Coulomb transitions

The results substantiate earlier observations for the liquid-liquid phase transition of Na + NH3. This system shows a transition to metallic states in concentrated solutions but in dilute solutions and near criticality, ionic states prevail [98], and the gross phase behavior seems to be in accordance with a Coulombic transition [37]. Crossover was found at f — 10-2 [46], and it seems to be much more abrupt than in the picrate systems. However, much depends on the subtle details of the data evaluation. Das and Greer [99] could smoothly represent the data by a Wegner series. 

We have designated as Coulomb transitions those intermultiplet transitions in which ALt O, i.e., transitions between levels derived from different Russell-... 

Coulomb repulsion between the electrons in the f shell and are much more sensitive to changes in the local environment than the spin-orbit transitions. They are therefore a useful probe of the way intra-atomic correlations are affected by the metallic state, particularly in the actinides. Nevertheless, there are relatively few investigations of Coulomb transitions in metals since their energies all exceed 500 meV and most exceed 1 eV, as can be seen in fig. 1. The lowest energies are found in Pr, Sm " and Tm, all of which have now been studied by neutrons (Taylor et al. 1988, Needham 1989, Osborn et al. 1990). Although Coulomb transitions are non-dipolar, they can have appreciable cross-sections at intermediate values of momentum transfer, and are, in many cases, stronger than the dipolar (i.e., J—>J 1) cross-sections at the same k. 

The recent observations of Coulomb transitions in actinide intermetallic compounds (McEwen et al. 1990, Osborn et al. 1990) are of particular interest because the 5f electrons are on the boundary between localised and itinerant behaviour. The neutron results give direct evidence of the persistence of strong intra-atomic correlations in, e.g., the heavy-fermion compound UPtj. The theoretical challenge is to reconcile this with the substantial evidence that the f electrons also form a coherent Fermi liquid (Fulde et al. 1988, Zwicknagl 1988). 

Praseodymium The Coulomb transitions with the lowest energies are found in the f contigura-... 

The energy of the lowest Coulomb transition in trivalent thulium, the Hg— F4 transition, is at just under 700 meV with transitions to the... 

Investigations of Coulomb transitions in intermediate valent thulium (and samarium) compounds are an obvious development in this field. 

The study of Coulomb transitions is especially valuable in actinide metals and intermetallic compounds (McEwen et al. 1990, Osborn et al. 1990). Because of the greater radial extent of the 5f charge distribution, the actinide f electrons tend to hybridise more strongly with band electron states than their lanthanide counterparts. In a number of actinide metals, it is evident that the f electrons contribute to the cohesive energy through the formation of 5f bands, either by direct f-f overlap, as in a-uranium, or by hybridisation with conduction bands, as in URUj or URhj (Oguchi and Freeman 1986, Johansson et al. 1987). In these cases, relativistic band theory is successful in predicting lattice constants, photoemission and Fermi surfaces (Arko et al. 1985) provided the f states are included as itinerant. 

In the lowest optieally excited state of the molecule, we have one eleetron (ti ) and one hole (/i ), each with spin 1/2 which couple through the Coulomb interaetion and can either form a singlet 5 state (5 = 0), or a triplet T state (S = 1). Since the electric dipole matrix element for optical transitions — ep A)/(me) does not depend on spin, there is a strong spin seleetion rule (AS = 0) for optical electric dipole transitions. This strong spin seleetion rule arises from the very weak spin-orbit interaction for carbon. Thus, to turn on electric dipole transitions, appropriate odd-parity vibrational modes must be admixed with the initial and (or) final electronic states, so that the w eak absorption below 2.5 eV involves optical transitions between appropriate vibronic levels. These vibronic levels are energetically favored by virtue... 

It is of special interest for many applications to consider adsorption of fiuids in matrices in the framework of models which include electrostatic forces. These systems are relevant, for example, to colloidal chemistry. On the other hand, electrodes made of specially treated carbon particles and impregnated by electrolyte solutions are very promising devices for practical applications. Only a few attempts have been undertaken to solve models with electrostatic forces, those have been restricted, moreover, to ionic fiuids with Coulomb interactions. We would hke to mention in advance that it is clear, at present, how to obtain the structural properties of ionic fiuids adsorbed in disordered charged matrices. Other systems with higher-order multipole interactions have not been studied so far. Thermodynamics of these systems, and, in particular, peculiarities of phase transitions, is the issue which is practically unsolved, in spite of its great importance. This part of our chapter is based on recent works from our laboratory [37,38]. 

The CNDO method has been modified by substitution of semiempirical Coulomb integrals similar to those used in the Pariser-Parr-Pople method, and by the introduction of a new empirical parameter to differentiate resonance integrals between a orbitals and tt orbitals. The CNDO method with this change in parameterization is extended to the calculation of electronic spectra and applied to the isoelectronic compounds benzene, pyridine, pyri-dazine, pyrimidine and pyrazine. The results obtained were refined by a limited Cl calculation, and compared with the best available experimental data. It was found that the agreement was quite satisfactory for both the n TT and n tt singlet transitions. The relative energies of the tt and the lone pair orbitals in pyridine and the diazines are compared and an explanation proposed for the observed orders. Also, the nature of the lone pairs in these compounds is discussed. 

It is notable that pyridine is activated relative to benzene and quinoline is activated relative to naphthalene, but that the reactivities of anthracene, acridine, and phenazine decrease in that order. A small activation of pyridine and quinoline is reasonable on the basis of quantum-mechanical predictions of atom localization encrgies, " whereas the unexpected decrease in reactivity from anthracene to phenazine can be best interpreted on the basis of a model for the transition state of methylation suggested by Szwarc and Binks." The coulombic repulsion between the ir-electrons of the aromatic nucleus and the p-electron of the radical should be smaller if the radical approaches the aromatic system along the nodal plane rather than perpendicular to it. This approach to a nitrogen center would be very unfavorable, however, since the lone pair of electrons of the nitrogen lies in the nodal plane and since the methyl radical is... 

---