Introduction

In recent years Density Functional Theory (DFT) has become the most popular method in quantum chemistry, accounting for approximately 90% of all calculations today. The reason for this preference is the extreme computational cost required to obtain chemical accuracy with multiple determinant methods. DFT scales with the same order as HF theory -- O(N).

This difference in speed is heightened by the fact that multiple determinant calculations require very large basis sets, with high momentum basis functions, whereas DFT can produce accurate results with relatively small basis sets. This is due to the poor behaviour of the HF wavefunction when the inter-electronic distance becomes very small. The cusp-condition [64,65,66,67] states that the wavefunction should increase linearly when moving away from r₁₂=0. The post-HF methods of section (1.6) try to account for this by introducing terms of r₁₂² and higher. Thus, the convergence of the correlation energy with the momentum in the basis set can be exceedingly slow, of the order of $(l+\frac{1}{2})^{-4}$ [68].

DFT avoids the expense of the more traditional methods, deriving the energy directly from the electron probability density, rather than the molecular wavefunction,thus drastically reducing the dimensionality of the problem.