Molecular hyperpolarizability components βzzz and βzxx under directional extensions of π conjugation: missing-orbital analysis and simplified sum-over-states calculations

The application of missing-orbital analysis to molecular hyperpolarizability β obtained by a simplified sum-over-states calculation, allows one to study the effects of the π conjugation extension on both diagonal βzzz and off-diagonal βzxx components for C2v molecules (the z-axis being the principal one). Extension of the z-length in aminonitropolyacetylenes by increasing the number of acetylene units increases βzzz but βzxx remains unchanged. Conversely, βzxx increases significantly with only a slight increase in βzzz if the π conjugation is extended mainly in the x-direction for 1,3-diamino-4,6-dinitrobenzene by replacing benzene with a fused-ring or inserting acetylene units between the substituents and benzene. These are ascribable to changes in the charge-transfer structure by the π extension.