# How does metallic bonding in alkaline earth metals work?

Metallic bonds are said to be delocalised.

Lithium crystals have each lithium atom in direct contact with eight other lithium atoms. Each atom could therefore be in a hybrid of eight chemical bonds with each other.

But a similar explanation does not work for atoms like beryllium.

Some possible arrangements of electrons that beryllium could be a hybrid of configurations of might be:

$$\ce{Be^{+} + Be^{-}}$$

$$\ce{Be^{2+}_2 + Be^{2-}_2}$$

$$\ce{Be^+ + e^-}$$

$$\ce{Be^{+}_2 + e^-_}$$

$$\ce{Be^{2+}_2 + 2e^{2-}_}$$

$$\ce{Be^{2+}_2 + e^{2-}_2}$$

$$\ce{Be^{2+}_2 + e^{2-}_2}$$

But beryllium is diamagnetic and all these suggest paramagnetic properties or a $e^{2-}_2$ pair which doesn't seem right to me although I'm not fully sure how the free electron hybrids would work.

Another possibility is that the electrons are dragged up into the p orbitals.

For example, the atoms would have valence electron configurations of:

$$\underset{sp}{[\uparrow \vert \uparrow]} \underset{p}{[\; \vert \; ]}$$

which would result in hybrids of $\ce{Be2}$ or $\ce{Be_4}$ I think.

However, the atoms would have to be dragged up really high so that they aren't paramagnetic.

Let me list out the molecular orbital theory bonding and antibonding orbitals for diberyllium.

$$\underset{\sigma}{[\uparrow \downarrow]} \underset{\sigma^*}{[\uparrow \downarrow]} \underset{\pi}{[\; \vert \;]} \underset{\sigma}{[\; ]} \underset{\pi^*}{[\; \vert \;]} \underset{\sigma^*}{[\;]}$$

If I wanted a bonding material that was not paramagnetic I'd have to lift up the energy to something like:

$$\underset{\sigma}{[\uparrow \downarrow]} \underset{\sigma^*}{[\;]} \underset{\pi}{[\; \vert \;]} \underset{\sigma}{[ \uparrow \downarrow]} \underset{\pi^*}{[\; \vert \;]} \underset{\sigma^*}{[\;]}$$

which is probably too high energy to matter for any purposes.

• Where did you get the information that "Lithium crystals have each lithium atom in direct contact with four other lithium atoms."? Everything I find says that its crystal structure at room temperature is body-centered cubic, where each atom has eight neighbors. – f'' Jul 24 '16 at 6:43
• That was a typo I meant 8 – Steven Stewart-Gallus Jul 24 '16 at 16:08

• But then why is beryllium diamagnetic? If beryllium is like $\ce{Be^+}$ in a sea of $\ce{e^-}$ then it should be paramagnetic. If it is like $\ce{Be^{2+} + 2e^{-}}$ shouldn't it still be paramagnetic? – Steven Stewart-Gallus Jul 24 '16 at 19:55
• So it is $\ce{Be^{2+} + e{2-}_2}$! But I thought pairs only happen in superconductors with Cooper pairs? – Steven Stewart-Gallus Jul 24 '16 at 21:39
• Most lanthanoids have $Ln^{3+}$ + 3$e^-$. – gsurfer04 Jul 25 '16 at 9:57