Hybrid Fock exchange/density functional theory functionals have shown to be very successful in describing a wide range of molecular properties. For periodic systems, however, the long-range nature of the Fock exchange interaction and the resultant large computational requirements present a major drawback. This is especially true for metallic systems, which require a dense Brillouin zone sampling. Recently, a new hybrid functional [HSE03, J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)] that addresses this problem within the context of methods that evaluate the Fock exchange in real space was introduced. We discuss the advantages the HSE03 functional brings to methods that rely on a reciprocal space description of the Fock exchange interaction, e.g., all methods that use plane wave basis sets. Furthermore, we present a detailed comparison of the performance of the HSE03 and PBE0 functionals for a set of archetypical solid state systems by calculating lattice parameters, bulk moduli, heats of formation, and band gaps. The results indicate that the hybrid functionals indeed often improve the description of these properties, but in several cases the results are not yet on par with standard gradient corrected functionals. This concerns in particular metallic systems for which the bandwidth and exchange splitting are seriously overestimated.

53 PBE0/GTO 386 604 540 353 71 B3LYP/GTO 389 617 547 340 71 PBE+U(4.5)/pw 392 618 −1435 e 549 −834 e 221 −20 53 PBE/pw f 383 608 −1573 547 −988 403 162 53 PBE/pw g 385 604 −1589 547 −999 409 168 53 a Reference 81. b Zero-point vibrational energy and thermal contributions to the heats of formation are very small (2.1 and 1.4 kJ/mol for CeO 2 and Ce 2 O 3 , respectively) and even smaller for reaction 2.1 (0.8 kJ/mol). Therefore, we use ΔE f,r ≈ ΔH f,r 0 (values from Table 2). c Experimental formation enthalpy of water at 0 K (−239 kJ/mol) has been taken from the literature. 82 d Reference 63. e Reference 80. Since GGA+U yields only the less stable γ phase of cerium, the energy difference between α and γ phase (−3 kJ/mol) has been added to the heats of formation. f PAW ansatz to describe the electron−ion interaction using plane waves. g LAPW+LO ansatz to describe the electron−ion interaction using plane waves, which can be considered as the benchmark method in the solid-state community. Both, PAW and LAPW are so-called full-potential methods.

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First-principles calculations based on hybrid Hartree-Fock density functionals provide a clear picture of the defect energetics and electronic structure in ZnO. Among the donorlike defects, the oxygen vacancy and hydrogen impurity, which are deep and shallow donors, respectively, are likely to form with a substantial concentration in n-type ZnO. The zinc interstitial and zinc antisite, which are both shallow donors, are energetically much less favorable. A strong preference for the oxygen vacancy and hydrogen impurity over the acceptorlike zinc vacancy is found under oxygen-poor conditions, suggesting that the oxygen vacancy contributes to nonstoichiometry and that hydrogen acts as a donor, both of which are without significant compensation by the zinc vacancy. The present results show consistency with the relevant experimental observations.

Present local and semilocal functionals show significant errors, for instance, in the energetics of small molecules and in the description of band gaps. One possible solution to these problems is the introduction of exact exchange and hybrid functionals. A plane-wave-based algorithm was implemented in VASP (Vienna ab-initio simulation package) to allow for the calculation of the exact exchange. To systematically assess the precision of the present implementation, calculations for the 55 molecules of the G2-1 quantum chemical test set were performed applying the PBE and PBE0 functionals. Excellent agreement for both atomization energies and geometries compared with the results obtained by GAUSSIAN 03 calculations using large basis sets (augmented correlation consistent polarized valence quadruple zeta for the geometry optimization and augmented correlation-consistent polarized valence quintuple zeta for the energy calculations) was found. The mean absolute error for atomization energies between VASP and the experiment is 8.6 and 3.7 kcalmol, as calculated with the PBE and PBE0 functionals, respectively. The mean deviations between VASP and GAUSSIAN are 0.46 and 0.49 kcalmol for the PBE and PBE0 functionals, respectively.