Half-metallicity and spin-contamination of the electronic ground state of graphene nanoribbons and related systems: an impossible compromise?

An analysis using the formalism of crystalline orbitals for extended systems with periodicity in one dimension demonstrates that any antiferromagnetic and half-metallic spin-polarization of the edge states in n-acenes, and more generally in zigzag graphene nanoislands and nanoribbons of finite width, would imply a spin contamination <linear span>S(2)<linear span> that increases proportionally to system size, in sharp and clear contradiction with the implications of Lieb's theorem for compensated bipartite lattices and the expected value for a singlet (S = 0) electronic ground state. Verifications on naphthalene, larger n-acenes (n = 3-10) and rectangular nanographene islands of increasing size, as well as a comparison using unrestricted Hartree-Fock theory along with basis sets of improving quality against various many-body treatments demonstrate altogether that antiferromagnetism and half-metallicity in extended graphene nanoribbons will be quenched by an exact treatment of electron correlation, at the confines of non-relativistic many-body quantum mechanics. Indeed, for singlet states, symmetry-breakings in spin-densities are necessarily the outcome of a too approximate treatment of static and dynamic electron correlation in single-determinantal approaches, such as unrestricted Hartree-Fock or Density Functional Theory. In this context, such as the size-extensive spin-contamination to which it relates, half-metallicity is thus nothing else than a methodological artefact.