Covalent-mixing parameters

In solids where cation-cation interaction is significant, by can be related to R, where R is the cation-cation separation. In cases where cation-anion-cation interaction is important, by is related to the covalent mixing parameter, X, of the cation-anion orbitals. For octahedrally coordinated cations, as in rocksalt and perovskite structures, the relevant mixing parameters are and in the following molecular wave functions... 

Finally, a a band on the itinerant-electron side of the Mott-Hubbard transition in the presence of localized t spins S = 3/2 signals covalent-mixing parameters X and therefore a cubic-field splitting (Eq. 5 of Goodenough, this volume) that approaches Aex- To test this deduction, hydrostatic pressure was used to induce a transition from the high-spin to the low-spin states in CaFeOs the transition was observed to occur at a pressure Pc 30 GPa [50]. 

The values of the TB parameters that reproduce the ab initio band structure are reported in Table 2 for a subset of materials the others show the same behaviour. The variation of Aa and p/Aa as a function of the mixing parameter of the hybrid functional is also depicted in Fig. 6. Trends are again very clear on increasing the fraction of HF exchange, the band gap Aa increases (the change is higher at the HF end of the series) this feature makes the material more ionic. The parameter p/Aa that is the TB definition of covalence in the materials, decreases systematically on moving from the pure DFT to the HF end of the series. 

The variation of the calculated value of Popt for BaTiOs, as a function of the mixing parameter in the hybrid F-BLYP series, is shown in Fig. 11. We observe a steady decrease of P as the HF-exchange component in the hybrid functional is increased, in agreement with the degree of Ti-0 covalence in each solution. This result confirms that the polarisation of the ferroelectric phase is dominated by the electronic polarisability, as described earlier. Correspondence with experimental results is achieved for a value of 0.55. 

It is also of interest to observe that in the frilly optimised tetragonal phase, the double maximum profile in the distortion energy as a function of the mixing parameter a, described for the pseudocubic phase, is no longer present. Removing the structural constraint of the cubic phase, the equilibrium structure is allowed to adapt to the relative ionic sizes, and its features are characterised only by the relative covalence in the Ti-0 bonding (the 15/Aa TB parameter shown in Fig. 6). The double minimum profile of Fig. 10 is therefore introduced in the constrained optimisation corresponding to the pseudocubic phase. 

The first part of this review deals with classical ESR results in metals. Here ESR can determine the site symmetry of the probe and measures CF effects in full detail. In this field of research ESR has made notable contributions. Some interesting physics developed from the comparison of the magnitude of the cubic fine structure parameter for metals and for insulators. The systematic differences are probably caused by covalent mixing contributions as a consequence of the conduction-electron hopping on and off the local moment site. In addition, ESR in metals is the only method to determine quantitatively the relaxation rates between the lattice, the band states and the impurities. It has been shown. 

To examine the effect of covalency on the QS, the values of the QS of some compounds have been calculated with the aid of the Extended Hiickel MO method (i 82, 61). In these calculations the values for the empirical parameters used were obtained from comparison with EPR experiments (see EPR studies). This method is suitable only for molecules with low symmetry, because effectsoof spin-orbit coupling and thermal mixing have been neglected. 

The triplet EPR spectra of the mixed dimers [ZnTPPS/TTAP] and [TPPS/ZnTTAP] also displayed in Figure 5 have the same characteristics as the free base dimer spectra (cf. Figures 3 and 5). A summary of the values of triplet parameters derived from the spectra is given in Table II. Included are literature values on face-to-face covalently-linked diporphyrins (8). 

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