Determination of spin Hamiltonians from projected single reference configuration interaction calculations. I. Spin 1/2 systems

The most reliable wave-function based treatments of magnetic systems usually start from a complete active space self-consistent field calculation of the magnetic electrons in the magnetic orbitals, followed by extensive and expensive configuration interaction (CI) calculations. This second step, which introduces crucial spin polarization and dynamic correlation effects, is necessary to reach reliable values of the magnetic coupling constants. The computational cost of these approaches increases exponentially with the number of unpaired electrons. The single-determinantal unrestricted density functional Kohn Sham calculations are computationally much simpler, and may provide reasonable estimates of these quantities, but their results are strongly dependent on the chosen exchange-correlation potential. The present work, which may be seen as an ab initio transcription of the unrestricted density functional theory technique, returns to the perturbative definition of the Heisenberg Hamiltonian as an effective Hamiltonian, and proposes a direct estimate of its diagonal energies through single reference CI calculations. The differences between these diagonal terms actually determine the entire Heisenberg Hamiltonian. The reference determinants must be vectors of the model space and the components on the other vectors of the model space are cancelled along the iterative process. The method is successfully tested on a series of bicentric and multicentric spin systems. The projected single reference difference dedicated Cl treatment is both accurate and of moderate cost. It opens the way to parameter-free calculations of large spin assemblies. (C) 2010 American Institute of Physics. [doi:10.1063/1.3458642]