Surface Formation Energy and Stability

Within the slab model approach, the surface formation energy is computed as 

In metals or small band gap semiconductors, convergence can be slower and numerical noise larger. In Eq. [87], total energies from 3-D and 2-D systems are used, and this in principle might create problems of equivalent accuracy in algorithms that are specific for 2-D and 3-D. As a cross check, we can use the following definition for the surface energy  

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