A theoretical analysis of third-order nonlinear optical properties of linear polyenes and benzene

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Abstract
An accurate and computationally tractable theoretical procedure for the calculation of the nonresonant, electronic components of the third‐order molecular polarizabilities, γ(0;0,0,0), γ(−3ω;ω,ω,ω), and γ(−2ω;ω,ω,0), can be constructed. This procedure partitions γ into a σ‐electron component (γσ) and a π‐electron component (γπ). The γσ term is evaluated using the bond‐additivity approximation; the γπ term is calculated using the semiempirical INDO all‐valence‐electron molecular orbital method combined with full single‐ and double‐excitation configuration interaction (SDCI) of singlet π‐electron configurations, and Orr and Ward’s sum‐over‐states expression for γ. The INDO‐SDCI method is also used to calculate one‐ and two‐photon spectroscopic properties of the 1ππ* states salient to γπ for the molecules of interest. It is shown that single‐excitation CI alone is not sufficient for the calculation of γπ for linear polyenes and benzene. Calculations of the effect of chain length and conformation on the values of γ for ethylene, cis and trans linear polyenes, and benzene indicate that γ is strongly influenced by conjugation chain length. A simple relationship can be established between the calculated value of γπ(0;0,0,0) for the trans linear polyenes investigated and that for ethylene, the molecule with the solitary π‐electron C–C bond: γπ(0;0,0,0)≂γπ(0;0,0,0)ethylene NC–C3, where NC–C=1,3,5,7, and NC–C is the total number of C=C and C–C bonds in the given polyene, i.e., the length of the π‐bonding network. As γ increases with chain length, so does the ratio γπ/γ. Virtual electronic transitions involving excited π‐electron states with extensive charge separation and double excited configurational character are important contributors to γπ for the linear polyenes and benzene. An approximation of γπ(0;0,0,0) for the linear polyenes can be written in terms of the linear π‐electron polarizabilities for the ground state and 1 1Bu π‐electron excited state. Although this approximation is strictly applicable to the centrosymmetric linear polyenes, it does suggest a very interesting criterion for the selection of organic molecules with large third‐order polarizabilities. Namely, the change in polarizability between the ground state and a strongly one‐photon absorbing excited state is an important factor to consider when selecting candidate molecules.