Vibrational Excitation of HDO Molecule by Electron Impact

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors present a theoretical (from first principles) study of the vibrational transitions in HDO molecule by electron impact.  Rate coefficients for all the transitions involving the 16 lowest vibrational levels are obtained, and analytical fits are provided to help modeling astrophysical media.  The results point to significant differences between HDO and H2O.  

This work is a valuable contribution to the field and is suitable for publication. However, I find the following minor issues that would benefit from clarification:  

Line 78 

• There is an inconsistency in the number of significant figures in the masses of D and H. Is there any reason for this? 

• Additionally, regarding the notation for atomic mass units, both ‘amu’ and ‘u’ denote the atomic mass unit, but they are not exactly the same and ‘u’ is the preferred in modern scientific literature.  

Table 2 

• Some (not all) numerical values presented in Table 2 are truncated compared to those in Table 2 of Reference [22]. For example, the energy level (040) should be 5420.04 instead of 5420, or the energy level (010) should be 1403.48 instead of 1403.5. Am I missing something? 

• Additionally, why do the levels (050), (210), and (130) calculated in the present work have nine significant figures, while the others have eight?  

 

Figure 7 

• Several data cited in Figure 7 are missing in the bibliography. In particular, I could not find: 

• Khakoo (2009), El-Zein (2000), Shyn (1988), Seng (1976), Nishimura (2004), Yousfi (1996) (and potentially others). The authors should verify that all cited references are included in the bibliography. 

• The discussion in lines 180–188 regarding Figure 7 could benefit from additional content. In particular, I notice that: 

• The new HDO cross-sections for stretching transitions are approximately twice the size of those for H2O in the 2024 calculation, yet they are similar to the 2021 results. 

• Experimental data for H2O are closer to the 2021 theoretical results than to the new 2024 calculations. 

Given these observations, what conclusions can be drawn about the behavior of HDO cross-sections compared to H2O? A more detailed interpretation of these results would benefit the discussion. 

 

References 

• There are differences in the formatting of references: some include DOI links, while others do not. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The present study provides electron impact cross sections and excitation/de-excitations rate coefficients of H2O and HDO molecules using the well-known R-matrix method. The present results of energies have been compared with both previously published experimental and theoretical data. The present work provides useful results related to astrophysical applications. The study warrant publication in a leading journal such as atoms, however a necessary revision is required to improve the merit and presentation of the manuscript.

 It is clear the superiority of the published results by Zobov et.al. where, their energies more accurate and identical to experimental results. The uncertainty in the energies calculations should be widely discussed by the authors in a manner of why their calculations showed higher uncertainty relative to experimental data.

 Despite authors focused on the astrophysical applications in the introduction but the used limited range of incident electron energy (up to 10 eV). In the interstellar and spacialobjects it is familiar to observe high energies for collisional processes. This point must be argued in details to explain why especially stopped at this range of collision energy?

What is the general symmetry group of HDO?

“Cluster Singles, Doubles and Triples (CCSD(T)) calculations with Hartree-Fock orbitals, followed by the optimization procedure in the C1 symmetry group” this sentence needs more explanation, may be using table or other tool to show how the number of energy levels increased by applying SD or T strategy.

 

Figures 5 & 6 explained the cross sections as a function of electron energy, that’s useful but a deep discussion of the physical meaning of phenomena needs to be lighted within the manuscript text. Just pointing to the figure or explaining it in brief sentences is not enough.  The same as for Figure 8. For rate coefficients for the excitation and (de-)excitation by electron impact.

 

We used a mass of 1.008 amu for the hydrogen atom and 2.0141018 amu for the deuterium. Reference is required.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This is a theoretical study of electron scattering by HDO molecules performed by using R-matrix code. The studied process is vibrational excitation/de-excitation, where cross sections and thermally-averaged rate coefficients are determined. The code has been applied for several geometries of the target molecule. Three-dimensional vibrational states of HDO were evaluated by solving the Schrödinger equation numerically and applying the vibrational frame transformation. This research is an extension of the previous study by the same authors published in A&A (2024) now applied to the system with a reduced symmetry point group. HDO properties, such as the equilibrium structure and vibrational frequencies have been obtained in this study and compared with experimental data. Four fixed geometry configurations have been obtained and the reactance K-matrix calculated for these geometries. Considered electron energy is below the excitation of the first excited electronic state of the molecule i.e. about 8.3 eV above the ground electronic state at the equilibrium geometry. Calculated energies of the lowest vibrational levels of HDO are in good agreement with experimental ones, with relative deviation less than 1%. Wave functions of several lowest vibrational levels are presented. The cross sections for the v’(v1’v2’v3’) ← v(v1v2v3) process and thermally-averaged rate coefficient α_(v’←v)(T) have been calculated and graphically presented together with the uncertainties assessment. Data are also given in tabular form in the appendix, what may facilitate the incorporation in different models of plasma or astrophysical observations.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have revised the original manuscript based on my previous comments and I believe it is ready for acceptance.

Author Response

Referee 2 wrote:

The authors have revised the original manuscript based on my previous comments and I believe it is ready for acceptance.

Response:

We would like to thank the referee for the attentive reading of the manuscript.