Calculation of linear and nonlinear electric susceptibilities of conjugated hydrocarbon chains

Abstract

We calculated the π electron contributions to the linear and nonlinear static electric susceptibilities of a linear conjugated hydrocarbon chain. We started from the Hückel equations for the π electrons in the presence of an electric field, and we expanded the equation in terms of the electric field by using perturbation theory. We solved the successive perturbation equations analytically, and we derived exact analytical expressions for the energy perturbations up to fourth order. We used these energy perturbations to derive values for χ⁽¹⁾_XX, χ⁽²⁾_XXX, and χ⁽³⁾_XXYY where the X axis is along the chain. We found that the molar linear susceptibility χ⁽¹⁾_XX is roughly proportional to the 2.8 power of N and that the nonlinear susceptibility χ⁽³⁾_XXXX is roughly proportional to the 5.3 power of N. For larger values of N the π electron contributions to the susceptibilities become much larger than the σ electron contributions.