Jahn-Teller coupling constant

Warren KD (1984) Calculations of the Jahn-Teller Coupling Constants for d Systems in Octahedral Symmetry via the Angular Overlap Model. 57 119-145 Warren KD (1977) Ligand Field Theory off-Orbital Sandwich Complexes. 33 97-137 Warren KD (1976) Ligand Field Theory of Metal Sandwich Complexes. 27 45-159 Watson RE, Perlman ML (1975) X-Ray Photoelectron Spectroscopy. Application to Metals and Alloys. 24 83-132... 

Warren, K. D. Calculations of the Jahn-Teller Coupling Constants for d Systems in Octahedral Symmetry via the Angular Overlap Model. Vol. 57, pp. 119-145. 

Here the constant b was assumed to have the same value for both the E and E states. This assumption is consistent with transition [2] being a narrow peak while transitions [3] and [4] are broader bands, as the structure of the near-infrared absorption of CuIJY demonstrates (Fig. 9). Transitions [2], [3], and [4] are assigned the observed frequencies 10900, 12700, and 14650 cm l, and transition [1] will be shown to be below 1000 cm-l. The energy difference between transitions [2] and [3] depends only on the Jahn-Teller coupling constant, which is determined to be b = 3600 cm- from the observed frequencies. The spin-orbit coupling constant X is equal to 829 cm l for the free Cu11 ion (23), but in Cu11 complexes assumes the value close to 400 cm l. In the present analysis the band centers are insensitive tj various choices of,X. With X = 400 cm and b2 = 3600 cm, the... 

Nevertheless, although the strong field formalism lends itself most readily and naturally to the evaluation of the Jahn-Teller coupling constants, there may still arise situations in which a weak field basis might be more appropriate. Moreover, in either basis it is frequently desirable to determine the influence of spin-orbit interactions and the present work therefore presents results for all the d ground states of ML6 0h systems in both the weak and strong field bases and considers specifically the consequences of spin-orbit coupling in either formalism. 

The necessary theory for the calculation of the linear Jahn-Teller coupling constants via the Angular Overlap Model has already been fully reported1-4) and is therefore only briefly rehearsed here. The coupling constant, c, is defined as... 

Calculations of the Jahn-Teller Coupling Constants via the Angular Overlap Model... 

Table 4. Jahn-Teller Coupling Constants for ML6, Oh, Systems in the Weak Field LSMlMs) Basis...

Table 7. Reduction Factors for the Jahn-Teller Coupling Constants and Stabilization Energies of MLj, O, Systems in the Strong Field Basis...

In Tables 4 and 5 are shown the results calculated for the Jahn-Teller coupling constants in the weak field scheme the former contains those derived in Oh symmetry, using the LSMlMs) basis set and the latter the constants found when spin-orbit effects are specifically included via the O LSJMj) basis. Similarly, Table 6 shows the coupling constants obtained in the strong field scheme in Oh symmetry whilst the reduction factors, both for the coupling constants and for Ejt, consequent upon the allowance for spin-orbit coupling (O symmetry) are listed in Table 7. 

Table 9. Illustrations of the Diagonal Sum Rule for the Jahn-Teller Coupling Constants of ML6, Oh and O Systems... 

The hv and Kj parameters are the harmonic vibrational frequency and anhar-monicity constant respectively of the vibrational Hamiltonian (Hq). The Aj and A2 parameters are the first-order and second-order Jahn Teller coupling constants respectively for the Jahn-Teller part of the Hamiltonian (Hjj). 

Table 3. Jahn-Teller coupling constants for transition metal ions commonly involved in metalloproteins ... 

Calculations of the Jahn-Teller coupling constants for systems in octahedral symmetry via the angular overlap model. K. D. Warren, Struct. Bonding (Berlin), 1984,57,119 (20). 

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