Assignment of electronic spectra of GdF by identifying families using the f-shell Omega decomposition method

A systematic method for identifying the electronic structures of diatomic molecules containing lanthanide atoms has recently been proposed by the authors. The difficulty arising from the multiconfigurational nature of the 4f electrons is overcome by this method, the ‘f-shell Omega decomposition’. The GdF molecule is treated as an example, and all the electronic states below 3.0 eV are assigned systematically by applying this method for wave functions given by the generalized open-shell configuration interaction calculations. The states are first classified by the excitation energies, then by the gross atomic orbital populations. Finally, based on the method described here, they are grouped into families which derive from the states of the highest Ω, called roots, giving the highest electronic angular momentum around the molecular axis. The eightfold degenerate ground states (Kramers partners included), for instance, are classified into a family named X 7/2[(4f7)(6s2)]Ω where the total angular momentum Ω decreases by one from 7/2 to 1/2 (−1/2 to −7/2). The 70–90th states (1.915–2.183 eV) are classified into five families: n 3/2[(4f7)(5d2)]Ω, o 15/2[(4f7)(5d2)]Ω, p 5/2[(4f7)(6s15d1 + 5d2)]Ω, q 9/2[(4f7)(6s15d1 + 5d2)]Ω, and r 5/2[(4f 7)(6s15d1)]Ω. The strengths of the transition spectra are also examined. The [15.8] transitions (15776.9 cm−1) identified by Kaledin et al. are assigned to transitions from the p 5/2[(4f7)(6s15d1 + 5d2)]Ω and q 9/2[(4f7)(6s15d1 + 5d2)]Ω families to the X 7/2[(4f7)(6s2)]Ω family. Since many other states lie close to these p and q families, the spectra are likely to be complicated. Other electronic transitions involving the A 7/2[(4f 7)(6s15d1)]Ω and c 11/2[(4f 7)(6s15d1)]Ω families (the 15–24th states located at 0.782–0.949 eV) are also examined and are found to be weak.