Electron distributions in radicals

Properties and potential applications of novel electron distributions, such as the charge densities associated with singlet and triplet electron pairs, ρ0(r) and ρ1(r), and the distributions of “effectively unpaired” spin-up and spin-down electrons, Δα(r) and Δβ(r), are discussed. Given the total spin S in an N-electron system described with a wave function which is a spin eigenfunction, ρ0(r) and ρ1(r) can be expressed as linear combinations of the charge and spin densities and are independent of the spin projection quantum number M. The proposed definition of the density of effectively unpaired electrons approaches the concept of electron pairing in a more general fashion than the traditional spin density. Distributions Δα(r), Δβ(r), and their sum Δ(r) are particularly suitable for open-shell singlet states and diradicals and can be used to describe the variation of the radicaloid character of a molecule along a reaction path. The discussion is illustrated by calculations on selected singlet and triplet states of the methylene (CH2) radical. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 316–323, 2000