The Face-to-Face σ-Hole⋯σ-Hole Stacking Interactions: Structures, Energies, and Nature

Round 1

Reviewer 1 Report

The reviewed work entitled “The Face-to-Face σ-Hole···σ-Hole Stacking Interactions: Structures, Energies, and Nature” by Yu Zhang and Weizhou Wang concerns the computational study of a few geometries extracted from crystal database which are potentially interesting due to the presence of σ-hole···σ-hole Br···Br stacking interaction. Results showed that these dihalogen contacts are driven by dispersion forces. These interactions were also checked in the context of their behaviour in large containers what is quite a unique approach. It turned out that these complexes confined in carbon nanotube may become more stable than in the original, crystal state. Moreover, the electronic properties of the containers are also improved by the presence of investigated dimers as indicated by the HOMO-LUMO analysis. Authors are experienced in the field of the noncovalent interactions examination and this work is a continuation of their previous studies (the future studies are also announced in current paper). This paper is competent piece of work which can be useful in deepening the knowledge of the σ-hole interactions. However, before publication it should be revised. These are my remarks:

1. I would like to know more details about CSD searching of investigated species. Were these 4 structures the only ones found in CSD of such structural motif or not? Why these four? What were the criteria of searching?
2. I wonder about Authors’ statement that there are no hydrogen bonds in these dimers. These structures are part of crystallographic units. The geometry within is propagated not only linear but across different planes. So, I assume that beside the dihalogen contacts there should be other interactions which stabilize this crystal unit (Br···H hydrogen bond between linear chains). Was this issue studied?
3. What are the other BCP properties from AIM analysis? I mean, the H parameter or the -V/G ratio? The minor issue is that the red dots commonly represent ring critical points while bond critical points are indicated normally by green dots (as default in AIMAll software). In this work BCP’s are red.
4. The importance of correlation presented in Fig. 4 seems to be marginal as induction energy play at most secondary role in the stabilization of these compounds according to SCS-SAPT0 decomposition.
5. I believe that captions under the Figures 2 and 3 are wrongly swapped.
6. If I understand correctly the DASKOX complex forms (in the gas phase) despite the negative sigma hole value. This interesting fact should be highlighted and studied in broader detail.

Author Response

1. I would like to know more details about CSD searching of investigated species. Were these 4 structures the only ones found in CSD of such structural motif or not? Why these four? What were the criteria of searching?

Reply: We thank the reviewer very much for pointing out this important issue. We did not carry out CSD searches in this study. The Br₁···Br₂ distances in Fiugre 3 are all less than the sum of the van der Waals radii of two Br atoms. However, the much smaller Br₁···Br₂ distance is not a necessary condition for the formation of the face-to-face σ-hole(Br)···σ-hole(Br) stacking interaction. The case is the same for the other face-to-face σ-hole···σ-hole stacking interactions. Therefore, the difficulty for the CSD statistical analyses lies in how to define the distance between the two atoms with σ holes. Up to now, we are still working on this issue. The main aim of this study is to exclude the possibility of the other noncovalent interactions and further to prove that the face-to-face σ-hole···σ-hole stacking interactions do exist and have unique properties.

There are many face-to-face σ-hole···σ-hole stacking interactions found in the crystal structures. We did not include the face-to-face σ-hole(I)···σ-hole(I) stacking interactions in this study because someone maybe question the effect of the well-known relativistic effect. On the other hand, we also did not consider the face-to-face σ-hole(S)···σ-hole(S) stacking interactions in this work because, accompanying the formation of the face-to-face σ-hole(S)···σ-hole(S) stacking interaction, the S atoms are always involved in the formation of the other noncovalent interactions. That is to say, we want to make the face-to-face σ-hole···σ-hole stacking interaction much “cleaner”, and give conclusive evidence of the existence of the face-to-face σ-hole···σ-hole stacking interaction.

As shown in Figure 3, the one-dimensional chain structures formed by the face-to-face σ-hole(Br)···σ-hole(Br) stacking interactions in the crystal structures of DASKOX and ENIVEC, which shows the important role of the face-to-face σ-hole(Br)···σ-hole(Br) stacking interaction in the crystal engineering. This is why we selected the two dimers DASKOX-D and ENIVEC-D. For the dimers BTRPYC-D and TPHMBR02-D, the angles in Figure 3 are all 180°, which means that they are formed by the perfect face-to-face σ-hole(Br)···σ-hole(Br) stacking interactions. This is why we selected the two dimers.

2. I wonder about Authors’ statement that there are no hydrogen bonds in these dimers. These structures are part of crystallographic units. The geometry within is propagated not only linear but across different planes. So, I assume that beside the dihalogen contacts there should be other interactions which stabilize this crystal unit (Br···H hydrogen bond between linear chains). Was this issue studied?

Reply: We agree with the reviewer on this point. The cooperativity or anti- cooperativity between the face-to-face σ-hole···σ-hole stacking interaction and the other noncovalent interaction is also an interesting topic. We simply discussed this issue in our previous paper (J. Chem. Phys. 2020, 153, 214302, doi:10.1063/5.0033470). The main aim of this work is to prove the existence of the face-to-face σ-hole···σ-hole stacking interactions.

When we selected the dimers from the crystal structures for this study, the first thing is to exclude those containing the short contacts between Br and the other atoms. Hence, the other noncovalent interactions such as the Br···H hydrogen bonds between linear chains have been excluded.

3. What are the other BCP properties from AIM analysis? I mean, the H parameter or the -V/G ratio? The minor issue is that the red dots commonly represent ring critical points while bond critical points are indicated normally by green dots (as default in AIMAll software). In this work BCP’s are red.

Reply: We used the AIM2000 software for AIM analysis in this work. We tried to change the color of BCP’s in accordance with the requirement of the reviewer, but it looks like the AIM2000 software do not have such option.

AIM analysis was performed to further prove the existence of the face-to-face σ-hole···σ-hole stacking interactions and nonexistence of the other noncovalent interactions. According to Bader’s AIM theory, for the closed-shell interactions (van der Waals interactions, hydrogen bonds, and ionic bonds), the values of the electron densities at the bond critical points are relatively small and their corresponding Laplacians are positive. Therefore, we only focused on the values of electron densities at the bond critical points and their corresponding Laplacians. Considering that the AIM analysis is a simple supplement to the other analyses, we did not list and discuss the other data in this work.

4. The importance of correlation presented in Fig. 4 seems to be marginal as induction energy play at most secondary role in the stabilization of these compounds according to SCS-SAPT0 decomposition.

Reply: For the other dispersion-dominated noncovalent interactions such as the π···π stacking interactions, the electrostatic energies always play secondary roles and the induction energies are always neglectable. Different from these dispersion-dominated noncovalent interactions, the induction energies of the face-to-face σ-hole···σ-hole stacking interactions play at most secondary role in the stabilization of these dimers. So we concluded that the face-to-face σ-hole···σ-hole stacking interactions has its own unique feature.

We have pointed out in the paper that the total interaction energies, electrostatic energies, and dispersion energies all do not correlate with the interatomic distances, and only the induction energies correlate with the interatomic distances. Figure 4 clearly show such a strong correlation. Without Figure 4, we do not know how strong the correlation is.

5. I believe that captions under the Figures 2 and 3 are wrongly swapped.

Reply: We are sorry for our mistake, and have corrected this error in the revised manuscript.

6. If I understand correctly the DASKOX complex forms (in the gas phase) despite the negative sigma hole value. This interesting fact should be highlighted and studied in broader detail.

Reply: Yes, the Br atom in the DASKOX-M has a negative σ-hole. In lines 105-110, we highlighted this issue using the following sentences:

“As pointed out earlier by Politzer and Murray, the σ-hole is a region of lower electronic density on the extension of a σ bond and it is incorrect to assume that a σ-hole has only the positive electrostatic potentials [40]. Therefore, the σ-holes of the Br atoms can be either negative or positive. Both the negative and positive σ-holes can be seen in Figure 2, although the absolute values of the surface maxima of the σ-holes of the Br atoms in DASKOX-M and TPHMBR02-M are not very large.”

In lines 207-216, we highlighted this issue using the following sentences:

“As shown in the third row of Table 1, the electrostatic terms are all attractive, which seems contradictory to the fact that the two face-to-face σ-holes have the same electron-density distributions. At the same time, it is noticed that the electrostatic energies in Table 1 do not correlate with the most positive potentials of the σ-holes in Figure 2. On the other hand, unlike the induction energies, the electrostatic energies do not correlate with the Br₁···Br₂ interatomic distances. In fact, such cases have been widely found in the study of the π···π stacking interactions [43]. Sherrill and coworkers have pointed out that the charge penetration is the cause of these counterintuitive effects [43]. The charge penetration effects play key roles for understanding the electrostatic components of both π···π stacking interactions and σ-hole···σ-hole stacking interactions.”

Reviewer 2 Report

The work of Yu Zhang and Weizhou Wang concerns of non-covalent bonding through interactions of bromine atoms.

The improvements to the article I suggest the authors:

1. the title of the paper is too broad. The authors studied only systems stabilized by a dihalogen (bromine) bond. Even if one were to limit oneself to dihalogen systems, one would have to extend one's research to systems stabilized with other halogens. A search of the CSD database provides over 1000 hits of systems stabilized by dihalogen bond (any halogen).
2. because of the important role of crystal lattice interactions on the stability of such systems, the Authors should attempt to optimize the geometry of dimers in the gas phase and/or in the solvent. This would allow one to estimate the strength of halogen-halogen interactions neglecting the influence of interactions in the solid.
3. i have doubts about the name face-to-face σ-hole···σ-hole stacking interactions used by the Authors. It has been accepted that stacking interactions describe interactions involving p electrons or possibly systems in which subunits form stacks with geometries referring to those observed for aromatic systems.
4. the numbering of Fig. 2 and 3 is confusing
5. i suggest to add ref concerning CSD database indicating the version of the database used to carry out the CSD search.

Author Response

1. the title of the paper is too broad. The authors studied only systems stabilized by a dihalogen (bromine) bond. Even if one were to limit oneself to dihalogen systems, one would have to extend one's research to systems stabilized with other halogens. A search of the CSD database provides over 1000 hits of systems stabilized by dihalogen bond (any halogen).

Reply: We thank the reviewer for very helpful comments. This work is an expansion and deepening of our previous study (Zhang, Y.; Wang, W. The σ-Hole···σ-Hole Stacking Interaction: An Unrecognized Type of Noncovalent Interaction. J. Chem. Phys. 2020, 153, 214302, doi:10.1063/5.0033470). As we mentioned in this study, the existence of the σ-hole···σ-hole stacking interactions was questioned because the other possible noncovalent interactions were not excluded in our previous paper. Hence, the main aim of this study is to exclude the possibility of the other noncovalent interactions and further to prove that the face-to-face σ-hole···σ-hole stacking interactions do exist and have unique properties. We did not carry out CSD searches in this study and this is not the aim of this study.

We did not include the face-to-face σ-hole(I)···σ-hole(I) stacking interactions in this study because someone maybe question the effect of the well-known relativistic effect. On the other hand, we also did not consider the face-to-face σ-hole(S)···σ-hole(S) stacking interactions in this work because, accompanying the formation of the face-to-face σ-hole(S)···σ-hole(S) stacking interaction, the S atoms are always involved in the formation of the other noncovalent interactions. That is to say, we want to make the face-to-face σ-hole···σ-hole stacking interaction much “cleaner”, and give conclusive evidence of the existence of the face-to-face σ-hole···σ-hole stacking interaction.

2. because of the important role of crystal lattice interactions on the stability of such systems, the Authors should attempt to optimize the geometry of dimers in the gas phase and/or in the solvent. This would allow one to estimate the strength of halogen-halogen interactions neglecting the influence of interactions in the solid.

Reply: In lines 137-144, we address the reviewer’s concern as follows:

“Although here we only focused on the face-to-face σ···σ stacking interactions in the crystal structures, one may want to know whether the geometries and interaction energies of these face-to-face σ···σ stacking interactions will change significantly in the gas phase. Selecting the BTRPYC-D as a model dimer, we fully optimized its geometries and calculated its interaction energy at the PBE0-D3(BJ)/def2-TZVPP theory level. It was found that in the gas phase the Br₁···Br₂ distance is 3.660 Å and the interaction energy is -1.30 kcal/mol, which are almost the same as the corresponding ones in the crystal structure.”

3. i have doubts about the name face-to-face σ-hole···σ-hole stacking interactions used by the Authors. It has been accepted that stacking interactions describe interactions involving p electrons or possibly systems in which subunits form stacks with geometries referring to those observed for aromatic systems.

Reply: The existence of the π···π stacking interaction (also called aromatic-aromatic interaction or aromatic stacking interaction) is well-known. Similarly, it is reasonable to assume the existence of the σ-hole···σ-hole stacking interaction.

The use of the term “σ-hole···σ-hole stacking interaction” is reasonable because the two σ-holes with the similar electron-density distributions are stacked with each other, which leads to the stacking of the two σ bonds and further the stacking of the two molecules (see Figure 3 and Figure 1).

4. the numbering of Fig. 2 and 3 is confusing.

Reply: The captions under the Figures 2 and 3 are wrongly swapped. We are sorry for our mistake, and have corrected this error in the revised manuscript.

5. i suggest to add ref concerning CSD database indicating the version of the database used to carry out the CSD search.

Reply: We thank the reviewer for this suggestion and have cited the references and added the version for the CSD used in this work.

Round 2

Reviewer 1 Report

Authors properly adressed all my points. The work has gained in quality and should be published.