CNDO/S‒CI Calculations of Hyperpolarizabilities. III. Regular Polyenes, Charged Polyenes, Di-substituted Polyenes, Polydiacetylene and Related Species

The analytic formula for the third-order hyperpolarizability γijkl(-3ω;ω,ω,ω) is derived from time-dependent perturbation theory. An approximate formula for γijkl in a static electric field is also presented. The γzzzz values (the chain axis components) for regular polyenes, charged polyenes, donor (D) - acceptor (A) disubstituted polyenes, polydiacetylene and related species are evaluated by the use of several quantities calculated for low-lying excited states by the CNDO/S-CI method. The signs and magnitudes of γzzzz and the effects of variations in chain length are investigated on the basis of the calculated results. For regular polyenes, the calculated γzzzz values are positive and a power law dependence on the chain length N is found with an exponent of 4.14. In contrast, the calculated values of γzzzz for charged polyenes (+) are negative, but possess a similar N-dependence with an exponent of 4.44. The signs, magnitudes and N-dependences of γzzzz for disubstituted polyenes with donor (D) and acceptor (A) groups and polydiacetylene are discussed in relation to the experimental data available.