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Henry Rzepa, Imperial College London[edit]

slides: DOI:b9r9

Benoît Braïda, Université Pierre et Marie Curie - Paris 6[edit]

slides: Slides


Henry (talk) 10:26, 19 July 2017 (CEST)[edit]

Hypervalency is defined[1] 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[2] where the description "“carbon can expand its octet of electrons to form this relatively stable molecule“ was used. Yet, in this latter case, octet expansion as defined above is in fact an illusion, as indeed are many examples that are cited[3], including SF6 itself and even the non-polar I.I7[4] and At.At7.[5]. The octet remains resolutely un-expanded for these species.

Here I will challenge with a tiny molecule CH3F2- where two extra electrons have been added to fluoromethane [6].

These electrons can be added in two basic ways.

  1. The electrons can 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 C2, 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 3 to 2 to 1 to 0. And of course all core shells contain populated bonding and antibonding pairs, which do not overall contribute to the bond orders.
  2. The electrons on carbon could instead (or as well as) 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 and for SF6 itself[7] the Rydberg occupancy is only 0.37e.

C-F mode

Highest occupied NBO for CH3F(2-)

Highest occupied NBO for BH3F(3-)

ELF Basin centroids for CH3F(2-)

ELF Basin centroids for BH3F(3-)

ELF Basin centroids for CH2F2(2-)

ELF Basin centroids for CH3F(1-)

Highest singly occupied NBO for CH3F(1-)

  • Adding two electrons to CH4 populates the anti-bonding orbital, thus reducing the Wiberg bond order of each of the CH bonds to 0.773 (ωB97XD/Def2-TZVPPD/scrf=water). The total Rydberg occupancy is <0.2e. [8]
  • ELF analysis for CH3F(2-)
    Adding two electrons to CH3F populates instead the Rydberg levels, thus increasing the Wiberg bond orders (CF 1.213, CH 0.980, ωB97XD/Def2-TZVPPD/scrf=water). The carbon Rydberg occupancy is 1.068e, the F 0.369e and the H 0.032e (total Rydberg 1.53e).
  • All 3N-6 vibrational modes are real[9] and an IRC can be located for e.g. the dissociation into CH3- and F-[10], but the minimum is only protected by a very small barrier.
  • Increasing the basis set to Def2-QZVPPD[11] gives a total Ryberg population of 1.55e (C, 1.09, F, 0.31, H, 0.05e).
  • An ELF analysis shows the existence of six "Rydberg" basins, integrating to 1.44e, and located some distance away from the atoms. These are the electrons contributing to the expanded octet. The “unexpanded” shell surrounding the carbon integrates to 7.23e, a “normal” octet.
  • ELF analysis for BH3F(3-)
    A second example [12] is the isoelectronic BH3F3- which has a total Rydberg population of 0.68e and an ELF basin distribution again showing inner and outer valence basins.
  • UV-Vis spectrum
    The vis-UV spectrum of this species calculated using Time-dependent DFT is shown on the right. The colour would be a very intense dark blue.[13]
  • CH2F22- also shows[14] a reduced effect, with a Rydberg population of 0.62e, but again with outer-shell ELF basins.
  • The mono-anion CH2F21- shows an interesting variation[15] in which the NBO Rydberg populations are 0.86 (F), 0.22 (C) and 0.01 (H). The Wiberg bond indices are 1.03 (F), 3.78 (C), 0.98 (H). For this system, the additional electron populates mostly the fluorine 3s and 3p Rydberg states, unlike the di-anion where the C states are more significantly populated. This is reflected in a very different ELF basin analysis for the mono-anion, showing just a single further basin (0.71e) extending the C-F axis.
  • The variation in calculated C-F bond lengths across the series from CH3F to CH3F2- is 1.392, 1.415, 1.422Å.
  • Other permutations such as NH3F1-, SiH3F2- or CH3Cl2- fail to exhibit these effects, with population of anti-bonding MOs resulting in barrierless bond dissociation.

I argue therefore that CH3F2- and BH3F3- represent examples of hypervalency as defined by octet (Rydberg) expansion at the level of an ωB97XD/Def2-TZVPPD/scrf=water model. The challenge is two fold:

  1. To what extent is this result a pure artefact of the method adopted (the functional, the basis set and the solvation model)?
  2. Can other examples of molecules exhibiting true hypervalency as defined here be identified, perhaps even stable ones that can be fully characterised by a variety of physical methods?


  1. https://en.wikipedia.org/wiki/Hypervalent_molecule
  2. H. Kudo, Nature, 1992, 355, 432 - 434. DOI:10.1038/355432a0
  3. H. S. Rzepa, Is CLi6 hypervalent?, 2013, DOI:cbrs
  4. H. S. Rzepa, 2010, DOI:cbrr for calculation and DOI:cbrq for analysis.
  5. H. S. Rzepa, 2010, DOI:cbr4 and DOI:cbrq for analysis.
  6. H. S. Rzepa, 2016, DOI:cbrv
  7. H. S. Rzepa, 2017, DOI:cbrt
  8. H. S. Rzepa, 2016, DOI:bc7j
  9. H. S. Rzepa, 2016, DOI:cbrw
  10. H. S. Rzepa, 2017, DOI:cbrx
  11. H. S. Rzepa, DOI:cb3n
  12. H. S. Rzepa, 2017, DOI:cbrz
  13. H. S. Rzepa, 2017, DOI:cb2m
  14. H. S. Rzepa, 2017, DOI:cbr2
  15. H. S. Rzepa, 2017, DOI:cbzq , DOI:10.14469/hpc/2944