The singular value decomposition of the n-particle excitation operator as determined by coupled cluster or perturbation theory is used to extract the dominant and interesting electron-electron correlations from complex molecular wave functions. As an example of the very general formalism, the decomposition of the T-2 operator obtained from coupled cluster doubles calculations is used to analyze the strength and character of pair correlations in a variety of molecules with interesting electronic structure. The magnitude of the largest singular value(s) determines the strength of the correlation(s), and the corresponding right- and left-hand singular vectors characterize the physical and spatial nature of the correlations. The primary advantage of this tool over natural orbital analysis is that it provides direct associations between the occupied and virtual geminals involved in the correlations. (C) 2004 American Institute of Physics.