The screened Coulomb hybrid density functional theory developed in this work extends the applicability of hybrid functionals to large molecules and solids. Traditional hybrid functionals have been applied to medium sized molecules and some insulating solids with excellent results. However, the fundamentally long range of the Hartree-Fock (HF) exchange interaction limits their use for biomolecules and semi-conducting or metallic solids. The large spatial extent of the HF exchange can be reduced by utilizing a screened Coulomb potential. Such potentials have been widely used in solid state physics. Efforts of employing them in quantum chemistry were not as successful due to the unsatisfactory accuracy of the resulting methods. This work takes a new approach by combining a screened HF potential with both short and long range screened density functionals. The Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional is designed to produce exchange energies comparable to traditional hybrids while only using the short range, screened HF exchange. The accuracy of the HSE functional is assessed on a wide range of molecules and solids. Enthalpies of formation, geometries and vibrational frequencies of the G3 set of 223 molecules are predicted with performance equivalent to the best traditional hybrids. A set of 21 insulating, semi-conducting and metallic solids was used to determine the accuracy of lattice constants and bulk moduli. Both properties show significantly improved accuracy, compared to pure density functionals. HSE also accurately predicts band gaps of semi-conductors whereas pure density functionals severely underestimate the band gaps. Benchmarking of HSE in several semi-conducting and metallic solids shows a drastic decrease in computational cost, compared to established hybrid functionals. HSE achieves linear scaling for medium size systems (greater than 15 A) whereas regular hybrids scale as O (N2.5) for systems up to 100 A and scale linearly only beyond that. This late cross-over makes it computationally prohibitive to treat complex solids with traditional hybrid functionals. HSE circumvents this bottleneck and produces superior results while increasing computational cost by a factor of only two to four, compared to pure density functional theory
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