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Theoretical Chemistry

Resizing the chemical elements

Researchers systematically recalculate the atomic and ionic radii of elements 1 to 96

by Stephen K. Ritter
September 5, 2016 | APPEARED IN VOLUME 94, ISSUE 35

Credit: Chem. Eur. J.

Ever stop to contemplate the size of an atom or ion? Martin Rahm, Roald Hoffmann, and Neil W. Ashcroft have. For consistency’s sake, these Cornell University scientists have just completed a systematic theoretical estimate of the atomic and ionic radii of the first 96 elements of the periodic table (Chem. Eur. J. 2016, DOI: 10.1002/chem.201602949).

They say the size question has been a natural one to ask over the past century, given that we have been collecting good experimental data on atoms in every form of matter and have increasingly reliable theories about the nature of atoms. Still, the Cornell group posits, there’s no unique answer to the query: “What is the size of an atom or an ion?”

One can just come up with carefully defined—but, in the end, arbitrary—criteria, Hoffmann says. And many researchers have. Ultimately, the validity of one or another definition is measured by how well it aligns with experimental data, in particular with crystal structures. The importance of having standardized estimates such as the Cornell team’s is to help understand ambiguities when rationalizing material properties, such as crystal packing and molecular structures.

Rahm, Hoffmann, and Ashcroft began by setting up a size limit. Building on prior estimates, they settled on a cutoff being the average distance from the nucleus where the electron density falls to 0.001 electrons per bohr3, where bohr is the Bohr radius, which is 0.53 Å. The radii were then derived using relativistic all-electron density functional theory calculations. This approach provides radii that “agree remarkably well” with experimental estimates of radii derived from crystal structures, the researchers note.



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Jeremy Wessel (September 6, 2016 4:21 PM)
Perfect timing! I just talked about atomic radii in my General Chemistry class this morning!
samantha glazier (September 8, 2016 11:41 AM)
I am writing quiz #2 right now. I think I am going to ask why group 2 and group 1 are odd.
Arturo Vergara (September 7, 2016 12:49 PM)
Bob (September 7, 2016 3:37 PM)
Why are group 2 radii higher than group 1? Seems very strange. Aren't the outer electrons drawn in more tightly in group 2?
Steve Ritter (September 9, 2016 3:40 PM)
Martin Rahm responds:
"This is a good question, and one to keep in mind. When considering the electron density as the sole measure of atomic radii, the group 2 radii are indeed larger than group 1. There are two electrons in the outermost s orbital, instead of one, which make the orbital expand. However, these outermost electron densities of isolated atoms have not been measured experimentally. Instead, crystallographic radii have been derived in clever ways from statistical analyses of crystal structures, i.e. from interacting atoms. In light of our calculations, a likely reason why the radii of group 1 de facto comes out larger than in group 2 experimentally, is that the outermost electron density of group 1 atoms acts "more repulsively". To understand why, one needs to consider the effect of electron spin. Electrons of equal spin cannot occupy the same space, and avoid each other to a larger degree than electrons of opposite spins. The outermost electron density (which we use to define the radii) of group 1 is special in that a single electron, with spin 1/2, dominates it. This is in contrast to atoms of all other groups, where the outermost electron density arises from multiple electrons, with largely canceling spins. This difference in same-spin repulsion between otherwise identical electron densities appears to translate into the solid state, effectively making group 1 atoms take up more space."
(September 8, 2016 11:30 AM)
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