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I am trying to calculate the cohesive energy of certain metal oxides. However, I am only able to find a formula that is applicable to systems with a single element (say $\ce{Cu}$ metal or $\ce{Si}$ crystal), that is

$E_\text{cohesion} = E_\text{bulk(per atom)} - E_\text{isolated_atom}$

(consider the example given here)

What will be the formula to calculate the cohesive energy for a metal oxide such as $\ce{CuO}$ or $\ce{SiO2}$?

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Calculate the total energy of the unit cell. Take each unique atom from your unit cell and calculate its energy in isolation. Take the full unit cell energy and subtract off the energy of each lone atom in your unit cell. That's the cohesive energy of your unit cell. Often you'll divide this by the number of formula units or atoms in the unit cell to obtain your cohesive energy per formula unit or atom, respectively.

Putting this all together \begin{align} E_{\mathrm{cohesion}} = \frac{E_{\mathrm{UC}} - \sum_{i}^{N} E_{i}}{F} \end{align} where $E_{\mathrm{UC}}$ is the total energy of the unit cell, $N$ is the number of atoms in the unit cell, and $E_{i}$ is the energy of the $i$-th atom in the unit cell. $F$ is either the number of formula units or number of atoms per unit cell, depending on how you'd like to express your cohesive energy.

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  • $\begingroup$ Note, that both E(UC) and E(i) must be calculated using the same methodology, or with very close methodology, considering we have to treat the crystal and the atom. $\endgroup$
    – Miro Iliaš
    Jun 3 at 18:57

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