Multi-electron calculations

Empedocles argues that (dKeldR) is relative insensitive to crudities in the wave function. In addition, is a one-electron quantity, a thing which simplifies multi-electron calculations considerably. Further, it must be pointed out that Eq. (5.37) (see Eq. 4.27) and Eq. (5.41) (see Eq. 4.28)... 

In the following, we shall demonstrate techniques for calculating the electronic potential energy terms up to the second order. For simplicity, we shall study the case of H2 molecule, the simplest multi-electron diatomic molecule. 

When multi-electron atoms are combined to form a chemical bond they do not utilize all of their electrons. In general, one can separate the electrons of a given atom into inner-shell core electrons and the valence electrons which are available for chemical bonding. For example, the carbon atom has six electrons, two occupy the inner Is orbital, while the remaining four occupy the 2s and three 2p orbitals. These four can participate in the formation of chemical bonds. It is common practice in semi-empirical quantum mechanics to consider only the outer valence electrons and orbitals in the calculations and to replace the inner electrons + nuclear core with a screened nuclear charge. Thus, for carbon, we would only consider the 2s and 2p orbitals and the four electrons that occupy them and the +6 nuclear charge would be replaced with a +4 screened nuclear charge. 

Nevertheless, the one-electron approach does have its deHciencies, and we believe that a major theoretical effort must now be devoted to improving on it. This is not only in order to obtain better quantitative results but, perhaps more importantly, to develop a framework which can encompass all types of charge-transfer processes, including Auger and quasi-resonant ones. To do so is likely to require the use of many-electron multi-configurational wavefunctions. There have been some attempts along these lines and we have indicated, in detail, how such a theory might be developed. The few many-electron calculations which have been made do differ qualitatively from the one-electron results for the same systems and, clearly, further calculations on other systems are required. 

Electron correlation is inherently a multi-electron phenomenon, and we believe that the retention of explicit two-electron information in the Wigner intracule lends itself to its description (i). It has been well established that electron correlation is related to the inter-electronic distance, but it has also been suggested (4) that the relative momentum of two electrons should be considered which led us to suggest that the Hartree-Fock (HF) Wigner intracule contains information which can yield the electron correlation energy. The calculation of this correlation energy, like HF, formally scales as N. ... 

Let us describe the key moments of the new, ah initio approach to relativistic calculation of the spectra for multi-electron superheavy ions with an account of relativistic, correlation, nuclear, radiative effects. 

The evaluation of the quantitative aspects of the splitting involves calculations which become quite involved for the terms of higher L value from multi-electron configurations. We only present the results for the ground terms of the d configurations. The splitting patterns of these are set out in Figure 9. 

For further accurate calculation, the many-electron effects like the multiplet structure should be taken into account. Although this type of calculation is feasible with the first-principles DV multi-electron method any details will not be described here. 

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