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If you compare the melting points of alkali and alkaline earth metals, you see that the latter have higher melting points. However, if you look at MO theory, then alkaline earth metals should have quite a considerable proportion of the antibonding part of the bands occupied (even if there is an overlap with the p-band). So, why should the bond in alkaline earth metals be stronger?

(I realise that according to the electron sea model you just say that alkaline earth metals contribute two electrons, not just one, wich solves the problem. MO theory should also be applicable, so what am I overlooking?)

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From "The Nature of the Interatomic Forces in Metals" by Linus Pauling

This qualitative description of the interactions in the metal is compatible with quantum mechanical treatments which have been given the of problem, and it leads to an understanding such properties as the ratio of about 1. 5 of crystal energy of alkali metals to bond energy of their diatomic molecules (the increase being the contribution of the resonance energy), and the increase in interatomic distance by about 15 percent from the diatomic molecule to the crystal. The alkaline earth metals, by assuming the configuration nsnp, are able to form twice as many bonds as the alkalis. Similarly the suc- ceeding elements in the periodic table can form bonds in increasing number.

You are right on the fact that alkaline earth metals should not bond if we only considered their highest atomic energy levels. The dissociation energy for diatomic clusters of alkaline earth metals is low.

However, the disassociation energy gets higher for tetra-atomic as shown in this computational study: http://www.sciencedirect.com/science/article/pii/0039602885902328

Now, the reason why alkaline earth metals have higher melting points to be due to the p orbitals. The previous study relates p hybridization with bond strength. And so does this study: http://scitation.aip.org/content/aip/journal/jcp/77/8/10.1063/1.444313

Both journals state that p orbitals are involved in bonding. And the more involved the p orbitals in bonding, the stronger the bond. This trend is shown for alkaline earth metals. Beryllium, which has the highest melting point, also has more p orbital character. Also, take a look at the density of states of alkali metals and alkaline earth metals: http://www.colorado.edu/engineering/MCEN/MCEN5024/

You can see that not all p orbitals are entirely above the s orbitals.

So, to answer your question. The reason why alkaline earth metals have higher melting points is due to p orbitals. As Pauli states in his review, the np orbitals "hybridize" with the s orbitals. This allows for more bonds to form.

I think that p orbitals participate in bonding in alkali metals. But I couldn't find information that compares p orbital "hybridization" of alkali and alkaline earth metals directly.

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    $\begingroup$ Thanks for the answer. Actually, I believe quite a number of chemistry textbooks introduce metallic bonds by just expanding normal LCAO MO theory (which says you get as many MOs as you have contributing AOs) to the (almost) infinite metal crystal. And they also talk about antibonding orbitals there. (see xbeams.chem.yale.edu/~batista/vaa/band.html for an english example of that description) -- So I was wondering where the problem comes from and whether this formal derivation from MO theory was missing some essential points. $\endgroup$ – Andrea Nov 19 '16 at 23:25
  • $\begingroup$ @Andrea My mistake. I thought of that as band theory. I realize that it also falls as a "subcategory" of MO theory. I'll go read some journals and post my findings. $\endgroup$ – CoffeeIsLife Nov 20 '16 at 3:06

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