Theoretical Surface Science Beyond Gradient-Corrected Density Functional Theory: Water at α-Al2O3(0001) as a Case Study

The quantum chemical description of the adsorption, vibrations, and reactions of molecules at periodic solid surfaces is frequently based on a methodological "standard model": density functional theory (DFT) in the generalized gradient approximation (GGA), using plane wave bases and three-dimensional supercells. Although the computationally efficient GGA functionals can be very successful, cases are known where they do not perform so well. Most importantly, activation energies for chemical reactions are typically underestimated, with the consequence of computed reaction rates being too large. In this work, we consider a well-studied model system: water or water fragments adsorbed on an Al-terminated alpha-Al2O3(0001) surface as a test bed for studying the performance of electronic structure methods, both from DFT and wave function theory. On the DFT side, we employ two GGA exchange correlation functionals: PW91 and PBE with and without dispersion corrections, whose results are then compared to those of hybrid functionals B3LYP and HSE06. Further, we follow a periodic wave function approach in the form of local second-order Moller-Plesset perturbation theory, LMP2, on a Hartree-Fock reference. En route, we address issues arising from the choice of the basis set. The key findings of our study are as follows: (i) DFT-GGA adsorption energies are in reasonable agreement with both hybrid-DFT and LMP2 values. In particular, the deviations between the relative energies, corresponding to different adsorption structures, are in the range of the error due to missing dispersion corrections or the basis set error. (ii) Harmonic DFT-GGA vibrational frequencies for oxygen hydrogen stretch modes are by several tens of wavenumbers red-shifted compared to corresponding hybrid-DFT values. The latter are in much better agreement with recent experimental data. (iii) The activation energy for a hydrogen diffusion reaction is grossly underestimated by GGA compared to hybrid-DFT or LMP2, which in turn are quite comparable.