Alkali polarizability

The alkali metals tend to ionize thus, their modeling is dominated by electrostatic interactions. They can be described well by ah initio calculations, provided that diffuse, polarized basis sets are used. This allows the calculation to describe the very polarizable electron density distribution. Core potentials are used for ah initio calculations on the heavier elements. 

A problem with studies on inert gas is that the interactions are so weak. Alkali halides are important commercial compounds because of their role in extractive metallurgy. A deal of effort has gone into corresponding calculations on alkali halides such as LiCl, with a view to understanding the structure and properties of ionic melts. Experience suggests that calculations at the Hartree-Fock level of theory are adequate, provided that a reasonable basis set is chosen. Figure 17.7 shows the variation of the anisotropy and incremental mean pair polarizability as a function of distance. 

PEO is found to be an ideal solvent for alkali-metal, alkaline-earth metal, transition-metal, lanthanide, and rare-earth metal cations. Its solvating properties parallel those of water, since water and ethers have very similar donicites and polarizabilities. Unlike water, ethers are unable to solvate the anion, which consequently plays an important role in polyether polymer-electrolyte formation. 

The alkali halides cire noted for their propensity to form color-centers. It has been found that the peak of the band changes as the size of the cation in the alkali halides increases. There appears to be an inverse relation between the size of the cation (actually, the polarizability of the cation) and the peak energy of the absorption band. These are the two types of electronic defects that are found in ciystcds, namely positive "holes" and negative "electrons", and their presence in the structure is related to the fact that the lattice tends to become charge-compensated, depending upon the type of defect present. 

Lamoureux G, Roux B (2006) Absolute hydration free energy scale for alkali and halide ions established from simulations with a polarizable force field. J Phys Chem B 110(7) 3308-3322... 

Figure 3.9 C44 elastic moduli vs. reciprocal polarizabilities for prototype alkali halide crystals.

Figure 9.1 Shows the linear correlation between hardness and reciprocal polarizability for 11 alkali halides. The polarizability data are from Ruffa (1963), and the hardness data from Sirdeshmukh et al. (1995).

It is also worth noting that Equation 9.1 indicates a connection between C44, hardness, and e. The dielectric constant, e depends on the polarizability, a of each alkali halide through the Clausius-Mossotti equation ... 

A. R. Ruffa, Theory of the Electronic Polarizabilities of Ions in Crystals Application to the Alkali Halide Crystals, Phys. Rev., 130,1412 (1963). 

Based on the ionic radii, nine of the alkali halides should not have the sodium chloride structure. However, only three, CsCl, CsBr, and Csl, do not have the sodium chloride structure. This means that the hard sphere approach to ionic arrangement is inadequate. It should be mentioned that it does predict the correct arrangement of ions in the majority of cases. It is a guide, not an infallible rule. One of the factors that is not included is related to the fact that the electron clouds of ions have some ability to be deformed. This electronic polarizability leads to additional forces of the types that were discussed in the previous chapter. Distorting the electron cloud of an anion leads to part of its electron density being drawn toward the cations surrounding it. In essence, there is some sharing of electron density as a result. Thus the bond has become partially covalent. 

Acceptors may be considered as either hard"or soft". Hard acceptors, such as the proton or alkali metal ions are hardly polarizable and tend to react preferentially with light donor atoms14, ls ... 

Polarized Raman spectra from the alkali fluorides LiF, NaF and CsF habe been observed with argon laser excitations by Evans and Fitchen 09). These spectra are of interest as an extreme test of lattice dynamics theories and polarizability models. 

Mayer I G. (1933). Dispersion and polarizability and the Van Der Waals potential in the alkali halides. J. Chem. Phys., 1 270-279. 

A number of useful properties of the Group 1 elements (alkali metals) are given in Table 8. They include ionization potentials and electron affinities Pauling, Allred-Rochow and Allen electronegativities ionic, covalent and van der Waals radii v steric parameters and polarizabilities. It should be noted that the ionic radii, ri, are a linear function of the molar volumes, Vm, and the a values. If they are used as parameters, they cannot distinguish between polarizability and ionic size. 

A precise quantitative theory of the mutual polarization of ions in molecules is not possible as long as one cannot take into account the inhomogeneity of the field of the polarizing ion and the dependence of the polarizability of the polarized ion on its surroundings. It is therefore attempted to correlate the observed dependence of the p values on r and the polarizability of the ions in a semi-quantitative and semi-empirical fashion. This proves to be successful for the alkali fluorides but explains only qualitatively why the degree of polarity is smaller for BaO than for SrO. 

Accordingly, the polarizability of the ions will, in general, change upon molecule formation. Taking into account the polarizabilities and polarizing abilities of the ions in Li+I- and Cs+F , it follows that the actual a + ac valid for the application of Eq. (4) is, relative to the free ions, diminished for Lil and increased for CsF. In fact, it was shown on the occasion of an earlier application of Eq. (4) to 9 alkali hahdes, including the only fluoride CsF, that Eq. (5) represents the experimental data better than Eq. (4). 

The capacity of inositol orthoformate derivatives 124 and 125 for binding to alkali metal ions was studied by electrospray ionization mass spectrometry (ESI-MS) gas-phase measurements <2001JOC8629>. The [5.5.5]-iono-phore 125 n = 3) possessed the highest Li /Na selectivity and the best affinity for Li. The results obtained proved to be in agreement with the size-fit concept. Other factors which influence the complexation are the orientation of the oxygen atoms, which are able to bind to metal, the basicity, and the polarizability of the heteroatoms around the perimeter of the binding cavity. 

Dipolar ions like CN and OH can be incorporated into solids like NaCl and KCl. Several small dopant ions like Cu and Li ions get stabilized in off-centre positions (slightly away from the lattice positions) in host lattices like KCl, giving rise to dipoles. These dipoles, which are present in the field of the crystal potential, are both polarizable and orientable in an external field, hence the name paraelectric impurities. Molecular ions like SJ, SeJ, Nf and O J can also be incorporated into alkali halides. Their optical spectra and relaxation behaviour are of diagnostic value in studying the host lattices. These impurities are characterized by an electric dipole vector and an elastic dipole tensor. The dipole moments and the orientation direction of a variety of paraelectric impurities have been studied in recent years. The reorientation movements may be classical or involve quantum-mechanical tunnelling. 

Up to this point we have discussed the formation of polarons in ionic crystals. Polarons of another type can also form in elements and other systems, such as the valence bands of alkali and silver halides, where the polarizability is not the relevant factor. In fact Holstein s (1959) original discussion of the small polaron was of this form. This kind of polaron is sometimes called a molecular polaron, and is illustrated in Fig, 2.3(a), and in Fig. 2.3(b) in the activated configuration of the atoms when the electron can move from one site to another. There is nothing analogous to the large polaron in this case in three-dimensional systems either a small polaron is formed or there is little effect on the effective mass from interaction with phonons. 

The electronic interaction is small if the metal used as an adsorbent has a work function low in relation to the polarizability of the adsorbed atoms. On adsorption of sodium atoms on an aluminum surface of = 4.08 volts, for instance, Brady and Jacobsmeyer (56) obtained a noticeable increase of the photoelectric emission only after five atom layers of sodium had been condensed. In this case the alkali layer itself and not the metal of the sublayer emitted the electrons. 

The purely hydrogen-bonded structures range from the acids to the polyhydroxyl compounds such as carbohydrates. In contrast the alkali h3rdroxides are not hydrogen bonded to any extent, but resemble more closely ionic compounds with polarizable ions. Even in alkaline earth hydroxides, except those of beryllium, no true hydrogen bonds are formed, and it is only in the hydr oxides of the third group, which are of amphoteric character, that the hydrogen bonds reassert themselves [I]. 

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