Posts Tagged ‘Hiberty and co’

Kekulé’s vibration: A modern example of its use.

Friday, June 6th, 2014

Following the discussion here of Kekulé’s suggestion of what we now call a vibrational mode (and which in fact now bears his name), I thought I might apply the concept to a recent molecule known as [2.2]paracyclophane. The idea was sparked by Steve Bachrach’s latest post, where the “zero-point” structure of the molecule has recently been clarified as having D2 symmetry.[1]

pc
Let me start with a ωB97XD/6-311G(d,p) calculation of this mode. Because the mode is a mixture of C and H motions (which differ according to the molecule), I am going to try to normalise the mode by reducing the mass of the all atoms except the core six to effectively zero. The mode itself looks as below with the H-weighting applied. The hydrogens are riding, massless, on each of the six carbons.kekule-mode

The results are presented in the table below for the paracyclophane, in three different spin states.

System Mass-weighted modes, s, a Reduced mass, sym Reduced mass, asym DOI
Benzene, singlet 1342 1318 [2]
paracyclophane, singlet 1335, 1330 1257 1237 [3]
paracyclophane, triplet 1413, 1418 1403 1394 [4]
paracyclophane, quintet 1566, 1563 1521 1522 [5]

There are three effects which manifest.

  1. The first is that the Kekulé mode is depressed in the cyclophane compared to benzene itself. I have previously discussed how even in benzene this mode is depressed from its expected value because of the natural tendency of the π-system to adopt a localised cyclohexatriene motif (a tendency that is overcome by the σ-framework). So we conclude that this tendency (famously highlighted by Shaik, Hiberty and co[6]) is even slightly stronger in [2.2]paracyclophane. One might presume that the two π-clouds, in an enforced proximity which is certainly repulsive, co-operate to enhance the effect (see below).
    Click for 3D

    NCI surface showing π-repulsions (yellow). Click for 3D

    Perhaps this cooperation would be even stronger were it not from the distinct distortion from planarity that the cyclophane bridges enforce, and which might discourage the π-tendency to form cyclohexatriene.

  2. The interaction between the two π-clouds splits the Kekulé mode into a symmetric and antisymmetric pair, by either 5 or 20 cm-1 depending on the mass weighting.
  3. As one promotes the π-electrons into antibonding orbitals (triplet, then quintet) one increasingly weakens the π-resistivity. The π-electrons no longer want to collect into double bonds and so resist the symmetrising tendency of the σ-electrons less. The splitting of the  Kekulé mode also decreases.

My point with this post was to show how interesting new effects can be teased out of systems of contemporary interest by invoking Kekulé’s famous (vibrational) mode. Whether this corresponds to what the man himself had in mind is quite another matter of course.

References

  1. H. Wolf, D. Leusser, M. Jørgensen, R. Herbst‐Irmer, Y. Chen, E. Scheidt, W. Scherer, B.B. Iversen, and D. Stalke, "Phase Transition of [2,2]‐Paracyclophane – An End to an Apparently Endless Story", Chemistry – A European Journal, vol. 20, pp. 7048-7053, 2014. https://doi.org/10.1002/chem.201304972
  2. S. Shaik, A. Shurki, D. Danovich, and P.C. Hiberty, "A Different Story of π-DelocalizationThe Distortivity of π-Electrons and Its Chemical Manifestations", Chemical Reviews, vol. 101, pp. 1501-1540, 2001. https://doi.org/10.1021/cr990363l

Tags:, , ,
Posted in Historical, Interesting chemistry | No Comments »

Kekulé's vibration: A modern example of its use.

Friday, June 6th, 2014

Following the discussion here of Kekulé’s suggestion of what we now call a vibrational mode (and which in fact now bears his name), I thought I might apply the concept to a recent molecule known as [2.2]paracyclophane. The idea was sparked by Steve Bachrach’s latest post, where the “zero-point” structure of the molecule has recently been clarified as having D2 symmetry.[1]

pc
Let me start with a ωB97XD/6-311G(d,p) calculation of this mode. Because the mode is a mixture of C and H motions (which differ according to the molecule), I am going to try to normalise the mode by reducing the mass of the all atoms except the core six to effectively zero. The mode itself looks as below with the H-weighting applied. The hydrogens are riding, massless, on each of the six carbons.kekule-mode

The results are presented in the table below for the paracyclophane, in three different spin states.

System Mass-weighted modes, s, a Reduced mass, sym Reduced mass, asym DOI
Benzene, singlet 1342 1318 [2]
paracyclophane, singlet 1335, 1330 1257 1237 [3]
paracyclophane, triplet 1413, 1418 1403 1394 [4]
paracyclophane, quintet 1566, 1563 1521 1522 [5]

There are three effects which manifest.

  1. The first is that the Kekulé mode is depressed in the cyclophane compared to benzene itself. I have previously discussed how even in benzene this mode is depressed from its expected value because of the natural tendency of the π-system to adopt a localised cyclohexatriene motif (a tendency that is overcome by the σ-framework). So we conclude that this tendency (famously highlighted by Shaik, Hiberty and co[6]) is even slightly stronger in [2.2]paracyclophane. One might presume that the two π-clouds, in an enforced proximity which is certainly repulsive, co-operate to enhance the effect (see below).
    Click for 3D

    NCI surface showing π-repulsions (yellow). Click for 3D

    Perhaps this cooperation would be even stronger were it not from the distinct distortion from planarity that the cyclophane bridges enforce, and which might discourage the π-tendency to form cyclohexatriene.

  2. The interaction between the two π-clouds splits the Kekulé mode into a symmetric and antisymmetric pair, by either 5 or 20 cm-1 depending on the mass weighting.
  3. As one promotes the π-electrons into antibonding orbitals (triplet, then quintet) one increasingly weakens the π-resistivity. The π-electrons no longer want to collect into double bonds and so resist the symmetrising tendency of the σ-electrons less. The splitting of the  Kekulé mode also decreases.

My point with this post was to show how interesting new effects can be teased out of systems of contemporary interest by invoking Kekulé’s famous (vibrational) mode. Whether this corresponds to what the man himself had in mind is quite another matter of course.

References

  1. H. Wolf, D. Leusser, M. Jørgensen, R. Herbst‐Irmer, Y. Chen, E. Scheidt, W. Scherer, B.B. Iversen, and D. Stalke, "Phase Transition of [2,2]‐Paracyclophane – An End to an Apparently Endless Story", Chemistry – A European Journal, vol. 20, pp. 7048-7053, 2014. https://doi.org/10.1002/chem.201304972
  2. S. Shaik, A. Shurki, D. Danovich, and P.C. Hiberty, "A Different Story of π-DelocalizationThe Distortivity of π-Electrons and Its Chemical Manifestations", Chemical Reviews, vol. 101, pp. 1501-1540, 2001. https://doi.org/10.1021/cr990363l

Tags:, , ,
Posted in Historical, Interesting chemistry | No Comments »

The weirdest bond of all? Laplacian isosurfaces for [1.1.1]Propellane.

Wednesday, July 21st, 2010

In this post, I will take a look at what must be the most extraordinary small molecule ever made (especially given that it is merely a hydrocarbon). Its peculiarity is the region indicated by the dashed line below. Is it a bond? If so, what kind, given that it would exist sandwiched between two inverted carbon atoms?

1.1.1 Propellane

One (of the many) methods which can be used to characterize bonds is the QTAIM procedure. This identifies the coordinates of stationary points in the electron density ρ(r) (at which point ∇ρ(r) = 0) and characterises them by the properties of the density Hessian at this point. At the coordinate of a so-called bond critical point or BCP, the density Hessian has two negative eigenvalues and one positive one. The sum, or trace of the eigenvalues of the density Hessian at this point, denoted as ∇2ρ(r), provides in this model a characteristic indicator of the type of bond, according to the following qualitative partitions:

  1. ρ(r) > 0, ∇2ρ(r) < 0; covalent
  2. ρ(r) ~0, ∇2ρ(r) > 0; ionic
  3. ρ(r) > 0, ∇2ρ(r) > 0; charge shift

The third category of bond was first characterised by Shaik, Hiberty and co. using valence-bond theory1 and they went on to propose [1.1.1] propellane (above, along with F2) as an exemplar of this type.2 Matching the conclusions drawn from VB theory was the value of the Laplacian. As defined above, for the central C-C bond, both ρ(r) and  ∇2ρ(r) have been calculated to be positive, supporting the identification of this interaction as having charge-shift character.3

The Laplacian represents one of those properties where quantum mechanics meets experiment, in that its value (and that of ρ(r) itself) can be measured by (accurate) X-ray techniques.4 This was recently accomplished for propellane,5 with the same conclusion that the Laplacian in the central C-C region has the significantly positive value of +0.42 au. The electron density ρ(r) at this point was measured as 0.194 au. Calculations5 at the B3LYP/6-311G(d,p) level report ρ(r) as ~0.19 and ∇2ρ(r) as +0.08 au. Whilst the former is in good agreement with experiment, the latter is calculated as rather smaller than expected. This was originally interpreted as indicating that the “the experimental bond path has a stronger curvature [in ρ(r)] than the theoretical” although more recent thoughts are that both experimental and theoretical uncertainty may account for the discrepancy.5,6 An experiment worth repeating?

A hitherto largely unexplored aspect of characterising a bond using the Laplacian is whether the value at the bond critical point is fully representative of the bond as a whole. The Laplacian is related to two components of the electronic energy by the Virial theorem;

2G(r) + V(r) = ∇2ρ(r)/4; H(r) = V(r) + G(r)

where G(r) is the kinetic energy density, V(r) is the potential energy density and H(r) the energy density. Charge-shift bonds exhibit a large value of the (repulsive) kinetic energy density, a consequence of which is that ∇2ρ(r) is more likely to be positive rather than negative. The relationships above hold not just for the specific coordinate of a bond critical point, but for all space. Accordingly, another way therefore of representing the Laplacian ∇2ρ(r) is to plot the function as an isosurface, including both the negative surface (for which |V(r)| > 2G(r)) and the positive surface [for which |V(r)| < 2G(r)].

Such an analysis is the purpose of this post, using wavefunctions evaluated at the CCSD/aug-cc-pvtz level (see DOI: 10042/to-5012). The values of ρ(r) and ∇2ρ(r) at the bcp for the central bond are 0.188 and +0.095 au, which compares well with previous calculations. The values for the wing C-C bonds are 0.242 and -0.491 respectively (and were measured5 as 0.26 and -0.48). Laplacian isosurfaces corresponding to ± 0.49 (the value at the wing C-C bcp), ± 0.47 and ± 0.2 (which reveals prominent regions of +ve values for the Laplacian) can be seen in the figures below (and can be obtained as rotatable images by clicking).


Laplacian isosurface contoured at ± 0.49

 –

Laplacian isosurface contoured at ± 0.47. Red = -ve, blue= +ve.

Laplacian isosurface contoured at ± 0.20

A significant feature is the isosurface at -0.47, which corresponds to the lowest contiguous Laplacian isovalued pathway connecting the two terminal carbon atoms (and which coincidentally is similar in magnitude to that reported5 as measured for these two atoms). Three such bent pathways of course connect the two carbon atoms. The energy density H(r) shows a minimum value of -0.21 au along any of these pathways. It is significantly less negative (-0.13) for the direct pathway taken along the axis of the C-C bond.

Energy density H(r) @-0.21

Energy density H(r) @-0.13

ELF isosurface @0.7

A useful comparison with this result is the ELF isosurface. This too is computed at the correlated CCSD/aug-cc-pVTZ using a new procedure recently described by Silvi.7 Contoured at an isosurface of +0.7, the ELF function is continuous between the two terminal atoms, much in the manner of Laplacian. Significantly, the ELF function at the bcp appears at the very much lower threshold value of 0.54, and forms a basin with a tiny integration for the electrons (0.1e). Since both methods provide a measure of the Pauli repulsions via the excess kinetic energy, the similarity of the Laplacian to the ELF function is probably not coincidental.

The issue then is whether a bond must be defined by the characteristics of the electron density distribution along the axis connecting that bond, or whether other, non-least-distance pathways can also be considered as being part of the bond.8 The former criterion defines a pathway involving a positive Laplacian (+0.095) and would be interpreted as indicating charge shift character for that bond. The latter involves three (longer) pathways for which the Laplacian is strongly -ve, and which would therefore per se imply more conventional covalent character for the interaction. Considered as a linear (straight) bond, it has charge shifted character; considered as three “banana” bonds, it may be covalent. Weird!

  1. Shaik, S.; Danovich, D.; Silvi, B.; Lauvergnat, D. L.; Hiberty, P. C., “Charge-Shift Bonding – A Class of Electron-Pair Bonds That
    Emerges from Valence Bond Theory and Is Supported by the Electron Localization Function Approach,” Chem. Eur. J., 2005,
    11, 6358-6371, DOI: 10.1002/chem.200500265 and references cited therein.
  2. W. Wu, J. Gu, J. Song, S. Shaik, and P. C. Hiberty, “The Inverted Bond in [1.1.1]Propellane is a Charge-Shift Bond,” Angew. Chem. Int. Ed., 2008,
    DOI: 10.1002/anie.200804965; 10.1002/cphc.200900633
  3. S. Shaik, D. Danovich, W. Wu & P. C. Hiberty, “Charge-shift bonding and its manifestations in chemistry”, Nature Chem, 2009, 1, 443-3439. DOI: 10.1038/nchem.327
  4. P. Coppens, “Charge Densities Come of Age”, Angew. Chemie Int. Ed., 2005, 44, 6810-6811. DOI: 10.1002/anie.200501734
  5. M. Messerschmidt, S. Scheins, L. Grubert, M. Pätzel, G. Szeimies, C. Paulmann, P. Luger. “Electron Density and Bonding at Inverted Carbon Atoms: An Experimental Study of a [1.1.1]Propellane Derivative, Angew. Chemie Int. Ed., 2005, 44, 3925-3928. DOI: 10.1002/anie.200500169
  6. L. Zhang, W. Wu, P. C. Hiberty, S. Shaik, “Topology of Electron Charge Density for Chemical Bonds from Valence Bond Theory: A Probe of Bonding Types”, Chem. Euro. J., 2009, 15, 2979-2989. DOI: 10.1002/chem.200802134
  7. F. Feixas , E. Matito, M. Duran, M. Solà and B. Silvi, submitted for publication. See also this abstract.
  8. See for example the work of R. F. Nalewajski

Rzepa, Henry S. The weirdest bond of all? Laplacian isosurfaces for [1.1.1]Propellane. 2010-07-21. URL:http://www.ch.ic.ac.uk/rzepa/blog/?p=2251. Accessed: 2010-07-21. (Archived by WebCite® at http://www.webcitation.org/5rOFp6EuM)

Tags:, , , , , , , , , ,
Posted in Hypervalency, Interesting chemistry | 4 Comments »

Quintuple bonds: part 2

Saturday, February 20th, 2010

In the previous post, I ruminated about how chemists set themselves targets. Thus, having settled on describing regions between two (and sometimes three) atoms as bonds, they added a property of that bond called its order. The race was then on to find molecules which exhibit the highest order between any particular pair of atoms. The record is thus far five (six has been mooted but its a little less certain) for the molecule below

A molecule with a Quintuple-bond

There are many ways of describing the electronic behaviour in that region called a bond, one being the ELF (Electron localization function) technique, which certainly sounds as if it is describing a bond! The ELF function for the molecule above however was distinctly odd, and this was attributed to the Cr-Cr bond being not so much a covalent bond, but another (much less recognized type) known as a charge-shift bond. In particular, two of the ELF basin centroids did not occupy the central region between the two atoms, but had in effect fled that region, and in the process had also each split into two. Other ELF basins did not much look like bonds, but retained much of their core-electron (i.e. non bonding) character. The issue now becomes whether the ELF method is sensible, or simply an artefact. In other words, it needs calibrating against other (homonuclear) molecules which might exhibit charge-shift behaviour.

Three such molecules are in fact the halogens, F2, Cl2, Br2 as discussed by Shaik, Hiberty and co (DOI: 10.1002/chem.200500265). So lets take a look at what an ELF analysis shows for these, and how it compares with the chromium quintuple bond.

ELF analysis for F2

ELF analysis for Cl2

ELF analysis for Br2

At the B3LYP/6-311G(d) level, the ELF function shows the (valence) electrons located in two regions. Firstly, what we might call the lone pairs are located in a torus surrounding each halogen atom (i.e. the molecule must be axially symmetric). The remaining electrons are in basins with centroids along the axis of each bond. The Br2 centroid is a single conventional disynaptic basin, with an integration of 0.77 electrons. With Cl2 however, something odd happens (and the effect was described in DOI: 10.1002/chem.200500265 ); the disynaptic basin splits into a close pair, each integrating to 0.33 electrons, and looking as if the two parts want to run away from one another. This was interpreted as indicating that the purely covalent description of the halogen bond is in fact repulsive and not attractive! The effect is enhanced for F2, with two very much split basins, each integrating to 0.08 electrons. This serves to remind us of how odd a bond the F-F one truly is (and how easily it is homolyzed)!

Now that we have our calibration, does it match to the Cr-Cr quintuple bond? Very much so! Again, the valence basins show very low integrations (compared to the nominal bond order), and again they appear to have split and run away from each other. Most of the valence electrons in that species prefer instead to masquerade as core-electrons. So we can conclude that by the ELF criterion, the Cr-Cr bond is not quintuple, and not covalent but charge shifted. Of course, this does seem at odds with the Cr-Cr internuclear distance, which is indeed very short! This shortening probably arises from electrostatic attractions in the charge-shifted valence bond forms. It simply goes to show that what the nuclei get up to and what the electrons do may not be one and the same thing!

Tags:, , , ,
Posted in Hypervalency | 5 Comments »