Analytical and ab initio studies of effective exchange interactions, polyradical character, unpaired electron density, and information entropy in radical clusters ( R ) N : Allyl radical cluster ( N =2–10) and hydrogen radical cluster ( N =50)

Abstract Analytical expressions of total energies, effective exchange integrals, polyradical character, spin density, unpaired electron density, and information entropy are derived for allyl radical dimers and trimers on the basis of the Hubbard model in order to elucidate interrelationships among several broken‐symmetry and symmetry‐adapted approaches to molecular magnetism. Ab initio unrestricted Hartree–Fock and hybrid density functional theory (DFT) calculations of allyl radical dimers to decamers are also carried out for confirmation of characteristics revealed by the analytical investigations. A mesoscopic hydrogen radical cluster with 50 radical sites is studied by the ab initio hybrid DFT methods to elucidate functional behaviors of the above quantities with change of interatomic distance. The potential curves for the lowest and highest spin states of the cluster by these methods are depicted for the purpose. Implications of the present computational results are discussed in relation to size‐consistent spin projection and size effects on effective exchange interactions in mesoscopic radical clusters. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002