Valence bond approach to exact nonlinear optical properties of conjugated systems

Abstract

Diagrammatic valence-bond (DVB) theory is extended to dynamic nonlinear susceptibilities of interacting π electrons in Pariser-Parr-Pople (PPP) or other quantum cell models whose correlated ground state ||G> is known. Corrections Φ⁽¹⁾(ω) and Φ⁽²⁾(ω₂,ω₁) to ||G> due to oscillating electric fields are found directly as linear combinations of VB diagrams. Any nonlinear optical coefficient is reduced to matrix elements that implicitly include all excited states, as verified for shorter polyenes. Static and dynamic χ⁽³⁾ coefficients for cis and trans polyenes to N=12 carbons illustrate the importance of retaining the full spectrum. The coefficients β_ijk(ω,ω) for second harmonic generation are found for polar molecules like aniline and nitroaniline. Divergent responses are treated by lifetimes Γ for the resonant states, as shown for third harmonic generation in hexatriene with Γ=0 and in octatetraene with Γ>0. Electron-electron interactions reverse the sign of γ_ijkl(ω,ω,ω) in linear polyenes, except for the largest xxxx coefficient along the chain, and strongly decrease their magnitude and size dependence. The DVB procedure is checked against transition moments, noninteracting π electrons in Hückel models, explicit sums over all excited states, and is compared to recent approximate PPP calculations for the nonlinear optical (NLO) coefficients of linear polyenes.