Analysis of optical absorption spectra of transition metal cluster ions by the spin-polarized DV-Xα method

Optical absorption spectra of cobalt cluster ions, Co⁺_n, and vanadium cluster ions, V⁺_n, were analyzed by a theoretical calculation based on the spin-polarized DV-Xα method, and their electronic and geometric structures were obtained. Relative absorption cross section associated with each electronic transition was calculated; the calculation enables a qualitative comparison of calculated spectrum with a measured one not only in its transition energy but also in its intensity profile. This analysis shows that Co⁺₄, Co⁺₃, and V⁺₄ have, respectively, a tetrahedral structure with a bond distance of 2.00 Å, an equilateral triangle with a bond distance of 2.30 Å, and a distorted tetrahedral structure with five bonds having a distance of 2.34 Å and one of 2.89 Å. The differences in the population between majority and minority spins (spin-difference) evaluated from the electronic structure thus obtained were 2.0, 1.7, and zero per atom in Co⁺₃, Co⁺₄, and V⁺₄, respectively. These spin differences indicate a ferromagnetic and an antiferromagnetic spin-coupling in the cobalt and vanadium cluster ions, respectively.