Correlation Between C–H∙∙∙Br and N–H∙∙∙Br Hydrogen Bond Formation in Perovskite CH₃NH₃PbBr₃: A Study Based on Statistical Analysis

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Referee report on the manuscript entitled: „Correlation between C─H∙∙∙Br and N─H∙∙∙Br Hydrogen Bond 1 Formation in perovskite CH₃NH₃PbBr₃: A Study Based on Statistical Analysis” written by Alejandro Garrote-Márquez, Norge Cruz Hernández and Eduardo Menéndez-Proupin.

 

This is a theoretical study based on statistical methods. The Authors used previously obtained molecular dynamics results (Ref. 33) to draw further conclusions associated with correlations of the hydrogen bonds present in the studied perovskite.

 

The Reviewer found the manuscript interesting and worth publishing. It could be consider as another way of post-processing in the MD studies. However, using statistics the Authors show how to work with so-called “big data”, which is a hot topic in the contemporary science.

 

However, before the manuscript will be published, The Reviewer would like to ask the Authors to add some Figures of perovskite and hydrogen bonds to make the study more clear for Readers. It would be nice to elaborate more about the number of hydrogen bonding via MD simulations (e.g. about it strength, disruption and formation etc.). According to the Reviewer it would be a good starting point for further statistical explanations.

 

This part of the study is very similar to Ref 33 “The X─H∙∙∙Br (X=C or N) HBs are revealed by regions of high numerical values of the combined distribution function (CDF)[34] of the distance H─Y and the angle Br─H─X. Based on the CDF, the condition for the existence of a N─H∙∙∙Br HB was defined as 𝑑(N−H)<3 Å, and 135º<∡(Br−H−N)<180° [33]. Furthermore, for C─H∙∙∙Br HBs the distance condition was defined as 𝑑(C−H)<4 Å, with the same range for the angle ∡(Br−H−C)” – this fragment should be rewritten and the Authors should revised their idea concerning N-H and C-H bond length. Please, check in some books the C-H and N-H bonds properties. The Reviewer understands that the approximation was taken from the MD simulations where the distances were changing as a function of time, but it is confusing. Please, explain properly what is the covalent bond, what is the hydrogen bond, what is the interatomic distance between heavy atoms involved in the hydrogen bond formation in the cases studied.

Author Response

Referee report on the manuscript entitled: „Correlation between C─H···Br and N─H···Br Hydrogen Bond 1 Formation in perovskite CH NH PbBr : A Study Based on Statistical Analysis” written by Alejandro Garrote-Márquez, Norge Cruz Hernández and Eduardo Menéndez-Proupin.

This is a theoretical study based on statistical methods. The Authors used previously obtained molecular dynamics results (Ref. 33) to draw further conclusions associated with correlations of the hydrogen bonds present in the studied perovskite.The Reviewer found the manuscript interesting and worth publishing. It could be consider as another way of post-processing in the MD studies. However, using statistics the Authors show how to work with so-called “big data”, which is a hot topic in the contemporary science.

Comment 1: However, before the manuscript will be published, the Reviewer would like to ask the Authors to add some Figures of perovskite and hydrogen bonds to make the study more clear for Readers.

Reply 1 :

We appreciate this important recommendation. In response, we have added two figures that visually clarify the structural context of the hydrogen bonds analyzed in this work:

• Figure 1: Displays a representative unit cell of CH₃NH₃PbBr₃, showing the relative positions of Pb, Br, and MA ions. The N–H···Br and C–H···Br HBs are explicitly marked, along with geometric details (angles and distances). This figure helps readers visualize the possible HB orientations inside the perovskite cavity.
• Figure 2: Shows a broader view of the structure as obtained from molecular dynamics, emphasizing the spatial distribution and connectivity of hydrogen bonds within the simulated system. Different colours distinguish N–H···Br and C–H···Br interactions.

These figures have been placed in the Introduction section and are referenced in the corresponding explanatory tex (page 2, line 45-65).

"Figure 1 shows a unit cell of the metal-organic halide perovskite CH₃NH₃PbBr₃. It can be described as a methylammonium cation, MA=CH₃NH₃, inside a cubo-octahedral cavity composed of 8 Pb cations 12 Br anions. This unit cell is repeated quasi-periodically as illustrated in Figure 2. The deviations from strict periodicity, apparent in Figure 2, are due to thermal motion, as these figures are snapshots from molecular dynamics (MD) simulation. Some effects of thermal motion are particularly strong in halide perovskites, such as disorder in cation orientation, large displacements of the halide anions, and a random network of HBs. The organic cation MA is agglutinated by covalent C–N, N–H and C–H bonds, which exhibit lengths of approximately 1.5 Å, 1.0 Å and 1.0 Å, respectively. These bond lengths fluctuate slightly due to thermal motion, but they remain confined within a narrow distribution. A covalent bond involves the pairing of two electrons with opposite spin projection resulting in increased electron density between two atomic nuclei. This also allows us to understand on qualitative grounds the positive charge of MA. The molecular energy is minimized by filling the valence shells of C and N atoms with eight electrons, and the valence shell of H with two electrons. This count includes the electrons shared with the covalently bound atom. The 5-electron valence shell of N is completed with the electrons shared by the C atom and two H atoms, leaving one lone pair. The neutral molecule is CH₃NH₂, but in the ionic PbBr₃ framework, charge neutrality and energy minimization are achieved by capturing a proton attracted by the lone pair of electrons on the N atom. This qualitative picture is strongly backed by numerical quantum mechanics calculations."

Comment 2: 

It would be nice to elaborate more about the number of hydrogen bonding via MD simulations (e.g. about it strength, disruption and formation etc.). According to the Reviewer it would be a good starting point for further statistical explanations.

Reply 2: 

From our point of view, this is explained in the paragraph starting on line 102, already present in the original version.

"The well-known rotational motion of the organic cation in metal-organic halide perovskites implies that HBs form and break dynamically. This process can be studied by means of MD simulations and it can be quantified by means of a dimer autocorrelation function, from which a lifetime (LT) can be derived [34]. It is natural to expect that the LT of N─H∙∙∙Br bonds are longer than for C─H∙∙∙Br bonds. However, MD simulations of CH₃NH₃PbBr₃ [33] have shown rather similar LTs across a wide range of temperatures for both kinds of HB. Notably, the LTs are finite even for the low temperature orthorhombic phase, where the cations do not rotate (at least the C—N axis). Moreover, the LTs dependence with temperature is consistent with the Arrhenius law, and the activation energies are also similar for both kinds of HBs. This similarity of LTs and activation energies seems difficult to reconcile with the idea of one kind of HB being stronger than the other kind. The existence of C─H∙∙∙Br bonds is supported by the electronic reduced density gradient calculations, but they do not manifest in the vibration properties or any other observable. The CH₃NH₃ cation is confined in a cubo-octahedral cavity limited by Pb and Br ions. When the ammonium group NH₃ binds to one, two or three Br ions, the opposite methyl group CH₃ has available Br ions to bind at the opposite side of the cavity. It might be possible that the driving force for the formation of C─H∙∙∙Br bonds were the N─H∙∙∙Br bonds at the opposite side of the cation. Henceforth, we present a study of the correlation between the two kinds of HBs of a single cation along the MD trajectory."

We belief that this paragraph is better understood with the help of the Figures 1 and 2 that have been added in the revised version. In the reply 3 we also explain how the numbers of HB were calculated. 

 Comment 3:

This part of the study is very similar to Ref 33: “The X─H···Br (X=C or N) HBs are revealed by regions of high numerical values of the combined distribution function (CDF)[34] of the distance H─Y and the angle Br─H─X. Based on the CDF, the condition for the existence of a N─H···Br HB was defined as ?(N−H)<3 Å, and 135º< angle (Br−H−N)<180° [33]. Furthermore, for C─H···Br HBs the distance condition was defined as (C−H)<4 Å, with the same range for the angle (Br−H−C)” – this fragment should be rewritten and the Authors should revise their idea concerning N–H and C–H bond length. Please, check in some books the C–H and N–H bonds properties. The Reviewer understands that the approximation was taken from the MD simulations where the distances were changing as a function of time, but it is confusing. Please, explain properly what is the covalent bond, what is the hydrogen bond, what is the interatomic distance between heavy atoms involved in the hydrogen bond formation in the cases studied.

Reply 3:

Thank you for this detailed observation. We have rewritten and expanded the paragraph (page 5, line 160), clarifying the distinction between the covalent bonds N–H and C–H, and the hydrogen bonds N–H···Br and C–H···Br (defined by geometric criteria), which fluctuate with time during MD simulations.

We have also explicitly described what a covalent bond and a hydrogen bond are, and distinguished between interatomic distances involving hydrogen and those involving heavy atoms (N–Br or C–Br), as the VMD analysis uses the latter.

The new text reads 

"In previous studies [29,33], the identification of HBs was based on two geometric criteria: the distance between the hydrogen atom and the bromide ion, and the angle formed by the donor-hydrogen-acceptor triplet. Specifically, N–H···Br interactions are defined by an H···Br distance shorter than 3 Å and an angle Br–H–N greater than 135°, while for C–H···Br interactions the distance threshold was extended to 4 Å, maintaining the same angular condition. These cutoffs reflect the observed maxima in the joint probability distributions obtained from the combined distribution function (CDF)[34] analysis, and they are consistent with the characteristic ranges found in previous computational studies of similar systems[29,45].

In this study, the graphics program Visual Molecular Dynamics (VMD)[35] has been used for both visualizing the HBs and for quantifying their numbers. In VMD, a X–H···Y HB is defined by the X—Y distance instead of the H—Y distance, and the above explained condition for the angle (X—H—Y). Because of this, the N—Br distance upper limit was set to 4 Å, that is, 1 Å larger than the H—Br distance limit. The same procedure was followed for the C—Br distance, setting its upper limit at 5 Å. The equivalence of the HB definition in terms of X—Y or H—Y distances was shown in Ref. [29]."

Moreover, with the introduction of Figures 1 and 2, we added the paragrpah already commentd in Reply 1, starting at page 2, line 45). There, the distinction between covalent bonds and HBs is clearsly expained. We have also changed the first part of the followin paragraph (starting in line 66 of page 2), that now reads

"A different matter is the interaction of the organic cation with the inorganic lead-halide framework. To a great extent, this interaction is ionic, given that the inorganic sublattice is negatively charged. However, the cation can rotate inside the cubo-octahedral cavity, except at low temperatures. In this context, non-covalent and non-ionic interactions modify the cation movement, and they also contribute to the cohesive energy of the perovskite crystal. One of the most important of these interactions is ...."

 

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript „Correlation between C─H∙∙∙Br and N─H∙∙∙Br Hydrogen Bond Formation in perovskite CH3NH3PbBr3: A Study Based on Statistical Analysis” by Alejandro Garrote-Márquez, Norge Cruz Hernández and Eduardo Menéndez-Proupin is an attempt to reveal probable relation between two hydrogen bonds (HBs), of possibly different strength, formed between the methylammonium cation and the surrounding bromide anions. Seemingly stronger N─H∙∙∙Br HBs are found to have similar life times as the weaker C─H∙∙∙Br HBs. Further statistical analysis indicates that no definitive correlation exists between these two structural features, which might seem unexpected, given the simple shape of the cation leaving small room for independent behavior. The most important weakness of the manuscript is that it relies on the previous molecular dynamics simulation (ref. [33]), not on its own data, however let us not consider this as a drawback – the authors try to analyze the existing data from a different angle, which is also a useful approach. Moreover, the results were validated in Ref. 33. Another weak point could be the use of a machine-learning force field, which means that looking for correlations we are in fact exploring the internal structure of a machine-learned potential – however, let us again assume that the testing of the MLFF protocol in previous studies was adequate. I find the manuscript interesting and I suggest its publication in “Solids” when the following minor issues are resolved:

 

1. It is necessary to provide a structural drawing indicating the system of interest and the HBs. It could be similar to the Figure 1 of Ref. 33.

 

2. It seems that the study is based on an analysis of the two HBs at the same frame, thus being unable to detect time-delayed behavior (for example, a case in which the breaking of the N─H∙∙∙Br contact results in the enforced breaking of the C─H∙∙∙Br HB after, say, 0.5 ps). This is beyond the scope of the current study, but I would like the authors to discuss this possibility – do they think it could be useful in this case? The related phenomenon is “causality”, recently discussed e.g. in: V. Tatto et al., “Towards a robust approach to infer causality in molecular systems satisfying detailed balance”, arXiv:2502.19384v1, https://arxiv.org/html/2502.19384

 

3. A short comment on the H-N-C-H dihedral angles should be given, e.g. their distribution function or time course. This would reveal whether at low temperatures the rotation along the C-N bond is free or significantly hindered.

 

4. Table 3 is partially based on Table 1 from Ref. 33 – please include this information.

 

End of reviewer remarks.

Author Response

The manuscript „Correlation between C─H···Br and N─H···Br Hydrogen Bond Formation in perovskite CH3NH3PbBr3: A Study Based on Statistical Analysis” by Alejandro Garrote-Márquez, Norge Cruz Hernández and Eduardo Menéndez-Proupin is an attempt to reveal probable relation between two hydrogen bonds (HBs), of possibly different strength, formed between the methylammonium cation and the surrounding bromide anions. Seemingly stronger N─H···Br HBs are found to have similar life times as the weaker C─H···Br HBs. Further statistical analysis indicates that no definitive correlation exists between these two structural features, which might seem unexpected, given the simple shape of the cation leaving small room for independent behavior. The most important weakness of the manuscript is that it relies on the previous molecular dynamics simulation (ref. [33]), not on its own data, however let us not consider this as a drawback – the authors try to analyze the existing data from a different angle, which is also a useful approach. Moreover, the results were validated in Ref. 33. Another weak point could be the use of a machine learning force field, which means that looking for correlations we are in fact exploring the internal structure of a machine-learned potential – however, let us again assume that the testing of the MLFF protocol in previous studies was adequate. I find the manuscript interesting and I suggest its publication in “Solids” when the following minor issues are resolved:

We thank the Reviewer for these constructive comments. We have revised the manuscript accordingly. Our point-by-point responses are detailed below.

Comment 1:

It is necessary to provide a structural drawing indicating the system of interest and the HBs. It could be similar to the Figure 1 of Ref. 33.

Reply 1:

Thank you for this suggestion, which also comes from other reviewers. We have now included the new Figures 1 and 2, clearly indicating both types of hydrogen bonds (N─H···Br and C─H···Br) and their respective distances and angles. 

Comment 2:

It seems that the study is based on an analysis of the two HBs at the same frame, thus being unable to detect time-delayed behavior (for example, a case in which the breaking of the N─H···Br contact results in the enforced breaking of the C─H···Br HB after, say, 0.5 ps). This is beyond the scope of the current study, but I would like the authors to discuss this possibility – do they think it could be useful in this case? The related phenomenon is “causality”, recently discussed e.g. in: V. Tatto et al., “Towards a robust approach to infer causality in molecular systems satisfying detailed balance”, arXiv:2502.19384v1, https://arxiv.org/html/2502.19384

Reply 2:

This is a very interesting comment on an aspect that we had not considered so far. We agree with the reviewer that time-delayed effects may be relevant and potentially indicative of causality. However, our current methodology is restricted to synchronous correlation analysis. We have included a discussion paragraph in the revised manuscript (end of Section 4), commenting on this limitation and suggesting time-lagged correlation. This added text as

“Finally, let us notice that correlation and causality are not the same phenomenon, although they are frequently difficult to distinguish. If the formation or breaking of C–H···Br bonds were caused by the formation of breaking of N–H···Br bonds, one could study the correlation between the corresponding data after applying a time shift. Our study considers no time delay, consistent with a rigid MA molecule view. The study could be extended considering time delay of the order of MA vibration period (10—40 fs). However, these times are one or two orders of magnitude smaller than the HB lifetimes (Table 3). Hence, we think that a causal relationship would manifest in the correlation analysis carried out in this work.”

Comment 3:

A short comment on the H-N-C-H dihedral angles should be given, e.g. their distribution function or time course. This would reveal whether at low temperatures the rotation along the C-N bond is free or significantly hindered.

Reply 3:

As suggested, we have included the Figure S13, presenting the time evolution and histogram of the H-N-C-H dihedral angle for different temperatures. This provides additional insight into the configurational dynamics of the methylammonium cation and its relation to hydrogen bond formation. On page 13, lines 437-440 we have added a short comment: 

“Moreover, 125 K is the lowest temperature for which we have observed relative rotation of the CH3 and NH3 groups, as inferred from the time dependence of the dihedral angle H—N—C—H shown in Figure S13 of the Supplementary Materials.”

Comment 4:

Table 3 is partially based on Table 1 from Ref. 33 – please include this information.

Reply 4: 

We thank the reviewer for this observation. Indeed, part of the data presented in Table 3—specifically the lifetimes of the hydrogen bonds—was taken directly from Table 1 of Ref. 33, as clearly acknowledged in our initial methodology. To make this source fully explicit to the reader, we have now added the following sentence to the caption of Table 3:

"Hydrogen bond lifetimes are reproduced from Table 1 of Ref. 33."

 

Reviewer 3 Report

Comments and Suggestions for Authors

The paper by Garrote-Marquez, Cruz Hernandez and Menendez-Proupin gives us an interesting molecular dynamics and statistical study on two different types of hydrogen bonds present in CH₃NH₃PbBr₃ perovskite. I find this work to be scientifically sound, well-executed, with good conclusions, and very well-written. The authors have carefully evaluated their somewhat unexpected findings (the fact that the results are highly dependent on data segmentation is particularly interesting) and provided good and reasonable explanations. However, I have one major objection to this paper, and it is related to the visualization. The authors have not presented the structure of CH₃NH₃PbBr₃ perovskite, they have not given any snapshot of their simulation, they have not presented any figure where interactions they are writing about are shown. Without that, it is very difficult to follow the discussion. Therefore, I recommend the revision of this manuscript, where additional figures should be added, with at least some description of the structure. Not everyone reading this paper would have the opportunity to download the authors' paper on similar topic, published in J. Phys. Chem. C (reference 33), where the structure is clearly presented. And after all, we should not have to look at some other paper to understand the one we are reading. 

Author Response

Comment:

The paper by Garrote-Marquez, Cruz Hernandez and Menendez-Proupin gives us an interesting molecular dynamics and statistical study on two different types of hydrogen bonds present in CH NH PbBr perovskite. I find this work to be scientifically sound, well-executed, with good conclusions, and very well-written. The authors have carefully evaluated their somewhat unexpected findings (the fact that the results are highly dependent on data segmentation is particularly interesting) and provided good and reasonable explanations. However, I have one major objection to this paper, and it is related to the visualization. The authors have not presented the structure of CH₃NH₃PbBr₃ perovskite, they have not given any snapshot of their simulation, they have not presented any figure where interactions they are writing about are shown. Without that, it is very difficult to follow the discussion. Therefore, I recommend the revision of this manuscript, where additional figures should be added, with at least some description of the structure. Not everyone reading this paper would have the opportunity to download the authors' paper on similar topic, published in J. Phys. Chem. C (reference 33), where the structure is clearly presented. And after all, we should not have to look at some other paper to understand the one we are reading.

Reply: 

We thank the reviewer for this very valuable comment, also suggest byt the other reviewers. We fully agree that the manuscript should be self-contained and accessible without requiring the reader to consult our previous work (Ref. 29 and 33). In response, we have included two new figures in the revised version of the manuscript to address this issue:
•    Figure 1 shows the unit cell of CH₃NH₃PbBr₃, including atomic positions and representative hydrogen bonds (N–H···Br and C–H···Br), clearly marked. Distances and angles relevant to hydrogen bonding are indicated.
•    Figure 2 presents a snapshot from the MD simulation, highlighting the hydrogen bond network formed between the organic cation and the bromide ions. Interactions are coloured according to their type (N–H···Br in bluish color, C–H···Br in red) for clarity.
A brief description of the structure and interactions has also been added to the Introduction section (pages 3–4) to guide the reader through the visual information. 

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have significantly improved their presentation by adding the appropriate figures and by describing the structures. I recommend the acceptance of this manuscript, with congratulations to the authors for writing such a good paper.