When Core Orbitals Act as Valence Orbitals: Linear and Bent Geometries of <i>MX</i> ₂ for <i>X</i> a Halogen and <i>M</i> an Alkaline Earth

Although the VSEPR model predicts the group 2 dihalides to be linear, it has long been known experimentally that the dihalides of the heavier group 2 metals are bent. High-level <i>ab initio</i> CCSD(T)/awQ(-PP) and CASPT2/awQ(-PP) calculations were performed for the ground states of MX₂ (<i>M</i> = Be, Mg, Ca, Sr, Ba, and Ra; <i>X</i> = F, Cl, Br, and I) to predict optimized geometries, inversion barriers, bending frequencies, and natural orbitals. The MF₂ for <i>M</i> = Be and Mg; the MCl₂ for <i>M</i> = Be, Mg, and Ca; the MBr₂ for M = Be, Mg, Ca, and Sr; and the MI₂ for <i>M</i> = Be, Mg, Ca, and Sr are predicted to be linear. SrCl₂ is linear at the CASPT2 level but is slightly bent (quasilinear) at the CCSD(T) level. Inversion barriers to linearity increase down the column for a given halogen. The bending harmonic frequencies of CaF₂ and SrCl₂ are comparable to the inversion barriers, so the molecules are predicted to be quasilinear at most temperatures and highly fluxional. Natural orbitals at the SA-CASSCF level show a mixing of the outer core p_n-1 orbitals of the alkaline earth with the valence s and p orbitals of the halides for MF₂ (<i>M</i> = Ca, Sr, Ba, and Ra), MCl₂ (<i>M</i> = Sr, Ba, and Ra), MBr₂ (<i>M</i> = Ba and Ra), and MI₂ (<i>M</i> = Ba and Ra), which drives the bending. BaF₂ and RaF₂ also exhibit mixing of the outer core s_<i>n</i>-1 orbitals with the 2s orbitals of F, which makes the bending more pronounced and the inversion barriers larger for these two molecules. All-electron calculations and population analysis suggest that the core d and valence d orbitals have only a small contribution to the bending. Ionicity increases down the column and decreases from the difluorides to the diiodides. Bending in these dihalides can be simply explained in terms of the outer core orbitals of the alkaline earth mixing with the valence of the halogens as they overlap the valence energy space of the halogens. Thus, the VSEPR model for predicting the bond angle for the Group 2 dihalides is good to on the order of ± 5 kcal/mol.