The B₂ Structural Motif as a Tool for Modulating Ring Currents in Monocyclic Li Clusters

Round 1

Reviewer 1 Report

In the manuscript entitled " The B2 structural motif as a tool for modulating ring currents in monocyclic Li clusters " (Chemistry-1338729) by Đorđević and Radenković, the authors investigate the magnetically induced current densities (MICD) in Li₃B₂^- and Li₄B₂ and perform the CTOCD-DZ based spectral decomposition of MICDs to identify the source of the diatropic ring currents in these clusters. According to author’s findings, unlike the parent planar Li₃⁺ and Li₄²⁺ systems which sustain negligibly weak current density circulation, the Li₃B₂^- and Li₄B₂ clusters exhibit a strong diatropic current density due to virtual translational excitations involving a pair of (quasi)degenerated HOMO-1 orbitals. In the conclusions Đorđević and Radenković claim that the B2 unit can be used for modulating the current density in cyclic Li-based clusters. Firstly, I have to admit that the manuscript is well written and pleasant to read. The ipso-centric approach is briefly explained and the references seem to be appropriate in this context. However, in my opinion the substantial content of this work is not publishable in the present form and authors have to reinvestigate the systems and fundamentally rethink their conclusions as well as make some additional changes to improve the text, taking into account the following points:

(1) It is true that in many cases NICS gives different predictions than MICD just because NICS is a single number that is unable to represent the complexity of tropicity patterns in a ring. It does not mean, however, that the MICD-based predictions are always correct. For instance, in coronene MICD wrongly predicts superbenzene-type delocalization pattern while NICS and ICSS correctly recognize the resonance electronic structure predominated by two Clar’s forms with three pi-sextets each. Can the authors explain why NICS gives negative values in Li₃⁺ and Li₄²⁺? The CMO/NBO-NICS analysis could be helpful in this context…

(2) The authors should bear in mind that electron delocalization (property of the unperturbed density matrix) is much more fundamental feature of all aromatics than the magnetically-induced diatropic ring current. And in both clusters Li₃⁺ and Li₄²⁺ electron delocalization patterns are determined by fully symmetric HOMO orbitals that formally represent 3c2e and 4c2e sigma-bonding, respectively. Admittedly, according to the NBO-NRT analysis, the former is represented by the superposition of three lone-pair isomeric resonance forms and the latter by the superposition of four lone-pair isomeric forms, which is in contrast to their organic pi-aromatic counterparts, C₃H₃⁺ (three pi-bond resonance bonds) and C₄H₄²⁺ (six pi-bond resonance forms). However, at the spin-restricted one-determinant level of the theory (M06-2X) the electronic-structure based criteria of aromaticity such as the multicenter index (MCI) or the electron density of delocalized bonds (EDDB) clearly show that both clusters are Li₃⁺ and Li₄²⁺ are certainly sigma-aromatic.

(3) Li₃⁺ and Li₄²⁺ should not be referred to as rings/monocycles since in both cases Coulson’s bonds orders between all atomic pairs are equal, which means that the ‘cross-ring’ interactions are no different from the ‘along-rings’ ones; in a sense, the cross-ring connections between atoms are indistinguishable from those along the ring.

(4) One of the systems is a monoanion. Did the authors check the character (Val/Ryd) of the frontier KS-orbitals in the calculations involving a basis set with diffuse functions?

(5) As mentioned by the authors, the NBO analysis reveals triple bond B≡B in both clusters, Li₃B₂^- and Li₄B₂. However, the full NBO-NRT analysis also shows that e.g., in the latter the density matrix is contributed in 62% by the resonance forms involving the Li-B-Li hyperbonding, while each of the remaining resonance forms containing the Li-Li bonds contributes no more than 1.3% (see Fig-1). This result clearly shows that cyclic delocalization of electrons in both systems is rather weak.

(6) A weak cyclic delocalization in Li₄B₂ suggests that the reported diatropic current density might come exclusively from the B≡B bond (being only slightly perturbed by the lithium atoms surrounding the diatomic molecule). The calculated magnitude of the magnetically-induced current density (MMICD) fully confirms that (see Fig-2), which contradicts the results of the ipso-centric based spectral decomposition presented in Figure 6 (BTW, I was unable to reproduce the KS-MOs presented in the figure – could the authors provide the corresponding input files used in the calculations?), and unfortunately it seems to falsify the main hypothesis included in the title of the article: “The B2 structural motif as a tool for modulating ring currents in monocyclic Li clusters”.

 

Comments for author File: Comments.pdf

Author Response

Here are the G09-input files requested by the referee:

%chk=Li3B2.chk
# NMR pop=nboread IOp(10/46=1) nosymm def2tzvp m062x

Title Card Required

-1 1
 B                 -0.00002400   -0.07049200   -0.76597200
 B                 -0.00001600   -0.07049000    0.76597400
 Li                 0.00027200    1.90844700   -0.00000200
 Li                 1.82571600   -0.83692900   -0.00000400
 Li                -1.82592000   -0.83654800    0.00000200
 Bq                 0.00002200    0.07832300   -0.00000100

$NBO NPA NBO NBOSUM BNDIDX E2PERT NLMO DIPOLE CMO NRT NCS <XYZ MO> $END

 

%chk=Li4B2.chk
# NMR pop=nboread IOp(10/46=1) nosymm def2tzvp m062x

Name

0 1
 B                  1.44463700    1.44530400   -0.76062500
 B                  1.44459600    1.44537100    0.76070300
 Li                 2.88930700    2.89052100    0.00015600
 Li                 0.00000000    0.00000000    0.00000000
 Li                 2.88994000    0.00078700    0.00000000
 Li                -0.00063300    2.89004200    0.00000000
 Bq                 1.44465350    1.44533750    0.00003900

$NBO NPA NBO NBOSUM BNDIDX E2PERT NLMO DIPOLE CMO NRT NCS <XYZ MO> $END

Author Response File: Author Response.pdf

Reviewer 2 Report

This is a very nice investigation revealing how the induced current densities in a cluster can be altered through coordination so that the B2(2-) coordinated clusters exhibit diatropic ring currents corresponding to aromaticity. However, I have two items I would like the authors to address before I can recommend acceptance:

1: How does the ring currents change if the B-B distances are elongated? It would be nice to see if the current density maps gradually turn from those displayed in Figures 3b and 4b to those in Figures 3a and 4a.

2: What is known experimentally about clusters like these? Have they ever been observed experimentally? If so, as transient intermediates or as stable and isolable compounds? If they have never been reported experimentally, could the authors provide information that would be useful for future experiments? E.g., what are the binding energies between Li3(+) and B2(2-) in Li3B2(-) and between Li4(2+) and B2(2-) in Li4B2? It should also be made clear in the Introduction whether the clusters earlier have been explored experimentally or not. 

Author Response

Our response is in the attached file. 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

(1) I agree that “the NICS(0)ZZ values cannot be used to compare the aromaticity of the target complexes and their reference Li3+/Li42+ systems.” But this is mainly because the correspondence between cyclic electron delocalization and the tropicity in this or another point/site of a ring/fragment is much more complicated as the induced ring-current densities represent the effect of “reorganization” of the resonance electronic structure due to response of the system to the external magnetic field rather than the resonance effect itself (to rephrase Prof. R.F. Nalewajski, “current density represents ‘becoming’ while electron delocalization represents ‘being’). In benzene, both the lowest lying orbital and the superposition of 2 HOMO orbitals give negative contributions to the NICS value, but due to the lower HOMO-LUMO gap the magnitude of the letter is higher. The argument based only on the analogy between topological characteristics of the ring, (3,-3) vs (3,+3), is inappropriate because as a consequence one should accept that the systems containing the 2-electron-n-center bonding orbitals like the H-based model sigma-aromatic analogues of C3H3(+) or C4H42+ (not to mention the entire families of the ground/excited-state aromatic all-metal clusters) are in principle not aromatic (at lease within the regime of one-determinant approaches like HF and DFT). In the paper that authors refer to, it is explained that in Li3(+) diatropic ring current is not observed because of CANCELATION with the local paratropic circulations. The cancelation or actually any kind of interference of the vector subfields means that we lose the correspondence between tropicity and aromaticity, and hence the fact that the ring current is observed or not has nothing to do with the effect of aromatic stabilization. Once again, a good example here is the coronene case, where the current-density cancellations inside leaves strong diatropic ring current outside which does not represent the real resonance structure of the system and its reactivity and other properties. To summarize this point, I cannot agree that in Li3/Li4 “rings” the ring-current based predictions are more reliable than the NICS-based ones. In fact, both suffer from the fact that due to interferences between the subfields of different tropicity they no longer correspond to the effect of cyclic delocalization of electrons or such correspondence is much more complicated and much less conclusive in the context of molecular aromaticity.

(2a) Again, I agree that the strong cyclic delocalization of electrons is a necessary but not sufficient condition for aromaticity. But the completing condition is the energetic stabilizing effect associated with delocalization rather then the fully orthogonal criterion involving the magnetic response. One should notice that both electron delocalization and energetic stabilization are associated with the electron density of the system and hence they correspond to the actual resonance electronic structure; in contrast, the induced current densities are associated with the perturbed electron density of the system under the external magnetic field. Moreover, I personally think that the real power of the aromaticity concept would be to predict the magnetic response of the molecular systems rather than to use the magnetic response criterion to redefine the concept of aromaticity. 

(2b) By definition, the text-book antiaromatic systems are those being destabilized by cyclic delocalization of electrons . But to ‘release their antiaromaticity’ they often undergo Jahn-Teller distortions (even at the cost of strains or Pauli repulsion increase), and therefore - quoting Prof. Steiner – the real antiaromatic systems actually do not exists! In this context, MCI performs pretty well showing lack of delocalization in C4H4. Additionally, MCI enables one to identify e.g. hyperconjugative stabilizing effects in the ground-state C8H8 system, which is commonly accepted to be a nonaromatic system in spite of following the Huckel’s rule for antiaromatic systems. 

(2c) I appreciate the authors calculated the multicenter index. However, to correctly address the cyclic delocalization of electrons the Iring index is preferred rather than MCI. But, nevertheless, in both cases the authors should provide the normalized versions of the index (e.g. the 1th-root of MCI) as the original one suffers from the size-extensivity issue and hence the values of MCI for systems of different size cannot be directly compared. How did the authors calculate MCI? Did they take into account all atoms or only the Li ones? In the former case the MCI^(1/n) column in Table 2 should contain 0.5954, 0.4657, 0.7631, 0.6575, and in the latter case it should collect of the following numbers 0.4213, 0.3178, 0.7631, 0.6575. This is rather a technical (but important) detail as the conclusions remain the same – cyclic delocalization is reduced when introducing the B2 unit, in full contrast to the ring-current based prediction.

(3) The point of my comment was that the system in which the cross-ring connections/interactions are of the same importance as the ‘along-ring’ ones the systems is topologically not a ring, but this is a semantic detail and I could eventually accept the term “ring”. As regards the Mayer’s (not Mulliken) bond-orders, they could be useful indicators only in the basis of well localized and polarized (effective) minimal-basis atomic orbitals. Unfortunately, the numbers taken directly from Mayer’s BO definition in the def2-TZVP basis are completely unreliable.

(4) I strongly urge the authors to recalculate at least NICS and MCI values using the augmented version of the def2-TZVP basis function; single-point calculations would be enough. Alternatively, just check if the frontier occupied KS-MOs in the anionic system have Rydberg character. If so, not even aromaticity would give this system enoguh stabilization to actually exist.

(5) OK

(6) I appreciate that in the current version of the manuscript the authors emphasize that the current density in both clusters is mainly determined by the π-electrons of the B-B bond. But here the visual comparison of Li3/Li4, B2, and the resulting clusters is crucial, and, when comparing separately Li cluster, B2 unit, and the entire complex, readers would probably conclude that Li atoms are just satellites that perturb a little bit the strong diatropic current originated from the B2 anion. Thus, I highly encourage the authors add to Figures 3 and 4 maps with the B2 anion (in the plane perpendicular to the bond ax and in the middle of the bond). Moreover, the results of the B-B elongation analysis at the DFT level are in my opinion meaningless; the calculations like this require multireference approaches but, as far I as know, this is not possible to perform the calculations and get these nice current-density maps at the post-HF level. 

Author Response

Dear Reviewer,

Thank you for your comments and suggestions. 

Please find our answers in the attached file.

Best regards,

 

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors have carried out appropriate changes to the manuscript in response to my earlier comments. I think the manuscript is ready for acceptance. 

Author Response

Dear Reviewer,

We thank you for your comments and support.

Best regards,