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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]


The 100 year-old history of the term hypervalency and its evolving meaning is excellently covered in a recent review of the topic.[1]. The original and often quoted[2] definition of the term relates to a molecule that contains one or more main group elements formally bearing more than eight electrons in their valence shell. One well-known example dating from 1992 of a molecule to which the term hypervalent was applied is CLi6[3], where the description carbon can expand its octet of electrons to form this relatively stable molecule appears. Yet, in this latter case, significant octet expansion as defined above is something of an illusion (due to significant Li-Li bonding).[4][5] For many other examples that are cited, including SF6 itself (the chosen Wiki logo for this topic) and even the less polar I.I7[6] and At.At7[7], any octet expansion may also be illusory, although their hypervalence may be real. Here I will challenge and explore these concepts using the molecule CH3F2-, where two extra electrons have been added to fluoromethane.[8]

These electrons can be added in two basic ways.

  1. The electrons can populate the antibonding molecular orbitals (MOs) formed from a valence basis comprised of just the 2s/2p AOs. For methane itself, there are four bonding MOs (into which the octet of electrons are placed in pairs) and four anti-bonding MOs, all constructed from the total of eight atomic orbitals for the five atoms. 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. This mode tends to reduce the bond index calculated for the carbon atom in methane from the value of 4.0; the overall valence count at this atom does not increase. In systems such as SF6, the coordination number at the central atom is clearly increased, but the individual S-F bond orders themselves decrease from 1 to 0.72 and the calculated bond index at S is ~4.3 rather than the 6 implied by the coordination number. Nowadays, such systems tend to be more commonly described as hypercoordinated rather than hypervalent, although this convention is neither standard nor consistently adopted.
  2. The electrons on carbon could instead (or as well as) expand the octet shell by populating molecular orbitals constructed using 3s or 3p higher Rydberg atomic orbitals (AOs) as well as the normal 2s and 2p valence 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[9] the Rydberg occupancy is only 0.37e. A molecule exhibiting significant Rydberg population probably does deserve the description hypervalent, and might be expected to exhibit associated properties such as exalted bond orders to and bond indices at the hypervalent atom. It would also be true to suggest that this is by far the rarer mode.

Computational procedures and FAIR data management[edit]

Calculations were all performed using the Gaussian 16 program. Input and output data from the calculations is managed using a FAIR (Findable, Accessible, Interoperable, Re-usable) data repository,[10] via the PID (persistent identifier, a DOI) for each dataset, and is given in the citation list. Such citable data is preferred to the more usual expedient of preparing a supporting information file in which coordinates are listed as part of a paginated PDF document.

Results and discussion[edit]

The focus here is to explore the properties of putative examples of Rydberg-based hypervalence, rather than hypercoordinate-based hypervalency which was the focus in the recent review.[1]

  • Adding two electrons to CH4 populates the anti-bonding LUMO, thus reducing the NBO-calculated Wiberg bond order of each of the CH bonds to 0.773 (ωB97XD/Def2-TZVPPD/scrf=water). The total Rydberg occupancy is 0.21e and the bond index at carbon is reduced to 3.1 (< 4). [11]
  • In marked contrast, adding two electrons to CH3F significantly populates the Rydberg levels (Figure 3) thus increasing the NBO-calculated 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 to give a total Rydberg population of 1.53e. The Wiberg bond indices are C; 4.15, H; 1.03 and F; 1.33.[12] All 3N-6 vibrational modes are real (Figure 4)[13] and an IRC can be located for e.g. the dissociation into CH3- and F-[14], but the minimum is only protected by a very small barrier. Increasing the basis set to Def2-QZVPPD[15] gives a similar total Ryberg population of 1.55e (C, 1.09, F, 0.31, H, 0.05e). An ELF analysis[16] (Figures 1 and 5) 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, whilst the “unexpanded” shell surrounding the carbon integrates to 7.23e, a “normal” octet.
    Figure 1. ELF analysis for CH3F(2-) with numerical values indicating basin populations
    • This Rydberg-expanded wavefunction is also derived from a CASSCF(12,12)/Def2-TZVPPD geometry optimisation (rC-F 1.417Å), for which ELF analysis based on the natural orbitals also produces outer shell ELF attractors with integrated populations of 1.94e and a C-F bond inner shell attractor with 0.9e.[17]
  • A second example [18] is the isoelectronic H3BF3- which has a similar NBO (Figure 6) encapsulating a a total Rydberg population of 0.68e and an ELF basin distribution again showing inner and outer valence basins (Figures 2 and 7).
    Figure 2. ELF analysis for BH3F(3-) with numerical values indicating basin populations
  • CH2F22- also shows[19] a reduced effect, with a Rydberg population of 0.62e, but again with outer-shell ELF basins (Figure 8).
  • The mono-anion CH2F21- shows an interesting variation[20] 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 (Figure 9). The singly occupied highest NBO is similar to the others (Figure 10).
  • 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.
  • Adding one electron to NH4+ to form the radical NH4[21] shows an interesting combination with Rydberg hypervalence. The total Rydberg population is a modest but significant 0.36718e, of which each hydrogen is 0.07872 and the nitrogen 0.05263e. The Wiberg bond indices are N 2.8242 and H 0.8372 (NBO configuration on H: 1S(0.65)2S(0.08)) indicating antibonding contributions from the additional electron which negate any hypervalence originating from the valence shell expansion. The ELF basins [22] reveal the additional electron is beyond the N-H axis, where it presumably does not violate the "octet" on the nitrogen itself. The value of the ELF function at the four centroids is 0.85, compared to eg 1.0 for a perfectly localized electron density. This reminds of molecular electrides!
    ELF analysis for N H4(•) with numerical values indicating basin populations

Interactive figures[edit]

These figures are displayed as interactive in-lined 3D models embedded in the Wiki pages only.

Figure 3. Highest occupied NBO for CH3F(2-)

Figure 4. C-F stretching mode for for CH3F(2-)

Figure 5. ELF Basin centroids for CH3F(2-)

Figure 6. Highest occupied NBO for BH3F(3-)

Figure 7. ELF Basin centroids for BH3F(3-)

Figure 8. ELF Basin centroids for CH2F2(2-)

Figure 9. ELF Basin centroids for CH3F(1-)

Figure 10. Highest singly occupied NBO for CH3F(1-)

Comment on HF(-), by Benoit[edit]

Henry, did you see this paper .[23] The authors classify HF(–), very similar to your suggestions, as the simplest hypervalent using Durrant’s definition of hypervalency. What do you think?

Reply to comment[edit]

  • Benoît Braïda has alerted me to a very recent article entitled Identification of a Simplest Hypervalent Hydrogen Fluoride Anion in Solid Argon [23] in which the bonding is claimed to be more covalent than ionic. Given that it represents the lower homologue of CH3F- described above, it was useful to see what a ωB97XD/Def2-TZVPPD calculation[24] calculation might reveal.
    1. The NBO-derived natural electron configurations are F [core]2S(1.93)2p(5.77)3S( 0.05)3p(0.04)3d(0.01) and H 1S(0.96)2S(0.12)2p(0.10) with a noticeably greater Rydberg population of the hydrogen than of the fluorine
    2. The Wiberg bond indices are 0.4758 for both F and H, with the HF bond order having the same value.
    3. There are therefore distinct differences between CH3F2- and to a lesser extent CH3- and HF-. In the former the Rydberg population increases the Wiberg bond indices and the Wiberg bond orders, whereas in the latter they decrease. As with NH4 , this molecule exhibits some aspects of both Rydberg hypervalence and anti-bonding character.
    4. The ELF function (ωB97XD/Def2-TZVPPD[25]) for HF•- is shown below, showing the nine valence electrons. The HF bond supports two covalent basins, one at ~ the mid-point of the bond and the other in the H core basin. An electron has been ejected along the HF axis beyond the hydrogen. A very unusual basin pattern, I have to say, but very similar to what happens with NH4.
ELF analysis for HF(1-) with numerical values indicating basin populations


I argue therefore that CH3F2- and BH3F3- represent rare 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 Rydberg hypervalency as defined here be identified, perhaps even stable ones that can be fully characterised by a variety of physical methods?


  1. 1.0 1.1 M.C. Durrant, "A quantitative definition of hypervalency", Chem. Sci., 2015, 6, 6614-6623. DOI:10.1039/c5sc02076j
  2. https://en.wikipedia.org/wiki/Hypervalent_molecule
  3. H. Kudo, Observation of hypervalent CLi6 by Knudsen-effusion mass spectrometry, Nature, 1992, 355, 432 - 434. DOI:10.1038/355432a0
  4. H. S. Rzepa, Is CLi6 hypervalent?, 2013, DOI:cbrs
  5. P.V.R. Schleyer, E.U. Wuerthwein, E. Kaufmann, T. Clark, and J.A. Pople, "Effectively hypervalent molecules. 2. Lithium carbide (CLi5), lithium carbide (CLi6), and the related effectively hypervalent first row molecules, CLi5-nHn and CLi6-nHn", J. Am. Chem. Soc., 1983, 105, 5930-5932. DOI:10.1021/ja00356a045
  6. H. S. Rzepa, 2010, DOI:cbrr for calculation and DOI:cbrq for analysis.
  7. H. S. Rzepa, 2010, DOI:cbr4 and DOI:cbrq for analysis.
  8. H. S. Rzepa, 2016, DOI:cbrv
  9. H. S. Rzepa, 2017, DOI:cbrt
  10. M. J. Harvey, A. McLean, H. S. Rzepa, A metadata-driven approach to data repository design, J. Cheminform, 2017, 9:4. DOI:10.1186/s13321-017-0190-6
  11. H. S. Rzepa, 2016, DOI:bc7j
  12. H. S. Rzepa, 2016, DOI:cbrw
  13. H. S. Rzepa, 2016, DOI:cbrw
  14. H. S. Rzepa, 2017, DOI:cbrx
  15. H. S. Rzepa, 2017, DOI:cb3n
  16. S. Noury, B. Silvi and R. J. Gillespie, Chemical Bonding in Hypervalent Molecules:  Is the Octet Rule Relevant?, Inorg/ Chem., 2002, 41, 2164-72. DOI:10.1021/ic011003v
  17. H. S. Rzepa, 2017, DOI:10.14469/hpc/3412
  18. H. S. Rzepa, 2017, DOI:cbrz
  19. H. S. Rzepa, 2017, DOI:cbr2
  20. H. S. Rzepa, 2017, DOI:cbzq , DOI:10.14469/hpc/2944
  21. H. S. Rzepa, 2017, DOI:cf78
  22. H. S. Rzepa, 2017, DOI:10.14469/hpc/3378
  23. 23.0 23.1 M.-C. Liu, H.-F. Chen, C.-H. Chin, T.-P. Huang, Y.-J. Chen & Y.-J. Wu, Nature, 2017, 7:2984, DOI:10.1038/s41598-017-02687-z
  24. H. S. Rzepa, 2017, DOI:10.14469/hpc/3274
  25. H. S. Rzepa, 2017, DOI:10.14469/hpc/3377