Origin of the Correlation Energy

Within the framework of the SCF-MO approach, the probability density of finding simultaneously two electrons with different spin in a certain space is given simply by a product of probability densities of the individual electrons. This independence of electrons with different spin is, however, physically unrealistic, because the in the Hamiltonian imposes a certain constraint, i.e,a certain correlation on the motion of all electrons in the system. Disregarding the electron correlation brings about the energy difference between the exact and SCF solutions which is called the correlation energy (Fig. 4.1). Here by the exact solution we imply the lowest energy attainable with the Hamiltonian (1,1) by a method which furnishes the 

This chapter is based partly on the reviews of I. Hubac with one of the authors237,238  

Nevertheless we shall see in the following section that the situation is not so hopeless as it might appear. 

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