A stabilization rule for metal carbido cluster bearing μ3-carbido single-atom-ligand encapsulated in carbon cage

Metal carbido complexes bearing single-carbon-atom ligand such as nitrogenase provide ideal models of adsorbed carbon atoms in heterogeneous catalysis. Trimetallic μ3-carbido clusterfullerenes found recently represent the simplest metal carbido complexes with the ligands being only carbon atoms, but only few are crystallographically characterized, and its formation prerequisite is unclear. Herein, we synthesize and isolate three vanadium-based μ3-CCFs featuring V = C double bonds and high valence state of V (+4), including VSc2C@Ih(7)-C80, VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78. Based on a systematic theoretical study of all reported μ3-carbido clusterfullerenes, we further propose a supplemental Octet Rule, i.e., an eight-electron configuration of the μ3-carbido ligand is needed for stabilization of metal carbido clusters within μ3-carbido clusterfullerenes. Distinct from the classic Effective Atomic Number rule based on valence electron count of metal proposed in the 1920s, this rule counts the valence electrons of the single-carbon-atom ligand, and offers a general rule governing the stabilities of μ3-carbido clusterfullerenes.


Point-by-point response to reviewer's comments:
Reviewer #1 (Remarks to the Author): This article reports the synthesis, isolation and structural characterization of two new endohedral fullerenes.The synthesis and isolation are rather routine but time consuming.
We thank the Reviewer for the critical comments, which helped us to improve our manuscript.
Comment 1: The structural characterization by X-ray crystallography is problematic.
The authors must report esds for bond distances, angle and site occupancies if refined.
Answer: We thank the Reviewer for the carefulness on checking the X-ray crystallographic data.We did refine all parameters, but omitted them for simplicity in the original version.Following the Reviewer's suggestion, we added all esds for bond distances, angle, and site occupancies for VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 in Figure 2, the main text and SI (Supplementary Figures 6-7, Table 3, 4 and 7).Please note that, after double checking all crystallographic data, subtle changes on the parameters of VSc2C@D3h(5)-C78 happened based on improved data.
Comment 2: Differentiation between Sc and V crystallographically is challenging because of their similar atomic numbers and similar scattering.Inside the fullerene there are many disordered sites for the metal ions.How did the authors choose to assign sites to V or Sc?The assumptions they may have made need to be specified.It is possible that Sc and V may occupy the same site.How can one tell?Site occupancies and disorder are poorly handled in the text itself and much is missing the SI.
Answer: We thank the Reviewer for the professional opinion.Indeed, based on crystallography theory, differentiation between Sc and V crystallographically (without specific requirement on how they are combined together) is challenging because of their similar atomic numbers and similar scattering.Fortunately, in our present work, because of the requirement of formation of planar triangular VSc2C cluster following "Supplemental Octet Rule", specific electronic configuration of [V 4+ (Sc 3+ )2C 4-] 6+ @[C2n] 6-and metal-carbon bondings (one double bond plus two single bonds, see Figure 3c) are required, enabling us to differentiate Sc and V unambiguously.
In our previous work (Proc.Natl.Acad.Sci. U. S. A. 119, e2202563119 (2022)), we already presented details on how to crystallographically distinguish the Sc and V sites within VSc2C@Ih(7)-C80, by comparing R1 and wR2 values obtained from different configurations of the VSc2C cluster combined with DFT calculations.Using the same method, we succeeded in distinguishing the Sc and V sites within VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78.Taking VSc2C@D3h(5)-C78 as an example, we describe in details how to distinguishing the Sc and V sites as follow.
First, it is necessary to determine all disorder sites of three encapsulated metals (one V and two Sc atoms) within VSc2C@D3h(5)-C78, as shown in Fig. R1.Next, to assign M1, M2, M3, we carried out additional study on refining possible configurations of the VSc2C cluster with differnent V/Sc sites within VSc2C@D3h(5)-C78.Since there are two Sc atom within VSc2C cluster, which should be identical, we optimized three possible conformations of the encapsulated VSc2C cluster within VSc2C@D3h(5)-C78 (A, B, C) by using DFT calculations (Table R1).Based on DFT calculation results, VSc2C@D3h(5)-C78-A in which V possesses the shorter bond lengths to the central carbon atom (around 1.8 Å) has the lowest relative energy with the smallest R1 and wR2 values (12.05%/35.24%).Besides, R1 and wR2 values both increase when changing the disordered V sites to other sites with longer bond length of approximately 2 Å with the central carbon (see Table R1).Therefore, combining the R1/wR2 values with DFT calculations, we concluded that VSc2C@D3h(5)-C78-A is the most stable one, in which the short V-C bond length is attributed to V=C double bond and the two Sc-C bonds are longer in the form of single bonds.As seen in Fig. R2, the V-C bond lengths and Sc-C bond lengths based on other minor sites (orientations B-D) also fall into the range of V=C double bond and Sc-C single bond, respectively.Overall, because of the distinct difference between V=C bond lengths and Sc-C bond lengths, in our present work it is feasible to distinguish V and Sc sites since it is hard for Sc and V atoms to occupy the same metal site.
VSc2C@D3h(5)-C78 VSc2C@D5h(6)-C80 VSc2C@Ih(7)-C80 Figure 8) to identify the principle C5 and C3 axes in VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78.For VSc2C@D3h(5)-C78, it can be seen that the C3 axis lies on the plane of VSc2C cluster (see Fig. R4, c and d).Comment 5: A second aspect of the paper is the discussion of an "expanded Octet Rule" for endohedrals containing a central carbide ion.I did not find this topic to have much merit.Generally the term 'expanded octet" was used for situations where valence bond theory suggested the participation of d orbitals for elements in the second or lower in the periodic table.Since carbon only has s and p electrons available in the valence shell, the octet rule pertains to carbon period!Answer: We thank the Reviewer for the critical comment with detailed explanation of the term "expanded Octet Rule".We carefully made a literature survey and confirmed that the concept of an atom with an "expanded octet" usually refers to a hypervalent atom, whose structure may indicate the availability of low-lying d-orbitals [J.Chem.Educ. 76, 1013Educ. 76, (1999))].Hence, using "expanded Octet Rule" in our present case is indeed inappropriate and may cause misleading problem, although our initial meaning is to "expand" the concept of "Octet Rule" used typically for covalent compounds to metal carbido complexes exemplified by μ3-carbido

clusterfullerenes (μ3-CCFs).
Considering the claim of Reviewer 1, to avoid misunderstanding, we changed the term of "expanded Octet Rule" to "Supplemental Octet Rule" (which is now solidified with additional theoretical studies, see details of our answer to Comment 1 of Reviewer 2), i.e., the classic Octet Rule commonly used for covalent compounds can now be applied for metal carbido complexes as demonstrated by our work and is thus regarded as "Supplemental".Besides, we changed the title to "A stabilization rule for metal carbido cluster bearing μ3-carbido single-atom-ligand encapsulated in carbon cage" to emphasize that the motivation of this work is to establish a general rule governing the stabilities of μ3-CCFs, which can not only interpret the stabilities of all μ3-CCFs reported so far but also would guide the exploration of novel μ3-CCFs or even other metal carbido complexes.In this way, we also clarify that the established demonstrates that the "Octet Rule" commonly used for covalent compounds can be also applied for metal carbido complexes exmplified by μ3-CCFs.Our finding with the establishment of "Supplemental Octet Rule" undoubtedly extends our understanding of the "Octet Rule", and is thus of high importance for μ3-CCFs and even metal carbido complexes.We hope that the Reviewer understands its significance.

Reviewer #2 (Remarks to the Author):
The authors present some newly synthesised cage compounds.I am not from the field but these compounds are certainly interesting and challenging to synthesise.It is noted that the newly synthesised compound has an octet configuration on the central μ3 carbon and this is used in an attempt to derive an expanded octet rule.Generally speaking, the compound synthesised is interesting.However, I don't believe that from the evidence presented one can really derive a general rule.The paper is generally well-presented but there is a bit too much jargon to reach a general audience.
We thank this Reviewer for her/his positive reviews with stimulating comments, which helped us to improve our manuscript.R5).According to these new results, clearly we can see that, for all 11 μ3-CCFs, configuration A bearing a central carbon with an eight-electron configuration is the most stable structure for all cases.Therefore, combined with the original 5 μ3-CCFs, we confirm that the "Supplemental Octet Rule" is a general rule for μ3-CCFs.
Table R5 (added as Supplementary Table 9).The relative total energy (ΔE, eV) of isolated  Given that this general rule is confirmed on the basis of additional study on all reported μ3-CCFs, we clarify briefly its applications and limits as follow.
1) It can interpret the stabilities of all μ3-CCFs reported so far, especially the necessity of involving non-rare earth metal (V, Ti, U) and formation of double bond between non-rare earth metal and the central carbon (M 4+ =C 4-) to satisfy the eight-electron configuration of the μ3-carbido ligand.
2  and VSc2C@D3h(5)-C78) for the first time, therefore is very important for establishing a general rule governing the stabilities of μ3-CCFs.
Comment 3: The authors should explain the level of theory used.Is PBE with a planewave basis really the optimal choice?Shouldn't one at least use a dispersion correction to model the cage?
Answer: We thank the Reviewer for the professional comment on the level of theory.
Actually, we did perform benchmark simulations (both geometric optimization and electronic structure calculations) at three different levels of theory, including the PBE functional, the HSE06 hybrid functional, and at the GGA level plus a dispersion correction (DFT-D3 method).As an example, Figure R5 plots the spin-resolved molecular levels and the spatial distributions of the frontier molecular orbitals of VSc2C@D5h(6)-C80 obtained by using the DFT-D3 method and the HSE06 functional.
We found that the optimized cages are not sensitive to the adopted functional and the bond length differences are less than 0.03 Å.Moreover, the arrangement of frontier molecular orbitals and their spatial distribution as well as the spin density are almost unchanged for different methods, although the energy level spaces are different.
Overall, this is a routine endohedral fullerene paper that reports the preparation and purification of three new molecules.The analysis of the crystallographic data leaves much to be desired.The application of the octet rule for carbon lacks novelty or substance.I do not recommend publication of this article in Nature Communications.
Publication in a more specialized venue might be possible after a more thorough and unbiased analysis of the crystallographic data.

Answer:
The Reviewer simply overlooked our efforts made in our last round revision (which are however well recognized by Reviewer 3 saying "Clearly, the authors have made an above and beyond effort to address all comments from all reviewers."),hence we respectfully disagree with her/him.As emphasized repeatedly, the novelty of our present work is that the classic Octet Rule commonly used for covalent compounds is applied for metal carbido complexes for the first time, which can not only interpret the stabilities of all reported μ 3 -CCFs reported so far but also would guide the exploration of novel μ 3 -CCFs or even other metal carbido complexes.
This significance has been well recognized by Reviewer 3 in the first round ("One of the novel features of this paper is the peculiar bonding of the encapsulated metal carbide complex.Even the authors themselves address the novelty perspective with their statement on page 12…"; "...such an expanded octet proposition is indeed credible.")and by Reviewer 2 in the second round ("I think this is challenging, interesting and well-performed work.").We do hope that Reviewer 1 can understand it.

Fig. R1 .
Fig. R1.Positions of the disordered metal sites and bond lengths between metal sites and the central carbon atom in VSc2C@D3h(5)-C78.According to Fig.R1, there are totally twelve metal sites in VSc2C@D3h(5)-C78.It is observed that M1a to M1d sites possess comparable bond lengths to the central carbon atom (1.86-1.91Å), which are distinctly shorter than those for other metal sites (1.99-2.12Å).Because the disordered sites of the same metal atom normally have similar bond lengths, it is reasonable to assign M1a to M1d sites to the same metal atom (M1) with different site occupancies.In addition, the other eight metal sites are distributed on both sides of the M1 disordered sites (see Fig.R1).Because the disordered sites of each metal atom are generally confined in the vicinity of the major sites, the four metal sites located on each side can be attributed to the disordered sites of the same metal atom (M2/M3).Therefore, each metal atom has four disordered sites, and the total twelve metal sites can be divided into four orientations of the encapsulated cluster VSc2C (differentiated by different bonding colors), which are depicted in Fig.R2.In different orientations, the corresponding bond lengths are comparable.Moreover, these
Considering the comment of Reviewer, we deleted Figures2c and 2din the original version since the key information of the VSc2C cluster is given in the zoomed Figures2e and 2fin the original version.Besides, we removed the bond angles in new Figures2c and 2dfor clarity, while the bond angles were given in Supplementary Information

Fig. R4 (
Fig. R4 (added as new Supplementary Figure 8).(a, b) Two views of the VSc2C@D5h(6)-C80.(a) Looking along the C5 axis of cage.(b) Looking perpendicular to the C5 axis of cage which is vertical in this view.(c, d) Two views of the VSc2C@D3h(5)-C78.(c) Looking along the C3 axis of cage.(d) Looking perpendicular to the C3 axis of cage which is vertical in this view.The carbon atoms with labels show the location of the C5/C3 axis within D5h(6)-C80/D3h(5)-C78 cage.

Comment 1 :
If the authors really derived a general expanded octet rule, then they should explain its applications and its limits.One compound, present in several different cages, can hardly be used to derive a new rule.Can the authors explain unexplained trends in the literature or make new predictions using their rule?Answer: We thank the Reviewer for the instructive suggestion.We agree with the Reviewer that more compounds are needed to deduce a new rule and it is important to discuss the applications and limits of this rule.In our original version, including three novel V-based μ3-CCFs, we just chose five representative μ3-CCFs based on three different types in terms of the non-rare earth metal (V, Ti, U), whose crystallographic structures are reported, to derive the general rule (see Supplementary TiM2C@C2n (M = Lu, Y, Nd, Gd, Tb, Dy, Er, Sc, 2n = 78, 80) with different electronic configurations and M=C bonds of TiM2C cluster.

Rev. 113 ,
5989-6113 (2013)).This notation has been widely used in fullerene community for more than 30 years, hence we cannot change it or reduce the usage of this jargon.Concerning the question why non-Ih-C80-based μ3-CCFs are important, it is because among all 16 reported μ3-CCFs most members are based on Ih-C80 cage, which is the most stable cage and has the highest yield as predicted theoretically and confirmed experimentally for trimetallic μ3-carbido clusterfullerenes (μ3-CCFs) and trimetallic nitride clusterfullerenes bearing intramolecular six-electron-transfer from the encapsulated cluster to fullerene cage (see Chem.Rev.113, 5989-6113 (2013)).For this reason, so far only few Ih-C80-based μ3-CCFs with relatively high yields have been crystallographically determined.This limits the systematic study of μ3-CCFs to derive a general rule.It is thus important to investigate whether non-Ih-C80-based μ3-CCFs, which have much lower yields than Ih-C80-based μ3-CCFs, can be isolated with considerable amount for crystal growth or not.Our study succeeded in isolating and determining crystallographically two non-Ih-C80-based μ3-CCFs (VSc2C@D5h(6)-C80

Figure R5 .
Figure R5.(a) The spin-resolved molecular levels and the spatial distribution of the frontier molecular orbitals of VSc2C@D5h(6)-C80 calculated by using the DFT-D3 (left) and hybrid HSE06 functional (right) method.(b) The corresponding spin density distributions.

Fig. R1 .
Fig. R1.Major and minor orientations including the respective Sc/V-C bond lengths of VSc 2 C cluster within VSc 2 C@I h (7)-C 80 (a), VSc 2 C@D 5h (6)-C 80 (b) and VSc 2 C@D 3h (5)-C 78 (c).Note that, although there may be a slight overlap between Sc and V sites in the minor orientations B, C of VSc 2 C@D 5h (6)-C 80 in terms of the short Sc2a-C and Sc2b-C bond lengths (see our answer to Comment 2 below for details), the major and most minor orientations all meet the requirement of specific metal-carbon bondings (one double bond [V=C] plus two single bonds [Sc-C]).

Fig. R3 .
Fig. R3.(a) Positions of the disordered metal sites with site occupancy (number aside the atom) and bond lengths between metal sites and the central carbon atom in VSc 2 C@D 3h (5)-C 78 obtained by constrained refinement model.(b) The positions of the major metal sites with the largest

motivation of our work is to establish a general rule governing the stabilities of μ3-CCFs, which can not only interpret the stabilities of all reported μ3-CCFs reported so far but also would guide the exploration of novel μ3-CCFs or even other metal carbido complexes. For
CCFs for the first time.Hence, our focus is not the central carbide ion itself and the number of surrounding metal ions, instead we focus "Supplemental Octet Rule" is applicable for the μ3-carbido single-atom-ligand coordinated with specific metals encapsulated within μ3-CCFs, thus the coincident misleading problem of "expanded Octet Rule" mentioned by this Reviewer can be excluded, since we focus on metal carbido cluster instead of covalent compounds containing elements in the second or lower row in the periodic table bearing d orbitals.Answer: We respectfully disagree with the Reviewer since we feel that the novelty and significance of our work might have been overlooked.Although for conventional metal carbido complexes the central carbon ion surrounded by 1 to 6 metal ions has been reported as mentioned in the Introduction section, the

on metal carbido cluster and manage to offer in-depth understanding of its unique structure and stability especially
the necessity of involving non-rare earth metal and formation of double bond between non-rare earth metal and the central carbon so as to satisfy the eight-electron configuration of the μ3-carbido ligand.To our knowledge, stabilities of organometallic complexes including metal carbido complexes have been commonly determined by Effective Atomic Number (EAN) rule (i.e., 18-electron rule) proposed in the 1920s, by studying μ3-CCFs as the simplest metal carbido complexes, our work

Table 6
13098-13107 (2016)).Considering the Reviewer's suggestion, we carried out additional theoretical calculations of the relative energies of other 11 reported Ti-based μ3-CCFs with different electronic configurations (see Table
Comment 4: The data in tableindicates that the authors constrained their crystallographic refinement so that the occupancies of sets of three metal atoms were made equal.The better way to address the problem without bias would be to allow the metal site occupancies to refine freely.I would like to see the results of a free refinement model.The present version is quite biased.

results of a free refinement model are unreasonable in this case.
2020)), thus the planar triangular configurations of VSc2C clusters within V-based μ3-CCFs are expected, as confirmed by DFT calculations.Hence, the These results suggest that the disorder of each metal atom is derived from the rotation of the entire planar VSc2C clusters (Chem.Eur.J. 22, 13098-13107 (2016); Chem.Commun.56, 3867-3870 (