Ab initio study of breakdown of the Condon approximation in the F2Σ+–A2Π electronic transition of AlO

Breakdown of the Condon approximation in the F2Σ+v′–A2Πv″ transition of AlO is studied from the ab initio band strengths and Franck–Condon factors (FCFs) for bands with vibrational quantum numbers v′ = 0–18 and v″ = 0–18. The band strength distribution is clearly different from the FCF distribution, indicating a breakdown of the Condon approximation. The breakdown is characterized by the small value (below 10−1) of the ratio of the relative band strength to the relative FCF relating to the FCF maximum bands in each v″-progression for v′ = 5–16. We analyzed the effect of the internuclear distance (R) dependence of the electronic transition moment on the band strengths for the FCF maximum bands for v′ = 1–16 by using a model of transition matrix element. The analysis shows that the variation of the electronic transition matrix element μ(R) with R in the regions represented by the R-centroids for the bands makes the greatest contribution to the breakdown. The variation of μ(R) around 4.1 a0, where μ(R) changes sign, is crucial to the large scale breakdown in the F–A transition.