Computational quantum chemistry for single Heisenberg spin couplings made simple: Just one spin flip required

We highlight a simple strategy for computing the magnetic coupling constants, J, for a complex containing two multiradical centers. On the assumption that the system follows Heisenberg Hamiltonian physics, J is obtained from a spin-flip electronic structure calculation where only a single electron is excited ( and spin-flipped), from the single reference with maximum (S) over cap (z), M, to the M - 1 manifold, regardless of the number of unpaired electrons, 2M, on the radical centers. In an active space picture involving 2M orbitals, only one beta electron is required, together with only one alpha hole. While this observation is extremely simple, the reduction in the number of essential configurations from exponential in M to only linear provides dramatic computational benefits. This (M, M - 1) strategy for evaluating J is an unambiguous, spin-pure, wave function theory counterpart of the various projected broken symmetry density functional theory schemes, and likewise gives explicit energies for each possible spin-state that enable evaluation of properties. The approach is illustrated on five complexes with varying numbers of unpaired electrons, for which one spin-flip calculations are used to compute J. Some implications for further development of spin-flip methods are discussed. (C) 2014 AIP Publishing LLC.