It has been shown, using a “model-potential” analysis, that −Cn/Rn dispersive terms can be an important part of the physical bonding in M+/Rg complexes (M+=atomic metal ion, Rg=rare gas atom) for M+ ions with large, polarizable outer-shell electron clouds. The model potential equation consists of all attractive terms (accurately calculated or estimated) out to 1/R8, as well as an Ae−bR repulsive term. From known De, Re, and ωe values, and the first and second derivatives of the model potential, the repulsive constants A and b as well as the effective charge Z of M+ in a particular M+⋅Rg electronic state, can be determined. For the typical M+⋅Rg states considered here, Z=1.02±0.07, indicating that no extra “chemical” effects are necessary to explain M+/Rg bonding. Furthermore, the trends in the derived Ae−bR repulsive curves make good qualitative sense. A term-by-term analysis for M+⋅Rg states where the M+ ion is small and unpolarizable [such as Na+(2p6)⋅Rg] shows that −Cn/Rn terms contribute only a few percent to the bond strengths, while for M+⋅Rg states where M+ is large and polarizable [for example, Mg+(3s)⋅Rg], the −CnRn terms can contribute on the order of 40%–50% to the bond strengths, thus rationalizing semiquantitatively several heretofore puzzling De, Re, ωe comparative values.

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Articles you may be interested inComparison of the interactions in the rare gas hydride and Group 2 metal hydride anions J. Chem. Phys. 140, 084304 (2014); 10.1063/1.4865749Higher order two-and three-body dispersion coefficients for alkali isoelectronic sequences by a variationally stable procedure J. Chem. Phys. 134, 144110 (2011); 10.1063/1.3577967Inelastic electronic excitation and electron transfer processes in collisions between Mg ( 3 S 0 1 ) atoms and K + ( S 0 1 ) ions studied by crossed beams in the 0.10-3.80-keV energy rangeThe effects of dispersive C n /R n -attraction on M+/Rg bonding (M+=atomic metal ion, Rg=rare gas atom) It has been shown, using a model-potential analysis, that the large permanent quadrupole moment of the excited Mg ϩ (3p) ion can play a significant role in the strong physical M ϩ /Rg bonding observed for Mg ϩ (3p)•Rg͓ 2 ⌸͔ ionic states. The four permanent quadrupole terms included in the model potential ͑two proportional to 1/R 6 , two to 1/R 8 ͒ contribute substantially to Mg ϩ (3p)/Rg attraction near the bond distances R e . In fact, our analysis indicates that the leading charge/induced-dipole 1/R 4 attractive term contributes only ϳ25-30 % to the physical bonding in the Mg ϩ (3p)•Ar excited state, in stark contrast to the conventional wisdom that this term is usually dominant in M ϩ /Rg bonding. Empirically derived Ae ϪbR repulsive terms also show that electron/electron repulsion for a given Mg ϩ (3p)•Rg excited state is less than for the analogous Mg ϩ (3s)•Rg ground state, consistent with the fact that the Rg atoms approach the excited 3p orbital of Mg ϩ along its nodal axis. For the Mg ϩ (3p)•Rg͓ 2 ⌺ ϩ ͔ excited states, however, three of the permanent quadrupole terms are repulsive ͑with twice the magnitude͒ and thus contribute significantly to the extremely weak bonds and very large bond distances for the 3p ionic states. In contrast, the much smaller quadrupole moments of open-shell d-orbital states of transition metal M ϩ ions appear to have very little effect on their physical bonding with the Ar atom, at least for the few states which have been well-characterized spectroscopically. For all the M ϩ /Rg states discussed above, our model-potential analysis indicates that no substantial chemical or charge-transfer interactions are needed to rationalize the bond strengths, the bond lengths, and the vibrational frequencies ͑the ''shapes'' of the potential curves near their minima͒.

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