Density functional theory (DFT) is a method that addresses the computational expense of the electron-electron repulsion. The large number of Coulomb and exchange integrals is inherent to Hartree-Fock theory. The cost of computation increases as N4 where N is the number of basis functions. DFT started out as an alternative method to the calculation of electron-electron interactions using an electron gas. These methods were not useful until the 1960s when the Hohenberg-Kohn theorems were proposed. The first theorem suggests a one-to-one correspondence between the nuclear positions and the density. This is known as the external potential term in the hamiltonian. The second theorem shows that DFT can operate using a variational principle. Beyond the H-K theorems s breakthrough was made in 1965 when the idea of calculating the density using Kohhn-Sham wave functions. This approach solves a major problem for DFT. On the one hand it makes DFT more like the Hartree-Fock theory in the sense that one first calculates molecular orbitals by obtaining molecular orbital coefficients. There is also a Self-concisent field (SCF) principle in operation for DFT theory.
DFT Applications
DFT methods have a wide range of applications in part because of the emphasis on electron density. The presentation discusses applicationa that can be compared to experiments. The vibrational Stark effect is an application of an electric field to vibrational spectra. The calculation of these effects involves both mechanical effects and anharmonic coupling. As second area for investigation is the electric field application to UV-visible spectra. This is known as electrochromism. One can compare these effects to solvation effects, which arise because of solvent electric fields. These are known as solvatochromism. A third example given in the presentation is vibrational spectroscopy, which includes vibrational and infrared spectroscopy.
