Electron-correlation repulsion

For the most part, however, it is fair to say that within a given series of compounds the behavior of group III adducts can be explained in classical terms of inductive electron release, resonance, and simple steric hindrance, e.g. F-strain. The same may be said generally for the interpretation of pKa s in aqueous solution and it is the interesting exceptions to such simple interpretations that have required the welter of factors such as solvation, B-strain, I-strain and electron-correlation repulsion described in the pages above. We may well imagine that as we move from one element to another in the periodic table new influences will be felt and that even this list of effects will be inadequate when the central atom is varied. 

Note added in proof For some time it has seemed likely that the basicity order for carbanions is primary > secondary > tertiary and this is supported by a very recent study (303a). This is easily interpreted in terms of inductive effects and/or the electron correlation repulsion approach. 

The electron correlation repulsion theory can be used to explain the configurations of many molecules. We have also used it to explain base strengths in cyclic compounds and the relationships of group Va, Via, and Vila bases. A. number of experiments come to mind to test its application to the latter problem, such as observing the effect of protonation on rotational barriers. It remains to be seen whether the facts will support this simple notion. 

One of the limitations of HF calculations is that they do not include electron correlation. This means that HF takes into account the average affect of electron repulsion, but not the explicit electron-electron interaction. Within HF theory the probability of finding an electron at some location around an atom is determined by the distance from the nucleus but not the distance to the other electrons as shown in Figure 3.1. This is not physically true, but it is the consequence of the central field approximation, which defines the HF method. 

The advantage of using electron density is that the integrals for Coulomb repulsion need be done only over the electron density, which is a three-dimensional function, thus scaling as. Furthermore, at least some electron correlation can be included in the calculation. This results in faster calculations than FIF calculations (which scale as and computations that are a bit more accurate as well. The better DFT functionals give results with an accuracy similar to that of an MP2 calculation. 

DFT methods compute electron correlation via general functionals of the electron density (see Appendix A for details). DFT functionals partition the electronic energy into several components which are computed separately the kinetic energy, the electron-nuclear interaction, the Coulomb repulsion, and an exchange-correlation term accounting for the remainder of the electron-electron interaction (which is itself... 

The term ( iv X.o) in Equation 32 signifies the two-electron repulsion integrals. Under the Hartree-Fock treatment, each electron sees all of the other electrons as an average distribution there is no instantaneous electron-electron interaction included. Higher level methods attempt to remedy this neglect of electron correlation in various ways, as we shall see. 

The correlation of electron motion in molecular systems is responsible for many important effects, but its theoretical treatment has proved to be very difficult. Thus many quantum valence calculations use wave functions which are adjusted to optimize kinetic energy effects and the potential energy of interaction of nuclei and electrons but which do not adequately allow for electron correlation and hence yield excessive electron repulsion energy. This problem may be subdivided into cases of overlapping and nonoverlapping electron distributions. Both are very important but we shall concern ourselves here with only the nonoverlapping case. 

It should be noted that the above conclusions have been reached on strictly electrostatic grounds a spin property has not been invoked for the two electrons. From the variation of i/i along the box it can be shown that the singlet state is of higher energy than the triplet because the two electrons are more crowded together for (S-state) than for (T-state). Thus there is less interelectronic repulsion m the T-state. The quantity 2J j. is a measure of the effect of electron correlation which reduces the repulsive force between the two electron (Fermi correlation energy). 

Next, let us explore the consequences of the charge of the electrons on the pair density. Here it is the electrostatic repulsion, which manifests itself through the l/r12 term in the Hamiltonian, which prevents the electrons from coming too close to each other. This effect is of course independent of the spin. Usually it is this effect which is called simply electron correlation and in Section 1.4 we have made use of this convention. If we want to make the distinction from the Fermi correlation, the electrostatic effects are known under the label Coulomb correlation. 

Two different correlation effects can be distinguished. The first one, called dynamical electron correlation, comes from the fact that in the Hartree-Fock approximation the instantaneous electron repulsion is not taken into account. The nondynamical electron correlation arises when several electron configurations are nearly degenerate and are strongly mixed in the wave function. 

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