Understanding the Bond Length Differences in sp3d and sp3d2 Hybridization

[jd12345]

Why are the bonds in sp3d hybridisation of different length? And why sp3d2 has bonds of equal length. For me sp3d should also contain all equal ond lengths with a symmetrical shape
but it doesnt. Why not?

 

[Mike H]

Are all of the bonds for a molecule with sp³d hybridization different lengths? Imagine, for example, PCl₅ as a representative molecule.

Insofar as a symmetrical shape, compare PCl₅ to something like SF₆, a representative molecule with sp³d² hybridization. Are they symmetric in exactly the same way?

 

[jd12345]

In PCl5 equatorial bonds adn axial bonds areof different lengths and hence of different bond energies. I was asking the reason for this since orbitals hybridise to from new orbitals of equal energies all bonds should have the same stabiltiy but it isn't in case of trigonal bipyramidal. Why?

 

[DrDu]

The question is interesting and I have to think about it. However in the case of a pentagonal bipyramid it is clear on geometrical grounds that not all 5 corners are equivalent.
Furthermore I would like to remark that nowadays neither in PCl5 nor SF6 d orbitals are believed to participate in bonding. So this discussion might be somehow reminiscent of that medieval discurse "how many angels can sit on the tip of a needle?" although there may be some transition metal complexes where such a description might be useful.

 

[Mike H]

The question is interesting and I have to think about it. However in the case of a pentagonal bipyramid it is clear on geometrical grounds that not all 5 corners are equivalent.

That was pretty much what I was thinking. I would feel that the geometric argument would be adequate, at least at a semi-qualitative level. Especially since consideration of the relative size/radii also can help to understand the resulting geometry, particularly in the examples I mentioned.

Furthermore I would like to remark that nowadays neither in PCl5 nor SF6 d orbitals are believed to participate in bonding. So this discussion might be somehow reminiscent of that medieval discurse "how many angels can sit on the tip of a needle?" although there may be some transition metal complexes where such a description might be useful.

I agree. Of course, I also still see general chemistry textbooks being written with these sorts of specious hybridization arguments to explain molecular geometry, amongst other minor and major sins. It's been a while since I last cranked through an inorganic chemistry textbook, but I even recall seeing similar arguments in a text I used ~ 10 years ago for my own brush with a formal inorganic chemistry class.

 

[AlchemistK]

This whole idea is based on the fact that orbitals arrange themselves so that there is minimum repulsion, but considering a 3 dimensional molecule with same bonds, shouldn't a spherical arrangement ensure minimum repulsion? That would make a structure with equal lengths and equal angles.(Which is how PCl5 should be according to my thinking.)

Chemical bonding was taught to us just a few months back, and if the things they are teaching us is not correct,without stating so, its a shame.

 

[DrDu]

I am explaining this in this forum every couple of months.
The reason is that chemistry teachers apparently worldwide aren't obligated to take some classes
in theoretical chemistry during their formation.
This whole concept of d electrons in main group elemental compounds goes back to the
influential books by the Nobel prize winner Linus Pauling, like "General Chemistry".
While the book was excellent, unfortunately at the time it was written it was out of scope to test these ideas quantitatively on a computer.
And invariably when this became possible some of his reasoning had to be revised.
Unfortunately, 99% of the chemistry teachers (and even textbook authors) are completely ignorant of this scientific development.

If you want to know how valence bond theory describes these molecules nowadays,
here is a link to start with
http://dx.doi.org/10.1016/S1380-7323(99)80022-3

 

[Mike H]

I am explaining this in this forum every couple of months.
The reason is that chemistry teachers apparently worldwide aren't obligated to take some classes in theoretical chemistry during their formation.

That there are apparently undergraduate chemistry programs (at least here in the US) which don't require a full year of physical chemistry for chemistry majors is not helping things. There is the occasional J. Chem. Ed. article urging the tossing of hybrid orbitals every so often, but it seems to be a no-go on the wider front.

Chemical bonding was taught to us just a few months back, and if the things they are teaching us is not correct,without stating so, its a shame.

Many chemists tend to be visual thinkers, in my anecdotal experiences. We love pictures. Many, though, get too attached to said pictures since they're simple and seem to "work" well in day-to-day issues.

 

[DrDu]

Mike, don't get me wrong. Actually I am a big fan of VB theory, but it makes me sick how it is taught nowadays as a purely qualitative concept, which is often not even distinguished from pre-QM models like Lewis structures. Then regularly in "advanced" classes some putative failiures of the VB method are shown and how MO theory triumphantly leads to correct answers.
In the meantime I looked up the sp3d concept in Paulings "The nature of the chemical bond". It mightstill be usefull to describe transition metal complexes like VF5.
While Pauling explains how sp3d2 orbitals are to be constructed, he does not go into details for sp3d.
However it is clear that there are actually two different hybrid orbitals, the apical and the equatorial ones which are different mixtures of s p and d orbitals. The exact mixing coefficients will depend somehow on how one exactly maximizes the localization of both orbitals simultaneously, but it can be shown that the best apical orbitals which can be costructed are more localized than the equatorial ones explaining already the stronger bond.

 

[Mike H]

DrDu - I think that we're on the same page regarding VB theory. My issue - as is yours, it would seem - is that it (and MO theory, at least in my experience) is presented in such a qualitative manner early on in the educational process (lower-division university chemistry courses here in the US, or its equivalent elsewhere) it feels that it's been 'cut off at the knees'. Still, people try to use this truncated description at that point to explain everything and anything about chemical structure, reactivity, and so on. My feeling is that - as was noted in a review by Hoffmann andShaik that I recall from a good while ago - both VB and MO are essential tools for understanding and inquiry, they just need to be taught and implemented properly. One might be more convenient to apply than the other for a particular problem, but one could use the other and converge upon the same answer.