Teoria funkcjonałów gęstości: podstawy, realizacja Kohna-Shama i pojęcia dla chemii

Thirty five years after Hohenberg and Kohn discovered in 1964 that the electronic density r(r) can be used as the basic quantity in the rigorous formulation od the theory of electronic structure of matter, the modern density functional theory (DFT) has developed into an already mature discipline, which offers both attractive computational tools for applications in physics, chemistry and molecular biology, and a new conceptual framework for predicting and rationalizing preferences in chemical processes. Computational advances, originating from the other, almost as old historical development by Kohn and Sham (KS) in 1965, have demonstrated that the accuracy of the modern DFT software in the mostly ground-state applications has reached the level of the 3chemical accuracy 1, comparable to that offered by the sophisticated and prohibitively expensive traditional quantum chemistry methods, which explicitly determine the correlated N-electron wavefunction of a molecular system. The importance of these two branches of computational quantum chemical methods in modern chemistry has been recognized by the 1998 Nobel Prize for Chemistry [W. Kohn (density theory) and J.A. Pople (wavefunction theory)]. The Hohenberg-Kohn/Kohn-Sham theories have been generalized to thermal ensembles, multicomponent systems, spin and orbital paramagnetism, and superconductivity. The recent developments also cover the relativistic and excited-states theories, time dependent systems and the DFT for sybsystems, the latter being of paramount importance for the theory of chemical reactivity. The applications of DFT range from the ground-state properties of solids, through calculations on molecular systems of chemical/biological importance to high temperature plasmas. A combinations of DFT with molecular dynamics has prompted a spectacular progress in calculations on the ion dynamics in solids and the equilibrium structures of large molecular clusters with up to ~10(2) atoms. Very recently, progress has also been made in developing approaches behaving linearly with the number of electrons, which show promise of handling truly large systems consisting of ~10(3) atoms This spectacular success of the computational DFT is matched by its conceptual significance in chemistry. DFT gave a new impetus for developing novel, more reliable reactivity criteria and offered a new thermodynamical outlook on elementary chemical processes. It has soon been discovered that DFT provides the rigorous basis for defining many classical chemical concepts, which had originally been introduced on intuitive/phenomenological grounds, e.g., the electronegativity and hardness/softness characteristics of the electronic distribution in molecules. It resulted in more rigorous theoretical justifications of important rules of chemistry, soon to be followed by general variational principles for chemistry, which both elegantly united many facets of the electronic structure/chemical reactivity facts, and allowed for more accurate predictions of behaviour of chemical species. Despite this success of DFT, the knowledge of its basic theorems and generalizations is not widespread among chemists, to the best knowledge of the Author. Even in the university quantum chemistry course this subject is rarely mentioned, with the methodological core usually covering exclusively the traditional Hartree-Fock (HF) molecular orbital theory and its configuration interaction (CI) extensions. Little is known, for example, about the conceptual advantages of the Kohn-Sham orbitals over their HF counterparts, and the physical interpretation of the former. This review article, written in response to a kind invitation of this Journal Editor, attempts to fill this gap. This monographical survey covers the Hohenberg-Kohn theorems and their ensemble extensions due to Mermin, elements of the Kohn-Sham and Kohn-Sham-Mermin theories, and rudiments on the crucial density functional for the exchange-correlation energy. The discussion of the KS approach includes the KS equations for the optimum canonical orbitals and an analysis of the physical significance of the KS molecular orbitals, corresponding to a fictitious system of non-interacting electrons. The general form of the crucial functional for the exchange-correlation energy E(xc)[r] is summarized and the density scaling argument for its Local Density Approximation and the first nonlocal (density gradient) correction is presented. A general form of E(xc)[r] in terms of the exchange-correlation hole is introduced and specific examples of the non-local exchange and correlation functionals are given. Finally, some advantages of the related orbital dependent functionals E(xc)[{fi[r]}] used in the Optimized Effective Potential method are briefly mentioned. An emphasis is also placed upon selected concepts for chemistry. In particular characteristics of the electronic "gas" in open molecular systems, covering the chemical potential (negative electronegativity), Fukui function, and the absolute measures of the chemical hardness (softness), are discussed in a more detail, including their behaviour in the zero temperature limit. It is argued that DFT facilitates a thermodynamical-like description of the polarization and charge-transfer phenomena in molecular systems, e.g., those accompanying interaction between reactants, adsorbate and substrate in heterogeneous catalysis, etc.