Four electron problem

The prototype system for all four electron problem is the H4 system, discussed in Section n. 

From all the applications we have done in recent years [10-12], we review those that show the essence of our methodology. After introducing the VB formalism, we study the four electrons problem, a cluster of hydrogen, in an unusual limit, in order to address the problem of insulator to metal transition in solid hydrogen under pressure. Then we proceed to the applications to neutral and anionic lithium clusters, which are systems with very delocalized bonds. 

We note that the four electrons problem, a cluster of four hydrogen atoms, is a prototype for testing correlation methods in electronic structure. McWeeny [2] had already addressed this problem in the context of a valence bond formalism and here we tackle the problem in a quite unusual range of intermolecular separations. 

It would appear that for a description of the four electron system it would be necessary to consider the superposition of the three given structures with different localizations of the valency bonds. However, it is still possible to make a further simplification. In the problem of three electrons, three structures also were possible with the bond between a and b and with a free atom c (spin function aj8a—jSaa) with a bond between atoms b and c and a free atom a (spin function aajS—ajSa) with the bond between atoms a and c and a free atom b (spin function aajS—jSaa). But we pointed out that these three functions were not independent, the third being a linear combination of the other two. Let us write down the appropriate functions for the four electron problems describing the states /, II and IIL The space coordinate part of any wave function of four electrons will have the form... 

Wc arc now in a position to set out in its general form the secular equation for the four electron problem. This will take the following form ... 

Many problems involving the electronic states of organic molecules can be dealt with by considering only the optical electrons, especially if they are located in the highest occupied orbital. Thus, in some cases an adequate description can be obtained by solving a two or, if there is a doubly degenerate orbital involved, a four-electron problem. The latter is just more tedious than the former, so in this section some pertinent aspects of the two electron problem will be discussed. 

J. J. C. Muldei Nouv. J. Ghint., 4, 283 (1980). Rotation Around the Double Bond in Ethylene A Four-Electron Problem. 

The possible bond eigenfunctions for the four-electron problem and the relations between them are illustrated graphically in Figure 13 1 (fromi... 

XIll. Resonance and the Structure op Complex Molecules Spin Theory and Bond Eigenfunctions, 232. Evaluation of the Integrals, 240. The Two-Electron Problem, 244. The Four-Electron Problem, 245. The Concept of Resonance, 248. The Resonance Energy of Benzene, 249. The Resonance Energy of Benzene by the Molecular Orbitals Method, 254. 

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