Defects open-shell

Open shell defects in rocksalt-structured matrices the observables of interest are in this case the hyperfine constants, measurable experimentally by EPR, which depend both on the defect structure and on the localisation of the defect states. 

We have finally shown that the use of experimental geometries and/or constrained optimisations can lead to fictitious results, especially for those observables that are strongly dependent on the interatomic distances, such as the magnetic coupHng constants J in magnetic oxides and the EPR parameters of open-shell defects. Whenever possible, theoretical predictions should be achieved without imposing structural constraints on the solution. 

Other properties in magnetic resonance may be mentioned here, for example, hyperfine couplings. As the isotropic hyperfine coupling also depends crucially on the spherical spin-density distribution around the nucleus in question, s-character in bonding and, thus, hybridization defects will be important. Obviously, for open-shell radicals the s-character of the singly occupied MO(s) is the most cmcial aspect, but spin polarization of doubly occupied MOs with core or valence s-character may also be relevant (e.g., when the singly occupied molecular orbital is of pure p-character at the given atom). 

The unrestricted and restricted open-sheU Hartree-Fock Methods (UHF and ROHF) for crystals use a single-determinant wavefunction of type (4.40) introduced for molecules. The differences appearing are common with those examined for the RHF LCAO method use of Bloch functions for crystalline orbitals, the dependence of the Fock matrix elements on the lattice sums over the direct lattice and the Brillouin-zone summation in the density matrix calculation. The use of one-determinant approaches is the only possibility of the first-principles wavefunction-based calculations for crystals as the many-determinant wavefunction approach (used for molecules) is practically unrealizable for the periodic systems. The UHF LCAO method allowed calculation of the bulk properties of different transition-metal compounds (oxides, perovskites) the qrstems with open shells due to the transition-metal atom. We discuss the results of these calculations in Chap. 9. The point defects in crystals in many cases form the open-sheU systems and also are interesting objects for UHF LCAO calculations (see Chap. 10). 

There is nothing in the above derivation that requires the open-shell orbitals to be degenerate. For example, the whole group of states arising from promotion of up to four electrons from the top two filled MOs of a closed-shell system into the lowest pair of empty MOs may be dealt with by this method on putting n = 4, n2 = 4. In this way it is possible to obtain MOs that are better adapted to the description of excited states than are the virtual MOs of a closed-shell calculation, whose defects for this purpose have been noted already (p. 172). 

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