Posts Tagged ‘Valence’

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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Hypervalence and octet-expansion in trimethylene-λ6-sulfane and related species.

Monday, November 27th, 2017

Previously: “Non-polar” species such as SeMe6, SMe6, ClMe3, ClMe5 all revealed interesting properties for the Se-C, S-C or Cl-C “single” bonds. The latter two examples in particular hinted at internal structures for these single bonds, as manifested by two ELF basins for some of the bonds. Here I take a look at the related molecule where a formal double bond between carbon and the central sulfur atom replacing the single-bond might also hint at octet expansions and hypervalence.

Starting with X=Y=Z=CH2,‡ the calculated (ωB97Xd/Def2-TZVPP) geometry has an interesting chiral D3-symmetric form. The density based ELF-basin centroids are shown below, with each formal C=S π-double bond represented by two ELF basins above and below the C-S axis and with each pair of ELF basins being twisted by 48° with respect to the other two pairs. The total valence shell count around the S is 10.98e and the octet is “expanded” (by ~3e).

The orbital-based NBO approach indicates little utilisation of higher (Rydberg) atomic orbital shells (S: [core]3S(1.13)3p(3.35)3d(0.11)4p(0.02); C: [core]2S(1.15)2p(3.77)3p(0.01)3d(0.01) ). Each S-C bond has a Wiberg bond order of 1.36 (significantly less than a double bond), and the central S has an overall bond index of 4.102. There is a real mis-match between the orbital partitioning (2*1.36 = 2.72e) and the ELF partitioning (2*1.83 = 3.66e) into the S-C bonds. The former indicates that ~two of the twelve valence electrons are entering into anti-bonding orbitals to reduce the total bond index from a possible six to just four, but that they still contribute to the electron-density based ELF disynaptic C-S basins. To cast light on this behaviour, successively one to three of the CH2 groups can be replaced by O.

For each “S=O” bond, we find the ELF basin population more or less halves and electrons instead populate the non-bonding O “lone pairs”. The S-C ELF populations in contrast remain approximately constant. These species therefore have “double” S=C bonds but just “single” S-O bonds. The Rydberg population increases slightly; S: [core]3S(1.06)3p(2.95)3d(0.16)4p(0.02)) and the S bond index is 4.18 for one oxygen and S: [core]3S(0.99)3p(2.67)3d(0.19)4p(0.02) and S bond index 4.16 for two oxygens.

Sulfur trioxide (below) seems best represented by S-O rather than S=O bonds. The Rydberg population is S: [core]3S(0.91)3p(2.41)3d(0.21)4p(0.03) and the S bond index is 4.32.

Just for good measure sulfur trisulfide S(S)3 shows rather lower lone pair population because of course it is less electronegative than oxygen, and hence has a slightly greater S-S ELF basin population. Rydberg, S: [core]3S(1.43)3p(3.73)3d(0.21)4p(0.03) and central S bond index 4.04.

It seems molecules where the electrons in a valence shell exceed the “octet” are only too happy to let the excess electrons leak out into adjacent electronegative atoms as lone pairs, where they are no longer classified as  “shared”. Trimethylene-λ6-sulfane does not have this option and the excess electrons remain in the region of the valence shell, but here they do not contribute to augmenting the bond index at the central atom.  In this specific interpretation, the octet is exceeded, but hypervalence is not induced. It is a slippery concept; one where general agreement about its properties may indeed be difficult to achieve!

‡The FAIR data DOI collection for this post is 10.14469/hpc/3316.

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VSEPR Theory: Octet-busting or not with trimethyl chlorine, ClMe3.

Sunday, November 12th, 2017

A few years back, I took a look at the valence-shell electron pair repulsion approach to the geometry of chlorine trifluoride, ClF3 using so-called ELF basins to locate centroids for both the covalent F-Cl bond electrons and the chlorine lone-pair electrons. Whereas the original VSEPR theory talks about five “electron pairs” totalling an octet-busting ten electrons surrounding chlorine, the electron density-based ELF approach located only ~6.8e surrounding the central chlorine and no “octet-busting”. The remaining electrons occupied fluorine lone pairs rather than the shared Cl-F regions. Here I take a look at ClMe3, as induced by the analysis of SeMe6.

The difference between ClF3 and ClMe3 is that octet-excess electrons (two in this case) in the former can relocate into fluorine lone pairs by occupying in effect anti-bonding orbitals and hence end up not contributing to the central atom valence shell.‡ With ClMe3 the methyl groups cannot apparently sustain such lone pairs, at least not distinct from the Cl-C bond region. So might we get an octet-busting example with this molecule? A ClMe3 calculation (ωb97xd/6-311++g(d,p)) reveals a molecule with all real vibrational modes (i.e. a minimum, FAIR data DOI: 10.14469/hpc/3241) and ELF (FAIR data DOI 10.14469/hpc/3242)† basins as shown below:

Density-derived approach: Two of the C-Cl bonds each exhibit two ELF basins; one disynaptic basin (0.94e) and one monosynaptic basin (0.20e) closer to the chlorine. The former pair integrate to 1.88e, density which largely arises from carbon (natural charge -0.84) and which contribute to a total integration for these carbons of 7.17e. The latter pair contributes to a total chlorine integration of 7.19e. The angle subtended at chlorine for the two 2.68e “lone pair” basins is 141°. Thus an inner, octet-compliant, valence-shell for chlorine is revealed, plus an expanded-octet outer one into which the two additional electrons go. The latter contribute to forming an octet-compliant carbon valence shell, but may be considered as not contributing to the valence shell of the other atom of the pair, the chlorine. An endo lone-pair rather than the more usual exo lone-pair if you will. These results reveal that the molecular feature we know as a (single) “bond” may in fact have more complex inner structures or zones, something we do not normally consider bonds as having. In this model, these zones are not invariably considered as shared between both the atoms comprising the bond.

Orbital-derived approach: NBO analysis (FAIR data DOI: 10.14469/hpc/3241) reveals the chlorine electronic configuration as [core]3S(1.83)3p(4.67)4S(0.01)3d(0.03)5p(0.02,) showing very little population of the Rydberg shells (4s, 3d, 5p) occurs (0.13e in total). This method of partitioning the electrons allocates a chlorine Wiberg bond index of 2.00 and the methyl carbon bond index of  3.83. If the regular valence of Cl is taken as 1, then the central chlorine can be regarded as non-Rydberg hypervalent (the electrons in the 0.94e basins are taken as contributing to the chlorine bond index).

The carbon-halogen bond internal structures simplify for Br (DOI: 10.14469/hpc/3248, 10.14469/hpc/3250) and I (DOI: 10.14469/hpc/3249, 10.14469/hpc/3247); for each only a single ELF basin is located and the NBO Br and I bond indices are respectively 2.10 and 2.1. This is not due to incursion of  Rydberg hypervalence (Br: [core]4S(1.83)4p(4.46)5S(0.02)4d(0.03)6p( 0.01); I: [core]5S(1.82)5p(4.29)6S(0.02)5d(0.02)6p(0.01) ) but of a merging of the carbon and halogen valence basin such that the ELF contributions to each cannot be deconvoluted. In each case the NBO bond indices of ~2 suggest hypervalency for the halogen.

What have we learnt?  That the shared electron (covalent) bond can have complex internal features, such as two discrete basins for the apparently shared electrons. How one partitions these electrons can influence the value one obtains for the total shared electron count and hence whether the octet is retained or expanded for main group elements such as the halogens. And finally, that hypervalence and hyper-coordination are related in the orbital model at least. Thus along the series MenI (n= coordination number 1,3,5,7), the values of the Wiberg bond index at the halogen progress as 1.0, 2.1, 3.1 (DOI: 10.14469/hpc/3236) and 4.01 (DOI: 10.14469/hpc/3238), or one extra atom bond index per electron pair.  Given this, it seems useful to retain the distinction between the terms hypervalence and hyper-coordination, but also recognize that we still may have much to learn about the former.

‡See the previous post on SeMe6 for a more detailed discussion.

† The FAIR Data accompanying this blog post is organised in a new way here. All the calculations are collected together with an over-arching DOI: 10.14469/hpc/3252 associated with this post, with individual entries accessible directly using the DOIs given above. The post itself has a  DOI: 10.14469/hpc/3255 and the two identifiers are associated with each-other via their respective metadata.  A set of standards (https://jats.nlm.nih.gov) with implementation guidelines for e.g. repositories, authors and publishers-editors  are expected in the future to establish infra-structures for cross-linking narratives/stories with the data on which they are based.

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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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Real hypervalency in a small molecule.

Sunday, February 21st, 2016

Hypervalency is defined as a molecule that contains one or more main group elements formally bearing more than eight  electrons in their  valence shell. One example of a molecule so characterised was CLi6[1] where the description "“carbon can expand its octet of electrons to form this relatively stable molecule“ was used. Yet, in this latter case, the octet expansion is in fact an illusion, as indeed are many examples that are cited. The octet shell remains resolutely un-expanded. Here I will explore the tiny molecule CH3F2- where two extra electrons have been added to fluoromethane.

Two such electrons added to e.g. such a methane derivative can be in principle accommodated in two ways:

  1. The electrons on carbon could expand the octet shell by populating molecular orbitals constructed using 3s or 3p atomic orbitals (AOs) as well as the normal 2s and 2p shells. This is also the normal "explanation" for expanded octets, the assumption being that as one moves down the rows of the periodic table (e.g. P, S, Cl, etc) these shells become energetically more accessible (e.g. the 3d or 4s shell for P, S, Cl etc). In fact, for e.g. PF5, the occupancy of such  "Rydberg" shells is only ~0.2 electrons, not a significant octet expansion.
  2. The electrons can instead or as well as populate the antibonding molecular orbitals (MOs) formed from just the 2s/2p AOs. For a methane derivative, there are four bonding MOs (into which the octet of electrons are placed) and four anti-bonding MOs all constructed from the total of eight AOs. Well known examples of populating antibonding MOs are the series N≡N, O=O (singlet), F-F, Ne…Ne where the additional electrons are added to anti-bonding MOs and have the effect of reducing the bond orders from 3 to 2 to 1 to 0. And of course all core shells contain populated bonding and antibonding pairs.

Here are some ωB97XD/Def2-TZVPPD/scrf=water calculations. All these species are molecules with all-real vibrations, being stable toward dissociation to e.g. CH3– + H– or CH3– + F–.  A transition state for this latter dissocation with IRC[2] can be characterised. In all cases the energy of the highest occupied MO or NBO is -ve, meaning that the electrons are bound, at least in part due to the solvent field applied.

Molecule Wiberg CH order Wiberg CF order Natural Populations E HONBO, au dataDOI
CH42- 0.773 –

C:[core]2S(1.98)2p(3.82)3S( 0.15)4d( 0.01)

H:1S( 1.00)

-0.144CH4 [3]
CH3F2- 0.980 1.213

C:[core]2S(1.05)2p( 3.20)3S(1.26)4p( 0.01)4d( 0.01)

H:1S( 0.84)2S( 0.01)2p( 0.02)

F:[core]2S(1.88)2p( 5.61)3S( 0.30)3p( 0.04)3d( 0.01)4p( 0.01)

-0.068
Click for 3D

Click for 3D

 [4]
CH2F22- 0.871 0.897

C:[core]2S(1.60)2p( 2.64)3S(0.39)3p( 0.01)4d( 0.01)

H:1S(1.19)2S( 0.06)

F:[core]2S(1.86)2p( 5.52)3S( 0.01)3p( 0.01)4p( 0.01)

-0.281
Click for 3D

Click for 3D

 [5]
CF42- – 0.801

C:[core]2S(1.94)2p( 1.96)3S( 0.19)3p( 0.04)5d( 0.01)

F:[core]2S(1.89)2p( 5.54)3p( 0.01)3d( 0.02)

 

-0.148CF4 [6]
  1. CH42- shows only small Rydberg occupancy (< 0.2e), but a significantly reduced bond order for the four C-H bonds (each C-H bonding NBO also has some antibonding character for the other three CHs) and hence the molecule is not truly hypervalent.
  2. CH3F2- in contrast shows quite different behavour. The C-H bond order is almost 1 and the C-F bond order is actually >1. Of the two extra electrons, ~1.28 now occupy carbon Rydberg AOs and the fluorine also has significant Rydberg population (~0.36e). So this is a real hypervalent system, in which the total valencies exceed that expected from an octet.
  3. CH2F22- is somewhere inbetween the previous two systems. The carbon has modest Rydberg occupancy (~0.4e) but there is also significant occupation of the antibonding MOs. Both the C-H and C-F bond orders are <1.
  4. CF42- shows a further reduction in the C Rydberg occpancy (<0.2) and the C-F bond order is also reduced. This reduction in bond order is also seen in other so-called hypervalent systems such as PF5.

So of these systems, CH3F2- can be reasonably called hypervalent, whilst the others have much less such character. It does appear that there is a fine balance between placing extra electrons into Rydberg orbitals to expand the "octet" and hence valencies, and placing them in anti-bonding orbitals where the individual valencies are actually reduced. It seems that substituting methane with just one fluorine encourages population of the Rydberg orbitals, but that more fluorines encourage instead population of the antibonding orbitals. What is remarkable is that CH3F2- actually has a (small) barrier to dissociation. The challenge now is to try to design a system which has a significant Rydberg population, a low antibonding population AND is stable to dissociation; this will require some inspiration. So do not hold your breaths!

 

References

  1. H. Kudo, "Observation of hypervalent CLi6 by Knudsen-effusion mass spectrometry", Nature, vol. 355, pp. 432-434, 1992. https://doi.org/10.1038/355432a0
  2. https://doi.org/
  3. H.S. Rzepa, "C 1 H 4 -2", 2016. https://doi.org/10.14469/ch/191837
  4. H.S. Rzepa, "C 1 H 3 F 1 -2", 2016. https://doi.org/10.14469/ch/191919
  5. H.S. Rzepa, "C 1 H 2 F 2 -2", 2016. https://doi.org/10.14469/ch/191918
  6. H.S. Rzepa, "C 1 F 4 -2", 2016. https://doi.org/10.14469/ch/191916

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VSEPR Theory: A closer look at trifluorothionitrile, NSF3.

Saturday, January 16th, 2016

The post on applying VSEPR ("valence shell electron pair repulsion") theory to the geometry of ClF3 has proved perennially popular. So here is a follow-up on another little molecue, F3SN. As the name implies, it is often represented with an S≡N bond. Here I take a look at the conventional analysis.

trifluoorothionitrile

This is as follows:

  1. Six valence electrons on the central S atom.
  2. Three F atoms contribute one electron each.
  3. One electron from the N σ-bond.
  4. Donate two electrons from S to the two π-bonds.
  5. Eight electrons left around central S, ≡ four valence shell electron pairs.
  6. Hence a tetrahedral geometry.
  7. The bond-bond repulsions however are not all equal. The SN bond repels the three SF bonds more than the S-F bonds repel each-other.
  8. Hence the N-S-F angle is greater than the F-S-F angle, a distorted tetrahedron.

Now for a calculation[1];  ωB97XD/Def2-TZVP, where the wavefunction is analysed using ELF (electron localisation function), which is a useful way of locating the centroids of bonds and lone pairs (click on diagram below to see 3D model).

Trifluorosulfonitrile

  • At the outset one notes that there are six ELF disynaptic basins surrounding the central S, integrating to a total of 7.05e. The sulfur is NOT hypervalent; it does not exceed the octet rule.
  • These six "electron sub-pair" basins are arranged octahedrally around the sulfur. The coordination is NOT tetrahedral, as implied above.
  • The three S-N basins have slightly more electrons (1.25e) than the three S-F basins (1.10e), resulting in …
  • the angle subtended at the S for the SN basins being 96° (a bit larger than octahedral) whilst the angle subtended at the S for the SF basins being smaller (89.9°). This matches point 7 above, but is achieved in an entirely different manner.
  • As a result, the N-S-F angle (122.5°) is larger than the ideal tetrahedral angle and the F-S-F angle (93.9°) is smaller, an alternative way of expressing point 7 above.
  • The S≡N triple bond as shown above does have some reality;  it is a "banana bond" with three connectors rather than two. Each banana bond however has only 1.25e, so the bond order of this motif is ~four (not six) but nevertheless resulting in a short S-N distance (1.406Å) with multiple character.

So we have achieved the same result as classical VSEPR, but using partial rather than full electron pairs to do so. We got the same result with ClF3 before. So perhaps this variation could be called "valence shell partial electron pair repulsions" or VSPEPR.

References

  1. H.S. Rzepa, "F 3 N 1 S 1", 2016. https://doi.org/10.14469/ch/191808

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