Theoretical physicists Steven O'Malley and Don Beck
Theoretical physicists Steven O'Malley and Don Beck
“Tech physicists unearth the secrets of atomic heavyweights”

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It's Not Elementary

by Marcia Goodrich

Michigan Tech researchers have nailed down a fundamental property of some of the biggest, baddest elements on the periodic table.

Physics Professor Don Beck's research team, including Research Associate Steven O'Malley, has calculated electron affinities for the lanthanides and the actinides, the twenty-eight heaviest elements which make up the last two rows of the periodic table.

Lanthanides, also known as rare earths, are used in the production of lasers and sunglasses. Actinides, the bottom dwellers of the periodic table, are arguably the scariest collection of elements on Earth, including as they do plutonium and other deadly substances.

"Electron affinity" is the amount of energy required to pluck an electron from an anion (an atom with an extra electron orbiting around its nucleus). Elements with low electron affinities (like iron) give away that extra electron easily. Elements with high electron affinities (like chlorine) hang onto it for dear life, so understanding electron affinity is critical for predicting the outcome of chemical reactions.

"I remember learning about electron affinities in tenth-grade chemistry," said O'Malley. "When I began working as a grad student in atomic physics, I was surprised to learn that many of them were still unknown."

They were, in fact, the lanthanides and actinides. In terms of atomic structure, these are perhaps the most complex of elements, which is why no one had been able to calculate their electron affinities before.

Here's what makes them so tricky. Electrons orbit in shells around an atom's nucleus, something like the layers of an onion, but in stranger shapes. Within each shell are a number of subshells. A subshell is like an egg carton: it can hold from one to a certain number of electrons, but no more.

Typically, as you work your way down and across the periodic table to larger and larger atoms, the inner shells fill up with electrons, and then new shells and subshells are formed sequentially and fill up pretty neatly.

That's not what happens with the lanthanides and actinides. Before one subshell in the sequence fills up, additional electrons begin making even more shells. Then, as you move across the periodic table to the heavier atoms, electrons finally occupy all the vacancies in that first shell.

Why would this matter for electron affinity? Several forces hold electrons in their orbits around the atom's nucleus. Two simple ones are electrons' attraction to protons in the nucleus and repulsion away from their fellow orbiting electrons, what Beck calls "the B.O. effect."

A full shell exerts forces that are pretty constant on the electrons orbiting farther from the nucleus, which had made it relatively easy to calculate the electron affinities of most elements. But if there are vacancies in a shell—as there are in the lanthanides and actinides—the electrons in that shell can shuffle around, playing musical chairs, as it were.

The forces exerted by an electron vary depending on which slot it occupies. And, in addition to simple electrical factors, there are other complex variables to contend with at the subatomic level, including relativistic and many-body effects.

Here's how it works with the lanthanides. Before the so-called 4f subshell fills up, the additional electrons begin making new shells. Then, as you move across the periodic table to heavier atoms in the lanthanide series, that 4f subshell is fully occupied with its maximum number of fourteen electrons.

With several electrons bouncing around in those fourteen slots, over two hundred different arrangements of electrons in the 4f subshell are possible in some of the lanthanides. "It's a nightmare," says Beck.

With funding from the National Science Foundation, his group of theoretical physicists began their work on electron affinities in 1994, focusing on the lanthanides. Then in 2007 they made a computational breakthrough that allowed them to drill into the "nightmare" middle of the row from both ends, one anion at a time. In just eighteen months, they found electron affinities for all the remaining lanthanides.

With the rare earths under their belt, the team decided to forge ahead with the actinides in 2009. "They were even more complicated," said O'Malley, since even more subshells are involved, and they, too, do not fill up neatly and cleanly.

"But having worked on the lanthanides, I knew what to expect."

Armed with advanced methodology and plenty of experience, the researchers finished calculating the electron affinities of the entire actinide row in about five months.

What's next? Their findings will be referenced in the next iteration of the classic text The Handbook of Chemistry and Physics, now in its ninetieth edition.

The team's theoretical results have already been partially verified by experimentalists, but the process may take awhile. "Universities don't like to deal with actinides—they are both radioactive and poisonous," Beck notes.