Electron pair correlation

For these reasons, in the MCSCF method the number of CSFs is usually kept to a small to moderate number (e.g. a few to several thousand) chosen to describe essential correlations (i.e. configuration crossings, near degeneracies, proper dissociation, etc, all of which are often tenned non-dynamicaI correlations) and important dynamical correlations (those electron-pair correlations of angular, radial, left-right, etc nature that are important when low-lying virtual orbitals are present). 

Of course, in the actual computation, one first has to go to all orders to establish the exact Xco, of Eq. (4) from which Eq. (7) follows. Nevertheless, in practice, for atomic and molecular ground states where the shell model holds well and the zero-order reference is a closed-shell, single deferminan-tal HE wavefunction, it remains true that the dominant contribution to the Ecorr comes from the double excitations (electron pair correlations), although for a given state, the exact magnitude of each term of Eq. (4) depends on the computational method and on the function spaces that are used. 

Fig. 5. Structure-skeletal electron pair correlation for closo, nido and arachno boranes...

Bardett R J and Silver D M 1975 Many-body perturbation theory applied to electron pair correlation energies I. Closed-shell first-row diatomic hydrides J. Chem. Phys. 62 3258-68... 

The physical interpretation of terms arising in C Mq Ci in terms of orbital relaxation and electron pair correlation effects has been carried out by several workers. To give some feeling for the physical content of the terms in (P2)ij we... 

The next step in a generalization of the independent electron-pair correlation is to include the interpair correlation contributions as well. The recipe of the general independent electron-pair approximation (lEPA) is hence to calculate independently the correlation-energy contributions Ecorr for any pair of spin orbitals, i. e. the correlation energy accounted for by the wave function... 

For the sake of completeness we can mention some other computational schemes, different from those explained here, that are also based on the idea of electron-pair correlation. There is e.g. the use of the following ansatz for the wave function... 

From the -electron wave function, we may compute what is called the electron pair correlation function FI (ri, l 2)-in short, a pair function defined as ... 

Condon, E. U., On pair correlation in the theory of atomic structure. Rev. Mod. Phys. 40 872 (1968) Nesbet, R. K., Electronic pair correlation in atoms and molecules, Int. J. Quantum Chem. S4 117 (1971). In the 1960 s there was a disagreement between Sin-anoglu and Nesbet about the origins of the lEPA. These two articles present complementary views of the history of the subject and make fascinating reading. 

The results for scattering by atoms are conveniently expressed by the electron density function p(r) and the electron-pair correlation function pXr). Using Dirac s 8 function, p may be written as a sum over all the electrons in the atom... 

The distribution function Diy) for an atom may thus be determined from electron-diffraction data. This was done for argon by Bartell and Brockway in 1953. Bartell and Gavin i pointed out that the inelastic part of the scattering should be sensitive to electron correlation [cf. equation (56)]. Thus it is possible to obtain the electron-pair correlation function, P r), experimentally in favourable cases. The theory was first applied to two-electron systems later the same authors estimated the effect of electron correlation on the total intensity scattered by beryllium. ... 

Electron Pair Correlation Energies. I. Closed-Shell First-Row Diatom Hydrides. 

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