Hybrid functionals and their application to small molecules and solids

Full text: Hybrid functionals, containing a fraction of the exact exchange, allow for a rather accurate treatment of e.g. small molecules and band gaps in bulk materials. A plane-wave based algorithm was implemented in VASP (Vienna Ab-initio Simulation Package) to accomplish the calculation of the exact exchange. Two functionals including exact exchange are presently available, i.e. the PBE0 (Perdew-BurKEX-Ernzerhof) and the HSE (Heyd-Scuseria-Ernzerhof). A rigorous assessment of the implementation was performed by geometry optimization and calculation of the atomization energies of the G2-1 quantum chemical test set, containing 55 molecules. Excellent agreement compared to corresponding Gaussian 03 data and good agreement with experiment was achieved. The mean absolute error (theory related to experiment) for the atomization energies calculated with the PBE and the PBE0 is 8.6 and 3.7 kcal/mol, respectively. To investigate the properties of bulk materials, the lattice constants and bulk moduli of twenty solids comprising ionic, semiconducting and metallic materials, have been calculated using the PBE, PBE0 and HSE functional, respectively. Additionally, full potential linearized augmented plane wave calculations were carried out with the WIEN2k package using the PBE exchange correlation functional. Both ab initio methods give very similar values, well below the deviations from experiment. Referring to the projector augmented wave results (VASP) the mean deviation of the lattice constants from experiment is 0.041 A, 0.026 A and 0.031 A for the PBE, PBE0 and HSE functional, respectively. In general, hybrid functionals seem to improve the description of insulating periodic systems in a way similar to that of small molecules. (author)