Second-order ab initio Møller-Plesset study of optimum chain length for total (electronic plus vibrational) β(-ω _σ;ω ₁,ω ₂) of a prototype push-pull polyene

Static as well as dynamic electronic and vibrational longitudinal first hyperpolarizabilities (β _L ^e and β _L ^v) of α,ω,-nitro,amino-polyacetylene oligomers, containing up to 16 unit cells, have been computed at the Hartree-Fock and second-order Møller-Plesset levels using the 6-31G atomic basis set. The curve of first hyperpolarizability per unit cell versus the number of unit cells presents a maximum that defines the optimal chain length for NLO applications. Modifications in electronic structure occurring when electron correlation is included lead to an increase in the height of the maximum β _L ^e by a factor of 2. A similar enhancement arises from the corresponding change in equilibrium geometry, which, in addition, shifts the position of the maximum toward longer chain lengths. Frequency dispersion also has a major effect on the position and magnitude of the optimal point. The contribution of the vibrational hyperpolarizability is relatively small when correlation and frequency dispersion are included. Our results are compared with experiment, as well as other calculations, and implications are drawn.