Theoretical determination of the intensities and splittings of4A2gto2Egvibronic transitions

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Abstract
The vibronic splitting and Zeeman effect of 4A2g to 2Eg* nu (t1u) and 4A2g to 2Eg* nu (t2u) vibronic transitions are considered theoretically. It is shown that when the excited state has pure orbital doublet character the 2Eg* nu (t1u) and 2Eg* nu (t2u) vibronic multiplets each split into 2T1u and 2T2u vibronic levels and the Zeeman splitting of the vibronic levels equals that of the parent electronic state. When the excited state also contains some orbital triplet character through spin-orbit interaction a further splitting becomes possible, giving a total of four levels. In this case the Zeeman splitting will no longer equal that of the parent electronic state, but can be calculated by diagonalising four 3*3 energy matrices. The relative intensities of 4A2g to 2Eg vibronic transitions are expressed in terms of two parameters. It is shown that, for the 2A2g(t23) to 2Eg(t23) transitions within a d3 ion, one of these parameters will be small. In this case the relative magnitudes of both the intensity and vibronic interaction parameters can be estimated and the likely vibronic splitting pattern predicted.