Application of Badger’s rule to third row metal diatomics

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Abstract
We extend the range of applicability of Badger’s rule, an empirical correlation between ωe and re , to diatomic molecules that include one or two metal atoms from the third row of the periodic table. For such M2 and MO species, the accuracy of the correlation competes with that of ab initio calculations in certain cases. We use the correlation along with experimental values of ωe to estimate re for two electronic states each of Cu+2 and of TiO+. For Cu+2 , we obtain 2.35±0.10 Å for X 2Σ+g and 2.22±0.15 Å for the excited 2Π state at T0=1.143 eV. For TiO+, we obtain 1.54±0.05 Å for X 2Δ and 1.57±0.05 Å for the B 2Σ+ state at T0=1.39 eV.