Fundamentals of Diatomic Molecular Spectroscopy

Round 1

Reviewer 1 Report

Author presents a discussion about the fundamentals of diatomic molecular spectroscopy, with emphasis in he interpretation of optical spectra rbased on quantum mechanics, with a especial understanding of the concept of angular momentum operators.

Some points need attention and a better explanation:

• In INtroduction, author says about the original contribution of Oskar Kleis' work, and it is not clear what is new in this contribution and what isactually based on Oskars' previous work. Please clarify that.
• The mathematical transformation on line 117 and following, including equations 8 and 9, are not clear enough. Please clarify it.
• The experimenta data on Figures 2 and 3 are depicted as vibrational spectra, but they are really rotovibrational spectra, and are not clearly discussed in the results. Please clarify it.
• What is the main point in item 3.3.2. (Comparisons with measured spectra)? Since there is no spectra, why this sentence with no meaning? Please add some comment on that.
• At the end, what is the main difference between this work and O. Klein's work? Why there is no comment on the concluding remarks on this? Or everything here is original?

Author Response

Responses to Reviewer 2:

Thank you for your comments, edits are highlighted in green text.

(1) I clarified Oscar Klein's work with respect to this review by including lines 53 to 59 over and above using 'review' in lines 9 and 48. And the clause in lines 65 and 66 further clarifies O. Klein's contribution, also emphasized in lines 92 to 94.

(2) Clarifications regarding the transformation (original manuscript: Line 117) are in lines 131 to 135.

(3) Descriptive text is included for clarifications regarding the presented spectra in Figures 2, 3 (and Fig.1) see lines 183-188.

(4) Sections 3.3.1 and 3.3.2 are now combined, title of Section 3 is slightly modified to 'Selected diatomic spectra'. Extra text is also included to describe computations, see lines 190-202.

(5) In the Discussion and conclusions Section (added 'and conclusions' in line 219), lines 226-227 emphasize O. Klein's original communication, and lines 228-229 remark on applications. In addition, lines 233-235 spell out that this review emphasizes that there is no mathematical justification of reversed angular momentum operators.

Respectfully,

Reviewer 2 Report

The work considers fundamental properties of angular momentum and its transformation upon "laboratory-molecular fixed coordinate systems transition" in diatomic asymmetric top. The author uses the so-called reversed internal angular momentum concept of Van Vleck (1951), where angular momentum referred to axes mounted on the molecule adheres to opposite-sign commutator algebra. The reversal of motion in quantum mechanics is described by an anti-unitary transformation, requiring sign change and complex conjugation. The author shows that the reversed angular momentum concept is misleading and quantum mechanics explains all possible contradictions, which one would think to be found.

To be honest many practical spectroscopists do not care much about these theoretical details in their analysis of molecular spectra using the rules established by Herzberg, Mulliken, Van Vleck, Lefebvre-Brion and Mizuchima. But nevertheless, this review is very useful from the fundamental point of view and fits very well to the issue of MDPI Fundamentals J. It can be recommended for publication without any doubts.

Few recommendations have to be mentioned, however. The author does not pay so much attention to the time-reverse and spin-splitting problems.  Thus, analysis of the C₂ molecular Swan system (d³Π_g → a³Π_u band) and the A-X band of OH radical does not consider spin splitting and lambda-doubling. It would better if the modern Fundamentals of Diatomic Molecular Spectroscopy will touch a bit the modern achievements in ab initio applications for electronic diatomic spectra, including fine structure and transition moments calculations, at least for C₂ and OH species, discussed as examples in this review. One ref. [38] is not enough for plane reader to comprehend all spectral aspects behind Fig. 2. The same concerns molecular laser-induced breakdown spectroscopy and only one reference [40]. Few sentences would be necessary to provide minimum explanation for the plane reader.

Author Response

I appreciate the comments by the reviewer, edits are in blue.

I understand that practical spectroscopists may not  care about the origin of rules established over decades. However it is important to realize that mathematics needs to be consistent with quantum mechanic theory and symmetry properties.

(1) Actually lambda doubling and spin splitting is included, added lines 238-239 in blue. In addition, added descriptive text in lines 190-202 to summarize the computing methodology.

(2) I agree with the expressed need of text regarding spectra, see lines 183-188, and lines 190-202, viz. more than in Ref 39 (was Ref 38 in the original manuscript).

(3) Regarding laser-induced breakdown spectroscopy, added text is in lines 210-218. Hopefully it is acceptable to include 'and references therein' in Ref 41 (as Ref 40 in the original manuscript) in response to more references than just Ref 39 and Ref 41 (were Refs. 38 and 40, respectively).

(4) Included as well reference to ab initio computations, see liens 119-122 and new Ref. 35.  [ The review in Ref 35 includes routine use of regular and anomalous commutator relations, maybe in a way that VanVleck writes in his 1951 paper (Ref 2) that an anomaly applied consistently is no anomaly at all - how can we require adherence to mathematics? Of course, in VanVleck era, approximations were necessary but now we can compute diatomic spectra without a priori  approximations. No further text is included, so the comment in square brackets is just for practical spectroscopists that care about mathematics.]

Respectfully,  

Reviewer 3 Report

This paper is good.

Author Response

I appreciate the recommendation by reviewer 3. Thank you.

Round 2

Reviewer 1 Report

Authors have done a very nice improvement to the manuscript, and it is ready now for acceptance.