This work deals with the Fukui and dual reactivity descriptors within the framework of the spin-polarized density functional theory. The first and second derivatives of the electron density and the spin density with respect to the total number of electrons N = N_α + N_β and with respect to the spin number N_s = N_α - N_β have been formulated by means of reduced density matrices in the representation of the spin-orbitals of a given basis set, providing the matrix extension of those descriptors. The analysis of the eigenvalues and eigenvectors of the Fukui and dual-descriptor matrices yields information on the role played by the molecular orbitals in charge-transfer and spin-polarization processes. This matrix formulation enables determining similarity indices which allows one to evaluate quantitatively the quality of the simple frontier molecular orbital model in conceptual density functional theory. Selected closed- and open-shell systems in different spin symmetries have been studied with this matrix formalism at several levels of electronic correlation. The results confirm the suitability of this approach.
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