Correlation energy definition

Exchange-correlation energy definition, interpretation and exact properties... 

According to Eq. 11.67, the correlation energy is simply defined as the difference between the exact energy and the energy of the Hartree-Fock approximation. Let us repeat this definition in a more precise form ... 

The use of the UHF method as the standard for the independent electron model also rationalises the definition of correlation energy (9). 

The definition of the one-body, two-body, three-body and four-body correlation energy terms at several levels of correlation, respectively, as follows ... 

Two key pieces of theoretical data are required to obtain an empirical estimate of the correlation energy from the experimental data collected in the preceding section the total molecular Hartree-Fock energy and the relativistic corrections . It is implicit in the definition of the correlation energy presented in Eq. (1) that the total electronic energy ofa given molecule, Ef, may be divided into three constituent parts,... 

The answer is yes, in a very general way, as has been discussed before [62,63]. Consider any parameter in the external potential, called y. For definiteness, we choose the internuclear separation in a diatomic molecule. Then the exchange-correlation energy depends parametrically on this quantity. Now imagine making an infinitesimal change in y. The differential change in is... 

Let us turn to the electron correlation energy. According to its definition... 

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