Other crystal fields

The above equations have been obtained on the assumption that no orbital states have energies close to that of the ground state. This means that they should be applicable to d3, d5, and d8 for crystal fields which are close to octahedral in symmetry. They should be applicable to d4 and d9 also, when the distortion from octahedral symmetry is tetragonal, since in this case matrix elements of are zero between the ground state and the nearby excited state, d2, d6, and d1 in octahedral symmetry must be treated in a manner similar to that used for dl in Sec. III.D. For other crystal-field symmetries, the treatment used depends on whether the crystal field gives low-lying excited states that have nonzero matrix elements of with the ground state. 

The data obtained for 6-amino-3-methyl-l,2,4-triazin-5-one (17) show the surprising result that the non-ionic structure (17a) contributes little to the resonance while the ionic structures (17b-f) have to be considered in the crystalline state, which is probably due to the stabilization of these structures by hydrogen bonding or other crystal fields acting on this molecule. 

Jahn-Teller distortion and other crystal fields... 

For Iran sition metals th c splittin g of th c d orbitals in a ligand field is most readily done using HHT. In all other sem i-ctn pirical meth -ods, the orbital energies depend on the electron occupation. HyperCh em s m oiccii lar orbital calcii latiori s give orbital cri ergy spacings that differ from simple crystal field theory prediction s. The total molecular wavcfunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals arc the residue of SCT calculations, in that they are deemed least suitable to describe the molecular wavefunction, ... 

Significant progress in the optimization of VDW parameters was associated with the development of the OPLS force field [53]. In those efforts the approach of using Monte Carlo calculations on pure solvents to compute heats of vaporization and molecular volumes and then using that information to refine the VDW parameters was first developed and applied. Subsequently, developers of other force fields have used this same approach for optimization of biomolecular force fields [20,21]. Van der Waals parameters may also be optimized based on calculated heats of sublimation of crystals [68], as has been done for the optimization of some of the VDW parameters in the nucleic acid bases [18]. Alternative approaches to optimizing VDW parameters have been based primarily on the use of QM data. Quantum mechanical data contains detailed information on the electron distribution around a molecule, which, in principle, should be useful for the optimization of VDW... 

Although Fc304 is an inverse spinel it will be recalled that Mn304 (pp. 1048-9) is normal. This contrast can be explained on the basis of crystal field stabilization. Manganese(II) and Fe" are both d ions and, when high-spin, have zero CFSE whether octahedral or tetrahedral. On the other hand, Mn" is a d and Fe" a d ion, both of which have greater CFSEs in the octahedral rather than the tetrahedral case. The preference of Mn" for the octahedral sites therefore favours the spinel structure, whereas the preference of Fe" for these octahedral sites favours the inverse structure. 

Tetrahedral complexes arc also common, being formed more readily with cobali(II) than with the cation of any other truly transitional element (i.e. excluding Zn ). This is consistent with the CFSEs of the two stereochemistries (Table 26.6). Quantitative comparisons between the values given for CFSE(oct) and CFSE(let) are not possible because of course tbc crystal field splittings, Ao and A, differ. Nor is the CFSE by any means the most important factor in determining the stability of a complex. Nevertheless, where other factors are comparable, it can have a decisive effect and it is apparent that no configuration is more favourable than d to the adoption of a tetrahedral as opposed to... 

As was the case with lanthanide crystal spectra (25), we found that a systematic analysis could be developed by examining differences, AP, between experimentally-established actinide parameter values and those computed using Hartree-Fock methods with the inclusion of relativistic corrections (24), as illustrated in Table IV for An3+. Crystal-field effects were approximated based on selected published results. By forming tabulations similar to Table IV for 2+, 4+, 5+ and 6+ spectra, to the extent that any experimental data were available to test the predictions, we found that the AP-values for Pu3+ provided a good starting point for approximating the structure of plutonium spectra in other valence states. However,... 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

Those electrons must not only avoid each other but also the negatively charged anionic environment. In its simplest form, the crystal field is viewed as composed of an array of negative point charges. This simplification is not essential but perfectly adequate for our introduction. We comment upon it later. 

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