Sum rules for generalized electron-pair moments

The existence of an exceptional rigorous sum rule for the second generalized electron-pair moments 〈q2〉a,b, which combines one- and two-electron properties of atoms and molecules described by any exact or approximate wave function, which are apparently independent of each other are discussed. The electronic kinetic energy decomposition into the electron-pair relative and center-of-mass motion contributions was illustrated. Hartree atomic units are utilized throughout.