2.6 Summary

The main problem of the Hartree-Fock and DFT methods is the underlying treatment of electron correlation. In the Hartree-Fock method, electron correlations beyond a mean field picture are entirely neglected, whereas in DFT they are included approximately via a functional $E_{XC}[n]$. DFT methods consequently require careful calibration to establish their accuracy (or inaccuracy) on a case by case basis. Both methods provide a relatively inexpensive route to performing computational physics, chemistry and materials science, provided only trends and not highly accurate quantitative predictions are required.

Post Hartree-Fock methods are potentially very accurate, but their poor scaling with system size limits their usefulness, restricting their application to small molecules and excluding most topics in condensed matter.

As will be discussed in chapter 3, Quantum Monte Carlo methods combine favourable scaling with system size with a very accurate treatment of electron correlation. This renders them ideal for correlated studies of large molecules and condensed matter systems when high accuracy is required.

An additional novel and very practical feature of Quantum Monte Carlo methods is that they provide a direct measure of the likely accuracy obtained. This feedback represents a fundamental advance over current density functional and quantum chemical methodology where the accuracy obtained is both unknown and variable. This is clearly advantageous when new systems are investigated, where there is little or no reference data.