The density of electron-spin angular momentum (erg-sec/cm3) at a point x, y, z in a paramagnetic molecule is ℏ Szρ(x, y, z), where Sz is the z component of the total electron spin angular momentum in units of ℏ. If the exact wave function for the molecule Ψ is built up from one-electron basis functions ψi, then the normalized spin density function ρ(x, y, z) can be expressed in terms of the ψi and the spin density matrix ρijρ(x,y,z)= ∑ ijρijψj*ψi.If the ψi are molecular orbitals, then ρij is the molecular orbital spin density matrix; if the ψi are atomic orbitals, then ρij is an atomic orbital spin density matrix. The equation of conservation of spin is Tr(Sρ)=1 where S is the non-orthogonality matrix, Sij=〈ψi|ψj〉. The elements of the spin density matrices are sensitive to overlap and electron correlation effects. This is illustrated by calculations of the spin density matrices of the ethylene positive ion radical, and of the allyl radical. The spin density matrix for the latter molecule is calculated using (a) the simple molecular orbital approximation, (b) the simple valence bond approximation, and (c) the complete π-electron interaction configurational treatment given by Chalvet and Daudel. It is shown that the general connection between σ-proton hyperfine splittings aN and the π-electron atomic orbital spin density matrix ρNN′, involves a (hyperfine interaction)-(exchange interaction) matrix QN′N″″N such that aN=Tr(QNρ).However, for practical calculations, observed hyperfine splittings may be used to estimate the diagonal elements of the spin density matrix, aN≈QρNN,where Q has the semiempirical value of —63 Mc or —23 gauss