Vibronic analysis of overlapping resonances and the third-harmonic-generation spectrum of β-carotene

Vibronic contributions to third-harmonic-generation (THG) are obtained in the Condon approximation for displaced harmonic oscillators in the region of overlapping three- and two-photon resonances, where enhanced THG intensity and explicit dependence on the relative signs of the displacements are found. The THG intensity and phase of β-carotene are then modeled in terms of four electronic states, including overlapping 2 1Ag and 1 1Bu resonances whose displacements are taken from two-photon and linear spectra, respectively, and a high-energy Ag state based on a Pariser–Parr–Pople (PPP) sum rule for transition dipoles. Relations between THG and other spectra show the limitations of three-state models and provide useful constraints on the excited-state structure of related conjugated systems such as polyenes and β-carotene.