Molecular first hyperpolarizability of push-pull polyenes: Relationship between electronic and vibrational contribution by a two-state model

Abstract

In this work we present a theoretical justification, based on a two-state model, of the recently observed close resemblance between the molecular first-order hyperpolarizability (${\mathrm{\ensuremath{\beta}}}^{\mathit{e}}$) obtained with traditional experimental or theoretical methods and the vibrational (or relaxation) contribution (${\mathrm{\ensuremath{\beta}}}^{\mathit{r}}$) for several classes of polyconjugated molecules. The vibrational hyperpolarizabilities have been evaluated according to a semiclassical model previously presented by the authors in which molecular polarizabilities are expressed in terms of vibrational (infrared and Raman) intensities. Here we prove that in the case of polyconjugated molecules, the analytic expressions of ${\mathrm{\ensuremath{\beta}}}^{\mathit{e}}$ and ${\mathrm{\ensuremath{\beta}}}^{\mathit{r}}$ are functions of the same physical parameters. This implies that ${\mathrm{\ensuremath{\beta}}}^{\mathit{e}}$ and ${\mathrm{\ensuremath{\beta}}}^{\mathit{r}}$ provide a measure of the same physical property. \textcopyright{} 1996 The American Physical Society.