Controversial Bond Orders

From bondslam
Jump to: navigation, search


Ángel Martín Pendás[edit]

Pedro Salvador Sedano[edit]


David L. Cooper[edit]


--Eduard (talk) 17:54, 20 July 2017 (CEST) In the last ten years, there has been a vivid discussion about the nature of the chemical bonding in the C2 molecule. Some people claim that this molecule goes beyond the classical C-C picture and the molecule exhibits a quadruple bond. Others have found this molecule to be less special and report proofs of double- or triple-bond character. In light of some new evidence, several authors have even changed their initial position regarding the bonding nature of C2. A recent discussion on Chemistry Views,[1] summarizes some of the clues behind the opposing views in this controversial molecule. Below we have made a selection of papers according to which side they take in this conundrum. Which side are you on?

In favor of a quadruple bond[edit]

- Quadruply bonded carbon. [2]

- Quadruple bonding in C2 and analogous eight-valence electron species. [3]

- One Molecule, Two Atoms, Three Views, Four Bonds? [4]

- Chemical bonding in carbon dimer isovalent series from the natural orbital functional theory perspective. [5]

- The Nature of the Fourth Bond in the Ground State of C2: The Quadruple Bond Conundrum. [6]

- Response to the Comment by J. Grunenberg on “The Nature of the Fourth Bond in the Ground State of C2: The Quadruple Bond Conundrum′′. [7]

- The Quadruple Bonding in C2 Reproduces the Properties of the Molecule. [8]

- A Response to the Critical Comments on “One Molecule, Two Atoms, Three Views, Four Bonds?” [9]

- Bonding in B2 and B2+: Insights from full configuration interaction and valence bond studies [10]

- Latent harmony in dicarbon between VB and MO theories through orthogonal hybridization of 3σg and 2σu [11]

- Intrinsic Resolution of Molecular Electronic Wave Functions and Energies in Terms of Quasi-atoms and Their Interactions [12]

- Chemical bonding motifs from a tiling of the many-electron wavefunction [13]

- The Art of the Chemical Bond [14]

In favor of a double or triple bond[edit]

- Bonding Conundrums in the C2 Molecule: A Valence Bond Study. [15]

- Critical Comments on “One Molecule, Two Atoms, Three Views, Four Bonds?”. [16]

- Comment on “The Nature of the Fourth Bond in the Ground State of C2: The Quadruple Bond Conundrum” [17]

- The Chemical Bond in C2 [18]

- C2 in a Box: Determining Its Intrinsic Bond Strength for the X1g+ Ground State [19]

- The Bond Order of C2 from a Strictly N-Representable Natural Orbital Energy Functional Perspective [20]

- New insights from domain-averaged Fermi holes and bond order analysis into the bonding conundrum in C2 [21]

Higher than triple bond[edit]

- Magnetic Shielding Studies of C2 and C2H2 Support Higher than Triple Bond Multiplicity in C2. [22]

Other views[edit]

- According to the local spin analysis, [23] C2 has diradicaloid character. [24]


Psalse (talk) 19:13, 30 August 2017 (CEST)[edit]

Some years ago we considered dicarbon, along with other diatomics, in the light of the so-called local spin analysis (LSA). The LSA is a wavefunction analysis tool by which essentially the expectation value of the spin-squared operator is decomposed into one-center (atomic/fragment) and two-center contributions. The method is able to quantify the existence of local spins (atomic terms) and their coupling (diatomic terms) even for pure singlet states. Thus, it is able to differentiate between a classical covalent bond and an anti-ferromagnetic system in which the spins are coupled to a singlet. The interpretation of the one- and two-center terms arising from the LSA is not as straightforward as for instance a population analysis of the spin density. Let us consider first the simplest case of a two-electron homonuclear diatomic system in the singlet state, consisting of two hydrogen-like atoms labeled A and B. In the dissociation limit, the LSA will provide the following results:


For the same system in a triplet state we would obtain


For such prototypical molecule one can easily obtain analytical expressions for the local spins and Mayer-Wiber bond orders in the framework of the three-dimensional space analysis. For a single-determinant description of the system the bond order is exactly 1 and the local spins zero. The two electrons are perfectly paired forming a classical covalent bond. When electron correlation is considered the BO decreases and the local spins increase monotonically. in fact, the extent of local spin is proportional to the deviation from the perfect covalent bond picture.


In the paper Chem. Eur. J. 2013, 19, 15267 we studied a number of diatomics, including dicarbon, at the full-valence CASSCF/cc-pVTZ level of theory. The results are gathered below.


The LSA analysis reveals a different signature for the CC bond, clearly pointing towards a diradicaloid, where both sigma and pi electrons contribute.

The slides can be found: Slides

Ampendas (talk) 20:53, 21 August 2017 (CEST)[edit]

Real space techniques may be used to obtain, simultaneously, energetic and bond-order-like insights (e.g. through IQA and real space delocalization descriptors). If this is done, four bonding components may be found in correlated descriptions of dicarbon, although its intrinsic bond energy turns out to be smaller than that in acetylene. Some data from CAS and FCI calculations can be found below:


--Henry (talk) 19:12, 23 August 2017 (CEST)[edit]

ELF centroids for C2 using MultiWFN

ELF centroids for C2 using TopMod

ELF function contoured at 0.811 showing just the endo C-C torus

ELF function contoured at 0.800 showing the combined endo and exo-torus

  • The wavefunction for C2 has been computed at the CASSCF(12,12)/6-311G(d,p) level and written using Gaussian16 as an (unsymmetrized) .wfn file using natural orbitals.[25] These show 12 orbitals that have significant fractional occupancy, reflecting the multi-reference character of the wavefunction. In particular orbital 7 (nominally with zero occupancy in a single-reference model) has occupancy of 0.3744405.
  • The ELF centroids computed from the density obtained from the .wfn file using the TopMod09 program are shown on the left. The total basin integration of the four centroids which are slightly exo to the C-C bond is 4.44e whilst the four central basins (typical of π bonds) are 3.4e and reflect a π-torus. It is difficult to compare the partition of the ELF function into bonds with other methods, but could these basins reflect the unusual character of the postulated two σ bonds; one a regular endo bond and the other more loosely coupled exo to the bond and very much weaker than the first?
  • The MultiWFN ELF basin analysis is based on constructing a far finer density grid than TopMod, in part because the former program does so in parallel on multiple processors. It captures a circular attractor for the endo-C-C region and is well on the way to apparently doing so for the two exo-CC regions. These three circular attractors tend towards describing the density in this molecule as far bulkier than e.g. ethyne itself. Perhaps not surprising given the amount of electron repulsion concentrated into this region. One has to ask whether a similar picture pertains to eg Cr2.

--Henry (talk) 15:29, 24 August 2017 (CEST)[edit]

Bernard Silvi has sent me a response to the above: The ELF=0.7 isosurface with in green the C-C bond and in red the carbon lone pairs is shown on the right. The problem with Gaussian and cartesian gaussian basis set is that the cylindrical symmetry D∞h is replaced by the point symmetry D4h. One has to take care of that and consider that there are three circle attractors instead of 12 point attractors. The results of my calculation of the population is V(C,C) 3.44 , σ2=1.92, V(C) 2.16, σ2=0.96. Therefore the "ELF bond order" deduced from the V(C,C) population is 3.44/2=1.72 which does not correspond to that expected from the bond length. Why is it too short? If I look at the covariance of the lone pair populations I find 0.20 which is a rather large value indicating a noticeable charge shift contribution (in VB language).

David L. Cooper: σ-weakening effects in C2[edit]

There is surely no reason to doubt the veracity of the breathing orbital valence bond calculations (and so on) that have been used to argue in favour of a fourth bond in ground state C2 at its equilibrium geometry [26]. In general terms, they show very clearly the presence of a conventional triple bond (resembling that in HCCH) plus two singly-occupied outwards-pointing hybrid orbitals. There is a further (smaller) energy lowering that can be associated with the interaction between these last two orbitals. To a large extent, the nature of the bonding in C2 could be deemed to have been settled: there is a triple bond augmented with a further stabilizing interaction that could arguably be called a fourth bond. Before fully accepting this "triple-bond-plus" model, there are some important further considerations. It turns out that various experimentally-derived data appear to indicate that the bonding in C2 is not only weaker than one might first have supposed for a triple-bond-plus arrangement, but it could in fact be weaker even than that associated with the formal triple bond of HCCH. This can of course be rationalized within the triple-bond-plus model in term of weakening associated with four σ electrons occupying much the same space (and similar arguments). At least in this sense, the bonding in ground state C2 at its equilibrium geometry could be described as triple-bond-plus, albeit modified by "σ-weakening".

Many alternative methodologies suggest that there are sufficient changes in the σ space on going from HCCH to C2 that the total σ interactions in C2 are weaker than those in HCCH. According to some approaches, the σ-weakening is sufficient for the bonding to be better described in terms of two electron-sharing π bonds plus one or two weaker σ interactions: "double-bond-plus". (On the whole, it does seem to be more fruitful to focus on the strength of the σ interactions rather than on counting the number of them.) As just one example [27], we mention the analysis of a spin-coupled (also known as full generalized valence bond) wavefunction for C2. Except for nontrivial non-perfect-pairing contributions in the spin space, the orbital description suggests a full σ bond, two π bonds and two singly-occupied outwards-pointing hybrids. Nonetheless, when the pair density from this calculation is analyzed using the domain-averaged Fermi hole approach, the anticipated full σ bond is no longer seen, presumably because of the σ-weakening associated with four σ electrons occupying much the same space.

The triple-bond-plus model does appear to be an excellent description of ground state C2 before full account has been taken of σ-weakening whereas various double-bond-plus models could arguably also be seen as useful descriptions after the full extent of the σ-weakening effects have been formally included.


  1. A. Deveson, D. Cremer, G. Frenking, M. Piris, S. Shaik, Chemistry Views, 17 March 2016, DOI: 10.1002/chemv.201600022
  2. J. Grunenberg, Nat. Chem., 2012, 4, 154-155. DOI: 10.1038/nchem.1274
  3. S. Shaik, D. Danovich, W. Wu, P. Su, H. S. Rzepa, P. C. Hiberty, Nat. Chem., 2012, 4, 195-200. DOI: 10.1038/nchem.1263
  4. S. Shaik, H.S. Rzepa, R. Hoffmann, Angew. Chem. Int. Ed., 2013, 52, 3020-3033 DOI: 10.1002/anie.201208206
  5. J. M. Matxain, F. Ruipérez, I. Infante, X. Lopez, J.M. Ugalde, G. Merino, M. Piris, J. Chem. Phys., 2013, 138, 151102. DOI: 10.1063/1.4802585
  6. D. Danovich, P. C. Hiberty, W. Wu, H. S. Rzepa, S. Shaik Chem. Eur. J., 2014, 20, 6220-6232. DOI: 10.1002/chem.201400356
  7. S. Shaik, D. Danovich, P. C. Hiberty, Chem. Eur. J., 2015, 21, 17126-17127. DOI: 10.1002/chem.201503882
  8. S. Shaik, D. Danovich, B. Braida, P. C. Hiberty, Chem. Eur. J., 2016, 22, 4116-4128. DOI: 10.1002/chem.201600011
  9. D. Danovich, S. Shaik, H.S. Rzepa, R. Hoffmann, Angew. Chem. Int. Ed., 2013, 52, 5926-5928 DOI: 10.1002/anie.201302350
  10. J. H. van Lenthe, R. W.A. Havenith, Computational and Theoretical Chemistry, 2017, DOI:10.1016/j.comptc.2017.02.001
  11. R. Zhong, M. Zhang, H. Xu and Z. Su , Chemical Science, 2016, 7, 1028-1032. DOI:10.1039/C5SC03437J
  12. A. C. West, M. W. Schmidt, M. S. Gordon, and K. Ruedenberg, J. Phys. Chem. A,, 2017, 1086-1105. DOI:10.1021/acs.jpca.6b10911
  13. Y. Liu, T. J. Frankcombe and T. W. Schmidt, PCCP, 2016, 18, 13385. DOI:10.1039/c6cp01188h
  14. S. K. Ritter, ACS Central Sci., 2016, 769-772. DOI:10.1021/acscentsci.6b00337
  15. P. Su, J. Wu, J. Gu, W. Wu, S. Shaik, P. C. Hiberty, J. Chem. Theory Comp., 2011, 7, 121-130 DOI:10.1021/ct100577v
  16. G. Frenking, M. Hermann, Angew. Chem. Int. Ed., 2013, 52, 5922-5925 DOI: 10.1002/anie.201301485
  17. J. Grunenberg, Chem. Eur. J., 2015, 21, 17126-17126. DOI: 10.1002/chem.201500130
  18. M. Hermann, G. Frenking, Chem. Eur. J., 2016, 22, 4100-4108. DOI: 10.1002/chem.201503762
  19. W. Zou, D. Cremer, Chem. Eur. J., 2016, 22, 4087-4099. DOI: 10.1002/chem.201503750
  20. M. Piris, X. Lopez, J.M. Ugalde, Chem. Eur. J., 2016, 22, 4109-4115. DOI: 10.1002/chem.201504491
  21. D. L. Cooper, R. Ponec, M. Kohout, Mol. Phys., 2016, 104, 1270-1284. DOI: 10.1080/00268976.2015.1112925
  22. P. B. Karadakov, J Kirsopp, Chem. Eur. J., DOI:10.1002/chem.201703051
  23. E. Ramos-Cordoba, E. Matito, I. Mayer, P. Salvador J. Comput. Theory Chem., 2012, 8, 1270-1279, DOI:10.1002/chem.201703051
  24. E. Ramos-Cordoba, M. Reiher, P. Salvador Chem. Eur. J., 2013, 19, 15267-15275, DOI:10.1002/chem.201703051
  25. H. S. Rzepa, 2017, DOI:cb5j
  26. Shaik, S.; Danovich, D.; Braïda, B.; Hiberty, P. C. The quadruple bonding in C2 reproduces the properties of the molecule. Chem. Eur. J., 2016, 22, 4116–4128. DOI:10.1002/chem.201600011
  27. Cooper, D. L.; Penotti, F. E.; Ponec, R. Why is the bond multiplicity in C2 so elusive? Comput. Theor. Chem., 2015, 1053, 189-194. DOI:10.1016/j.comptc.2014.08.024