Superconductivity, quantum hydrogen bonds, and rotten egg gas

I thought these three things had nothing to do with each other. Howevever, they do! Two enduring interests of mine, and commonly featured in this blog, are superconductivity and hydrogen bonding, particularly the role of quantum nuclear motion in the latter. The former is related to my beginnings as a condensed matter physicist and the latter more to my attempt, over the past decade, to become a chemical physicist. But, this post discusses how they can be intimately related.

About a year ago, a group reported superconductivity at 200 K, in a sulfur hydride compound under the incredibly high pressures above 100 Gigapascal (about 1000 kbar, which only a few years ago was not feasible). A nice commentary by Igor Mazin puts the discovery in context.

Aside: the starting compound H2S is commonly known as "rotten egg gas".

A longer paper is helpful and here I reproduce some of the abstract.

What superconducts in sulfur hydrides under pressure and why 
N. Bernstein, C. Stephen Hellberg, M. D. Johannes, I. I. Mazin, and M. J. Mehl

Intriguingly, superconductivity in the observed pressure and temperature range was predicted theoretically in a similar compound, H3S. Several important questions about this remarkable result, however, are left unanswered: 

(1) Does the stoichiometry of the superconducting compound differ from the nominal composition, and could it be the predicted H3S compound? 

(2) Is the physical origin of the anomalously high critical temperature related only to the high H phonon frequencies, or does strong electron-ion coupling play a role? 

We show that at experimentally relevant pressures H2S is unstable, decomposing into H3S and S, and that H3S has a record high Tc due to its covalent bonds driven metallic, which make this compound rather similar to MgB2, but unlike most other good conventional superconductors.

One thing that is striking is that there are few experiments (due to the high pressures) and the important role that theory (specifically, computations based on DFT-approximations) are playing. People are even debating differences of 20% in predictions of Tc!

The paper that particularly got my greatest interest was this one

Quantum Hydrogen-Bond Symmetrization and High-Temperature Superconductivity in Hydrogen Sulfide
Ion Errea, Matteo Calandra, Chris J. Pickard, Joseph Nelson, Richard J. Needs, Yinwei Li, Hanyu Liu, Yunwei Zhang, Yanming Ma, Francesco Mauri

It shows (again using DFT-based computations) that at the high pressures H3S undergoes a phase transition from a structure with a mixture of S-H covalent and S-H...S hydrogen bonds to a structure where the proton is delocalised between the two S atoms.

This structural phase transition is completely analogous to what happens in ice under pressure (and has a natural description in a simple model of H-bonding). Also there the quantum nuclear motion of the protons plays a significant role, leading to significant isotope effects (as observed in the superconductivity experiments).

Based on experience with these strong H-bonds, a couple of cautions are in order.

The S-H stretch vibrations (phonons) are highly anharmonic.

Computational results can vary significantly depending on what approximation (density functional or level of theory) is used.