Spin-orbit coupling coefficient/constant

The single electron spin—orbit coupling constant , / is fundamentally a positive quantity. The term coefficient XLS can be of either sign... 

The spin-orbit splitting coefficient v f = - Asf, proportional to the spin-orbit coupling constant, is used in place of the free-atom spin-orbit splitting parameter I. 

ESR parameters of the complex show its distortion upon entrapment, depending on the geometry of the intrazeolite space. In ZSM-5, the decreased effective spin-orbit coupling constants and molecular orbital coefficients for in-plane n binding are indicative of increased covalency between Cu and en, due to distortion from planarity upon encapsulation. This distortion from planar geometry is confirmed by a red shift in the energy-level diagrams at least for the zeolites with the smaller pores (ZSM-5 Beta). An intensity enhancement of the d-d bands occurs in parallel. 

The tensorial structure of the spin-orbit operators can be exploited to reduce the number of matrix elements that have to be evaluated explicitly. According to the Wigner-Eckart theorem, it is sufficient to determine a single (nonzero) matrix element for each pair of multiplet wave functions the matrix element for any other pair of multiplet components can then be obtained by multiplying the reduced matrix element with a constant. These vector coupling coefficients, products of 3j symbols and a phase factor, depend solely on the symmetry of the problem, not on the particular molecule. Furthermore, selection rules can be derived from the tensorial structure for example, within an LS coupling scheme, electronic states may interact via spin-orbit coupling only if their spin quantum numbers S and S are equal or differ by 1, i.e., S = S or S = S 1. 

The spin-orbit coupling constant A is the coefficient of the operator term LZSZ in the effective Hamiltonian. It arises from the operator 3t in equation (7.71) we have seen in section 7.4.4 how the matrix elements of this operator lead to first-, second- and higher-order contributions in the effective Hamiltonian,... 

Fig. 11. The calculated dependence of the MCD intensity upon the rhombic distortion parameter, V, at low-spin Fe(III) in heme. As is the MCD intensity at 4.2 K and 5 T corrected to be linear in-field, e is the extinction coefficient in isotropic light, and X is the spin-orbit coupling constant of Fe(III) (60) c is the coefficient of the 3d, , orbital in the ground state.

A molecular orbital calculation (Figure 10.7) has shown that the antibonding coefficients, and (eTT ), of vanadyl porphyrins vary as a function of dv->p (Figure 10.8). Since the spin-orbital coupling constant 5 and the anisotropic gj and tensors for a given vanadyl chelate are constant, and from the first order approximation,... 

One phenomenon which made its appearance early on in this work is the fact that chemical bonds do not appear to break gradually, but on the contrary, are little affected by increasing bond distances until a critical value is reached, when large changes are observed to occur in the wave function over a very short intemuclear distance 0.5deformation characteristic of bond formation and at the same time the spin coupling coefficients also vary rapidly. This occurs at an interatomic distance of 4.5oo. which remains surprisingly constant for many different species and processes. Indeed, one might assert that in a chemical reaction. 

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