A theoretical analysis of the origin of the second-order nonlinear optical properties of octupolar molecules. The case of triamino-trinitrobenzene

The off-resonant π-electronic component of the β tensor, β_π, is calculated and analyzed for an octupolar molecule with D_3h point group symmetry, l,3,5-triamino-2,4,6-trinitrobenzene (TATB), and the related dipolar molecule with C_2V point group symmetry, para-nitroaniline (pNA). The βπ' for TATB and pNA are calculated using the semi-empirical INDO/S Hamiltonian combined with single- and doubleexcitation configuration interaction of singlet π-electron configurations, and Orr and Ward's sum-overstates expression for β. The sum-over-states approach permits one to identify the salient ¹ππ^∗ states participating in the virtual electronic excitations that define the off-resonant β_π's for TATB and pNA. It is found that in addition to the ground electronic state, a pair of doubly degenerate ¹ππ^∗ states contribute strongly to the off-resonant β_π for TATB This finding is in contrast to the single ¹ππ^∗ charge-transfer state that principally defines the off-resonant β_π for dipolar, conjugated π-electron molecules like pNA. The natures of the two doubly-degenerate ¹ππ^∗ states important to the off-resonant β_π for TATB are analyzed in terms of their electronic spectroscopy and π-electron charge distributions. The familiar two-state, singleterm approximation of β_π used for dipolar molecules is not sufficient for octupolar molecules, and a multistate, multi-term approximation is derived for TATB.