Is science sometimes in danger of getting tunnel vision? Recently published ebook author, Ian Miller, looks at other possible theories arising from data that we think we understand. Can looking problems in a different light give scientists a different perspective?

Dative Bonds And Theory

It seems to me there are two purposes for theory: to enable the calculation of things of interest so that predictions can be made, or to lead to understanding so that even if calculations are not practical, at least educated guesses can be made to guide further action. At the risk of drawing flak from the computational chemists, I think the second purpose is of more importance to chemists. The problem is, chemistry is based on a partial differential equation that cannot in general be solved, if for no other reason than the equations relating to a three-body problem involving a central field cannot be solved exactly. That leaves the question, if you cannot solve that, what can you do? What chemists have done is to take solutions from what can be solved (the hydrogen atom) and base models on those. Thus we have orbitals that correspond to the excited state solutions of the hydrogen atom. The perceptive reader of my previous posts will realize I have argued that the actual orbitals do not exactly correspond, nevertheless the wave functions I argue for (essentially superpositions of waves with fewer nodes based on the principle that separation is possible provided all components have quantized action) are essentially the same in terms of angular distributions, so that issue is irrelevant to the present issue, which is what to do with these orbitals relating to dative bonds? Most chemists are familiar with one answer relating to dative bonds: models based on arrows, etc.
 
Recently, we have seen a debate about dative bonds in Angew. Chem. In. Ed. (2014, 53, 370 – 374; 2014, 53, 6040 – 6046.). There seem to be several points being made, but they tend to boil down to the use of arrows, what the dative bond is, and what model is worth following. This discussion attracted the heretic in me!
 
First, why models? One of the protagonists (Frenking) used this quote: Bonding models are not right or wrong but they are more or less useful. This raises the issue, what do we mean by "right or wrong", and when can a model that is known to be wrong continue to be used? In the first case a model can be seen to give useful outputs and can be used while there are no known examples of it being wrong, and, of course, there is nothing wrong with using a model that you know to be an approximation, as long as everyone accepts that it is an approximation. Another time when the model is strictly wrong but can still be used (in my opinion anyway) is when it is only wrong when a given external condition is imposed that gives a known effect, in which case it can be used when that effect is absent. The most obvious example is Newtonian mechanics. Newton assumed action at a distance was immediate. It is not, and when that is relevant we have to resort to Einstein's mechanics, but when motion is such that the effects of light speed can be considered as effectively instantaneous, you would be mad not to use Newtonian mechanics.
 
However, back to the dative bond. What is it? Seemingly Haaland (Angew. Chem. Int. Ed. 1989, 28, 992 – 1007.) considered: The basic characteristics of a dative bond, depicted with an arrow “→”, are its weakness, the substantially longer bond length compared to typical single bonds, and a rather small charge transfer. My personal view is this does not help much. What does " substantially longer bond length compared to typical single bonds" mean? In this sense, it must be recalled that bond lengths vary, and the dative bond does not have a non-dative counterpart. Both parties to this discussion used the example of borazane (NH3→BH3). Right – what is the length of a non-dative nitrogen-boron single bond free of other complications, including lone-pair interactions? The next question, though, is, if we write it like that, what does the arrow mean? What I was taught as an undergrad, and it seems reasonable enough, is that a two-electron bond forms using both electrons from the nitrogen lone pair. Now, part of this discussion then focused on, what does that mean?
 
A lot of people seem to think that what happens is that the nitrogen transfers an electron to the boron atom, then the two electrons pair. The net result is that the molecule is a zwitterion, with N and B- charges on the relevant atoms, with a little subsequent polarization of the hydrogen atoms. That would seem to contradict Haaland in that such a distribution would give a very strong dipole moment, but note now what Frenking says: "Writing ammonia borane H3N-BH3 as a zwitterion yields a negative charge at boron and a positive charge at nitrogen, while the partial charges exhibit the opposite polarity." What exactly does that mean? From what I can make out from a cursory glance at the literature, borazane has a dipole moment of 5.2 D. Now, which way is that likely to go? I cannot see a sufficient electron transfer to get that dipole moment from boron to nitrogen, so it seems reasonable to me to assign the direction of flow to be from the lone pair of nitrogen towards boron, as the arrow indicates. Accordingly, I find this discussion just a little misleading. However, I also do not feel that the concept of the nitrogen transferring an electron to boron, and the two pairing is very helpful either.
 
So, how do I see the dative bond? In my picture, the nitrogen atom has a lone pair, and those electrons are described by a wave function that has a barrier at infinity, while boron, if it hybridizes, can create an sp3 configuration with an empty wave function, which I shall describe as a hole. If the nitrogen atom approaches such that the lone pair wave function is directed towards the hole on the boron atom, the boron atom now provides a barrier to the lone pair wave function, perhaps described as the vacant sp3 orbital "capturing" the lone pair and reducing the range over which the electrons can roam by the boron atom providing a turning point. As positional uncertainty is lowered, momentum increases, kinetic energy increases, and by the virial theorem, total energy is lowered. In that picture, the arrow is a great way of describing it, and the lone pair mechanics are now determined both by the nitrogen atom and the boron atom, and to maintain the sp3 hybridization, the lone pair has to spend increased time away from the nitrogen atom, hence the high dipole moment. Note that that is also more valence-bond type thinking than molecular orbital thinking. As to why I put that here, apart from highlighting the debate, the sort of thinking of this last model, which is essentially that the dative bond forms as a cosnequence of the change to boundary conditions applied to a lone pair helps me; whether it helps anyone else is, I suppose, a more interesting question.
Posted by Ian Miller on Nov 9, 2014 8:59 PM Europe/London

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