Theoretical Considerations of Surface Energies

In theoretical studies, such as with DFT, the T = 0 value of is typically calculated, also assuming that contributions due to zero-point vibrations as well as the pV term are negligible, that is, is calculated. In terms of a periodic slab calculation, 

E is more conveniently defined with regard to surface area. A, as 

18) It turns out, however, that extreme care must be taken in order to ensure that the surface energy, which is a small energy difference between two much larger total energies is computed reliably. All the issues that can affect the accuracy of the computational set-up, such as basis set, treatment of core electrons, integration 

Studies on jeUium surfaces provide a partial explanation for why LDA outperforms GGA for the calculation of the surface energy of metals. Specifically, they show that the exchange-correlation contribution to the surface energy is calculated more reliably with the LDA because of a favorable cancellation of errors LDA overestimates the exchange contribution to the surface energy, but underestimates the correlation contribution, whereas PBE underestimates both quantities [138-140], Since these results on jellium surfaces are apparently transferable to real metals, it is reasonable to anticipate that functionals that are superior to LDA for jellium surfaces will also be superior to LDA for real metal surfaces. In this regard, it appears that the meta-GGA TPSS, PBE-WC, and a functional from Mattsson and coworkers based on a subsystem functional approach offer some promise [28,140, 141]. However, whether these functionals live up to expectations for real metal surfaces and solid surfaces in general remains to be seen. 

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