Who would have thought that in the year 2022, the size/volume of an atom is still open issue!
"... Yet, from an electrical field perspective, Mg2+ should be significantly larger than Mg0, because the electric field ultimately depends on the ratio of the number of protons-to-electrons. In other words, the area affected by a cation should be large, while the density of electrons should be small. Hence, the Mg2+ example serves as an illustration that the field-defined size is not “atomic size” in the conventional sense and provides different insights than other existing atomic size models. ..."
From the abstract:
"Chemical shape and size play a critical role in chemistry. The van der Waals (vdW) radius, a familiar manifold used to quantify size by assuming overlapping spheres, provides rapid estimates of size in atoms, molecules, and materials. However, the vdW method may be too rigid to describe highly polarized systems and chemical species that stray from spherical atomistic environments. To deal with these exotic chemistries, numerous alternate methods based on electron density have been presented. While each boasts inherent generality, all define the size of a chemical system, in one way or another, by its electron density. Herein, we revisit the longstanding problem of assessing sizes of atoms and molecules, instead through examination of the local electric field produced by them. While conceptually different than nuclei-centered methods like that of van der Waals, the field assesses chemically affected volumes. This approach implicitly accounts for long-range fields in highly polar systems and predicts that cations should affect more space than neutral counterparts."
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