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If I have the energy per atom $e=7.37 $ eV, how can I estimate the energy of the single covalent bond in the diamond?

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I've no idea here you get the number of $7.37\:\mathrm{eV}$ from.

The bond dissociation of a single bond in carbon can be estimated as follows. The Enthalpy of Atomisation of carbon is $+717\:\mathrm{kJ/mol}$ and a $\mathrm{mol}$ contains four bonds. Atomisation turn carbon into a mono-atomic gas, so all bonds are broken.

So if we divide $+717\:\mathrm{kJ/mol}$ by the Avogadro Number, then divide by $4$ and convert to $\mathrm{eV}$ we get an estimate of $1.86\:\mathrm{eV}$ per covalent bond.

The bond dissociation Enthalpies of various types of carbon-carbon bonds can also be found in this table (page 2). Convert to $\mathrm{eV}$ as above.

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You can find this easily by counting atoms and bonds.

In the diamond lattice each atom has bonds to 4 neighbor atoms, and each bond is between 2 atoms. Hence, in a diamond crystal with $N_{atom}$ atoms you have $N_{bond}=N_{atom}\cdot 4/2=N_{atom}\cdot 2$ bonds.

Therefore the energy per bond is half the energy per atom: $7.37\text{ eV}/2 = 3.685\text{ eV}$

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