Development of approximate spin projection method and its application for elucidation of electronic structures, molecular structures and physical properties of polynuclear metal complexes

Abstract

A broken-symmetry (BS) method is now widely used for systems that involve (quasi) degenerate frontier orbitals because of their lower cost of computations. The BS method splits up-spin and down-spin electrons into two differentspatial orbitals. Within the BS method, therefore, a singlet spin state of the degenerate system is expressed as a spinpolarized state e.g. a singlet diradical. However the spin-polarized wavefunction suffers from a serious problem calleda spin contamination error. An approximate spin projection (AP) method can eliminate the error from the BS solution by assuming the Heisenberg model, and one can obtain molecular energies and its derivatives without the error. In thisaccounts, we illustrate a theoretical background of the BS and AP methods, starting from a bond dissociation of the simplest H₂ molecule. And we also show some examples of its application especially for Cr(II)₂ complex that is a typicalspin-polarized system with a multiple bond.