Electron correlation methods interelectronic distance

For systems containing three or more electrons very little is so far known about the foundation for the method of correlated wave functions, and research on this problem would be highly desirable. It seems as if one could expect good energy results by means of a wave function being a product of a properly scaled Hartree-Fock function and a correlation factor" containing the interelectronic distances ru (Krisement 1957), but too little is known about the limits of accuracy of such an approach. 

We have already indicated two of the ways in which we may provide for instantaneous electron correlation. One method is to introduce the interelectronic distances r into the wave function (Section 9.4). This method is only practicable for systems with a few electrons. 

In the Hylleraas-CI method, the Hylleraas idea has been exploited when designing a method for larger systems. The electronic wave function is proposed as a linear combination of Slater determinants, and in front of each determinant (1, 2, 3,..., N), we insert, next to the variational coefficient c , correlational factors with some powers v,u,...) of the interelectronic distances between electron m and electron n, etc.) ... 

The term Hyg/Vo S local energy Ei. In determining ( ), it is not necessary to carry out analytic integrations and, since only differentiation of the trial wavefunction is required to evaluate the local energy, the trial wave-function may take any desired functional form. It may even include interelectron distances explicitly. Thus, relatively simple trial functions may incorporate electron correlation effects rather accurately and produce expectation values of the energy well below those of the Hartree-Fock limit. Except in the limit of a large number of terms the VQMC method is not an exact method. 

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