Vibrational Properties and Vibrational First-Hyperpolarizability of an Octupolar Molecule Based on a Valence-Bond Three Charge-Transfer (VB-3CT) Model

Various vibrational characteristics and vibrational first-hyperpolarizability of the octupolar molecule are theoretically described by using a simple four-state (valence-bond and three charge-transfer) model. As the equilibrium value of the bond length alternation coordinate increases by introducing stronger donor and acceptor in the octupolar molecule, (i) the vibrational force constant of the symmetric stretching mode exhibits a nonmonotonic behavior, (ii) that of the asymmetric stretching mode decreases, (iii) IR and Raman intensities of the asymmetric modes increase, and (iv) Raman intensity of the symmetric mode shows a nonmonotonic pattern. Furthermore, it is found that the vibrational hyperpolarizability (β) increases with respect to the equilibrium BLA, and this pattern is qualitatively identical to that of the electronic β.