A Problem with Bond Additivity
In a previous post (http://my.rsc.org/blogs/84/1702) I made the case that the covalent bonds of the group one metals were characteristic of the element, i.e. the energy of any A – B bond was the arithmetic mean of the A – A and the B – B bond energies. I also asked " What do you think? Are you interested?" So far, no comments. Does this mean that nobody can see a glaring problem, or does it really mean that chemists as a whole have little interest in the nature of the chemical bond?
First, the glaring problem. How can the energies be the arithmetic mean? Thus from de Broglie, we know
pλ = h
We have also established that the covalent radius is characteristic of the atom, which means that λ on the bond axis is constant. We also know that on average, there are no net forces on the nucleus, otherwise they would accelerate in the direction of the force. (Zero point motion is superimposed on such an equilibrium distance, but the forces average to zero.) With no net forces, the average wavelength as determined on the other axes should also be constant. You may protest (correctly) that the wave may have only one wavelength, but that is only true if the wave is not separable. For example, one might argue the medium changes on the bond axis due to the change in particle density due to wave interference.
Thus the constant covalent radius implies a constant wavelength for the valence electron in different molecules. But since the total energy will involve a term (p1 p2)^2 minus the original energies, and since the square of a sum does not equal the sum of the squares, and since the path length must change between, say, Li2 and LiCs, the bond energies should not be the linear sum of the components if the waves are delocalized over the whole molecule. For a simple two-electron wave function that arises from pairing, no new nodes are placed in the wave function (other than the antibond or excited states) so the path length must change significantly. To me, this strongly suggests that the molecular orbital theory is not soundly based. Yes, they can get the right answers by adjusting the parameters/constants within the calculations, but that does not prove the theory is correct. Instead there should some algebraic reason why such additivity arises naturally.
Is there any? The answer to that, in my opinion, rests on the reason why the energy levels are stable anyway. Under Maxwell's electromagnetic theory, an accelerating electron should emit electromagnetic radiation, and this occurs always, except for the stationary states of atoms and molecules. From the Schrödinger equation, such stable states occur only when the action is exactly quantized. If the action about each atom must be quantized for σ-bonded molecules for the molecule to be stable, then we get the additivity of the energy of such simple molecules if the covalent radius is constant. Thus we have a physical reason, independent of calculations, for the observation. The importance of this is that it gives a new relationship to aid calculations, which also shows why the functional group actually occurs. Is such a potentially new physical relationship of sufficient interest to be worth further investigation?
Any comments? Please!
Posted by
Ian Miller on Mar 20, 2016 10:54 PM Europe/London
