Topology of electron-electron interactions in atoms and molecules. II. The correlation cage

Abstract

The concept of the correlation cage provides new insights into electron–electron interactions in atoms and molecules. The cage constitutes the domain in the space of interelectron distance vectors R within which correlation effects are substantial. Its shape and size are entirely determined by the topological properties of the electron intracule density I(R), thus avoiding any references to ill-defined “uncorrelated” quantities. Integration of observables related to I(R) over the correlation cage affords quantitative measures of electron correlation. The number of strongly correlated electron pairs Mcorr[I], their electron–electron repulsion energy Wcorr[I], and the cage volume Vcorr[I] that characterizes the spatial extent of electron correlation are functionals of I(R). The ratio κ[I] of I(0)Vcorr[I] and Mcorr[I], which measures the strength of short-range correlation effects, is small for systems such as H− and closer to one for those with weaker correlation effects.