Orbital degenerate

Vibrational stmcture is, at best, only partially resolved. The stmcture in the first and second systems is complex which could be due, in part, to there being a Jahn-Teller effect in each of them. Such an effect may arise when a molecule is in an orbitally degenerate E (or T) state. The Jahn-Teller effect involves a distortion of the molecule in order to destroy the... 

The effect of axial ligands on ground state properties of complexes with orbitally degenerate ground terms. G. A. Webb, Coord. Chem. Rev., 1969, 4,107-145 (151). 

Orbitally degenerate grormd states, in general, cannot be treated in the spin-Hamiltonian approach. In this case, SOC has to be evaluated explicitly on an extended basis of spin-orbit functions. However, in coordination chemistry and bioinorganic chemistry, this is only of marginal importance, because the metal centers of... 

Orbitally Degenerate Ground States. For all orbitally degenerate ground states the g values are calculated to be markedly anisotropic and to deviate substantially from 2. Thus, writing the effective orbital reduction factor as k (equivalent to k of Section 4), the g values are found (101) to be as follows for the systems shown -... 

Exchange Coupling in Systems Containing Orbitally Degenerate Lanthanides 21 1.5... 

We wish to introduce here some of the problems which are encountered when dealing with exchange coupling in systems containing orbitally degenerate ions. 

In 1937 Jahn and Teller applied group-theoretical methods to derive a remarkable theorem nonlinear molecules in orbitally degenerate states are intrinsically unstable with respect to distortions that lower the symmetry and remove the orbital degeneracy.37 Although Jahn-Teller theory can predict neither the degree of distortion nor the final symmetry, it is widely applied in transition-metal chemistry to rationalize observed distortions from an expected high-symmetry structure.38 In this section we briefly illustrate the application of Jahn-Teller theory and describe how a localized-bond viewpoint can provide a complementary alternative picture of transition-metal coordination geometries. 

The final application of LFMM concerns a subtle yet unexpectedly significant Jahn-Teller effect. The classic examples of Jahn-Teller distortions are associated with d9and high-spin d4 systems with orbitally degenerate ground states of E symmetry... 

For the moment we assume that the ground state is not orbitally degenerate. Thus, for to be nonzero we require an... 

It is clear from Eqs. (21 and 22) that the MCD due to C terms will be temperature dependent with increasing intensity as the temperature is lowered. This form of MCD will occur only if the ground state of the molecule under investigation is orbitally degenerate. 

In this section we have described the calculation of u (1) and 1) with TDDFT perturbed by a magnetic field. These quantities, in combination with u/0) and (0) obtained from an unperturbed TDDFT calculation, can be used with Eqs. (11, 17, 30, or 32) as appropriate to evaluate, respectively, Bj, Aj, Cj 1, or C/° 2 and thus an MCD spectrum using Eq. (33). We have explicitly avoided orbitally degenerate ground states and therefore cannot yet calculate classical C terms. This problem will be discussed in Section II.C.4 but before doing so, we will describe the calculation of MCD intensity from the imaginary part of the Verdet constant where the MCD intensity itself is calculated rather than parameters associated with the various MCD terms. 

In the context of orbitally degenerate ground states the alternative reference was termed a transformed reference via an intermediate configuration (TRIC) and the overall method was called TRIC-KS TDDFT or TRICKS-TDDFT (88). 

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