Posts Tagged ‘Valence electron’

What are the highest bond indices for main group and transition group elements?

Sunday, March 4th, 2018

A bond index (BI) approximately measures the totals of the bond orders at any given atom in a molecule. Here I ponder what the maximum values might be for elements with filled valence shells.

Following Lewis in 1916[1] who proposed that the full valence shell for main group elements should be 2 (for the first two elements) and 8 (the “octet“), Bohr (1922[2]), Langmuir (1919-1921[3]) and Bury (1921[4]) extended this rule to include 18 (the transition series) and 32 (the lanthanides and actinides). If we assume no contributions from higher Rydberg shells (thus 3s, 3p, 3d for carbon etc) and an electron pair model for orbital population (which amounts to the single-determinantal model), then the maximum bond index for hydrogen (and helium) would be 1, it would be 4 for main group elements, and then what?

For the special case of hydrogen, I have previously identified (for a hypothetical species) a bond index of 1.33, due mostly to a high Rydberg occupancy of 1.19e. The more normal BI is <1.0, as noted for this hexacoordinated hydride system. My current estimate for the maximum bond index for main group elements is <4.5. Thus for SF6, it has the value of ~4.33 and that includes a modest occupancy of Rydberg shells of 0.36e = 0.18 BI. Exclude these and it is close to 4.

Move on from group 16 to group 6 and you get compounds such as Me4CrCrMe44- or ReMe82- where the metal bond indices are ~6.5.‡ Compounds such as Cr(Me)6 (BI = 5.6)  and W(Me)6 (BI = 6.1) are rather lower. This is a long way from 18/2 = 9. The lanthanides and actinides[5] are unlikely to reveal many large BIs (32/2= 16 maximum value) since they are often ionic and the wavefunctions may be too complex to allow a simple index such as a BI to be safely computed.

So if we are hunting for record BIs, the transition elements are the place to hunt. Can a BI of 6.5 be beaten? Can it even approach 9, its maximum value? Does anyone know of candidate molecules? 

‡FAIR Data doi: 10.14469/hpc/3352.

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. N. Bohr, "Der Bau der Atome und die physikalischen und chemischen Eigenschaften der Elemente", Zeitschrift f�r Physik, vol. 9, pp. 1-67, 1922. https://doi.org/10.1007/bf01326955
  3. I. Langmuir, "Types of Valence", Science, vol. 54, pp. 59-67, 1921. https://doi.org/10.1126/science.54.1386.59
  4. C.R. Bury, "LANGMUIR'S THEORY OF THE ARRANGEMENT OF ELECTRONS IN ATOMS AND MOLECULES.", Journal of the American Chemical Society, vol. 43, pp. 1602-1609, 1921. https://doi.org/10.1021/ja01440a023
  5. P. Pyykkö, C. Clavaguéra, and J. Dognon, "The 32‐Electron Principle", Computational Methods in Lanthanide and Actinide Chemistry, pp. 401-424, 2015. https://doi.org/10.1002/9781118688304.ch15

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More tetrahedral fun. Spherical aromaticity (and other oddities) in N4 and C4 systems?

Thursday, March 2nd, 2017

The thread thus far. The post about Na2He introduced the electride anionic counter-ion to Na+ as corresponding topologically to a rare feature known as a non-nuclear attractor. This prompted speculation about other systems with such a feature, and the focus shifted to a tetrahedral arrangement of four hydrogen atoms as a dication, sharing a total of two valence electrons. The story now continues here.

What emerged during comments about H42+ was that a density functional (DFT) derived wavefunction seemed to predict it to be a stable minimum, but that wavefunctions derived from coupled cluster or CASSCF methods predicted it to be a three-fold degenerate transition state instead. So I asked myself if perhaps other similar tetrahedral molecules less susceptible to such method ambiguity might be found. Here I record some of the species I investigated. 

  1. N4 in a tetrahedral allotropic arrangement of the element (ωB97XD/Def2-TZVPP DFT method: 10.14469/hpc/2217 and CCSD(T)/Def2-TZVPP 10.14469/hpc/2216). I found this intriguing, because each nitrogen has a lone pair of electrons and such an arrangement of eight electrons might be spherically aromatic according to the rule: 2(n+1)2, where n=1[1]. N4 itself is indeed a true minimum (rN-N  1.460Å) with all positive force constants at both the DFT (767, 1005 and 1443) and CCSD(T) (726, 940 and 1304 cm-1) levels, but with a free energy ~185 kcal/mol higher than dinitrogen. The electronic topology is uneventfully classical, with six line (bond) critical points along each N-N axis (magenta), four ring critical points (green) and one cage point (inner blue sphere); there is no non-nuclear attractor present.The NICS value at the centre of the tetrahedron (coincident with the cage critical point) is -73 ppm, which does suggest aromaticity.
  2. C4 in a tetrahedral allotropic arrangement of this element is also a minimum as closed shell singlet (rC-C 1.646Å) again with positive force constants (ωB97XD/Def2-TZVPP DFT, 10.14469/hpc/2224, 434, 715, 1052 cm-1) and the same electronic topology as N4.
    The magnetic shielding at the ring centre is -1685 ppm, a value clearly perturbed by core ring currents or other factors; the molecule does not map to the 2(n+1)2 spherical aromaticity rule, which only allows values of 2,8,18, 32… electrons. I tried applying the ELF procedure using the computed WFN file (either direct or symmetrised, using both TopMod and MultiWFN) but the results did not have Td symmetry.‡
  3. C42+ with two fewer electrons is also a minimum as a closed shell singlet (rC-C 1.521Å) tetrahedral species (ωB97XD/Def2-TZVPP: 10.14469/hpc/2218, 1132, 1136, 1448 cm-1; CCSD(T)/Def2-TZVPP 10.14469/hpc/2225 showing rather different normal mode energies of ~330, 592, 1126 cm-1 ) which can be thought as mapping to the spherical aromaticity formula 2(n+1)2, where n=0. The electronic topology is slightly different from C4 itself, with four ring points (green) very close to the cage point in the centre.The ELF function now behaves itself in terms of symmetry, and produces a result in fact very similar to the H42+ molecule which started this topic rolling. There is an ELF basin with 0.14e located in the centroid and six equivalent basins (2.25e) spanning each pair of carbon atoms, although these C-C bonds are hugely banana shaped! That central electron basin closely resembles the one found in H42+ itself. The magnetic shielding at the centre of 3349 ppm is not meaningful in deciding if the molecule is indeed “aromatic”.
  4. C41-  is again a tetrahedral minimum, this time as a quartet 4A1 state (ωB97XD/Def2-TZVPP: 10.14469/hpc/2219, 918, 1024, 1377 cm-1; CCSD(T)/Def2-TZVPP 10.14469/hpc/2237, 824, 895, 1303 cm-1). The electronic topology is the same as before.Open shell spherical aromaticity[2] is given by the 2N2 + 2N + 1 (with S = N + ½) rule. A quartet state has S=3/2, hence N=1 and the formula stipulates 5 delocalizable electrons for aromaticity, which this species has! The isotropic magnetic shielding is 695 ppm, which again is not immediately helpful.The ELF analysis ((above) shows just two types of basin, with four “lone pairs” at each carbon vertex (1.24e) and eight associated with the C-C “bent” bonds (1.95e). 

What did I learn?

  • Firstly, that the (very unstable) tetrahedral allotrope of nitrogen might be a spherical aromatic.
  • Secondly, that tetrahedral closed-shell singlet C4 has a very odd wavefunction; this needs further work.
  • Thirdly that tetrahedral C42+  closely resembles H42+  in having a basin of electrons at the very centre, but that unlike H42+ it does appear to be a stable minimum.
  • Finally, that the radical anion C4– might be perhaps the smallest possible example of an open shell spherical aromatic.

And perhaps also in trying to answer some simple questions, I have also raised several more puzzles. Onwards and occasionally upwards.

‡This wavefunction is clearly odd, and needs further analysis.

References

  1. A. Hirsch, Z. Chen, and H. Jiao, "Spherical Aromaticity inIh Symmetrical Fullerenes: The 2(N+1)2 Rule", Angewandte Chemie, vol. 39, pp. 3915-3917, 2000. https://doi.org/10.1002/1521-3773(20001103)39:21<3915::aid-anie3915>3.0.co;2-o
  2. J. Poater, and M. Solà, "Open-shell spherical aromaticity: the 2N2 + 2N + 1 (with S = N + ½) rule", Chemical Communications, vol. 47, pp. 11647, 2011. https://doi.org/10.1039/c1cc14958j

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What’s in a name? Carbenes: a reality check.

Sunday, September 11th, 2016

To quote from Wikipedia: in chemistry, a carbene is a molecule containing a neutral carbon atom with a valence of two and two unshared valence electrons. The most ubiquitous type of carbene of recent times is the one shown below as 1, often referred to as a resonance stabilised or persistent carbene. This type is of interest because of its ability to act as a ligand to an astonishingly wide variety of metals, with many of the resulting complexes being important catalysts. The Wiki page on persistent carbenes shows them throughout in form 1 below, thus reinforcing the belief that they have a valence of two and by implication six (2×2 shared + 2 unshared) electrons in the valence shell of carbon. Here I consider whether this name is really appropriate.

carbenes

Let us start by counting the electrons in the 2p atomic orbitals on the ring atoms of 1, forming what we call a π-system. There are six; two from the carbons shown connected by a double bond, C=C and a further four from the two nitrogen lone pairs. Now in benzene, we also have six π-electrons in a ring and this molecule is of course famously aromatic due to the diatropic ring current created by the circulation of these six electrons. Moreover, all the C-C bonds are equal in length, ~1.4Å long (although the reasons for this equality are subtle).

So does 1 behave similarly? A ωB97XD/Def2-TZVPP calculation[1] shows the following calculated structure, in which all the bonds are clearly intermediate between single and double. The N-C(“carbene”) length of 1.357Å in particular is much shorter than a C-N single bond (~1.44AÅ), which tends to suggest that the resonance form 2 is a better representation than 1. This form is also pretty similar to pyrrole, itself a well-known hetero-aromatic species.nhc1

An alternative reality check is crystal structures. There are 42 examples (no errors, no disorder, R < 0.05) in the Cambridge structure database (CSD) and the distribution of C-N bond lengths below is indeed quite similar to the calculation shown above for the unsubstituted parent, with the lhs “hot-spot” almost exactly coincident. The C-C length similarly corresponds.

nhc2

nhc3

Let us try a technique for explicitly counting electrons, the ELF (electron localisation method), which works directly on a function of the electron density to identify the centroids of localized “basins” containing the integrated density. The three surrounding the “carbene” atom sum to 7.54e (with small seepage also into the carbon 1s core; 2.08e). A “normal” carbon on the C=C bond is 7.65e. The localization below turns out to closely resemble resonance structure 2 above.

nhc4

Further in-silico experiments can be carried out with species 3 and 4, in which a carbon atom replaces each of the nitrogens. This reduces the total electron count by two and now this poor molecule has a difficult choice to make. Should it be the π-system that sacrifices these two electrons, or could it be the σ-lone-pair found on the two-coordinate carbon? We will let the quantum mechanical solution decide[2] (with a constraint that the molecule be planar). The electrons arrange themselves to resemble the resonance form 4, choosing to retain the six π-electrons and sacrifice the carbene “unshared pair”. The 2-coordinate carbon as a vinyl cation now does have ~6 valence electrons (ELF indicates 5.23e). nhc5

What about the other choice? By promoting two electrons from HOMO to LUMO one can also calculate 3 (again constrained to planarity)[3] which finally does correspond to the classical description of a carbene.

nhc6

The arrow connecting 3 and 4 in the scheme at the top is NOT in this case an electronic resonance, but a a real equilibrium between two different species separated by an energy barrier. With only four π-electrons in a cycle it is also antiaromatic, and so the two localised alkene bonds avoid any conjugation with each other. This form has a free energy some 5.7 kcal/ml higher than the aromatic form. In fact, the molecule is very keen to avoid all antiaromaticity and hence if the planar constraint is lifted, it will distort with no activation to a non-planar diene (just as cyclo-octatetraene does to a non-planar tetra-ene). And to complete the tale, even though 4 is aromatic, it too distorts without activation to an odd-looking non-planar form with no symmetry[4],[5],[6] (but that is another story).

The final word should be that the naming of these types of persistent carbene does need a reality check; they should not be called this at all! They are really dipolar species or carbon-ylides as shown in 2. As it happens, a very closely related species in which one sulfur replaces one nitrogen is a very familiar compound, vitamin B1 or thiamine. The only example of a stable deprotonated thiamine derivative is referred to as a carbene[7], perhaps because with an acid catalyst it can dimerise in the manner expected of a real carbene. Significantly however, without acid catalyst this does not happen; a true carbene would not require such a catalyst.

References

  1. H. Rzepa, "NHC wfn", 2016. https://doi.org/10.14469/hpc/1473
  2. H. Rzepa, "butadiene carbene aromatic -192.700746", 2016. https://doi.org/10.14469/hpc/1581
  3. H. Rzepa, "butadiene carbene antiaromatic guess=alter -192.691607", 2016. https://doi.org/10.14469/hpc/1582
  4. H. Rzepa, "C5H4 non-planar, Cs symmetry", 2016. https://doi.org/10.14469/hpc/1583
  5. H. Rzepa, "C5H4 non-planar, C2 symmetry", 2016. https://doi.org/10.14469/hpc/1584
  6. H. Rzepa, "C5H4 non-planar, no symmetry", 2016. https://doi.org/10.14469/hpc/1585
  7. A.J. Arduengo, J.R. Goerlich, and W.J. Marshall, "A Stable Thiazol‐2‐ylidene and Its Dimer", Liebigs Annalen, vol. 1997, pp. 365-374, 1997. https://doi.org/10.1002/jlac.199719970213

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What's in a name? Carbenes: a reality check.

Sunday, September 11th, 2016

To quote from Wikipedia: in chemistry, a carbene is a molecule containing a neutral carbon atom with a valence of two and two unshared valence electrons. The most ubiquitous type of carbene of recent times is the one shown below as 1, often referred to as a resonance stabilised or persistent carbene. This type is of interest because of its ability to act as a ligand to an astonishingly wide variety of metals, with many of the resulting complexes being important catalysts. The Wiki page on persistent carbenes shows them throughout in form 1 below, thus reinforcing the belief that they have a valence of two and by implication six (2×2 shared + 2 unshared) electrons in the valence shell of carbon. Here I consider whether this name is really appropriate.

carbenes

Let us start by counting the electrons in the 2p atomic orbitals on the ring atoms of 1, forming what we call a π-system. There are six; two from the carbons shown connected by a double bond, C=C and a further four from the two nitrogen lone pairs. Now in benzene, we also have six π-electrons in a ring and this molecule is of course famously aromatic due to the diatropic ring current created by the circulation of these six electrons. Moreover, all the C-C bonds are equal in length, ~1.4Å long (although the reasons for this equality are subtle).

So does 1 behave similarly? A ωB97XD/Def2-TZVPP calculation[1] shows the following calculated structure, in which all the bonds are clearly intermediate between single and double. The N-C(“carbene”) length of 1.357Å in particular is much shorter than a C-N single bond (~1.44AÅ), which tends to suggest that the resonance form 2 is a better representation than 1. This form is also pretty similar to pyrrole, itself a well-known hetero-aromatic species.nhc1

An alternative reality check is crystal structures. There are 42 examples (no errors, no disorder, R < 0.05) in the Cambridge structure database (CSD) and the distribution of C-N bond lengths below is indeed quite similar to the calculation shown above for the unsubstituted parent, with the lhs “hot-spot” almost exactly coincident. The C-C length similarly corresponds.

nhc2

nhc3

Let us try a technique for explicitly counting electrons, the ELF (electron localisation method), which works directly on a function of the electron density to identify the centroids of localized “basins” containing the integrated density. The three surrounding the “carbene” atom sum to 7.54e (with small seepage also into the carbon 1s core; 2.08e). A “normal” carbon on the C=C bond is 7.65e. The localization below turns out to closely resemble resonance structure 2 above.

nhc4

Further in-silico experiments can be carried out with species 3 and 4, in which a carbon atom replaces each of the nitrogens. This reduces the total electron count by two and now this poor molecule has a difficult choice to make. Should it be the π-system that sacrifices these two electrons, or could it be the σ-lone-pair found on the two-coordinate carbon? We will let the quantum mechanical solution decide[2] (with a constraint that the molecule be planar). The electrons arrange themselves to resemble the resonance form 4, choosing to retain the six π-electrons and sacrifice the carbene “unshared pair”. The 2-coordinate carbon as a vinyl cation now does have ~6 valence electrons (ELF indicates 5.23e). nhc5

What about the other choice? By promoting two electrons from HOMO to LUMO one can also calculate 3 (again constrained to planarity)[3] which finally does correspond to the classical description of a carbene.

nhc6

The arrow connecting 3 and 4 in the scheme at the top is NOT in this case an electronic resonance, but a a real equilibrium between two different species separated by an energy barrier. With only four π-electrons in a cycle it is also antiaromatic, and so the two localised alkene bonds avoid any conjugation with each other. This form has a free energy some 5.7 kcal/ml higher than the aromatic form. In fact, the molecule is very keen to avoid all antiaromaticity and hence if the planar constraint is lifted, it will distort with no activation to a non-planar diene (just as cyclo-octatetraene does to a non-planar tetra-ene). And to complete the tale, even though 4 is aromatic, it too distorts without activation to an odd-looking non-planar form with no symmetry[4],[5],[6] (but that is another story).

The final word should be that the naming of these types of persistent carbene does need a reality check; they should not be called this at all! They are really dipolar species or carbon-ylides as shown in 2. As it happens, a very closely related species in which one sulfur replaces one nitrogen is a very familiar compound, vitamin B1 or thiamine. The only example of a stable deprotonated thiamine derivative is referred to as a carbene[7], perhaps because with an acid catalyst it can dimerise in the manner expected of a real carbene. Significantly however, without acid catalyst this does not happen; a true carbene would not require such a catalyst.

References

  1. H. Rzepa, "NHC wfn", 2016. https://doi.org/10.14469/hpc/1473
  2. H. Rzepa, "butadiene carbene aromatic -192.700746", 2016. https://doi.org/10.14469/hpc/1581
  3. H. Rzepa, "butadiene carbene antiaromatic guess=alter -192.691607", 2016. https://doi.org/10.14469/hpc/1582
  4. H. Rzepa, "C5H4 non-planar, Cs symmetry", 2016. https://doi.org/10.14469/hpc/1583
  5. H. Rzepa, "C5H4 non-planar, C2 symmetry", 2016. https://doi.org/10.14469/hpc/1584
  6. H. Rzepa, "C5H4 non-planar, no symmetry", 2016. https://doi.org/10.14469/hpc/1585
  7. A.J. Arduengo, J.R. Goerlich, and W.J. Marshall, "A Stable Thiazol‐2‐ylidene and Its Dimer", Liebigs Annalen, vol. 1997, pp. 365-374, 1997. https://doi.org/10.1002/jlac.199719970213

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