Electron-crystal

The single-electron crystal-field picture may be a crude over-simplification because Coulomb repulsion and SOC can lead to a situation where the ground term is a composite mixture of = 1/2, 3/2, and 5/2 states that does not derive from a single configuration [71, 72] the corresponding physical description is obtained from proper quantum chemical calculations [73-75]. 

High-valent iron can occur in a wide variety of electronic configurations. Figure 8.25 (a-c, e-i) presents a summary of the corresponding one-electron crystal-field states for the 3(/, 3J, and 3J electron configurations, allocated to HS and LS states in distorted octahedral and tetrahedral symmetry. Part d, in addition, depicts the case of low-low-spin iron(IV) found in some trigonal... 

Fig. 8.25 Schematic presentation of the one-electron crystal-field states for the Set, Set, and Set electron configurations of iron(IV), (V), and (VI). Case (g) has not been observed yet...

Dorset, D. L. and Moss, B., Electron crystal structure analysis of linear polymers - an appraisal, in Polymer Characterization, Carver, C. D. (Ed.), Advances in Chemistry Series, Vol. 203, American Chemical Society, Washington, DC, 1983, 409-416. 

Doped DNA (by this we mean DNA strands whose electrical charge and electron count have been varied by transfer from electron donors or electron acceptors) can be thought of by analogy to doped electron crystals, but once again the narrow bandwidth and disorder characteristic of DNA make the problem more complex. 

A further variation on the theme of emission is circularly polarized emission, where chiral interactions, for example between a lanthanide complex and a chiral ligand in solution, can be studied. Selection rules have been given619 based on S, L and / values for 4/states perturbed by spin-orbit coupling and 4/ electron-crystal field interactions, and four types of transition were predicted to be highly active chiroptically. These are given in Table 12. 

The failure is not limited to metal-ammonia solutions nor to the linear Thomas-Fermi theory (19). The metals physicist has known for 30 years that the theory of electron interactions is unsatisfactory. E. Wigner showed in 1934 that a dilute electron gas (in the presence of a uniform positive charge density) would condense into an electron crystal wherein the electrons occupy the fixed positions of a lattice. Weaker correlations doubtless exist in the present case and have not been properly treated as yet. Studies on metal-ammonia solutions may help resolve this problem. But one or another form of this problem—the inadequate understanding of electron correlations—precludes any conclusive theoretical treatment of the conductivity in terms of, say, effective mass at present. The effective mass may be introduced to account for errors in the density of states—not in the electron correlations. 

S. Brazovski and P. Monceau, editors. Proceedings of the Internationa Workshop on Electronic Crystals ECRYS 99, volume 9 of Journal de Physique IV Proceedings. Societe Francaise de Physique, 1999. 

The problem of phase separation in cuprates superconductors has been longely debated [1-8], Recently, several experiments show the formation of electronic crystals at critical densities [9, 10], These results provide a strong experimental support for the scenario proposed some years ago (11-14) for the phase diagram of cuprate superconductors where generalized Wigner... 

La tilled skutterudites 8 14.2. Electron crystals and phonon glasses 28... 

The filled skutterudite antimonides appear to represent excellent examples of electron-crystal, phonon-glass materials. The incoherent rattling of the loosely bound lanthanide atoms in these materials is inferred from the large values of the ADP parameters obtained in single-crystal structure refinements. This rattling lowers the thermal conductivity at room temperature to values within two to three times Km... 

Fig. 6. Variation of the crystal-field parameters of LaCl3 Pr3+ under pressure. Solid lines correspond to the conventional one-electron crystal field, utilizing only the 4f2 wavefunctions as the basis set. S denotes the mean deviation as defined in the text. Dashed lines represent the results derived from the inclusion of the 4f15d1 configuration interactions.

The underlying assumption of the superposition model is that the one-electron crystal field is additive and can be regarded as a superposition of the contributions from individual ions... 

In sect. 4.1 the one-electron crystal-field model for the f configurations was introduced. Though this model is very successful in providing a description of the crystal-field splittings, certain anomalous multiplets are poorly fitted. Prominent examples are the Di multiplet of Pr3+, the 2H(2)n/2 multiplet of Nd3+, and the 3Ks multiplet of Ho3+. Almost independent of the host crystal, the calculated crystal-field levels of these multiplets show a much larger deviation from the experimental ones than all the other levels. 

As for the one-electron crystal field, the GfQ are treated as parameters, whereas the angular... 

Another possibility to address the problem of the correlation crystal fields is an approach based on different wavefunctions for the spin-up and spin-down electrons. This spin-correlated crystal-field model merely doubles the number of crystal-field parameters and thus can be applied in most cases. Shen and Holzapfel (1995c) presented a high pressure study on spin-correlated crystal fields in MFCl Sm2+ (M = Ba, Sr, Ca). In particular, they considered the splitting ratio R of the 5Di and 7Fi multiplets, which should be equal to 0.298 within the conventional one-electron crystal-field theory and independent of the host crystal. In a first step, Shen and Holzapfel (1995c) considered ambient pressure as well as high pressure data of the isoelectronic Eu3+ ion. In this case they found a ratio of R = 0.238, which could be explained by taking into account a spin-correlated crystal-field parameter C2 = —0.007(3). 

Applying the model to the high-pressure data also distinctly improved the quality of the fits for both samples and at all pressures. A striking example is the D2 multiplet of Pr3+, where the rms error rises from 14.8 cm-1 at ambient pressure to a maximum value of 20.1 cm-1 at 8 GPa, when using solely the one-electron crystal-field parameters. On the contrary, if the 5-function model is included, a maximum rms error of only 0.9 cm-1 is found at ambient pressure and even smaller values are found at higher pressures. 

Furthermore, a very interesting property of these fits concerns the one-electron crystal-field parameter of Nd3+ in LaCH. In this case large difficulties were encountered in deriving the... 

Indeed, focusing on this low thermal conductivity, Slack et al. have investigated boron cluster compounds like beta boron, YB66 among others, as possible embodiments of the "electron crystal phonon glass" systems that they have proposed (Slack et al., 1971 Cahill et al., 1989). 

The one-electron crystal field Hamiltonian does not take into account electron correlation effects. For some systems, it has been useful to augment the crystal field Hamiltonian with additional terms representing the two-electron, correlated crystal field. The additional terms most commonly used (see, for example, Peijzel et al., 2005b Wegh et al., 2003) are from the simplified delta-function correlation crystal field model first proposed by Judd (1978) that assumes electron interaction takes place only when two electrons are located at the same position (hence the name delta-function ). This simplified model, developed by Lo and Reid (1993), adds additional terms, given as,... 

Gorller-Walrand and Binnemans (1996) have compiled the most complete listing of 4f-electron crystal field parameters across the lanthanide series. However, additional high quality crystal field level measurements for individual ions have been made since 1996 (see, for examples (De Leebeeck et al., 1999), for Nd LiYF4, or (Wegh et al., 2003), for Er LiYF4). 

George S. Nolas, Glen A. Slack, and Sandra B. Schujman, Semiconductor Clathrates A Phonon Glass Electron Crystal Material with Potential for Thermoelectric Applications... 

Graphite fluoride (CF) has unique properties, which include heat-resistance, electrical capabilities, and solid lubrication. Numerous studies on (CF) have been performed from the view points of electronic/crystal structures and chemical states/properties [1-5]. For example, Motoyama et al. [5] have... 

The introduction of the concept of one-electron crystal orbitals (CO s) considerably reduces difficulties associated with the many-electron nature of the crystal electronic structure problem. The Hartree-Fock (HF) solution represents the best possible description of a many-electron system with a one-determinantal wavefunction built from symmetry-adapted one-electron CO s (Bloch functions). The HF approach is, of course, only a first approximation to the many-particle problem, but it has many advantages both from practical and theoretical points of view ... 

Ab initio Closed Shell Formalism.—The method for calculation of HF CO s in polymers and crystals at the ab initio level has been discussed many times 1-5 therefore, we repeat here only the basic expressions to allow a self-contained discussion of the procedures applied. We will work entirely in configuration space, writing down the many-electron crystal wavefunction as a Slater-deter-... 

The cationic complex [(n -CsH5)Re(NO)(PRi3)] (Z) is capable of binding carbonyls either t, through the -ir-system, or by o--bonding through the lone pair electrons. Crystal structures of Z(phe-nylacetaldehyde) and Z(acetophenone) clearly show the two different modes of complexation (Figure 36). 

Because the photon momentum is negligible compared to the electron crystal momentum, the momentum conservation requirement simplifies to ... 

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