Reduced-order models different forms

In order to get significant results, the initial data must be formed by a set of clearly non-A -representable second-order matrices, which would generate upon contraction a closely ensemble A -representable 1-RDM. It therefore seemed reasonable to choose as initial data the approximate 2-RDMs built by application of the independent pair model within the framework of the spin-adapted reduced Hamiltonian (SRH) theory [37 5]. This choice is adequate because these matrices, which are positive semidefinite, Hermitian, and antisymmetric with respect to the permutation of two row/column indices, are not A -representable, since the 2-HRDMs derived from them are not positive semidefinite. Moreover, the 1-RDMs derived from these 2-RDMs, although positive semidefinite, are neither ensemble A -representable nor 5-representable. That is, the correction of the N- and 5-representability defects of these sets of matrices (approximated 2-RDM, 2-HRDM, and 1-RDM) is a suitable test for the two purification procedures. Attention has been focused only on correcting the N- and 5-representability of the a S-block of these matrices, since the I-MZ purification procedure deals with a different decomposition of this block. 

Che and Naccache (199) have studied the kinetics of 02 formed on slightly reduced anatase using EPR. They found that the adsorption could be explained on the basis of different formation rates for 02 adsorbed at different sites, with zero- and first-order kinetics for the oxygen and Ti3+ concentrations, respectively. Using the same approach, Hauser (200) has extended this work and proposed different models to explain the kinetics based on the formation of 02, O2-, and 02 ions for which activation energies around 1 kcal/mol were obtained. Nikisha et al. (201) have studied the oxygen adsorption kinetics using EPR, conductivity, and volumetric measurements. 

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