Crystal-field effect

Chemists want to learn from NQR experiments about the chemical bond within the molecule. Let us consider an example  

NQR frequencies for 3SC1 at 77 °K in ortho-, meta- and para-dichlorobenzene are given in Table II.3. The interpretation of the results runs into difficulties because of the crystal field effects. These influences are very difficult to evaluate. They certainly change from substance to substance. Qualitatively, we can characterize the crystal field effect in the following way 76). 

Electrostatic forces between the molecules. These forces may be composed of  

A quantitative treatment of these effects on NQR is outside the scope of today s solid state theory. Therefore a qualitative estimation of the crystal field effect seems to be necessary. This justifies classifying the crystal field 

The condensation of the molecules into the solid state taken as a rigid, ordered arrangement of molecules. 

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Electronic absorption spectra are produced when electromagnetic radiation promotes the ions from their ground state to excited states. For the lanthanides the most common of such transitions involve excited states which are either components of the ground term or else belong to excited terms which arise from the same 4f" configuration as the ground term. In either case the transitions therefore involve only a redistribution of electrons within the 4f orbitals (i.e. f—>f transitions) and so are orbitally forbidden just like d—>d transitions. In the case of the latter the rule is partially relaxed by a mechanism which depends on the effect of the crystal field in distorting the symmetry of the metal ion. However, it has already been pointed out that crystal field effects are very much smaller in the case of ions and they... 

In view of the magnitude of crystal-field effects it is not surprising that the spectra of actinide ions are sensitive to the latter s environment and, in contrast to the lanthanides, may change drastically from one compound to another. Unfortunately, because of the complexity of the spectra and the low symmetry of many of the complexes, spectra are not easily used as a means of deducing stereochemistry except when used as fingerprints for comparison with spectra of previously characterized compounds. However, the dependence on ligand concentration of the positions and intensities, especially of the charge-transfer bands, can profitably be used to estimate stability constants. 

Crystal field effects are of the order of the free ion interaction thus they cannot be treated as a small perturbation as in the lanthanides. Whereas the crystal field splitting in the oxidation state +3 is comparable to that for the lanthanides, it is significantly increased in the progression... 

As seen in Fig. 8 the experimentally determined magnetic moments at room temperature are in general much lower than the free ion values. To extract the contribution of orbital reduction, the influence of intermediate coupling, crystal field effects and j-j mixing must be considered. 

Accommodation of metal atoms of widely differing ionic radii into the same overall structure creates interesting possibilities for the doping of metal ions into a common matrix for spectroscopic examination under nearly constant crystal field effects. 

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,... 

We note that three spin-allowed electronic transitions should be observed in the d-d spectrum in each case. We have, thus, arrived at the same point established in Section 3.5. This time, however, we have used the so-called weak-field approach. Recall that the adjectives strong-field and weak-field refer to the magnitude of the crystal-field effect compared with the interelectron repulsion energies represented by the Coulomb term in the crystal-field Hamiltonian,... 

The mixing coefficients a and b in (4.10) depend upon the efficiency of the spin-orbit coupling process, parameterized by the so-called spin-orbit coupling coefficient A (or for a single electron). As A O, so also do a or b. Spin-orbit coupling effects, especially for the first period transition elements, are rather small compared with either Coulomb or crystal-field effects, so the mixing coefficients a ox b are small. However, insofar that they are non-zero, we might write a transition moment as in Eq. (4.11). 

Of course, in real systems, the relative contributions of Coulomb and crystal-field effects are such as to place chromophores somewhere inbetween the weak-and strong-field limits. In that case, a real Txg F) A2g transition is not a pure two-electron jump, so that some intensity is observed. 

Again, we restrict discussion to spin-allowed transitions here. In general, of course, crystal field effects compete with interelectron repulsion for all d" configurations, exceptfor n = 1 or 9. 

Theoretical analyses (75-77) of the matrix-induced changes in the optical spectra of isolated, noble-metal atoms have also been made. The spectra were studied in Ar, Kr, and Xe, and showed a pronounced, reversible-energy shift of the peaks with temperature. The authors discussed the matrix influence in terms of level shift-differences, as well as spin-orbit coupling and crystal-field effects. They concluded that an increase in the matrix temperature enhances the electronic perturbation of the entrapped atom, in contrast to earlier prejudices that the temperature dilation of the surrounding cage moves the properties of the atomic guest towards those of the free atom. 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

Gatti, C., Saunders, V.R. and Roetti, C. (1994) Crystal field effects on the topological properties of the electron density in molecular crystals the case of urea, J. Chem. Phys., 101, 10686-10696. 

Sreerama N, Woody RW, Callis PR (1994) Theoretical study of the crystal field effects on the transition dipole moments in methylated adenines. J Phys Chem 98 10397-10407... 

I shall take the simple view that most metal oxide structures are derivatives of a closest packed 02 lattice with the metal ions occupying tetrahedral or octahedral holes in a manner which is principally determined by size, charge (and hence stoichiometry) and d configuration (Jj). The presence of d electrons can lead to pronounced crystal field effects or metal-metal bonding. The latter can lead to clustering of metal atoms within the lattice with large distortions from idealized (ionic) geometries. 

While the enthalpy of formation is the property of interest in chemical thermodynamics of materials, many books focus on the lattice enthalpy when considering trends in stability. The static non-vibrational part of the lattice enthalpy can be deconvoluted into contributions of electrostatic nature, due to electron-electron repulsion, dispersion or van der Waals attraction, polarization and crystal field effects. The lattice enthalpy is in the 0 K approximation given as a sum of the potential energies of the different contributions ... 

In general, overlap of incompletely filled p orbitals results in large deviations from pure ionic bonding, and covalent interactions result. Incompletely filled / orbitals are usually well shielded from the crystal field and behave as essentially spherical orbitals. Incompletely filled d orbitals, on the other hand, have a large effect on the energetics of transition metal compounds and here the so-called crystal field effects become important. 

Wehrli, W. Ansamycins Chemistry, Biosynthesis and Biological Activity. 72, 21-49 (1977). Weiss, A. Crystal Field Effects in Nuclear Quadrupole Resonance. 30, 1-76 (1972). 

A variety of systems are known in which there are observable crystal-field effects on the configuration about a double bond. Thus, acetaldehyde phenylhy-drazone occurs in solution as an equilibrium mixture of syn and anti forms (in benzene the ratio is 3 2), but in the crystal only the anti isomer is found (60). 

We now turn to the question of sensitivity of chemical constitution to crystal-field effects. Here the distribution of the various possible species in a system will be determined by bond-breaking and -forming processes. Except for the case of proton tautomerism, which we will treat at the end of this section, these processes are of high energy. Nevertheless, a variety of systems showing such sensitivity have been encountered. 

All lanthanide ions, with the exception of gadolinium(III) and europium(II), are likely to be relaxed by Orbach-type processes at room temperature. In fact, the f" configurations n l) of lanthanides(III) give rise to several free-ion terms that upon strong spin-orbit coupling, provide several closely spaced energy levels. Table III reports the multiplicity of the ground levels, which varies from 6 to 17, and is further split by crystal field effects. 

The crystal field effect is due primarily to repulsive effects between electron clouds. As we have already seen, the repulsive energy is of opposite sign with respect to coulombic attraction and the dispersive forces that maintain crystal cohesion. An increase in repulsive energy may thus be interpreted as actual destabilization of the compound. 

An appreciation of the crystal field effect on the vibrations of the Bravais cell which is repeated to build the crystal is extremely important when interpreting the vibrational spectra of many substances, since in the presence of a crystal field influence the number of observed bands in the spectrum cannot be directly determined from the formula unit which goes to make up the unit cell. In other words, there is almost always a larger number of bands to account for when investigating solid state samples. The solid state effects often cause degenerate bands to split in the same degree as symmetric and antisymmetric stretching modes split. 

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