# How to model a doped surface?

I want to start studying some single-atom catalysts doping with a transition metal. However, I do not what protocol I should follow.

Based on the articles that I read, I should dope my surface only after I already optimized my unit cell and created my surface, however, how do I should decide what sites I will choose to make the substitution in my surface?

For example, how to decide that this is the better substitution:

• Surface mixing energy which evaluates the segregation propensity of each SAA surface w.r.t bulk. The dopant cannot even appear at the surface if it's positive. $$$$E_{\mathrm{mix}} = E_{\mathrm{D}_1\mathrm{H}} + \tilde{E}_{\mathrm{bulkH}} - (E_{\mathrm{H}} + \tilde{E}_{\mathrm{bulkD}})$$$$ where $$E_{\mathrm{D}_1\mathrm{H}}$$ and $$E_{\mathrm{H}}$$ are the energies of the SAA slab and the pure host slab, respectively, $$\tilde{E}_{\mathrm{bulkH}}$$ and $$\tilde{E}_{\mathrm{bulkD}}$$ are the per-atom energies of the bulk host and the bulk dopant, respectively.
• Aggregation energy which evaluates the aggregation propensity of the dopant atoms forming clusters (e.g. dimers and trimers) on the host metal surface. A dispersed SAA phase cannot be formed if it's negative. $$$$E_{\mathrm{agg}} = E_{\mathrm{D}_n\mathrm{H}} + (n-1)E_{\mathrm{D}} - nE_{\mathrm{D}_1\mathrm{H}}$$$$ where $$E_{\mathrm{D}_n\mathrm{H}}$$ are the energies of an alloy slab with a surface cluster of $$n$$ dopant atoms, $$E_{\mathrm{D}}$$ is the enenrgy of the pure dopant slab.