Statistical angular correlation coefficients and second electron-pair moments for atoms

Abstract

Statistical correlation coefficients ͓ f ͔ introduced by Kutzelnigg et al. ͓Phys. Rev. 172, 49 ͑1968͔͒ provide overall measures of the difference between the electron-pair density and the product of single-electron densities, where f ϭ f (r) is a probe function. It is shown that the angular correlation coefficient ͓r͔, a particular case of ͓ f ͔ for f (r)ϭr, is simply expressible in terms of the generalized electron-pair moments ͗q 2 ͘ (a,b) with two real-valued parameters a and b. Especially, the relation for aϭbϭ1 means that ͓r͔ is nothing but the difference between the center-of-mass motion and relative motion contributions in the second electron-pair moments. Conversely, the electron-pair moments ͗q 2 ͘ (a,b) are obtained from the single-electron moment ͚͗ i r i 2 ͘ and the correlation coefficient ͓r͔. The same is also true in momentum space.

Electron-pair radial sum and difference moments in atoms

“…It is also found that the statistical angular correlation coefficient [19][20][21][22] s½r is bounded as À hs 2 i À ht 2 i hs 2 i þ ht 2 i 6 s½r 6 þ…”