Missing-orbital analysis on hyperpolarizability β of organic molecules. Enhancement of the off-diagonal component βzxx using multiple substitutions

The first-order hyperpolarizability components, βzzz and βzxx, for C2v molecules (the z axis being the principal axis) are analyzed after simplified sum-over-states calculations. Compared with p-nitroaniline (PNA), βzxx is three times enhanced by x-extended π conjugation realized by a bulky substrate in 9-amino-10-nitroanthracene (ANA) and by multiple substitutions in 1,5-diamino-2,4-dinitrobenzene (DDB). While ANA shows βzzz unchanged because its z-directed charge transfer (CT) is similar to PNA, DDB has a βzzz 13 of PNA, which is reduced by two weak CTs introduced by two ortho-positioned donor-acceptor pairs on both sides of the z axis.