrational wavepacket states, while
the bath quantum harmonic oscillator (QHO) states are expanded in a
superposition of coherent states (CS). Using a non-adiabatically coupled
three-level model, we show that quadratic system-bath coupling induces
non-reversible internal conversion when the bath QHO wavepacket representation
is highly non-Gaussian. The quadratic coupling results in a broadened and
asymmetrically squeezed bath QHO wavepackets in the coordinate-momentum phase
space. Additionally, we found that computational effort can be reduced using
degenerate CSs to represent the initial bath wavepackets.
