  The electron-hole correlation length serves as an intrinsic length scale for
analyzing excitonic interactions in semiconductor nanoparticles. In this work,
the derivation of electron-hole correlation length using the two-particle
reduced density is presented. The correlation length was obtained by first
calculating the electron-hole cumulant from the pair density,and then
transforming the cumulant into intracular coordinates, and finally then
imposing exact sum-rule conditions on the radial integral of the cumulant. The
excitonic wave function for the calculation was obtained variationally using
the electron-hole explicitly correlated Hartree-Fock method. As a consequence,
both the pair density and the cumulant were explicit functions of the
electron-hole separation distance. The use of explicitly correlated wave
function and the integral sum-rule condition are the two key features of this
derivation. The method was applied to a series of CdSe quantum dots with
diameters 1-20 nm and the effect of dot size on the correlation length was
analyzed.
