The freeon theory of magnetism. I. The Heisenberg interaction

The freeon theory of magnetism is a viable alternative to the well-known Heisenberg theory. In particular, the freeon-exchange theory provides a deeper insight into the nature of the magnetic interaction than does the spin-exchange theory. In addition, it avoids the superfluous M_S quantum number in zero-field splitting, the overcounting of spin states, the spin frustration, and the spin paradigm. The freeon-exchange theory employs the algebra of the symmetric group and/or the unitary group in place of the spin algebra. The basis vectors of freeon theory are the Gel'fand states which are uniquely labeled by Gel'fand diagrams; the latter provide both the electron configuration and the spin quantum number. Both the spin and the freeon formulations support the Landé interval rule. In this article, we apply freeon theory to transition-metal dimers, trimers, and tetramers; these are examples of molecular magnets which have applications to microcircuitry. The freeon theory follows the permutation-group principle laid down by Herman Weyl over one-half a century ago. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 287–297, 1997