Semi-empirical Orbital-Dependent Exchange-Correlation Functionals

5 Semi-empirical Orbital-Dependent Exchange-Correlation Functionals 

Given the complexity of the first-principles implicit correlation functionals of Sect. 2.4, one is automatically led to look for simpler and thus more efficient semi-empirical alternatives. Two functionals of this type have been suggested for use within the 0PM. 

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Two semi-empirical orbital-dependent xc-functionals are reviewed in Sect. 2.5. Both functionals had been in the literature for quite some time before it was realized that they should be understood as imphcit density functionals in the same sense as the exact exchange. The first is the self-interaction corrected (SIC) form of the LDA [22], and the second is the CoUe-Salvetti correlation functional [23]. 

We shall see that the method of Kohn and Sham in density functional theory actually provides a sound theoretical base for this method which has been used Over the years simply as a numerical convenience. The density functional method uses a set of fictional molecular orbitals which do not themselves have any physical interpretation and whose only property is to generate an electron density which is exact. The whole of the experimental calibration procedure is thrown into the generation of a potential (the exchange/correlation potential) which can, in principle, be universal that is, not dependent on the particular molecule under study. The huge number of parameters required in earlier semi-empirical methods (some for every atom) is replaced by choice of a form for this potential and a few universal parameters (up to a dozen). 

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