  We introduce a quantum information analysis of vibrational wave functions to
understand complex vibrational spectra of molecules with strong anharmonic
couplings and vibrational resonances. For this purpose, we define one- and
two-modal entropies to guide the identification of strongly coupled vibrational
modes and to characterize correlations within modal basis sets. We evaluate
these descriptors for multi-configurational vibrational wave functions which we
calculate with the n-mode vibrational density matrix renormalization group
algorithm. Based on the quantum information measures, we present a vibrational
entanglement analysis of the vibrational ground and excited states of CO2,
which display strong anharmonic effects due to the symmetry-induced and
accidental (near-) degeneracies. We investigate the entanglement signature of
the Fermi resonance and discuss the maximally entangled state arising from the
two degenerate bending modes.
