Hohenberg-Kohn-Sham density functional theory

The emergence of a family of computational methods, known under the label ‘density functional theory∈dex theory! density functional ' or ‘DFT', revolutionalized the field of computer modelling of complex molecular systems. Many computational schemes belonging to the DFT family are currently in use. Some of them are designed to be universal (nonempirical) whereas other to treat specific systems and/or properties (empirical). This review starts with the introduction of the formal elements underlying all these methods: Hohenberg-Kohn theorems∈dex theorem! Hohenberg-Kohn, reference system∈dex reference system of noninteracting electrons∈dex reference system! noninteracting electrons, exchange-correlation energy∈dex energy functional! exchange-correlation functional∈dex functional, and the Kohn-Sham equations∈dex equation! Kohn-Sham. The main roads to approximate the exchange-correlation-energy functional based on: local density approximation∈dex approximation! local density (LDA), generalized gradient approximation∈dex approximation! generalized gradient (GGA), meta-GGA∈dex energy functional! exchange-correlation! meta-GGA, and adiabatic connection∈dex adiabatic connection formula (hybrid functionals∈dex energy functional! exchange-correlation! hybrid ), are outlined. The performance of these approximations in describing molecular properties of relevance to intermolecular interaction∈dex interactions! intermolecular s and their interactions with environment in condensed phase (ionization potential∈dex potential! ionization s, electron∈dex electron affinities∈dex electron! affinity, electric moments∈dex electric moment, polarizabilities∈dex polarizability ) is reviewed. Developments concerning new methods situated within the general Hohenberg-Kohn-Sham framework or closely related to it are overviewed in the last sectio