An Introduction to Density Functional Theory

Research Institute, North Carolina Supercomputing Center, MCNC, Research Triangle Park, North Carolina 27709 

Density functional theory is equivalent to solving Schrodinger s equation and is, therefore, an exact theory for describing the electronic structure and properties of matter. An important difference between DFT and WFT is the principal quantity of interest. In DFT this quantity is the electron density which, unlike the wavefunction, is an observable. As a result, quantities not readily accessible through WFT are conveniently defined. The computational 

Reviews in Computational Chemistry, Volume 7 Kenny B. Lipkowitz and Donald B. Boyd, Editors VCH Publishers, Inc. New York, 1996 

Considerable advances in the formal development of DFT as well as in its practical application have been made these last few years. In this chapter, we will not attempt to provide a comprehensive review of the subject, but rather provide an introduction to DFT, covering many of the important attributes that pertain to chemical problems. In the next section, we provide some of the basic calculus associated with functionals. Then some early models used in DFT are presented, followed by a formal presentation of DFT and the formalism used in practical applications. Finally, in the last section, we discuss the ability of DFT to compete with WFT in electronic structure calculations. A more detailed and comprehensive discussion of DFT can be found in the 1989 book by Parr and Yang. In what follows, we assume the Born-Oppenheimer nonrelativistic approximation and use atomic units throughout. Since the nuclei are assumed to be fixed in space, we will not explicitly show this dependence in equations and variables. 

---

Libero J. Bartolotti and Ken Flurchick, An Introduction to Density Functional Theory. 

Bartolotti LJ, Flurchick K. An introduction to density functional theory. In Lipkowitz KB, Boyd DB, eds. Reviews in Computational Chemistry. Vol. 7. New York VCH, 1995 187-216. 

J. M. Seminario, An Introduction to Density Functional Theory in Chemistry, in Modem Density Functional Theory a Tool for Chemistry, edited by J. M. Seminario and P. Politzer (Elsevier Science, Amsterdam, 1995). 

W. Kohn and L. H. Sham, Phys. Rev. A, 140, 1133 (1965). Self-Consistent Equations Including Exchange and Correlation Effects. M. Levy, Proc. Natl. Acad. Sci. U.S.A., 76, 6062 (1979). Universal Variational Functionals of Electron Densities, First-Order Density Matrices, and Natural Spin-Orbitals and Solution of the v-Representability Problem. R. G. Parr and W. Yang, Eds., Density Functional Theory of Atoms and Molecules, Oxford University Press, New York, 1988. J. Labanowski and J. Andzelm, Eds., Density Functional Methods in Chemistry, Springer Verlag, Heidelberg, 1991. L.J. Bartolotti and K. Flurchick, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1995, Vol. 7, pp. 187-216. An Introduction to Density Functional Theory. 

---