Studies of local spin in Hilbert and three-dimensional physical spaces

A. TORRE; L. LAIN; D.R. ALCOBA; R.C. BOCHICCHIO

Santiago de Compostela

Congreso; Ninth Triennial Congress of the World Association of Theoretical and Computational Chemists (WATOC-2011); 2011

World Association of Theoretical and Computational Chemists

The decomposition of the expectation value of the spin-squared operator < S2 > corresponding to an N-electron system into one- and two-center components provides the evaluation of local spins. These quantities turn out to be very useful to determine the spin state of an atom of group of atoms in a molecule as well as to describe magnetic interactions between the atoms which compose the system. This information becomes particularly interesting in the study of complexes of transition metal which play an important role in various disciplines as catalysis, enzyme chemistry, etc. The partitioning of the < S2 > quantity can be performed using different approaches. One of them proposes to partition the value < S2 > by means of projection operators1. Alternatively a direct partitioning of that expectation value has also been reported2 and the comparison of results arising from both procedures has been discussed in detail3. In a previous work4 we have described the partitioning of the expectation value < S2 > in terms of the elements of the spin-density matrix and those of the cumulant matrix of the second-order reduced density matrix. The results obtained  in the Hilbert space of atomic orbitals in selected molecules and radicals in triplet and doublet states show a good agreement with the genuine chemical behavior.  The main aim of this work is to go beyond describing our treatment in the three-dimensional physical space using the domains associated with the Bader atoms-in-molecules theory and the technique of fuzzy atoms. A critical analysis of all these results is discussed in detail. [1]A.E. Clark, E.R. Davidson, J. Chem. Phys. 115, 7382 (2001) [2]I. Mayer, Chem. Phys. Lett. 440, 357 (2007) [3]M. Podewitz, C. Herrmann, A. Malassa, M. Westerhausen, M. Reiher, Chem. Phys. Lett. 451, 301 (2008) [4]A. Torre, D.R. Alcoba, L. Lain, R.C. Bochicchio, J. Phys. Chem. A 114, 2344 (2010)