Orbitals magnetic

For the first group of magnetic parameters ic, Ag and aN, depending explicitly upon the magnetic field, we need a wave function P(B)) correct to the first order in the magnetic field. The Hamiltonian to be used for its derivation adopts the form of 

The LCAO coefficients, correct to the first order in the magnetic field, can be written in the form 

The LCAO coefficients are determined by solving the modified Roothaan equations [3] 

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Figure 29. Relative orientations of magnetic orbitals of the Cu(II) ion (d c2 2) in the x,y plane relative to that of the half-occupied Jt orbital of the phenoxyl radical. Here a is the Cu-O-C bond angle and P the dihedral angle between the x,y plane and the plane of the phenyl ring of the coordinated phenoxyl and St is the expected electronic ground state (204).

It should be emphasised that it is the rule rather than the exception for p to change markedly with crystal structure (Table 8.2). It is therefore unwise to assume that various metastable allotropes can be given the same value of P for the stable structure. In some cases values of p can be extrapolated from stable or metastable alloys with the requisite crystal structure, but in others this is not possible. A significant development is that it is now possible to include spin polarisation in electron energy calculations (Moruzzi and Marcus 1988, 1990a,b, Asada and Terakura 1995). This allows a calculation of the equilibrium value of to be made in any desired crystal structure. More importantly, such values are in good accord with known values for equilibrium phases (Table 8.2). It has also been shown that magnetic orbital contributions play a relatively minor role (Eriksson et al. 1990), so calculated values of P for metastable phases should be reasonably reliable. 

Diquat insecticides, 34 1-2 Direct exchange, 38 426 magnetic orbitals, 38 435 Directly bonded complexes, 21 202-207 Direct oxide reduction, in actinide metal preparation, 31 6-7, 21-22, 25 apparatus, 31 29... 

Magnetic orbitals, 38 430 direct exchange, 38 435 Magnetic resonance, spin equilibria dynamies investigation, 32 14-16... 

Due to the spin polarization effect, the magnetic orbitals can be difficult to identify from a spin-unrestricted calculation. Since the total energy of a Kohn—Sham determinant is invariant under unitary transformations between the spin-up orbitals among each other and spin-down orbitals among each other, one can arrange each spin-up orbital to overlap at most with each spin-down orbital on the basis of the corresponding orbital transformation (COT) (88—90). Then, the molecular orbitals (MOs) are ordered into pairs of maximum similarity between spin-up and spin-down orbitals and can be separated into three groups (i) the MOs with spatial overlap close to one (doubly occupied MOs),... 

The third quantum number, mb describes the orientation of the electron orbital relative to an arbitrary direction. Because an external magnetic field (such as might be induced by a neighboring atom) provides a convenient reference direction, mt is usually called the magnetic orbital quantum number. It can take an integral value from —l to /. 

Figure 41 (a) schematic representation of the molecular structure of [CuVO((fsa)2en)(MeOH)] (185) 911 (b) relativ symmetries of the magnetic orbitals 911 (c) schematic representation of the geometry around V02+ in the trinuclet... 

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