Ab initio study of band strength distribution for the D2Σ+–A2Π transition of AlO and the effect of R dependence of the electronic transition moment on the distribution

The band strength distribution for the D2Σ+ v′–A2Π v″ electronic transition of AlO, and the effect of R dependence of the electronic transition moment on the distribution, are studied based on the ab initio band strengths and the Franck–Condon factors (FCFs) for bands with vibrational quantum numbers v′ = 0–18 and v″ = 0–18. The band strength distribution exhibits a Condon parabola of the bands involving v′ = 0–9 and 11 of all the inner-well levels of the D2Σ+ double potential well. Five unobserved bands calculated among the ten largest band strength bands are found to involve the v′ levels near the D2Σ+ potential barrier top. The effect of the R dependence is examined for the FCF maximum bands in the v″-progressions for v′ = 0–9 and 11–18 (excluding v′ = 10 of the D2Σ+ outer-well level) by using the ratio of the band strength to the FCF, both relative to the 0–0 band. Large (small) ratios of value 1.276–1.559 (0.619–0.841) are found for ratio > 1 (ratio < 1) bands with v′ = 8, 9 and 11–18. An analysis using a model of transition matrix element shows that the difference between (1) the electronic transition moment in the region represented by the R-centroid for each large ratio band and (2) that for the 0–0 band makes the greatest contribution to the ratio. The R-centroids do not properly represent the important R regions (R < 3.0a0) for the small ratio bands with v′ = 11–18; a possible explanation is discussed. The results imply that the avoided crossings influence the band strength distribution. The Einstein A coefficients have been evaluated for the D–A bands with v′ = 0–9 and 11 and v″ = 0–18 from the calculated band strengths and transition energies.