Nonlinear optical properties of the linear quadrupolar molecule: Structure-function relationship based on a three-state model

Theoretical descriptions of the molecular polarizability and second hyperpolarizability (alpha and gamma) of the linear quadrupolar molecule are presented. By using a valence-bond and two charge-transfer states, three eigenfunctions of a quadrupolar molecule are obtained as linear combinations of these basis states. The analytic expressions for alpha and gamma are obtained, and the physical picture on the nonlinear optical (NLO) response of the quadrupolar molecule is presented. By introducing the bond-length-alternation coordinates into the model Hamiltonian, the relationships of various vibrational characteristics, such as IR, Raman, and hyper-Raman intensities and vibrational frequencies, with respect to the molecular structure are established. The vibrational second hyperpolarizability is also compared with the electronic one, and the two quantities show similar trends as the charge-transfer character changes. A number of distinctive features are discussed by comparing the results with those of the linear push-pull polyene. The NLO properties of a series of quadrupolar molecules are calculated by using the ab initio method, and also a few more examples of quadrupolar molecules are suggested.