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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 | A version of this story appeared in Volume 94, Issue 35

A periodic table showing calculated radii of elements 1 through 96.
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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