LINEAR SCALING IN MANY-BODY SYSTEMS

Chemistry is primarily concerned not with the properties of single molecules but with periodic trends, homologous series, functional groups, and the like. 

In chemistry, the systematization of the properties of a series of molecules is just as important as the determination of all of the properties of one particular species. Theoretically, therefore, it is important that any method which is applied to the problem of molecular electronic structure leads to expressions for expectation values which are directly proportional to the number of electrons in the system being studied. Meaningful comparisons of atoms and molecules of different sizes are then possible. [1,2] 

In his Nobel Lecture, the late Professor Sir John Pople, frs, discussed size-consistency in limited configuration interaction studies (ciD and ciSD)  

In this chapter, we consider the linear scaling of the energy and other expectation values for many-body systems in atomic and molecular physics and quantum 

The essential property of any true many-body theory of electronic structure is a linear scaling of the energy components, E, with the number of electrons, N, in the system. 

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