Pseudo-spin formalism

With all semi-empirical methods, HyperChem can also perform pseudo-RHF calculations for open-shell systems. For a doublet state, all electrons except one are paired. The electron is formally divided into two half electrons with paired spins. Each half elec-... 

Some compounds of these ions with formal octahedral or pseudo-octahedral stereochemistries have Ueff 1.8 BM, corresponding to the low-spin 2T2g ground term, with the presence of AT of some magnitude. 

By an inspection of Table 3 some qualitative predictions can be made. Strong coupling is expected in copper-proteins, particularly in pseudo-tetrahedral sites (the so-called blue centers), in low-spin iron(III) and high-spin iron(II) proteins and molybdo-proteins, where the high strong formal charge provides large e values ). 

Hamiltonians formally similar to Eq. (2.4) are encountered not only in the central problems of lattice dynamics and electron propagation, but also in a large variety of other problems. Among them we mention the Frenkel theory of excitons, the coupled electron-lattice impurities in the entire range of coupling, the Jahn-Teller (or pseudo-Jahn-Teller) systems, interacting spins, and so on. 

Ruthenium complexes are excellent reagents for protein modification and electron-transfer studies. Ru +-aquo complexes readily react with surface His residues on proteins to form stable derivatives [20, 21]. Low-spin pseudo-octahedral Ru-complexes exhibit small structural changes upon redox cycling between the Ru + and Ru + formal oxidation states [3, 22]. Hence, the inner-sphere barriers to electron transfer (Ai) are small. With the appropriate choice of ligand, the Ru + + reduction potential can be varied from <0.0 to >1.5 V versus NHE [23]. Ru-bpy complexes bound to Lys and Cys residues have been employed to great advantage in studies of protein-protein ET reactions. The kinetics of electron transfer in cytochrome 65/cytochrome c [24], cytochrome c/cytochrome c peroxidase [12], and cytochrome c/cytochrome c oxidase [25] complexes have been measured with the aid of laser-initiated ET from a Ru-bpy label. 

In the A -operator formalism the relations (35), (37) and (38) are built in to the excitation operators. A full definition is given by Jensen et al. [38] who introduce the pseudo quantum number Mk to play the role of the non-relativistic Ms quantum number. This number is defined as Mk = (M - M 2 with M and Mp the number of occupied unbarred and barred spinors, respectively. The analogue of the non-relativistic spin-restricted excitation operators are now those that preserve Mk, either by disallowing spin flips... 

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