Vibronic intensities and rotational line strength factors for the three-photon absorption spectrum of ammonia

Abstract

A perturbation theory approach is used to analyze the rovibronic structure of the three-photon resonant absorption of ammonia. The vibronic selection rules are presented in a convenient pyramid mnemonic in terms of irreducible representations of the rotation group and of the D3h point group. The analysis is presented for each possible situation, namely, all three photons are different, two photons are identical and one different, and all three photons are identical. The experimentally important case of three identical photons implies only two polarizations and two vibronic tensor elements for each symmetry type. With both the B̃ and C̃′ systems of ammonia one expects a ratio of 5 to 2 in the absorbance for circularly versus linearly polarized light for the N, O, S, and T branches. For the P, Q, and R branches one expects a 21 to 4 ratio of the weight-1 versus weight-3 tensor contributions to the C̃′ system in linearly polarized light (21 to 6 for B̃). Weight-1 terms are absent with circularly polarized light. These predictions are confirmed experimentally. The complete set of rotational line strength factors for three-photon absorption are given in algebraic form for the first time. The combination of vibronic factors, rotational line strengths, and statistical weights allows one to predict the three-photon absorption spectrum. Such calculated spectra are presented for ammonia at 45 K and they compare very favorably with the experimental spectra for both the B̃ system (a perpendicular band) and for the C̃′ system (a parallel band) in both linearly and circularly polarized light.