Correlation Coefficients for Electronic Wave Functions

Abstract

Electron correlation in atoms and molecules can be analyzed in terms of correlation coefficients similar to those used in probability theory and mathematical statistics. Different correlation coefficients can be defined for angular, radial, and momentum correlation in atoms and for axial (left-right), equatorial, and radial (in-out) correlation in molecules. The correlation coefficients are closely related to certain coefficients of the so-called natural expansion of the wave function. Nonvanishing correlation coefficients are obtained for the Fermi correlation in the independent-particle model as well as for electron correlation proper. Numerical examples show that the correlation coefficients for atoms are of the order of -0.05, suggesting that the correlation is usually small and negative, as compared with ±1 for "perfect" correlation. However, positive correlation coefficients may occur, in particular for excited states. Correlation in supersystems consisting of two nonoverlapping systems at large distances, and the distinction between interorbital and intraorbital correlation, are also discussed.