APPLICATIONS OF THE EFFECTIVELY UNPAIRED ELECTRON DENSITY MATRIX TO THE STUDY OF ELECTRONIC CORRELATION

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

Santiago de Compostela

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

World Association of Theoretical and Computational Chemists

Population analysis studies performed with the density matrix of effectively unpaired electrons show the suitability of this device to determine the extent of the radical and diradical character of molecules and related species of any spin multiplicity. The connection of this matrix with the valence and the free valence indices has promoted a rigorous study [1] of its mathematical properties which allows one to know the abilities and limitations of its applications. Likewise, we have reported a relationship between this matrix and the contracted spin-free cumulant matrix of the second-order reduced density matrix [2], which provides links between different tools used in quantum chemistry [3]. In this work we propose a decomposition of the effectively unpaired electron density matrix into two terms. One of them depends on the well-known spin-density matrix, which contains information over the unpaired electrons due to spin. The other term is a one-electron matrix which is related with the degree of correlation of the wave function used to describe the N-electron system. We report values of the trace of this matrix along with the energies determined in systems of several spin symmetries described at the level of configuration interaction using different excitations. The results confirm a direct relation between the value of this trace and the correlation of the wave function utilized. We have also regarded other formulation of the effectively unpaired electron density matrix recently suggested [4], based on the particle-hole matrix formalism. We discuss both formulations analyzing their ability to account for the electronic correlation. 1 V.N. Staroverov, E.R. Davidson, Chem. Phys. Lett. 330, 161 (2000) 2 L. Lain, A. Torre, R.C. Bochicchio, R. Ponec, Chem. Phys. Lett. 3 46, 283 (2001) 3 L. Lain, A. Torre, D.R. Alcoba, R.C. Bochicchio, Chem. Phys. Lett. 476, 101 (2009) 4 P. Karafiloglou, J. Chem. Phys. 130, 164103 (2009)