Traditionally theories of the electronic structure of matter have used approximations to the many-electron Schroedinger wave-function Ψ. These theories have been very successful for small molecules and clusters but encounter a fundamental problem where the number of atoms Na becomes large: The complexity of Ψ grows exponentially in Na, effectively representing an insurmountable wall when Na exceeds a number of order of 10.

More recently, Hohenberg, Kohn and Sham have shown that the density distribution of the electrons in the groundstate, n(r), in principle determines all properties of the system. From this they developed a density-based theory of electronic structure called Density Functional Theory (DFT). This theory offers a complementary point of view Ψ-based theories and has the practically important capability of treating much larger systems, up to Na = 0(10³).

The two approaches will be compared and recent applications of DFT will be described.