For "Part 1: Background" click here. For "Part 2: Introduction to Relativistic Quantum Chemistry" click here.

In this post I will be applying the lessons of Part 2 on relativistic quantum chemistry to discuss papers which publish significant (relativistic) electronic structure calculations of astatine. To date, I have only found two which I would put in this category; they are referenced at the end of the paper. Articles of lesser direct significance will be referenced as they come up. I will attempt to keep this blog post updated as I become aware of other articles or as they are published. If anyone is aware of any relevant articles, I would greatly appreciate if you leave a reference or link in the comments below.

**Calculations of HAt**

Saue *et al.*, though older, does a nice job of using a primarily molecular-orbital based approach
to deal with the influence of spin-orbit coupling in astatine, in particular in HAt. In HAt the unfilled 6*p* orbital from the astatine will form molecular orbitals with the unfilled 1*s* orbital from the hydrogen. When considering the contribution of the *p* orbital, we must consider the contribution of two orbitals; the *p*_{1/2} and the *p*_{3/2}. The former corresponds to the case where the unpaired electron's spin is opposite its angular momentum, while the later corresponds to where its spin is aligned with its angular momentum. Since the *p*_{3/2} has a higher electronic angular momentum in the *z*-direction, it will have stronger spin-orbit interactions and hence be of higher energy.

Saue *et al.* report that while HI can still be well described by Russel-Saunders coupling, it breaks down for HAt. Their Dirac-Hatree-Fock (DHF) calculations indicate that the *p*_{1/2} and *p*_{3/2} energies in HAt are much farther apart than in HI, and hence do not mix in molecular orbitals as well. This causes the hydrogen to preferentially bind with the larger *p*_{3/2} orbital. This yields the paradoxical result that spin-orbit coupling actually lengthens the bond in heavier hydro-halogens, the opposite result seen previously due to the increased speed of the core electrons. Thus the relativistic changes in bond length for astatine compounds may be expected to not be of as great significance as for other (in particular close shelled) heavy elements.

They further calculate the dipole moment to be a mere 0.06 D **with the negative charge on the hydrogen**. This is clearly indicative of covalent bonding, and if anything is more in line with the results expected from a metal than a halogen.

**Calculations of Condensed Astatine**

Until recently, there was a distinct lacuna of any sort of high level calculations of the properties of condensed astatine. Although earlier works often speculated that condensed astatine would behave as a metalloid, or potentially even a metal, there was no strong evidence to this effect. That is where the 2013 paper by Hermann *et al.* features. In their paper, the authors report the results of relativistic DFT calculations on poly-atomic astatine. The paper is, as far as I can tell, generally considered to be the most authoritative treatment of condensed astatine published to date. The use of DFT should give us reason to take the findings with at least a small grain of salt, though considering the size of the system under question it may have been the only logical approach to keep the problem tractable.

Halogens in the condensed state will exist as ordered bimolecular pairs, and will behave as insulting non-metals. As pressure is increased on the halogen, two events occur: (1) The material's band gap narrows, causing it to eventually become a conductor, and (2) the inter- and intra-molecular distances become closer in size, eventually resulting in the full metallization of undifferentiated bonds across the entire material. Importantly, (1) is calculated to take place at lower pressures than (2), resulting in a pressure regime of paired atoms and yet a metallic state.

The pressure necessary for both (1) and (2) steadily decreases as we move down group 17. Iodine is calculated to close its band gap at 16 GPa, and to reach the fully atomic phase at 21 GPa. For comparison's sake, diamonds are created in the laboratory at pressures usually around or somewhat above 10 GPa.

Hermann *et al.* began by running scalar relativistic DFT calculations on condensed astatine, i.e. DFT calculations which include the relativistic change in orbital size but neglect spin-orbit coupling. These calculations found astatine to be rather similar to iodine, and to remain non-metallic up to 9 GPa. However, when spin-orbit effects where calculated, **astatine was calculated to be a fully atomic metal at atmospheric pressure**. This is an extraordinary change for merely introducing spin-orbit effects, and it leads me to suspect that there are issues with at least one, and potentially both of the DFT calculations. However, without any other calculations (such as coupled-cluster) to compare the results with, I can't say where the problems may lie.

**Conclusions**

In conclusion, we are left with Bresler's observation that "the properties of the metal and the halogen are curiously combined in this element." It would appear that in solution astatine exhibits both metallic and halogenous qualities. **Current electronic structure calculations indicate that in the condensed phase astatine will most probably exhibit purely metallic characteristics at or slightly above atmospheric pressure. However, I believe that there is a clear need for more sophisticated and computationally expensive calculations to be run on condensed astatine** (no small task, I admit). Until such time as said calculations are run, it is my opinion that the reported characteristics of condensed astatine should be treated as speculative. Hmmm, maybe time to talk to my PI about my next project...

**References**

(1) T. Saue, K. Faugri, and O. Gropen, *Relativistic effects on the bonding of heavy and superheavy hydrogen halides* Chemical Physics Letters **263**, 360-366 (1996) available here.

(2) A. Hermann, R. Hoffmann, and N.W. Ashcroft, *Condensed Astatine: Monatomic and Metallic
* Physical Review Letters **111**, 116404 (2013) available here.