Superconductivity in RbH$_{12}$ at low pressures: an \emph{ab initio} study

1. This is a very detailed, careful and accurate calculation of potential superconducting properties in a binary hydride with a potentially "low-pressure" high Tc

2. Both zero point fluctuations and anharmonicity, often overlooked in calculations of this kind, have been accounted for.

3. The paper is extremely well written and easy to read. Because of this, I would expect it to gain a wide audience, not only for its specific content (RbH12) but for the clear presentation of methodology and explanation of results which are generalizable to other compounds

1. The results themselves are somewhat underwhelming as they don't vary from earlier results even with all the extra work and detail supplied by SSCHA

One extremely trivial matter:

In the last paragraph of the introduction the phrase "leaving *to* Immm and Cmcm phases to emerge" occurs. The "to" is odd. Is it supposed to be "two"? Or maybe "the"?

Publish (meets expectations and criteria for this Journal)

1. The authors employ an advanced method to study the superconducting properties of the RbH12 polyhydride. The calculations are sound.
2. The authors employ a clever trick to estimate the Raman activity of phonon modes in the system despite it being a metal.

1. The article does not propose a new material, nor it improves substantially the understanding of an existing one.
2. There are a few worrying methodological aspects. They are detailed in the requested changes. One important point is that the authors stretch the metastability range of this hydride, dismissing imaginary phonon frequencies as an interpolation error. The fact that SSCHA suggests that this system should be dynamically stable at a significantly lower pressure is one of the core points of the paper. It appears to be rather weak, in light of the fact that the interpolated phonon frequencies are imaginary.

1. In the abstract, and later in the results, the authors write that the Immm and P63/mmc phases will be dynamically stable down to a certain pressure even though their phonon dispersion exhibit imaginary phonons. The reason, verbatim, is “these are probably interpolation issues”. They refer to the fact that a point for which the SSCHA matrices were computed has become stable, while another for which they were interpolated remained unstable. It is very hard to consider this argument as reliable evidence to support the claim that the structure is metastable at this pressure. I understand that the a larger supercell may be too expensive to compute, but this is not a valid argument to claim stability at that pressure.
2. The authors estimate the Raman activity of the phonon modes in a rather unconventional way. Since in metals the polarizability is not defined, they take a random tensor, symmetrize it, and compute some intensities. This is a clever trick, but I do not think that showing a simulated spectrum that is wrong (by the authors’ own admission) is a good idea. I suggest they just show the peak centers as vertical lines with different colors to mark which one is active or not (by symmetry).
3. The smearing on the DOS in Fig. 5 appears to be the 0.02 Ry used to compute the charge density. The result unfortunately is a DOS which is all smeared out. I suggest they employ the 0.008 Ry smearing which they used for the matrix elements, which also gives an indication if the chosen k-grid is reasonable.
4. There is an inconsistency between the y axis label of Fig. 1 and what the authors write (“Fig. 1 shows the Gibbs free energy”). I think it’s because they take it at T = 0, but distinguish it from enthalpy because there is the zero point energy. However this is all very misleading. At T = 0 it makes no sense to call this a free energy. The zero-point energy is not part of the free energy, even though one may include it in the expression for Fh.
5. Concerning Fig. 4, it is also rather worrying that the lines are so irregular, and that they include so few points, especially since these are done with plain DFT calculations which should be very cheap. Moreover, there should also be a “RbH+11H” line, or something similar, i.e. a line showing how much higher are the proposed structure from the most important points in the convex hull. Showing only the enthalpy (or free energy) compared between RbH12 phases may mislead the reader into thinking that there is one RbH12 phase on the hull even at ambient pressure, which is not the case.
6. A minor point is that the authors write that “a first ab initio prediction of high-temperature superconductivity was done for H3S, followed immediately by the experimental confirmation”. The real story is slightly more complicated, as the group of Eremets had been working on hydrogen sulfide independently, and tried multiple times to double-check the validity of the experiment. In fact, in the time between Duan’s and Eremets’ arXiv papers there are only a few days, which would not have been enough to do all those experiments. This was written by Eremets himself in Physics Reports 856, 1-78 (2020). I think it would be right to give the late Eremets credit for that.
7. The authors used a mu* of 0.1 to solve the isotropic Eliashberg equations. In Ref. Nature Reviews Physics 6 509–523 (2024) it is clearly argued that this is inappropriate if the goal is to compare the results with the McMillan formula, as that formula assumes a mu* with a different cutoff on the Matsubara frequencies. Please take it into account.

Accept in alternative Journal (see Report)