15 Feb 2011


Submitted by Adam R. Johnson, Harvey Mudd College
I told my students I would poll inorganic chemists the answer to this question.  How many bonds does PF5 have?


I used to believe fervently in d-orbitals for main-group hypervalent molecules and then a colleague helped me "see the light."  I am now a proud reformed member of the no d-orbitals club.


Help me see the light because I still believe!

Sibrina Collins, PhD College of Wooster

So what do your students think of the results thus far? I would love to hear the story behind this question.


I ask my students to do the MO diagram for PF5 (or a similar expanded-octet molecule) every year on a homework.  i have them draw the MO diagram using only valence s and p orbitals on the central atom, and then I have them consider the effects of including the virtual d orbital.  Without giving away the complete answer, I still firmly believe based on my MO diagrams that PF5 has but 4 bonds.  Maybe I'll post the question a a learning object...

Sibrina (and others seeking enlightenment):

Here is an interesting take on the question of hypervalence in PF5 that was published in J. Chem. Ed. a few years ago and that could be used in either Gen Chem or in Inorganic if you don't want to go into the MO theory.  While I usually make the point to students that NF5 and OF6 don't exist, perhaps due to the small size of the central atom, I forget to emphasize as this paper does that PH5 and SH6 also do not exist (and that has to be based on something more than size).

Tracy A. Mitchell, Debbie Finocchio, and Jeremy Kua, "Predicting the Stability of Hypervalent Molecules," J. Chem. Educ. 2007, 84, 629-634.

Flick Coleman provides a great summary of the literature on this topic in his recent "JCE Featured Molecules" article: "Structure and Bonding in Hypervalent Iodine Compounds," J. Chem. Educ. 2010, 87 (9), 999–1000.

I do a similar exercise, but with SF6.


Christian R. Goldsmith Auburn University Department of Chemistry and Biochemistry

If one defines "bond" as "a contact between two atoms with a distance shorter than the sum of the VdW radii", then it obviously has five bonds, one from P to each F.  If one defines "bond" as "a filled bonding molecular orbital in the MO diagram", then of course there are only four.  When I teach I try to refer to the former as "bonding interactions" and the latter as "filled bonding MOs" to differentiate those concepts.

The importance of the nature of the outer atoms, and so the reason that PH5 isn't stable, is also revealed in the MO diagram.  The 5th pair of electrons in the MO diagram exist as one of many non-bonding MOs delocalized around the outer five atoms.  (In a Lewis structure of PF5, one expects 10 bonding electrons and 30 "non-bonding" electrons in the lone pairs.  In the MO diagram, it turns out to be 8 and 32.)  So that's an extra pair of electrons that don't contribute to bonding and need to be stablized: they'll obviously be more happy on a small, high Zeff, high electronegativity, low energy orbital element like F than on something like H or a lower halogen.  Hence, PF5 is stable, but PH5 and PI5 are not.

Steve, the options were "4", "5", and "Niether 4 nor 5; I am a crazy person". Naturally, you invented option d: "Both 4 *and* 5; I am a crazy person."

I think this is actually a really nice way of laying this out for students, and I'll try using the distinction between "bonding interactons' and "filled bonding MOs" this fall and see if my students nibble at the idea. I also like the examples of PH5 and PI5...I'd never thought of those counterexamples. 

But I'm comforted that you agree that the d-orbitals are doing a whole lot of nothing in the bonding of PF5. And while you say "of course there are only four", I think you'd be suprised by the number of people who have yet to see the light!

I've been puzzling over this question for a while, and though I am in the 4 bonds camp, I cannot make heads or tails of the results of the electronic structure calculations that I've performed on it (both DFT and MP2).  If take a look at the molecular orbital diagram for PF5, I'm pretty sure I'm seeing bonding ligand group orbitals that bear a striking resemblence to those that would overlap with dxy, dx2-y2, and dz2.  I also see LGOs that correspond to overlap with px and py, except there doesn't seem to be any phosphorus contribution in those MOs.  The only one that seems to makes sense is the A2'' LGO that overlaps with pz.  I don't see any A1' set that corresponds to the s orbital.

Does anyone have experience relating the MO diagrams of hypervalent compounds to the concepts that are generally taught in class?  I know there's a way to talk about it using generalized valence bond theory, but that still makes my head hurt.

Edit:  OK, I think I have it figured out.  If you perform Natural Orbital analysis on the final wavefunction and look at those, all of the expected orbitals appear.  You can even see the A1' LGO that the non-existent dz2 orbital on phosphorus would line up with, essentially forming the non-bonding orbital that you would expect to see if you treated the equitorial atoms as being part of a 4-center-6-electron bonding scheme.  

Now I just need to figure out a way to teach that to undergrads.

I was trolling the most recent issue of Inorganic Chemistry tonight and came across this paper debunking hypervalency in the sulfate ion based on both theoretical and experimental evidence.

Inorg. Chem. 2012, 51, 8607-8616. (http://pubs.acs.org/doi/abs/10.1021/ic301372m)

I can't say I follow the arguments too well, but I am convinced that we need to start working on changing the textbooks that always draw expanded octets even when they are not required as in sulfate. 


Ah, the debate continues. While the above paper does put the argument against hypervalency into an experimental and theoretical context, the question remains as to what effect the crystal binding energy has on the electron density.

This is an old question. I guess it goes back to Rundle (J. Chem. Phys 1949, 17, 671-675) and Pimentel (J. Chem. Phys. 1951, 19, 446-448.) who developed the idea of three center two electron bonds. Rundle expanded these ideas to the xenon fluorides (JACS 1963, 85, 112-113.) and postulated that the bonding of XeF2 and XeF4 involves delocalized three center four electron bonds using only p-orbitals on Xe (note: he did not consider Xe s orbital contributions). There have been many discussions of the importance (or lack thereof) of d orbitals in the bonding of hypervalent main group compounds. M.J.S. Dewar published one of these under the provocative title of "Why Life Exists" (Organometallics, 1982, 1, 1705- 1708). I find Chapter 6 "How Important are d-Orbitals in Main Group Chemistry" in Burdett's "Chemical Bonds: A Dialog" Wiley, 1997, to be pretty good. 

As d-functions must be included in the basis sets of second row atoms, "Hypercoordinate Molecules of Second-Row Elements: d Functions or d Orbitals" by Magnusson (JACS, 1990, 112, 7940-7951) is interesting.

The question of d-orbital participation in oxoanions also has a long history. While there may be multiple bond character, I believe that back donation into anti-bonding orbitals on the central atom is more important that any d-pi p-pi interaction.