Posts Tagged ‘Octet’

Octet expansion and hypervalence in dimethylidyne-λ6-sulfane.

Tuesday, November 28th, 2017

I started this story by looking at octet expansion and hypervalence in non-polar hypercoordinate species such as S(-CH3)6, then moved on to S(=CH2)3. Finally now its the turn of S(≡CH)2.‡

As the triple bonds imply, this seems to represent twelve shared valence electrons surround the sulfur, six from S itself and three from each carbon. The octet is clearly expanded from eight to twelve. But is all as it seems?

The linear form reveals the following localized orbitals. Six NBOs are localized to the S-C regions, of which four are bonding, two σ and two π. The remaining four electrons are in two non-bonding lone pairs, with a mild anti-bonding S-C component. So the bond order comes out as ~four, not six! This corresponds to the story told in the earlier blogs that the electrons in excess of the octet tend to occupy either non or antibonding orbitals.

In fact the full NBO analysis gives a value of 4.0920 for the S bond index and little Rydberg character; S: [core]3S(1.02)3p(3.61)3d(0.13).

Next, the ELF analysis, based not on orbitals but the derived electron densities. Each S-C region shows an ELF circular attractor integrating to 5.44e (or 10.88e for the S valence region). So the ELF reflects not only the density arising from bonding orbitals, but the non-bonding ones as well! 

Take a look at the ELF basin for the two hydrogen atoms; at 2.42e each this shell is ALSO expanded from the normal 2! Apart from the normal C-H localised NBO orbital, one can also see small C-H bonding contributions from the four NBOs labelled B above as well. So ELF analysis of the shared electrons in this species seems to show octet expansion for S and similar shell expansion for H. But we now know that simply taking the ELF basin population and dividing by two to get the bond or valence index can be misleading. The ELF analysis includes non or even anti-bonding density contributions and so it cannot be used to infer hyperbonding (hypervalence).

I must now confess to withholding some vital information from you. The linear HC≡S≡CH molecule is not a minimum, having four computed negative force constants, the normal mode of one of which is animated  below. 

The true minimum has C2 symmetry as follows and it corresponds to that mysterious structure shown at the top and hitherto not mentioned. This form is 14.6 kcal/mol lower in free energy than the linear variety. 

The ELF analysis confirms this species as bis(carbene), with two “lone pairs” on S. All the octet expansion has vanished; of the ~six electrons hitherto located in each C-S region, four have morphed into lone pairs, leaving only ~two in the S-C regions. The sulfur is now allocated 7.44e, a  “normal” octet.

At this point, I remind that the great G. N. Lewis himself, the original coiner of the eight electron valence rule, pondered whether acetylene might have a related bis(carbene) form. It is nice to come up with an example of this more than 100 years after his original suggestion.

‡FAIR Data DOI for the collection: 10.14469/hpc/3333

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Hypervalence and octet-expansion in sulfur hexafluoride.

Monday, November 20th, 2017

Following on from discussing octet expansion in species such as SeMe6, ClMe3 and ClMe5, I felt impelled to return to SF6, often used as an icon for hypervalence.

With this molecule we have twelve electrons to partition, six from sulfur and one each from six fluorines (the other six electrons on each F are presumed to form three sets of lone pairs). Recollect the two ways of dealing with them:

  1. To place them in pairs firstly into bonding MOs formed from using a 3s/3p valence atomic orbital basis on the S and a 2s/2p AO basis on F and to place any remaining electron pairs into antibonding orbitals constructed from the same basis. This would tend to reduce individual S-F bond orders.
  2. To place four pairs into bonding MOs and the remaining two pairs into MOs constructed using higher or Rydberg valence shells on S. This would tend to increase S-F bond orders by forming hyperbonds.

I will start with (delocalized) molecular orbitals (FAIR data DOI: 10.14469/hpc/3283). The HOMO (highest occupied MO) and the next 16 are in fact various variations of orbitals which can be regarded as fluorine lone pairs. The first of interest to us is the A1g-symmetric HOMO-17, which certainly looks as if it is antibonding along the six F-S bonds. But the heavy delocalization of the MOs makes it really difficult to comment on bonding/antibonding character.

So next, the more localized NBO orbitals (FAIR Data DOI: 10.14469/hpc/3284), which tends to “collect” the wavefunction into localized regions of bonds and lone pairs. There are twelve equivalent F lone pairs of the following type:

Next the remaining six F lone pairs, which are oriented axially along the S-F bonds. They have distinct S-F anti-bonding character.

Finally six S-F bonding pairs (“acorn” orbitals). But note that whilst they are bonding along one S-F bond, they are mildly antibonding along the opposing S-F bond. 

The Rydberg occupancy is S:[core]3S(0.98)3p(2.13)3d(0.24)4p(0.03)4f(0.01) and F: [core]2S(1.91)2p(5.51)3d(0.01), which gives a total  Rydberg occupancy of 0.35177e.  Adding up these effects, the NBO analysis tells us that the individual S-F bond orders are 0.7213. Six times this gives the Wiberg bond index at sulfur:  4.3276. This is close to the value of 4 expected from utilising an atomic orbital basis of one 2s and three 2p AOs on sulfur. One can think of this in another way.

  1. Start with a valence shell of twelve electrons to form six two-electron S-F bonds. The sulfur would have a bond index of six. Then promote either two electrons into fully antibonding orbitals (5-1=4) or four into non-bonding orbitals (F lone pairs) or possibly intermediate solutions, thus reducing the sulfur bond index by ~two bonds to give a bond index of four. Since the antibonding orbitals in this case are not fully antibonding, the bond index emerges a bit higher at 4.3276, a value also augmented by 0.35177/2 = 0.175885 due to Rydberg occupancy.
  2. One might usefully then ask if a bond index for sulfur of ≥ 4 can be usefully described as “hypervalent sulfur“? As usual in bonding theory, we need a reference state for non-hypervalent sulfur. If this is taken as two valencies, with a bond index of two, then this molecule is definitely hypervalent. If you assume that you can only construct the equivalent of four two-electron bonds using just a 3s1/3p3 atomic orbital basis, then it is merely mildly hypervalent; the four two-electron bonds are then distributed of course across six S-F regions, or 0.667 bonds per S-F region. The value of 0.7213 actually calculated is exalted by contributions in part from Rydberg orbitals. 

What about the octet? 6*0.7213*2 = 8.66e, a mildly expanded octet. I am now going to use the ELF method as an alternative counting procedure. This is based not on orbitals but on the electron density (a more direct experimental observable than orbitals). Six disynaptic basins are located totalling 6.5e. The remainder of the electrons populate the F lone pairs shown below as four distinct monosynaptic basins per F. This is an artefact of the resolution of the cube of ELF values and how the basin centroids are located. These are in fact circular and not point ELF attractors, forming a circular ELF torus around each fluorine.

So, ELF suggests that the sulfur “octet” is not exceeded and in this form of analysis the compound is merely hypercoordinate. In contrast the orbital-based approach indicates mild hypervalency in which the total bond index at S modestly exceeds 4. If you regard the normal valency of sulfur to be two, this is clearly hypervalent. But no substantial octet-expansion beyond the modest Rydberg type is needed to rationalise this species and certainly not up to twelve!

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