Effective crystal field

Figure 4.6. Lowest triplet state orderings for different metal complexes showing the relative positions of the d-d, n-n, and MLCT states as a function of metal, ligand, and effective crystal field strength. (Reprinted with permission from Ref. 7. Copyright 1991 American Chemical Society.)...

Similarly, Ru(bpy)2(CN)2 emits well at room temperature while [Ru(bpy)2(CN)Cl]+ does not. The main factor is the much lower effective crystal field strength of Cl versus CN. 

Since in the FHCF(L) the effective crystal field is given in terms of the l-system Green s function, the natural way to go further with this technique is to apply the perturbation theory to obtain estimates of the /-system Green s function entering Fqs. (22) and/or (25). It was assumed and reasoned in [29] that the bare Green s function for the /-system has a block-diagonal form ... 

M. Jacek and Z. Gajek, The Effective Crystal Field Potential, Elsevier, New York,... 

The EHCF theory [65] relates the dominating covalent contribution to the effective crystal field to the properties of the delocalized canonical MO of the /-system. Following the calculations presented in [65-69] the covalent contribution yields about 80-90% to the splitting of the (/-electrons eq. (2.122). The remaining 10-20% is provided by the Coulomb interactions with the effective charges on the ligand atoms. 

The unitary transformation from the basis of the CMOs to the basis of the LMOs of the /-system does not change the covalent contribution to the effective crystal field. According to numerical estimates the resonance integrals (,/. between d-AO and LPs of the donor atoms by I0-H00 times overcomes the resonance integrals between d- AO and any other LMOs and thus dominates the resonance interaction of the d- and /-systems. So, as it has been shown in [71], restricting the summation in eq. (4.82) by the sum of diagonal elements (L = L) over only the LPs results in error in the estimated splitting of the (/-levels of 0.1 eV. This precision is comparable to that of the EHCF method itself. This estimate is described by the formula ... 

However, as we have already pointed out, the value of Sgg — t2g is quite insensitive to the electronic configuration (2). Therefore, in the present paper, we approximated all of these effective crystal-field splittings by the value of eg — t2g Calculated in the ground state. On the other hand, the Racah parameters represent the electron-electron repulsion interaction and can be calculated by the radial part of the pure 3d atomic orbitals of the impurity chromium ion (1). After evaluating the value of these parameters, the multiplet structure of ruby can be obtained by diagonalizing the Tanabe-Sugemo matrices. 

The Eu3+ ion of [Eu(Tp)3] is coordinated according to a singlecrystal X-ray analysis in the first coordination sphere by nine N atoms in the shape of a tricapped trigonal prism, resulting in an effective crystal field (CF) of symmetry D3h. The absorption spectrum of powdered [Eu(Tp)3] was recorded at approximately 5 K, and the luminescence spectrum at 77 K. On this basis an experimental CF splitting... 

Solvent Effects, Crystal Fields. - This report is concerned with molecular properties and full coverage of intermolecular effects and solid state susceptibilities is not attempted. The papers reviewed in this section have been selected because they contain material closely related to the calculated properties of individual molecules. For example, calculations based on the electronic band structures of semiconductors etc. are excluded, but a few papers relating molecular crystal susceptibilities to the molecular hyperpolarizabilities are included. 

Phosphors are composed of the host lattice and the activator, which are discussed in detail in the following section. The optical properties of phosphors are mainly affected by several effects including the nephelauxetic effect, crystal field splitting, energy transfer, and thermal effect. These factors must be considered in practical and actual applications. We also list the suitable phosphors combined with UV- or blue-chip sources that have been developed and extensively used in lighting according to the excitation spectra. Other important factors, such as intensity (quantum efftciency), durability, thermal stability, and bandwidth, are discussed for the representative applications of phosphors. 

Free ion Nephelaiixetic effect Crystal field Stokes shift... 

In contrast, if the divalent ion is smaller than iron(II), as is the case for cobalt(Il) and nickel(II), which have ionic radii of 0.072 and 0.070 nm respectively, then substitution will place iron in a smaller than expected lattice site. In this case the positive lattice pressure will produce shorter iron-ligand bonds, and a stronger effective crystal field potential which will favour the low spin configuration and/or a higher spin crossover temperature. This is exactly what is observed in a series of... 

The crystal field environment of the d system in the series of iron(III) dithiocarbamate complexes may be expressed in the form of a potential with octahedral symmetry with a small trigonal component. Therefore, we may write for our purpose in this paper the effective crystal field potential, V(r), in terms of a series of spherical harmonics for the transition of metal ion as ... 

For the T2 level we need to consider the contribution to the nmr shift by the term proportional to X Xj the Fermi interac tion. Since in these compounds the effective crystal field environment of the iron atom is approximately of octahedral symmetry with a small most likely trigonal component(11,12) we shall assume that the form of the Fermi contact interaction is as given in reference (1). The magnetic susceptibility components Xi. and can be determined from the appropriate equations in ref.(13). (We shall neglect bonding in this paper determining x... 

The crystal field is something like a mystery and therefore it is commonly called the effective crystal field. Strictly speaking the crystal electric field acting on the open-shell electrons of a paramagnetic ion is basically due to the electrostatic field generated by the remaining ions of the crystal. Thus the 4f electrons possess an electrostatic potential energy that may be expanded in terms of spherical harmonics... 

Fig. 33.3. Energy splitting of the / ground state in the LnP phases due to an effective crystal field.

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