Role of σ-π interactions on linear and nonlinear susceptibilities in polyenes

Abstract

The validity of the σ-π separability approximation has been well established for some properties of the low-lying states in long polyenes. However, properties such as polarizabilities and hyperpolarizabilities apparently depend upon the entire excitation spectrum of the molecule and a detailed study of the σ-π separability approximation is warranted. We find from model calculations of the exact dynamic and static polarizability, α, and third-harmonic-generation (THG) coefficient, τ, in butadiene that the contribution of σ-electrons to the total polarizability is ≈30% while their contribution to THG coefficients is ≈10%. The σ-electrons make a positive contribution to α while their contribution to τ is small and negative. It is, therefore, likely that the excited states contributing to α are not the same as those contributing to τ. The σ-π separability approximation improves with increase in conjugation length and our calculations, being restricted to butadiene, provide an upper limit on the contribution of the σ-electrons.