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Crystal Slater parameters

On the other hand, electrostatic models regard the ligands or the whole crystal as polarizable units and thereby lead to weaker Coulomb and spin-orbit interactions. In a dielectric screening model (DSM) from Morrison et al. (1967) the f element is placed within an empty sphere with radius Rs which is embedded into an infinite medium with dielectric constant e. This leads to a reduction AFk of the Slater parameters (Newman, 1973) ... [Pg.530]

These differences are the well-known Slater integrals, which determine how the orbital moments orient themselves for a free ion. hi a real crystal, there will always exist a competition between the crystal field parameters (described by the am s) and integrals hke those appearing in Eq. 52 which will condition the ionic state. [Pg.227]

Fig. 7.29. Fourth-order crystal field parameter times the lattice constant, a, raised to the fifth power for a number of lanthanide monopnictides. The solid line is the point charge model prediction with Z = -1.2 and (r" ) equal to that obtained from a Dirac-Slater calculation (after Birgeneau et al., 1973). Fig. 7.29. Fourth-order crystal field parameter times the lattice constant, a, raised to the fifth power for a number of lanthanide monopnictides. The solid line is the point charge model prediction with Z = -1.2 and (r" ) equal to that obtained from a Dirac-Slater calculation (after Birgeneau et al., 1973).
Usually, it is assumed that pressure effects under the hydrostatic limit are isotropic, which causes a proportional decrease of all distances in the lattice without a change in the local symmetry of the Ln ion. As the result, a standard assumption is that angular factors C (0, (j>) in the crystal-field Hamiltonian are pressure independent and that the only pressure-sensitive parameters are the Slater integrals, spin-orbit coupling, and radial crystal-field parameters (R)- Then, in most cases, pressure causes small linear shifts of the sharp-lines luminescence related to f-f transitions in the Ln " and Ln ions. [Pg.90]

The values of the Slater parameters and the spin-orbit coupling constant for transition metal ions in crystals and molecules are smaller than the values found in the free ion. The extent of this reduction has been used as a measure of the covalency of the complex [44]. Newman has... [Pg.266]

Some years ago, Ng and Newman (1985, 1987a,b), calculated all the contributions up to second order in perturbation theory to the crystal-field and Slater parameters. A complete list of perturbations are described in clearly organized tables. The perturbation basis contains the ligand outer orbitals and 49 metal states. The electronic excitations which are considered are the following ... [Pg.295]

The method was applied to the system Pi LaCl3. The authors identified new contributions to rank-6 crystal field one-electron cfp originating from the correlated mechanisms Bl k, k2). They stated that neither covalency nor ligand polarization could significantly contribute to the reduction of Slater parameters in crystals and identified probable influential excitations namely 4f —> nf. The quality of the final match between experimental and calculated intrinsic parameters is moderate 180/607, 38.8/30.3 and 15.8/9.12cm for A, and A, respectively, in Pr LaCl3. The paper is rather a theoretical reference to be consulted as to which process contributes most to the cjp and which one is therefore worth calculating. [Pg.295]

Slater parameters) Vv scalar crystal-field strength... [Pg.122]

So far we have assumed that the electronic structure of the crystal consists of one band derived, in our approximation, from a single atomic state. In general, this will not be a realistic picture. The metals, for example, have a complicated system of overlapping bands derived, in our approximation, from several atomic states. This means that more than one atomic orbital has to be associated with each crystal atom. When this is done, it turns out that even the equations for the one-dimensional crystal cannot be solved directly. However, the mathematical technique developed by Baldock (2) and Koster and Slater (S) can be applied (8) and a formal solution obtained. Even so, the question of the existence of otherwise of surface states in real crystals is diflBcult to answer from theoretical considerations. For the simplest metals, i.e., the alkali metals, for which a one-band model is a fair approximation, the problem is still difficult. The nature of the difficulty can be seen within the framework of our simple model. In the first place, the effective one-electron Hamiltonian operator is really different for each electron. If we overlook this complication and use some sort of mean value for this operator, the operator still contains terms representing the interaction of the considered electron with all other electrons in the crystal. The Coulomb part of this interaction acts in such a way as to reduce the effect of the perturbation introduced by the existence of a free surface. A self-consistent calculation is therefore essential, and the various parameters in our theory would have to be chosen in conformity with the results of such a calculation. [Pg.6]

Model Hartree-Fock calculations which include only the electrostatic interaction in terms of the Slater integrals F0, F2, F and F6, and the spin-orbit interaction , result in differences between calculated and experimentally observed levels596 which can be more than 500 cm-1 even for the f2 ion Pr3. However, inclusion of configuration interaction terms, either two-particle or three-particle, considerably improves the correlations.597,598 In this way, an ion such as Nd3+ can be described in terms of 18 parameters (including crystal field... [Pg.1105]

In this section we show how the general form of Renner-Teller interaction matrices can be obtained at any order in the phonon variables and with electron orbital functions of different symmetry (p-like, < like, /-like, etc.). For this purpose, we use an intuitive approach [18] based on the Slater-Koster [19] technique and its generalization [20] to express crystal field or two-center integrals in terms of independent parameters in the tight-binding band theory [21] then we apply standard series developments in terms of normal coordinates. [Pg.47]

Here E (fd) and G7(fd) stand for the direct and exchange Slater integrals for the Coulomb interaction between the 4f and 5d electrons (Cowan, 1981). The f(dd) parameter is related to the spin-orbit interaction for the 5d electron. The interaction between 5d electron and crystal field is described by the following term ... [Pg.6]

The energies of the d-d-excitations in this model are obtained by diagonalizing the matrix of the Hamiltonian constructed in the basis of rid-electronic wave functions (nd is the number of d-electrons). Matrix elements of the Hamiltonian are expressed through the parameters describing the crystal field and those of the Coulomb repulsion of d-electrons, which are Slater-Condon parameters Fk, k = 0,2,4, or the Racah parameters A, B, and C. In the simplest version of the CFT these quantities are considered empirical parameters and determined by fitting the calculated excitation energies to the experimental ones. [Pg.148]

When one considers complex systems, for which no exact results are available, parameters are usually obtained from a simple similar system and then transferred to the more complex system in question using the Slater-Koster rules [30] and some other empirical formulas which are known to be roughly obeyed. The results were often encouraging, but the lack of a solid theoretical background to justify the procedure left some fundamental questions unanswered. For example, how could one simulate the crystal-... [Pg.18]

Explicit account of the electron interaction within a self-consistent approach modifies the interpretation of the parameters. Slater s notion of the average of configurations and fractional occupation will be consistently applied in the grand canonical ensemble form. The one-particle reduced density matrix retains the symmetry of the crystal field and spin-orbit matrices, thus... [Pg.46]

This basic parameterization scheme, used at the time of the last A.C.S. symposium on lanthanide and actinide chemistry ( 5), has been discussed in detail by Wybourne 06). In applying the scheme, the free-ion Hamiltonian was first diagonalized and then the crystal-field interaction was treated as a perturbation. This procedure yielded free-ion energy levels that frequently deviated by several hundred cm from the observed energy levels.a In addition, the derived parameters such as the Slater radial integral, f(2), and the spin-orbit radial integral did not follow an expected systematic pattern across the lanthanide or actinide series ( 7). ... [Pg.344]


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See also in sourсe #XX -- [ Pg.268 ]




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