Crystal field scale factor

Obviously, these structural changes make the transfer of force-constants from the neutral B3 molecule to the B3+ radical inadequate. Instead, we tentatively transferred the scale factors optimized for the neutral molecule to the quantum-mechanical force-field of B3+ and calculated the corresponding scaled normal frequencies. We obtained a clear correspondence between many of the frequencies experimentally observed in Cl doped B3 crystals (Fig. 3(a)) and the calculated scaled frequencies (Fig. 3(b)). We also observed that some of the calculated scaled frequencies in the neutral B3 molecule are present in the spectra of the Cl doped crystals (Fig. 3(c)). This fact tells us that there is some portion of unoxidized B3 molecules in the sample and gives additional proof for the validity of the SQMF calculations performed on the neutral B3 molecule. 

Magnetic anisotropies xlz (l/3)Tr/ for R = Ce-Yb except Pm, Gd (0.002 < AFj < 0.06, table 9) have been computed with eq. (58) and using five contact contributions Sfj (i = H9, H11-H14) and the geometrical G factors obtained from the crystal structures of (HHH)-[/ Co(L5)3]6+ (R = La, Lu). A qualitative good agreement (AF = 0.23) is obtained between the experimental magnetic anisotropies (scaled to -100 for Dy(III) and corrected for the variation of the crystal-field parameter near the middle of the series (vide supra), table 9) and Bleaney s factors (table 3). Further non-linear least-squares refinements of the molecular... 

As seen from table 4, inclusion of scaling factor significantly decreases the value of It is expected to decrease more significantly for RE ions in crystals, since all./ manifolds are split by crystal field and number of levels N increases drastically. For example, when similar analysis has been performed for the lowest levels of LaF3 Eu3+ by Brik et al. (2006), the value of arms turned out to be 21.6 cm-1. The consistency in energy values and their assignments... 

Crystal-field parameters would be expected to change across the series roughly in proportion to the radial integrals r2 and r4 (and r6 for 4f electrons). These integrals decrease dramatically across the lanthanide series for the 4f electrons (because their orbitals contract dramatically) but only by a few percent for the 5d electron. Thus, crystal-field parameters determined for Ce3+ may be used across the lanthanide series, with only a small scaling factor for the heavy ions. 

The most remarkable aspect of Eq. (14-10) is that the dependence upon bond length and therefore, the dependence upon which alkali halide is being considered—has cancelled out. Another consequence is that the ion. softening does not depend upon pre.ssurc. This explains why theories of the crystal-field splitting and its pressure dependence that arc based upon hard ions have been successful the 0.51 factor can be absorbed in an undetermined scale parameter, depending upon the shape of the orbitals being split, since the factor 0.51 does not change with distortion. 

Numerous crystals doped by ionic impurities such as main element ions or / element ions offer very attractive photophysical properties. One of the key questions is to identify the factors that make a host-impurity combination efficient. This requires the knowledge of energy levels. In many cases, the energy scheme of the electronic levels can be nicely imderstood by taking into account the proper electronic and crystal field interactions in standard crystal-field theory [161], that uses some effective parameters extracted from experimental data. However, ab initio methods are interesting tools as they ideally aim at studying and understanding physical phenomena, at the atomic scale. They are only based on first principles and fundamental constants, and can therefore. 

Visible spectra of (a) [Co(OH2)6] and (b) [CoCLj] - Note that the intensity scales differ by a factor of 50, the tetrahedral complex giving a much more intense band. The energy of the transition is smaller for the tetrahedral complex, reflecting the smaller crystal-field splitting in this case. Redrawn with permission from [12]. Copyright 1999 John Wiley Sons. 

Tc = Curie temperature Tn = Neel temperature Vc - crystal-field potential W = scale factor for the crystal-field splitting of the J ground-state energies X = symbol for an anion, N, P, As, Sb or Bi... 

For Ce, one starts with d = n representing a single electron in a Friedel sum rule. The T serves as a phenomenological scaling factor which incorporates the mass enhancements. The final term represents crystal field and spin-orbit splittings as well as quasiparticle interactions, which is generally ignored (see below). 

N. The N dependence of fis/N 0.15 has previously been found [145] for the same potential and the polyene alternations 8 = 0.07. The measured [111]/values for the 0-0 line of PDA crystals in Fig. 6.14 are around 0.6 per repeat unit, or 0.15 per tt electron. The 0-0 line is several times more intense at 10 K than the O-I sidebands. The total oscillator strength of the exciton is /ib 0.7-0.8 per repeat unit, or 0.18-0.20 per 8 electron, slightly above the PPP estimate. As there are no adjustable parameters or scale factors, oligomers with molecular V(R) account directly for the polymer intensity. Local field and other corrections will be needed for more stringent comparison. 

A Fermi hyperfine constant for a nucleus i bJ crystal-field parameters of rank k spherical tensor operators of rank k Cj Bleaney s factor of lanthanide j (scaled to -100... 

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