States in Solids

We begin with a general discussion of the nature of d stales in solids and a survey of implications with respect to properties. This discussion covers transition metals as well as transition-metal compounds. We then turn to specific systems compounds arc discussed first, in Chapter 19, since they are somewhat simpler to understand. Transition metals themselves arc discussed in Chapter 20. 

In titanium, at the left end of the transition series, the 3d states will be much more like. S and p valence states and will contribute to the bonding. Even at the far left of the 5/ series, the / levels will behave as valence states and will form bands in metallic thorium (Freeman and Koelling, 1974). These two trend.s—a decrease in the extent of localization as we move left in each series and as we move down in the periodic table constitute the two most important trends in the transition series. They will show up in different ways in different systems, but have the same origin. 

We have seen, particularly in the discussion of covalent crystals in terms of pseudopotentials, the importance of recognizing which matrix elements or effects are dominant and which should be treated as corrections afterward. Tliis is also true in transition-metal systems, and different effects arc dominant in different transition-metal systems thus the correct ordering of terms is of foremost importance. For many transition-metal systems, we find that band calculations, particularly those by L. F. Mattheiss, provide an invaluable guide to electronic structure. Mattheiss uses the Augmented Plane Wave method (APW method), which is analogous to the OPW method discussed in Appendix D. 

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Our intention is to give a brief survey of advanced theoretical methods used to detennine the electronic and geometric stmcture of solids and surfaces. The electronic stmcture encompasses the energies and wavefunctions (and other properties derived from them) of the electronic states in solids, while the geometric stmcture refers to the equilibrium atomic positions. Quantities that can be derived from the electronic stmcture calculations include the electronic (electron energies, charge densities), vibrational (phonon spectra), stmctiiral (lattice constants, equilibrium stmctiires), mechanical (bulk moduli, elastic constants) and optical (absorption, transmission) properties of crystals. We will also report on teclmiques used to study solid surfaces, with particular examples drawn from chemisorption on transition metal surfaces. 

Both sets of investigators also carried out work on Mn(MeCp)2, but this was found to show low-spin behaviour (vide infra) in solid solution in Mg(MeCp)2 or Fe(MeCp)2 (68), or in toluene or methylcyclohexane glasses at 4.2 K (65). Moreover, Ammeter et al. (68) also found Mn(Cp)2 itself to show a low-spin, 2A(ct2 S3) ground state in solid solution in Fe(Cp)2 or Ru(Cp)2, and this system is dealt with in detail later. 

Fig. 7.2. Calculated [40] relative ion population as a function of ion charge state in solid Ti heated at temperatures ranging from 10 to lOOeV. Also shown in the same plot is the separation energy of the 2p-ls transitions as a function of the ion charge. Higher ionization stages from B-like Ti to O-like Ti are expected to emit in the range between 4,550 and 4,750 eV...

Ionic States, in Solid Saturated Hydrocarbons, Chemistry of (Kevan and... 

The most common valence state in solid compounds is -i-3. A +4 valence state is known for the metal in its dioxide, Tb02, and tetrafluoride, TbF4. Terbium also forms several nonstoichiometric oxides of approximate composition Tb407. 

A concept related to the localization vs. itineracy problem of electron states, and which has been very useful in providing a frame for the understanding of the actinide metallic bond, is the Mott-Hubbard transition. By this name one calls the transition from an itinerant, electrically conducting, metallic state to a localized, insulator s state in solids, under the effect of external, thermodynamic variables, such as temperature or pressure, the effect of which is to change the interatomic distances in the lattice. 

One is familiar with the idea of discrete and definite electronic stales in molecules, as revealed by molecular spectroscopy. Each electronic stale possesses a number of vibrational states that are occupied to a great extent near the ground state at normal temperatures. Each vibrational state has, if the stcric conditions are enabling, a number of rotational states associated with it, and for gas molecules both the vibrational and the rotational states can easily be observed and measured spectroscopically. Correspondingly, the distribution of the vibrational states in solids (phonon spectra) is easily measurable. 

Emission from transition metal complexes obey Kasha s rule and originate from the lowest excited state which are (i) 3(n, n ) state in [Rh (phen)3] (C104)3 in water-methanol glass (ii) d, iz ) state in [Ru (bpy)J Clj in ethanol-methanol glass, and (iii) d d) state, in solid [RhClj (phen)J Cl. Their characteristics differ in details and are given in Figure 8.16-Sometimes weak fluorescence is also observed, from Cr + complexes. K [Co(CN)t] is highly luminescent. The 4>p and 7p are temperature... 

J. A. Pople, in Computational Methods for Large Molecules and Localized States in Solids , ed. F. Herman, A. D. McLean, and R. K. Nesbet, Plenum Press, New York, 1973, p. 11. 

Krueger and Weitz [1992] measured the diffusion coefficient of oxygen atoms in the ground 3P state in solid xenon by using the fluorescence of XeO excimers to monitor the 0(3P) concentration. The experimentally determined values are 5.4 x 10-18 and 2.0 x 10 17 cm2/s at 32 and 40 K, respectively. These diffusion coefficients are only about three orders of magnitude smaller than for hydrogen atoms ( 10 14cm2/s at 50 K), as... 

CTL emission is also observed during recombination of carriers originating from surface states formed by the chemisorbed adsorbates produced in the course of catalytic oxidation of a gas. As the recombination takes place through the electronic states in solid, the CTL spectrum is independent of the kind of gas, but depends on the kind of catalyst or the doped activator. This type of CTL emission has been reported for Th02 [6], Th02 activated with Tb or Pr [7], BaS04 activated with Eu [9], and y-AfeOs activated with Dy [18]. 

Di Bartolo, B. (1992) Optical Properties of Excited States in Solids, Plenum. 

Bagus, P. S., Liu, B., McLean, A. D., Yoshimine, M. Ab initio computation of molecular structures through configuration interaction. In Computational methods for large molecules and localized states in solids. Herman, F., McLean, A. D., Nesbet, R. K. (eds.). New York Plenum Press 1973, pp. 87-115... 

The study of distribution function characterization of a solid surface is still in its infancy for lack of heterogeneous isotherms, but, in principle, theories and techniques are available to foster the development of this important bridge between the infinite and finite state in solid surface chemistry. 

Phosphorescence is most easily attained in a solid state rather than in the liquid state. In solid-state dissipation of energy by virtue of collision is minimised and time to the excited state increased. This result in increase in probability of inter system crossing and consequently to phosphorescent. Solid like rigidity and phosphorescence can also be attained by absorption of molecule on a surface or by using a Micelle to stabilise the molecules. 

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