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

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 M-corr[I], their electron-electron repulsion energy W-corr[I], and the cage volume V-corr[I] that characterizes the spatial extent of electron correlation are functionals of I(R). The ratio kappa[I] of I(0)V-corr[I] and M-corr[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. (C) 1999 American Institute of Physics. [S0021-9606(99)31004-7].