Condon locus

The Franck-Condon factors (FCFs) for the strongest bands of a band system are located in a (v, v") table such that a parabola (the Condon locus) often tracks through them [1-3]. The tilt of this parabola, and its latus rectum, can be calculated from the spectroscopic constants of the upper and lower electronic states of the transition. It is relatively rare that the spectroscopic constants and the FCFs are available for any given molecule the availability is most common for isoelectronic sequences. Hence, we calculate these two properties for the Condon loci of similar band systems for the molecules in isoelectronic sequences. The hypothesis of the work is that these loci will manifest the periodicities of the constituent atoms in the diatomic molecules. 

Here, we provide formulas that will enable the calculation of the Condon locus in terms of molecular constants for parabolic potential energy fiinctions. Figure 8.1 shows schematically the parabolic energy curves of two simple harmonic oscillators and their discrete vibrational energy levels. 

The obvious starting point would be to compute the data (the angle and the length of the latus rectum) for the Condon locus of the band systems of each fixed-period diatomic molecule (e.g., both atoms from period 2). This procedure suffers from a severe lack of such data. The density of data is greater among isoeiectronic series. Table 8.1 shows the isoeiectronic series and related data. 

Fig. 8.2 The Condon locus for the B-X band system of CN with simple harmonic potentials assumed for the upper and lower states. A Franck-Condon factor lies at each integer intersection. The curve is calculated from the numerical values given in the text. The tixis of the parabola mtikes an angle of 46.29° with the v" axis, and the length of the latus rectum is 0.129 v units. In what follows, this Condon parabola would be described as narrow ...

Table 8.1 Total electron count of isoelectronic sequence, member molecules, atomic number difference, spectroscopic constants, latus rectum, and angle of the Condon locus symmetry angle from v"... 

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