ABSTRACT
The introduction of efficient and capable versions of density functional theory (DFT) in the 1990s has altered computational chemistry profoundly. It is fair to say that computational study of medium-sized organometallic systems and rather large organic systems is now dominated by density functional methods. The popular B3LYP method has usually proved comparable to MP2 calculations in quality of characterization of structures and energetics, and by good fortune produces harmonic vibrational frequencies closely comparable with observed vibrational absorptions. DFT often is competitive with far more demanding coupled cluster methods. Density functional methods rest on the assertion that the electron density
distribution is sufficient to define exactly the ground state of a system of electrons and nuclei. Wave functions, our focus to this point, play no necessary role in the description of molecular systems according to this point of view. The object of investigation is the ‘‘functional’’ of the density which actually accomplished the specification of the exact energy. Density functional theory has a sound basis in the Hohenberg-Kohn
theorem [1,2] and its refinement by Levy [3] which guarantees that there is some definite link between the density and the exact ground state energy. The development of DFT is the story of the invention of functionals which contain the physics of electron exchange-correlation. There is no systematic way to improve exchange-correlation functionals such as is provided in wave function-based electronic stricture theory by the variation method. Functionals can be chosen to obey certain proved constraints on the exact functionals, to capture the behavior of fully understood limiting cases such as the homogeneous electron gas, and (by the incorporation of disposable parameters) to represent faithfully collections of well-established experimental data. This last requirement, so central to the success of the methods in applications, is not generally compatible with such desirable features as simplicity of mathematical form or computational efficiency. In this chapter, we wish to provide some of the historical background
which laid the groundwork to the modern implementations of DFT, to
describe some of the strategems which lead to functionals capable of very accurate estimates of energy, to provide some guidance on which functionals are effective choices for particular tasks, and to describe what we might expect as the field advances. We are indebted to Peter Gill’s [4] survey of the early days of density functional theory and the unified view he gives of electronic structure theories which are orbital-based, density-based, and mixtures of the two. A useful and compact guide to the past 15 years of development is provided by Koch and Holthausen’s book [5], a very accessible guide to the performance of some of the most popular functionals. We will draw on these sources and augment them. Additional information is found, in the guide to GAUSSIAN-by Foresman and Frisch [6], and in the review by Perdew and Schmidt [7]. More recent advances are discussed by Jensen [8]. A second purpose of this chapter is to survey the conceptual and practical
challenges and current preoccupations in this rapidly developing field of research. One way to organize this survey has been provided by Perdew’s fanciful image of a hierarchy of DFT formulations leading from earth (Hartree-Fock theory) to heaven (chemical accuracy).
