In my last post, I presented evidence that the covalent radius of a Group 1 metal was constant in the dimeric compounds. I also asked whether anyone was interested. So far, no responses, and I suspect the post received something of a yawn, if that, from some because, after all, everyone "knows" there is a constant covalent radius. There is, of course a problem. Had I included hydrides, the relation would not have worked. Ha, you say, but the hydrides are ionic. Well, the constant covalent radius of hydrogen simply does not work for a lot of other compounds either. Try methane, ammonia and water. There are various alternative explanations/reasons, but let us for the moment accept that hydrogen does not comply with this covalent radius proposition.
If the covalent radius of an atom is constant, then there should be a characteristic wavelength for each given atom when chemically bound, which in turn suggests from the de Broglie relation that the bonding electrons will provide a constant momentum value to the bond. While that is a little questionable, if true it would mean the bond energy of an A – B molecule is the arithmetic mean of the corresponding A – A and B – B molecules. Now, one can argue over the reasoning behind that, but much better is to examine the data and see what nature wants to tell us.
Pauling, in The Nature of the Chemical Bond stated clearly that that is not correct. However, if we pause for thought, we find the arithmetic mean proposition depends on no additional interactions being present in addition to those arising from the bonding electrons forming the covalent bond. Thus atoms with a lone pair would be excluded because the A – A bonds are too weak, such weakness usually attributed to lone pair interactions. Think of peroxides. Then, bonds involving hydrogen would be excluded because the covalent radius relationship does not hold. Bonds involving hybridization may produce other problems. This is where the Group 1 metals come to their own: they do not have any additional complicating features. Far from "not being very interesting" as one editor complained to me, I believe they are essential to starting an analysis of covalent bond theory. So, what have we got?
The energies of the A – A bonds are somewhat difficult to nail down. Values are published, but often there is more than one value, and the values lie outside their mutual error bars. With that reservation, a selection of energies (in kJ/mol) are as follows: Li2 102.3; Na2 72.04, 73.6; K2 57.3; Rb2 47.8; Cs2 44.8
The observed bond energies for A – B molecules are taken from a review (Fedorov, D. A., Derevianko, A., Varganov, S. A. J. Chem Phys. 140: 184315 (2014)) Below, the calculated value, based on the average of the A – A molecules are given, then in brackets, the observed energy, then the difference δ expressed as what has to be added to the calculated value to get the observed value.
Mean Obs δ
Li – Na 88.0 (85.0) -3.0
Li – K 79.8 (73.6) -6.2
Li – Rb 75.1 (70.9) -4.2
Li – Cs 73.6 (70.3) -3.3
Na – K 65.5 (63.1) -2.4
Na – Rb 60.7 (60.2) -0.5
Na – Cs 59.2 (59.3) 0.1
K – Rb 52.6 (50.5) -2.1
K – Cs 51.1 (48.7) 3.4
Rb – Cs 46.3 (45.9) -0.4
The question now is, does this show that the bond energies are the arithmetic means of the A – A and B – B molecules? Similarly to my last post, there are three options:
(1) The bond energies are the sum of the atomic contributions, and the discrepancies are observational error, including in the A – A molecules.
(2) The bond energies are the sum of the atomic contributions, and the discrepancies are partly observational error, including in the A – A molecules, and partly some very small additional effect.
(3) The bond energies are not the sum of the atomic contributions, and any agreement is accidental.
What do you think? Are you interested?
