Estimates of Quantum Tunneling Effects for Hydrogen Diffusion in PuO₂

Round 1

Reviewer 1 Report

In present manuscript, the diffusion and quantum nuclear vibration tunneling of hydrogen diffusion in PuO2 re studied by density functional theory and quantum double well approximation. The research work showed that the choice of the exchange correlation function has little influence on the calculation results, and when the PuO2 lattice is fixed at the experimental density, the expression of spin in the system and the extended Hubbard U correction have little influence on the formation energy of hydrogen point defects. The approximate activation energies of transitions between hydrogen gap sites seeded by the semi empirical quantum model are calculated, and the quantum tunneling enhancement relative to the classical dynamics rate is determined. The model study found that under environmental conditions, the diffusion rate in H/PuO₂ system can be increased by more than an order of magnitude, and these effects still exist at high temperatures. The research work can be used as a rapid evaluation and screening tool for possible quantum nuclear vibration effects in condensed phase materials and surfaces, and is of great significance. The work is very interesting. The data in this manuscript are full and accurate, the analysis and interpretation are reasonable, and the results and the data set can well support the conclusions obtained. It can be accepted for publication as it is.

Author Response

We thank the reviewer for their comments and for recommending publication of our manuscript as is.

Reviewer 2 Report

In the present manuscript, the authors performed an exhaustive DFT computational study across different levels of theory, employing various exchange-correlation functionals to study point defect formation energies for hydrogen in PuO₂, and then utilizing the obtained data to predict hydrogen diffusion rates for different diffusion pathways, explicitly considering quantum tunneling effects in contrast to classic diffusion models and comparing with the latter.

The authors showed that all utilized functionals and different magnetic models (including noncollinear models) yield essentially comparable results in terms of lattice geometry and band gap energies, which is an important contribution for future studies of PuO₂ and related materials in terms of the accuracy/expense tradeoff. In the diffusion rate prediction part, the authors show that quantum tunneling effects play a significant role particularly for diffusion scenarios where bond breaking and formation occur, and provide a recipe for potential future assessment of the magnitude of quantum effects in various systems.

The study is very solidly designed and exhaustive, taking into account a multitude of parameters and systematically evaluating their impact. All results are presented clearly and in sufficient detail, and back up the conclusions drawn by the authors. Stylistically, the paper is written fairly well and is easy to read, notwithstanding the occasional typo (which will most certainly be sorted out during the proof).

In summary, both the scientific and stylistic quality of the manuscript is laudably high throughout, and the proposed method is of certain interest to the computational solid state physics/chemistry community.

I thus recommend publication in the present form.

Author Response

We thank the reviewer for their comments and for recommending publication of our manuscript as is.

Reviewer 3 Report

Type of manuscript: Article
Title: Estimates of Quantum Tunneling Effects for Hydrogen Diffusion in PuO2
Journal: Applied Sciences

Authors estimate the activation energies and quantum vibrational tunneling effects for hydrogen diffusion in PuO2. By using Density Functional approach authors show that results are relatively insensitive to exchange-correlation functionals and have only a small effect with the presence of spin in the system and the Hubbard U correction.  Then by using quantum double well approximation, the activation energies for transitions between hydrogen interstitial sites are calculated and the quantum tunneling enhancement is determined.  Enhancements of diffusion rates in H/PuO2 system at ambient conditions are suggested.

There may be a considerable effect due to other factors such as nuclear vibration and contributions of atomic masses towards hydrogen quantum tunneling of those systems, did the authors were able to address those effects to some extent?

Fig 1 should be updated to show supercell, interstitial, and octahedral in a single row and labeled as a, b, c. Then add the color balls legend by side to show which element is which, then reader can easily identify the system.

PuO2 has been determined experimentally…. This paragraph says about (labeled oct) and (labeled int), I don’t see it on fig 1.

It says “Lattice optimizations were performed for different PBE functionals and magnetic states. What kind of optimization did they perform, by keeping the same symmetry, or does it allow to do full optimization including lattice parameters and angles? It seems that the cubic structure is not maintained, then your structure is different from the original. Is it true? Detail optimization process should be added to the supplemental. Did they check pressure studies to see which structure gives you ground-state results?

Explain why DFT Hubbard U is different from DFTB/ChIMES and why they show comparable results for both U. Anything that authors can think of scientifically to this change?

Table 2 should be compressed by doing compressed rows on Latex. The whole manuscript takes a lot of space for plots and tables that are not organized well to compress results and small space. You can adjust them more readable than this. F.U is not defined anywhere.

What basis set did they use in DFTB/ChIMES? I think the results may deviate accordingly. Is there any way to improve that?  Do they use periodic boundary conditions or open boundary conditions with confined potentials?

Table 3: is this without SP? Is Table 4 with SP but without GGA+U and SOC? It is confusing to keep track of those for the reader. I would suggest adding that to the description of the table.

The authors discuss formation energies and activation energies but have not shown how those will be calculated in the manuscript. It is better to discuss those. 

Fig 5: re-organize them to be on the same row with legends. Axis labeling should be clearly visible and may be larger font than shown.

 

All the tables and figures need to be presented in a better way, by compressing the space and including all labeling, legends, and so on.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf