Hartree-Fock theory is a useful tool for many problems. Results can be systematically improved through an increasingly rigorous choice of basis set (AIMPRO is limited in this respect by overcompleteness problems; if the basis set becomes too large then it becomes difficult for the system to achieve self-consistency). It gives good structures and vibrational modes for small molecules, although tends to underpredict bond lengths with a corresponding overprediction of frequencies.
A major flaw with the method is the lack of electron correlation (leading to zero density of states at the Fermi level for Jellium). This precludes the use of Hartree-Fock theory in problems such as, for example, metallic systems. The difference in correlation between ground and excited states in real systems means that Hartree-Fock greatly overpredicts the width of the band gap.
Hartree-Fock provides the basis for methods covering a wide spectrum of accuracies. At the lower level there are semi-empirical methods such as MINDO/3, MNDO, etc., which are described in more detail below. These attempt to compensate for the lack of correlation through their parameterisation methods, additionally fitting to experimental ionisation energies and/or heats of formation of molecules. At the other end of the scale, many computationally expensive improvements can be utilised to overcome the correlation problem, such as the configuration interaction (CI) method [15], where the wavefunction is constructed from a combination of determinants. These are only really viable for small molecular systems at present.
In addition, the calculation size scales as O(N4), i.e. doubling the system size leads to a 16-fold increase in calculation time. This poor scaling with system size, coupled with the heavy computational cost of Hartree-Fock theory, currently limits it to smaller systems. Nonetheless, Hartree-Fock based calculations (when incorporating the high level corrections such as CI) often provide the benchmarks that other theoretical methods aspire to.