Posts Tagged ‘quintuple bond’

Quintuple bonds: resurfaced.

Sunday, January 31st, 2016

Six years ago, I posted on the nature of a then recently reported[1] Cr-Cr quintuple bond. The topic resurfaced as part of the discussion on a more recent post on NSF3, and a sub-topic on the nature of the higher order bonding in C2. The comment made a connection between that discussion and the Cr-Cr bond alluded to above. I responded briefly to that comment, but because I want to include 3D rotatable surfaces, I expand the discussion here and not in the comment.‡

Firstly, a quick update. Since the original post, quite a few Cr-Cr quintuple bonds have been reported. In searching the crystal structure database, I used the text "quintuple" as a text search term (since specifying a quintuple bond as such is not supported) along with a Boolean AND using the sub-structure Cr-Cr (with any type of bond allowed). The result is shown below. It is striking that in fact these "quintuple" bonds cluster into a set with a bond distance of ~1.74Å and another with 1.83Å. Are these valence bond isomers?

 

Now to the system shown at the top (one of the 1.74Å set). My original post discussed the results of a density functional evaluation of the properties of the electron density in the Cr-Cr region. Most striking was the value of the Laplacian ∇2ρ(r) of this density, the value of +1.45au being the largest ever reported for a pair of identical atoms. I should remind that ∇2ρ(r) is used as one measure of the character of a bond, being the balance between electronic kinetic energy density and potential energy density along a bond. But it is well recognised that the bonding between such transition metals has what is called multi-reference character; the wavefunction is not well described by just a single doubly occupied electronic configuration. More electronic configurations have to be included, and hence a MC-SCF (multi-configuration) self-consistent description of the wavefunction is needed. So as a response to the comment noted above, I decided to carry out CASSCF/6-311G(d) calculations, in which an active space of electrons and molecular orbitals is specified, and using the geometry previously obtained at the DFT level. Thus a CASSCF(8,8) calculation takes 8 electrons and evaluates all possible configurations arising from placing them into an active space of eight molecular orbitals. With metals unfortunately the active space is likely to be large, and so I decided to computed (10,10), (12,12) and (14,14) CASSCF as well to see if any convergence might occur. The last is close to the limit offered by the program. The values shown below are at the QTAIM line (bond) critical point along the Cr-Cr axis.

Active space ρ(r) ∇2ρ(r) Total energy, Hartree % of CS config Calculation DOI
8 .303 1.720 -2383.48049 63 [2]
10 .308 1.612 -2383.68830 61 [3]
12 .308 1.612 -2383.70398 60.6 [4]
14 .308 1.612 -2383.72161 59 [5]
DFT .313 1.45 – 100 [6]

From the trend above, we might safely conclude that the CASSCF active space IS convergent, at least for the density if not for the energy. Also convergent are the properties of the density such as ∇2ρ(r), and noteworthy is that the value of this property is even higher than was obtained using single-configuration DFT theory. So the claim that this system has a record such property does not change. Negative values of the Laplacian are normally taken to indicate a conventionally covalent bond, whereas +ve values show the bond has what is called charge-shift character.[7] So these Cr-Cr quintuple bonds must be amongst the most charge-shifted exemplars!

I show some surfaces (click on the image to get a rotatable model) computed from the CASSCF(14,14) density. Firstly the electron density ρ(r) itself, contoured at 0.25au, showing the high value between the chromium atoms.

Next, ∇2ρ(r) contoured at ±1.5, revealing its high value in the Cr-Cr region (blue = +ve, red = -ve) and then below at ± 0.25 which includes the covalent bonds of the ligands.

Finally, the ELF (electron localisation function) function which tries to gather the electron density into localised ELF basins (numbers are the integration of the electron density in this basin). This looks very similar to that shown previously and is striking because there is no basin in the Cr-Cr region. Instead, the localisation is along the Cr-N bonds. One might describe this as saying that the Cr-Cr region is very highly correlated.

‡It is a limitation of the WordPress system that such objects cannot be included in comments.

References

  1. C. Hsu, J. Yu, C. Yen, G. Lee, Y. Wang, and Y. Tsai, "Quintuply‐Bonded Dichromium(I) Complexes Featuring Metal–Metal Bond Lengths of 1.74 Å", Angewandte Chemie International Edition, vol. 47, pp. 9933-9936, 2008. https://doi.org/10.1002/anie.200803859
  2. H.S. Rzepa, "C 2 H 6 Cr 2 N 4", 2016. https://doi.org/10.14469/ch/191860
  3. H.S. Rzepa, "C 2 H 6 Cr 2 N 4", 2016. https://doi.org/10.14469/ch/191857
  4. H.S. Rzepa, "C 2 H 6 Cr 2 N 4", 2016. https://doi.org/10.14469/ch/191858
  5. H.S. Rzepa, "C2H6N2O2", 2016. https://doi.org/10.14469/ch/191855
  6. H.S. Rzepa, "C 2 H 6 Cr 2 N 4", 2010. https://doi.org/10.14469/ch/4156
  7. S. Shaik, D. Danovich, W. Wu, and P.C. Hiberty, "Charge-shift bonding and its manifestations in chemistry", Nature Chemistry, vol. 1, pp. 443-449, 2009. https://doi.org/10.1038/nchem.327

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A (very) short history of shared-electron bonds.

Tuesday, March 26th, 2013

The concept of a shared electron bond and its property of an order is almost 100 years old in modern form, when G. N. Lewis suggested a model for single and double bonds that involved sharing either 2 or 4 electrons between a pair of atoms[1]. We tend to think of such (even electron) bonds in terms of their formal bond order (an integer), recognising that the actual bond order (however defined) may not fulfil this value. I thought I would very (very) briefly review the history of such bonds.

  1. 1916: G. N. Lewis[1] proposed a model for carbon involving a cube with one electron at each corner, thus making an octet.‡ A single bond would be created by two atoms sharing a common edge (= 2 shared electrons), and a double bond by sharing a common face (= 4 shared electrons). The recognition that the formal bond order of two could be partitioned into one electron pair of σ symmetry and one of π was not achieved until ~1929 (by Hückel). It is also now recognised that whilst most bonds of order 1 are of type σ, a rare few can be π (these are called homo or “suspended” bonds).
  2. 1916: Lewis also speculates about a rather less well-known model comprising “eight electrons in which pairs are symmetrically placed about a center gives … the model of the tetrahedral carbon atom.” He then points out that two tetrahedra, attached by one, two or three corners each would represent the single, the double and the triple bond. The latter “represents the highest possible degree of union between two atoms“. He chooses acetylene as an example, representing it as H:C:::C:H and two “tautomers” (we would now call them valence bond isomers)† with lower bond orders, these being what we now call a bis-carbene and a biradical:Lewis
  3. 1965: It took a remarkable wait of 49 years (a span which encompasses the development and maturity of quantum mechanics) to extend the “highest possible degree of union” to the quadruple bond, identified by Cotton in the previously known compound [Re2Cl8]2-.[2].
    Click for 3D

    Click for 3D

    In fact, Mulliken had drawn a quadruple bond between the two carbons in C2 back in 1939[3] (see Table 1, p 779) but he probably thought of it as a very high energy excited state and that it did not merit further discussion. The latest thoughts are that C2  does indeed have (a weak) fourth bond[4] in its ground electronic state.

  4. 2005: Another 40 years elapsed before quintuple or “fivefold” bonding was discovered by Power[5] in ArCrCrAr. There has been a bit of a race since to discover the shortest example of this genre.
    Click for 3D

    Click for 3D

  5. 2013: Unlike the lower bond orders, where direct structural data for larger molecules is available, speculation about sextuple bonds is limited largely to theoreticians, who have been at it for quite a while. The latest thinking is summarised here[6] (also doi: 10.1039/C2CP43559D). The current best candidates for a sextuple bond include Mo2 and W2.
  6. What is the limit of the formal integer bond order? I do not believe anyone thinks that septuple or octuple bonds (formal or otherwise) will be discovered (or even speculated upon) any time soon, but there is no fundamental law which would prohibit them.[7] Quite possibly if we get beyond element 120 in the periodic table, examples might emerge!

‡A formula for predicting the filled electron shells is 2(N+1)2, which gives the values 2, 8, 18, 32[8],[9] 50. It is also, as it happens, the rule for 3D aromaticity in clusters.

†A bis-carbene form, whilst not appropriate for carbon, may indeed become more realistic as one proceeds down column 14 of the periodic table. Thus [10], where Ar-Sn≡Sn-Ar has a C-Sn-Sn bond angle of 125°.

Click for 3D.

Click for 3D.

Or perhaps an even better example[11] with a C-Sn-Sn angle of 98°. There is also an example of C-Pb-Pb[12] with an angle of 94°.

References

  1. G.N. Lewis, "THE ATOM AND THE MOLECULE.", Journal of the American Chemical Society, vol. 38, pp. 762-785, 1916. https://doi.org/10.1021/ja02261a002
  2. F.A. Cotton, "Metal-Metal Bonding in [Re<sub>2</sub>X<sub>8</sub>]<sup>2-</sup> Ions and Other Metal Atom Clusters", Inorganic Chemistry, vol. 4, pp. 334-336, 1965. https://doi.org/10.1021/ic50025a016
  3. R.S. Mulliken, "Note on Electronic States of Diatomic Carbon, and the Carbon-Carbon Bond", Physical Review, vol. 56, pp. 778-781, 1939. https://doi.org/10.1103/physrev.56.778
  4. S. Shaik, H.S. Rzepa, and R. Hoffmann, "One Molecule, Two Atoms, Three Views, Four Bonds?", Angewandte Chemie International Edition, vol. 52, pp. 3020-3033, 2013. https://doi.org/10.1002/anie.201208206
  5. T. Nguyen, A.D. Sutton, M. Brynda, J.C. Fettinger, G.J. Long, and P.P. Power, "Synthesis of a Stable Compound with Fivefold Bonding Between Two Chromium(I) Centers", Science, vol. 310, pp. 844-847, 2005. https://doi.org/10.1126/science.1116789
  6. F. Ruipérez, M. Piris, J.M. Ugalde, and J.M. Matxain, "The natural orbital functional theory of the bonding in Cr<sub>2</sub>, Mo<sub>2</sub>and W<sub>2</sub>", Phys. Chem. Chem. Phys., vol. 15, pp. 2055-2062, 2013. https://doi.org/10.1039/c2cp43559d
  7. G. Frenking, and R. Tonner, "The six-bond bound", Nature, vol. 446, pp. 276-277, 2007. https://doi.org/10.1038/446276a
  8. I. Langmuir, "Types of Valence", Science, vol. 54, pp. 59-67, 1921. https://doi.org/10.1126/science.54.1386.59
  9. J. Dognon, C. Clavaguéra, and P. Pyykkö, "Towards a 32‐Electron Principle: Pu@Pb<sub>12</sub> and Related Systems", Angewandte Chemie International Edition, vol. 46, pp. 1427-1430, 2007. https://doi.org/10.1002/anie.200604198
  10. A.D. Phillips, R.J. Wright, M.M. Olmstead, and P.P. Power, "Synthesis and Characterization of 2,6-Dipp<sub>2</sub>-H<sub>3</sub>C<sub>6</sub>SnSnC<sub>6</sub>H<sub>3</sub>-2,6-Dipp<sub>2</sub> (Dipp = C<sub>6</sub>H<sub>3</sub>-2,6-Pr<sup>i</sup><sub>2</sub>):  A Tin Analogue of an Alkyne", Journal of the American Chemical Society, vol. 124, pp. 5930-5931, 2002. https://doi.org/10.1021/ja0257164
  11. Y. Peng, R.C. Fischer, W.A. Merrill, J. Fischer, L. Pu, B.D. Ellis, J.C. Fettinger, R.H. Herber, and P.P. Power, "Substituent effects in ditetrel alkyne analogues: multiple vs. single bonded isomers", Chemical Science, vol. 1, pp. 461, 2010. https://doi.org/10.1039/c0sc00240b
  12. L. Pu, B. Twamley, and P.P. Power, "Synthesis and Characterization of 2,6-Trip<sub>2</sub>H<sub>3</sub>C<sub>6</sub>PbPbC<sub>6</sub>H<sub>3</sub>-2,6-Trip<sub>2</sub> (Trip = C<sub>6</sub>H<sub>2</sub>-2,4,6-<i>i</i>-Pr<sub>3</sub>):  A Stable Heavier Group 14 Element Analogue of an Alkyne", Journal of the American Chemical Society, vol. 122, pp. 3524-3525, 2000. https://doi.org/10.1021/ja993346m

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