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Exact Exchange

We will now describe the exact exchange (EXX) functional [77,78,79]. A common misconception amongst non-specialists is that HF and EXX are the same thing. It is true, of course, that both functionals treat exchange ``exactly'' in the sense that the exchange energy is given in terms of the orbitals by Equation (3.3). The difference arises from the fact the orbitals themselves are different - in EXX the orbitals are eigenstates of a Hamiltonian with a local potential, while in HF they are eigenstates of a Hamiltonian with a non-local potential. This leads to very different results, notably in the calculation of band structures, where, as we will see in Chapter 4, HF performs disastrously while EXX performs very well indeed [79]. EXX also includes treatment of correlation in the style of the LDA, which is not the case in standard HF. Although LDA correlation can be added to HF, this does not improve the band structure problem, the reason for which will become clear in the discussion in Section 5.3.


Subsections
next up previous contents
Next: Definition of the Exact Up: Theory of Non-Local Functionals Previous: Efficient Procedure for HF   Contents
Stewart Clark 2012-08-09