On Two Different Objectives of the Concepts of Ionic Radii

Abstract

Experimentally and theoretically derived interatomic distances (D) and ionic radii (R) of more than a hundred monomeric (AX), dimeric (A2X2, ABXY), and crystalline ([AX]) alkali halide species (A=Li, Na, K, Rb, Cs, Fr; X=H, F, Cl, Br, I, At) have been analyzed. Chemists use the word "atomic radius" for two antithetic concepts. Let D(CiEE'jj') be the "billion" of distances i between two adjacent atoms in the millions of known compounds C from a hundred different elements E in bonding states j. The common chemical aim is partitioning D approximately into increments R(Ej) +R(E'j'). This can be achieved with a few (say <thousand) predictive constants R(Ej). An antipodal aim is specifying in hindsight an electron density feature in the "billion" of different bonds i, by partitioning them into "two billions" of exact bonded radii R(E)(Ci) + R(E')(Ci). The constant incremental and the variable bonded radii concepts with the same generic name are useful in different fields of research. Different concepts should be well distinguished, since they have different meaning, different numerical values, and different purposes.

Theoretical Studies on Hexanuclear Oxometalates [M6L19]q−(M = Cr, Mo, W, Sg, Nd, U). Electronic Structures, Oxidation States, Aromaticity, and Stability

“…Table 1 lists the optimized bond lengths of the O h structures, which increase from Cr through Sg and a bit further to Nd and U. Assuming the concept of gauged ionic radii, 38 45 (b) 12O b : The six metal atoms are netted and kept together by 24 W−O b bridges, each with a two-center O b -2p σ →W-5d z2 σ-donor bond ( Figure 2d) and with a half of an "aromatic" three-center W-5d xy ←O b -2p π →W-5d xy π-bond ( Figure 2e) and a half of an "aromatic" three-center W-5d z2 ←O b -2p π →W-5d z2 πσ-mixed bond ( more, forming rather weak three-center W-5d z2 ←O c -2p→W-5d z2 σ-interactions ( Figure 2g). The W···O c distances of 232 pm correspond to vanishing covalence, when extrapolating Pyykko's covalent radii to zero valence.…”

Additive Covalent Radii for Single-, Double-, and Triple-Bonded Molecules and Tetrahedrally Bonded Crystals: A Summary

“…Similarly, the "CR" set has 126 and 119 pm for oxide and fluoride, respectively. For recent summaries, see Gibbs et al 13 or Liu et al 14 A further option, not discussed here, is to go beyond these simply additive "hard-sphere radii" and to introduce "soft-sphere radii" with further parameters, see Lang and Smith, 15 or to make a Schomaker−Stevenson 16 electronegativity correction. 17 With more parameters per element, improved fits could be hoped for.…”

Quantifying the Tetrad Effect, Shape Components, and Ce–Eu–Gd Anomalies in Rare Earth Element Patterns

“…We follow the convention used by O'Neill (2016) of using the eightfold coordinated "ionic radius" from Shannon (1976), itself based on an earlier structure determination of simple lanthanide fluorides (Greis and Petzel 1974). Whether these values are sufficiently accurate and admissible as representative values for the entire field of geochemistry is still debatable, while being mindful that the "ionic radius" of an element varies based on the local environment and that ions are not rigid balls (Liu et al 2013;Gibbs et al 2013). There is ongoing work attempting to refine REE ionic radius values (Gagné 2018), and it is possible that slightly different radii will be used in future versions of the tools presented here.…”