Yes, you can relate Mulliken spin density to the odd electron population on atomic sites in a molecule. When using the Unrestricted Hartree-Fock (UHF) method, you obtain separate wavefunctions for the alpha (↑) and beta (↓) spins, which allows you to calculate the spin density at each atomic site. The spin density is determined by the difference between the populations of the alpha and beta electrons at each atom, given by the formula:

\[

\rho_{\text{spin}}(i) = n_{\alpha}(i) - n_{\beta}(i)

\]

where \(n_{\alpha}(i)\) and \(n_{\beta}(i)\) are the Mulliken populations of the alpha and beta electrons at atomic site \(i\). The odd electron population, particularly the unpaired electrons that contribute to a radical species, can also be derived from these spin densities, specifically from the sites that exhibit a non-zero spin density, indicating the presence of unpaired electrons.

Thus, you can directly connect the Mulliken spin density to the odd electron population by analyzing the spin density values: if an atom has a significant spin density, it suggests that it contributes to the odd electron population, which may reflect the reactivity or magnetic properties of the molecule. To quantify the odd electron population at each site, you can sum the contributions of the unpaired electrons (from the alpha or beta populations) based on their respective spin densities. In this way, the analysis of spin density can provide insights into the localization and distribution of odd electrons across atomic sites in a molecule.