N-State Interpretations of the First and Second Hyperpolarizabilities of Cyanobiphenyl-Based Liquid Crystal Molecules

Electronic structure calculations on the frequency-dependent hyperpolarizabilities of 5-alkyl cyanobiphenyl have been performed using the AM1 Hamiltonian and time dependent Hartree-Fock theory. Both the average first and second hyperpolarizabilities decrease with increasing twist angle, O, between the two phenyl groups, and increase with increasing incident frequency. While the nonlinear optical properties of materials are frequently interpreted within the framework of two and three state models for the electronic spectrum, systems with a more complex electronic structure require an approach which can denote state importance. The linear optical properties of 5CB are dominated by two low-lying charge transfer transitions from the ground state, which would seem suitable to a three state model. However, large state dipole moments offset of low oscillator strengths for other transitions allowing them to also become significant contributors to the nonlinear optical properties.