O'Malley Completes the Lanthanide Anion Series

March 12, 2009

Postdoctoral Research Associate Steve O'Malley has finished calculating the electron affinities (EA) of the entire lanthanide row. Previous work had been done on the endpoints of the row, but O'Malley's breakthrough design of the 4fⁿ subgroup has permitted the first accurate calculations for the complex middle-row lanthanides. Relativisitic configuration interaction methods were required for proper treatment of the heavy atoms. Calculations which would have taken months or a year were accomplished in a day. The results are being published in two papers in Phys. Rev. A.

Filling in Some Age-Old Blanks: Physicists Calculate a Fundamental Property of the Rare Earths
Physics Professor Don Beck's research team, including Research Associate Steven O'Malley, has filled in some longtime blank spaces on the periodic table. They have calculated electron affinities for the lanthanides, a series of 15 elements commonly known as rare earths...READ MORE
Tech Today, March 12, 2009

According to O'Malley, “I remember learning about electron affinities in 10th grade Chemistry class, and when I began working as a grad student in Atomic Physics I was surprised to learn that many of them were still unknown. Our group has always pushed the boundaries of the complexity of our Atomic Physics calculations where others have been content with dealing with much simpler systems. At some point I realized that it was simply unacceptable, given today's computational capabilities, that no one was even making an attempt at these calculations.”

Interview with Dr. Steve O'Malley

Q: How long did the entire set of lanthanide EA calcs take?

A: These calculations represent about one year of my time, an additional year prior was spent building up the set of codes that was needed to tackle them.

Q: I take it you don't use the "lanthanoid" term over "lanthanide".

A: Lanthanide is an older term. The powers that be in scientific nomenclature prefer lanthanoid because the “-ide” suffix generally denotes a negative ion (which I'm focusing on here even though I refer to the neutral atoms as lanthanides). Perhaps chemists use the newer term, but I just searched the APS site (Physical Review series of journals), and I found >250 papers using “lanthanide” and none using “lanthanoid”. Interestingly, the spellchecker of the Open Office program I'm using to edit this rtf file recognizes “lanthanide” but not “lanthanoid.”

Q: EA's for lanthanides have been difficult to predict because their negative ions are unstable.

A: They are not unstable, I'm reporting anion states that lie below the neutral ground state. Calculations have been difficult due to the computational complexity of the configurations.

Q: EA's for lanthanides are very tiny, traditionally listed as about 50 kJ/mol, or half an eV for any of them. What was that estimate based on?

A: Partially on semi-empirical estimates, most recently, say last 20-30 years, there were AMS (atomic mass spectrometry measurements) that couldn't directly measure the EA's, but could measure the small relative yield of these anions compared to other elements, which led to the smaller estimates of EA's. Newer experiments are capable of identifying energies of individual transitions in the photo-detachment spectra, but often the identification of the corresponding anion state and neutral threshold involved are less than straightforward. Hopefully the composition of our calculated anion states will be useful to experimenters in performing this analysis.

Q: How have similar calculations compared to yours?

A: We actually agree quite well with some earlier calculations that exist, though improvements in the amount of correlation we can add generally results in greater binding (higher EA), even compared to work from our own group from the early 90's. The complexity of the configurations, though, restricted earlier computational groups to the ends of the row. Our values for Nd^– through Er^– are the first ab initio EA's available for these anions.

Q: Can you give a sense of the expense of a calculation, plus the computing resources?

A: Our computers are actually quite modest by today's standards (2.5 GHz processor). The important achievement here was the set of restrictions made on the 4f subgroup of each atom/anion. For this study the most complex individual calculations took about 1 day of CPU time (the trick is building up the basis set rather than the final execution of the code). By my estimates, however, if I could actually re-dimension the main RCI code to accommodate the level of correlation here without using my new data preparation techniques (4f restrictions) and dramatically expand the RAM to allow such an expensive calculation, the data presented in these two papers would represent a solid decade of CPU time even on a much faster PC.

Q: Are there specific applications for negative ions, or was your intention to complete the chemical trends in the periodic table?

A: At this point I think the value is purely scientific in terms of completing our understanding of EA's of the whole periodic chart, however, we hope that the methods we've used here could eventually be expanded to lanthanide neutral atoms and positive ions which would have more practical uses in areas such as molecular, solid state, or plasma physics. The 4f restrictions lend themselves very well to describing the lowest few states of the neutral atom and attachments of an electron to them. If one wants to look higher up in the energy spectrum of an atom or ion, the computational savings would be less dramatic.

Q: The relativistic component of the energy calculation is critical because the trend would be qualitatively incorrect without it.

A: Yes. Heavier elements must be treated relativistically. For the lighter atoms, say iron (Fe Z=26) or smaller, one can use nonrelativistic techniques, perhaps with some small corrections, but for elements near the bottom of the chart a fully relativistic formalism is the way to go.

Q: Do you anticipate that the EA values will start appearing in periodic tables?

A: I doubt you will soon see companies printing posters of the periodic chart with our data on them. However, we have some contact with experimental groups at Denison University in Granville, Ohio and University of Nevada, Reno, and our hope is that they will take up the experimental side of the lanthanide anion study as they have in the last decade or so. Once there is experimental verification (and we expect some adjustment of our values) we would expect more formalized acceptance of these results.

Q: Are there any controversies about the numbers within the atomic community?

A: There is some question in several cases in disagreement with the UNR experimental group who have reported EA measurements of several lanthanides of 1.0 eV or more over the last decade or so. However, we believe that their results are being misinterpreted in many cases, identifying peaks in their energy spectra with the neutral ground state when they, in fact, correspond to excited neutral thresholds much higher up in the atomic energy spectrum. This misidentification drastically overestimates the EA. In at least one case, Ce^–, the Denison group seems to have confirmed our re-interpretation of these data.

Q: What's left in this series, and then what's next for your research?

A: Well, we have stated in the second paper of this study that we've identified all the lanthanide anion configurations, and that future experimental work will likely just shift our EA values up or down a modest amount, say 0.03 eV or less, resulting in perhaps a few more or less bound states for each anion. Our work so far has been primarily on ab initio energy calculations. If we can expand this work to photodetachment calculations (which requires dealing with excited thresholds in the neutral spectra), we can directly compare our data with the experimental photodetachment spectra to verify our re-interpretation of their data, as was the case in our earlier Ce^– work.

Currently, however, I'm working on an analogous study of the actinide row.

Q: How about a little bio—you've been doing research here for several years.

A: I got my BS in Physics at the University of Michigan and originally came to Tech intending to get a MS in Mechanical Engineering. I found that the ME professors that everyone else in my classes found to be too tough were the ones I liked best (they were doing full derivations of every equation and perhaps using a bit more calculus than others would have preferred). When I realized these courses were being taught like a Physics course (IMHO), I decided to continue pursuing Physics. Most of my work with Don Beck as a graduate student was also with transition metal anions and the ends of the lanthanide row. After I got my PhD at Tech, I stayed on as a postdoc with Don Beck and more recently have worked as an instructor for the department. I've struggled in recent years with the decision to continue with Atomic Physics or move on to something different. I think this series of papers tackling all the rare earth elements may make a nice cap to my contribution to the Atomic Physics community as I contemplate new directions for my career.