Interelectronic repulsion effect

These SCF MOs incorporate average interelectronic repulsion effects, but do not include instantaneous electron correlation, which is the tendency for electrons to stay at any time as far removed as possible from each other. Without this correlation, electrons get in each other s way to a greater extent than they should. This is the reason why SCF calculations give energies, especially transition energies, which are much too high. 

Seen from the point of view of quantum chemistry, this model divides the interelectronic repulsion effects into two categories the intra-atomic effects which are approximated by an analytic function corresponding to a smoothly varying valence state energy as function of ionicity, and interatomic effects which are represented by the Madelung potential valid for spherically symmetric, non-overlapping ions. 

This is probably not a good value for carbonium ions (or carbanions) because cf nonself-consistent fields and uncertainties with respect to the overall interelectronic repulsion effects. 

Brickstock, A., and Pople, J. A., Phil. Mag. 44, 705, The spatial correlation of electrons in atoms and molecules. IV. The correlation of electrons on a spherical surface." Two examples—four electrons of the same spin and eight paired electrons—have been studied to compare the effects of the exclusion principle and the interelectronic repulsion. 

The nephelauxetic effect calculation and accuracy of the interelectronic repulsion parameters /, cubic high spin d1, d3, d7 and d systems. E. Konig, Struct. Bonding (Berlin), 1971, 9, 175-212 (64). 

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). 

The approach we have adopted for the d configuration began from the so-called strong-field limit. This is to be contrasted to the weak-field scheme that we describe in Section 3.7. In the strong-field approach, we consider the crystal-field splitting of the d orbitals first, and then recognize the effects of interelectron repulsion. The opposite order is adopted in the weak-field scheme. Before studying this alternative approach, however, we must review a little of the theory of free-ion spectroscopy... 

We note that three spin-allowed electronic transitions should be observed in the d-d spectrum in each case. We have, thus, arrived at the same point established in Section 3.5. This time, however, we have used the so-called weak-field approach. Recall that the adjectives strong-field and weak-field refer to the magnitude of the crystal-field effect compared with the interelectron repulsion energies represented by the Coulomb term in the crystal-field Hamiltonian,... 

Again, we restrict discussion to spin-allowed transitions here. In general, of course, crystal field effects compete with interelectron repulsion for all d" configurations, exceptfor n = 1 or 9. 

Konig E (1971) The Nephelauxelic Effect. Calculation and Accuracy of the Interelectronic Repulsion Parameters I. Cubic High-Spin d2, d, d and dg Systems. 9 175-212 Kopf H, see Hopf-Maier P (1988) 70 103-185... 

Figure 1.1 Effect of interelectronic repulsion, spin-orbit coupling and magnetic field on the energy levels arising from a given 4fn configuration for a free-ion Ln3+. The magnetic field effect is estimated assuming a 1 T field.

In simple crystal field theory, the electronic transitions are considered to be occurring between the two groups of d orbitals of different energy. We have already alluded to the fact that when more than one electron is present in the d orbitals, it is necessary to take into account the spin-orbit coupling of the electrons. In ligand field theory, these effects are taken into account, as are the parameters that represent interelectronic repulsion. In fact, the next chapter will deal extensively with these factors. 

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