Post-HF calculations electron correlation

Electron correlation is the phenomenon of the motion of pairs of electrons in atoms or molecules being connected ( correlated ) [56]. The purpose of post-HF calculations is to treat such correlated motion better than does the HF method. In the HF treatment, electron-electron repulsion is handled by having each electron move in a smeared-out, average electrostatic field due to all the other electrons (sections 5.2.3.2 and 5.2.3.6b), and the probability that an electron will have a particular set of spatial coordinates at some moment is independent of the coordinates of the other electrons at that moment. In reality, however, each electron at any moment moves under the influence of the repulsion, not of an average electron cloud, but rather of individual electrons (in fact current physics regards electrons as point particles - with wave properties of course). The consequence of this is that the motion of an electron in a real atom or molecule is more complicated than that for an electron moving in a smeared-out field [57] and the electrons are thus better able to avoid one another. Because of this enhanced (compared to the HF treatment) standoffishness, electron-electron repulsion is really smaller than 

Bridged the classicai Ion is not a stationary point at this level 

Hartree-Fock calculations are sometimes said to ignore, or at least neglect, electron correlation. Actually, the HF method allows for ra/ne electron correlation two electrons of the same spin can t be in the same place at the same time because their spatial and 

A measure of the extent to which any particular ab initio calculation does not deal perfectly with electron correlation is the correlation energy. In a canonical exposition [59] Lowdin defined correlation energy thus The correlation energy for a certain state with respect to a specified Hamiltonian is the difference between the exact eigenvalue ofthe Hamiltonian and its expectation value in the HF approximation for the state under consideration. In other words, the correlation energy for a calculation on some molecule or atom is the energy calculated by some perfect quantum mechanical procedure, 

Basis No. basis functions HF energy Method Energy 

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