Interelectronic repulsion

If we compare the calculated total ionization potential, IP = 4.00 hartiees, with the experimental value, IP = 2.904 hartiees, the result is quite poor. The magnitude of the disaster is even more obvious if we subtract the known second ionization potential, IP2 = 2.00, from the total IP to find t c first ionization potential, IPi. The calculated value of IP2, the second step in reaction (8-21) is IP2 = Z /2 = 2.00, which is an exact result because the second ionization is a one-election problem. For the first step in reaction (8-21), IPi (calculated) = 2.00 and IPi(experimental) = 2.904 — 2.000 =. 904 hartiees, so the calculation is more than 100% in error. Clearly, we cannot ignore interelectronic repulsion. 

Cl calculations can be used to improve the quality of the wave-function and state energies. Self-consistent field (SCF) level calculations are based on the one-electron model, wherein each electron moves in the average field created by the other n-1 electrons in the molecule. Actually, electrons interact instantaneously and therefore have a natural tendency to avoid each other beyond the requirements of the Exclusion Principle. This correlation results in a lower average interelectronic repulsion and thus a lower state energy. The difference between electronic energies calculated at the SCF level versus the exact nonrelativistic energies is the correlation energy. 

Assignment of (he observed bands to these transitions, provides an estimate of B, the Racah interelectron repulsion parameter. Its value (Table 23.6) is invariably below that of the fiee-ion (1030cm ) because (he expansion of d-electron charge on complexation reduces the inteielectronic repulsions. 

Craig, D. P., Proc. Roy. Soc. [London) A202, 498, Electronic levels in simple conjugated systems. I. Configuration interaction in cyclobutadiene. (ii) All the interelectron repulsion integrals, three- and four-centered atomic integrals, are included. 

Brickstock, A., and Pople, J. A., Phil. Mag. 44, 697, The spatial correlation of electrons in atoms and molecules. III. The influence of spin and antisymmetry on the correlation of electrons/ A discussion is made of the refinement needed, if the interelectronic repulsion is taken into account beyond the single determinant, b. 

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. 

Finally, we must remember that just as a d-d spectrum is not properly described at the strong-field limit - that is, without recognition of interelectron repulsion and the Coulomb operator - neither is a full account of the energies or number of charge-transfer bands provided by the present discussion. Just as a configuration... 

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