On the inner and outer radial density functions

Abstract

Starting from the two-electron radial density D2(r1,r2), a generalized partitioning of the one-electron radial density function D(r) into two component densities Da(r) and Db(r) is discussed for many-electron systems. The literature partitioning (Koga and Matsuyama Theor Chem Acc 115:59, 2006) of D(r) into the inner D (r) radial densities is shown to minimize the average variance \((\sigma ^{2}_{a} + \sigma ^{2}_{b})/2\) of the two component density functions Da(r) and Db(r). It is also found that the average radial separation halved, \( \langle|r_{1} - r_{2}|\rangle /2\), constitutes a lower bound to the standard deviation σ of D(r).