Is science sometimes in danger of getting tunnel vision? Recently published ebook author, Ian Miller, looks at other possible theories arising from data that we think we understand. Can looking problems in a different light give scientists a different perspective?

Astatine – Relativistic Effects Needed?

The recent Chemistry World highlighted a recent publication on astatine, in which the paper predicted that due to relativistic effects on the inner electrons, it would be metallic and monoatomic in the solid state. As some may recall, in previous posts I have questioned such relativistic corrections since I had previously published a paper ( in which I showed that ionization energies and lower excited state energies could be related through reasonably simple relationships involving quantum numbers. In this, the s electron of gold was actually more "normal", if that means agreement with the required relationship is better, than either copper or silver.
The reason I regard astatine as annoying comes from this consideration. In my paper cited above, the ionization potentials of valence electrons could be calculated from simple relationships involving only quantum numbers when there was only one electron in the level, while an additional term was required for others that approximated to a term only in the quantum number , but in practice was better with a minor empirical correction for each group. The important point was that this term was constant for a given column of elements in the periodic table, and there are relationships between groups. (This term is conceptually due to additional quanta of action being generated through the waves exploring all available space, and attenuates as increases because the number of orbitals to explore increases the number of cycles before the required quantum of action is completed. This lies outside standard quantum mechanics, and I shall elaborate my alternative interpretation in future posts.) Now, in principle if my alternative interpretation is correct and relativistic correction is not required, the ionization energies of the elements I did not calculate should still be given by the published relationships. (I regard the equations as predictions, even if I did not evaluate them.)
The relationships were not exact. There were two unexplained small regularities. The first involved a small term (st for this post) the sign of which depended on whether n and were odd or even, the magnitude of which increased with the distance from shell completion. There was also a positive term (+T for this post) that applied only to paired p electrons following d shell completion, thus Se, Br, Kr, then Te, I and Xe all required +T, as did Po. Recently ionization potentials have been measured for At and Rn, so how do my functions perform?
The prediction for astatine, with +T was 9.7606 ev; without it, 9.1893 ev; the observed value is 9.3175 ev. What should I make of that? Suppose we consider radon. Without +T, the predicted IP is 10.7457 ev; the observed value is 10.747 ev, which in my view, is fairly close, so my obvious conclusion is that there is some interaction with the d electrons that applies to Po when n = 6, not for Rn, and annoyingly, somewhere in between for At. In my opinion, admittedly somewhat biased since I am supporting my own theory, this would indicate that if the "non-hydrogen-like" wave functions are correct, there is no need for relativistic corrections here. Finally, it may be of interest that the IP of Fr is predicted without st to be 3.903 ev; the observed value is 3.938 ev.  These calculated values are based solely on the wave nature, without any terms for interference with other waves or resonances. The value of st required for Fr is of very similar magnitude to that for Rb and Cs, except that Cs is of opposite sign. Then, to confuse everything, the ionization potential for radium is such that some further effect might be operating, and that could be relativistic in origin.
What relativistic corrections are suggested? In one account (Chem. Rev. 112: 371-384) without relativistic corrections, the ionization potential of gold was 7.057 ev, and with it, 9.147 ev (observed, 9.2254 ev). Thus it would appear that contraction of the inner orbitals adds over 2 ev, and this should increase as the charge on the nucleus increases. I am sorry, but for me, this does not add up.
Perhaps chemistry would solve this issue? My calculation of the bond distance in At2 is 150 pm, and the bond energy of hydrogen astatide is 273 kJ/mol. Would that settle the question? Perhaps, but annoyingly I can't see the data coming any time soon because the most stable isotope of astatine has a half-life of 8.1 hrs. 
Posted by Ian Miller on Nov 18, 2013 4:28 AM Europe/London

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