Hartree-Fock theory, total energy computations

The density functional theory (DFT) [32] represents the major alternative to methods based on the Hartree-Fock formalism. In DFT, the focus is not in the wavefunction, but in the electron density. The total energy of an n-electron system can in all generality be expressed as a summation of four terms (equation 4). The first three terms, making reference to the noninteracting kinetic energy, the electron-nucleus Coulomb attraction and the electron-electron Coulomb repulsion, can be computed in a straightforward way. The practical problem of this method is the calculation of the fourth term Exc, the exchange-correlation term, for which the exact expression is not known. 

A classic illustration of the quality of a calculation is provided considering the effect of the basis set of say, a Hartree-Fock (HF) calculation. (See Sect. 3 for further discussion of the HF method). For MO schemes like HF theory, the variational principle states that the lower the computed total energy, the better the result [1]. The energy can be lowered by increasing the basis set size and so large basis set calculations are often described as good quality. However, this need not imply that experiment is also well reproduced. If the basic assumptions of the HF approximation are inappropriate, then it may not be possible to predict experimental data reliably, irrespective of the basis set size. As will be seen later, this is often the case for HF calculations on TM systems. 

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