Operator Zeeman

Fig. 12. Zeeman Operator Energy Level Diagram for d1 and d5 Systems in CMV Symmetry...

Fig. 14. Zeeman Operator Energy Level Diagrams for d1 and d9 Systems in Cxv Symmetry...

We now let the molecule interact with an external magnetic field Bo. The interaction energy, as far as the orbital is concerned, is given by the orbital Zeeman operator... 

Eq. (1.36) is called the Van Vleck equation. In that form the Zeeman operator operates only to first order. Indeed, we should include the second order Zeeman term, which allows the interaction between the ground S multiplet (j functions) with all the excited ones ([Pg.18]

The involvement of the matrix elements of the Zeeman operator in the interaction matrix... 

If the total angular momentum is derived only from an isotropic electron spin, that is, J=S, the Zeeman operator can be rewritten as... 

S2 possesses the eigenvalues S(S + 1). For a spin-1/2 dimer (S can be 0 or 1), the same values are obtained from the derivation of the Bleaney-Bowers equation. For spin systems in an external magnetic field, the Zeeman operator Hmag = -g/ BB S accounts for Zeeman splitting. The isotropic Heisenberg Hamiltonian for multiple spin centers can be expanded by adding the individual coupling pairs ... 

Within the spin-only basis and without distortions on [Fe(CN)g] , the Zeeman operator Hzi is represented by the matrices given in (50-52), which directly show the coupling of the local g-tensors of Fe and Cu . 

Table 3. Matrix Elements of Zeeman Operators within f Ground States.

In conclusion, the diagonal matrix elements of the electron Zeeman operator are... 

Notice that in the transformed basis set the z-component of the Zeeman operator is no longer diagonal there are off-diagonal matrix elements of the type P i Hf Pj).) The full spin Hamiltonian matrix Hy is then diag-onalised. The obtained eigenvalues ,-(/ ) are expanded in powers of B, yielding the van Vleck coefficients. 

The application of a parallel (x or 7) component of the Zeeman operator (which is non-diagonal in the /w,) /n5) basis set) should bring about the same result. 

The spin-orbit couphng constant / used to be reduced in magnitude by the amount k as compared to the free-ion value The Zeeman operator can be expressed with the help of the relationship... 

Since the (spin) Zeeman operator in the basis set of coupled spin angular momenta functions magnetic energy levels are easy to generate (Table 10.8)... 

However, some second-order van Vleck coefficients are non-zero due to the fact that certain magnetic states are coupled through the Zeeman operator... 

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