MANY-BODY THEORIES FOR ATOMS AND MOLECULES

In the first section of this chapter, we emphasized the importance of linear scaling with the number of electrons in the system when developing approximate descriptions of many-body systems. We showed that both the exact solutions of the many-electron 

Schrodinger equation and the solutions supported by an independent electron model, scale linearly with electron number. Approximate treatments of electron correlation effects may not necessarily scale linearly with electron number. Approximations which display such a linear scaling are termed many-body methods. In the previous section, we described the many-body perturbation theory which is the basic ingredient of all many-body theories. It provided a fundamental tool for both the synthesis and the analysis of many-body methods. In this section, we consider some many-body theories of atomic and molecular structure and some theories which contain unphysical terms which scale nonlinearly with electron number. 

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