Polarizability Group 1 elements

The frozen-core approximation is one basic assumption underlying all ECP schemes described so far. Especially for main group elements, where a large-core ECP approximation works fairly well if not too high accuracy is desired, the polarizability of the cores (Fig. 14) has nonnegligible effects for elements from the lower part of the periodic table. Within the ECP approach it is indeed possible to account for both static (polarization of the core at the HF level) and dynamic (core-valence correlation) polarization of the cores in an efficient way. Meyer and coworkers [202] proposed in the framework of AE calculations the... 

The electron affinities (in kJ mol ) of some main group elements. Recommended values for the polarizability volumes a (in 10 m ) of some atoms and monatomic ions in the gas phase. 

The static dipole polarizabilities for the Pq ground state of the neutral group-14 elements C, Si, Ge, Sn, Pb, and element Z = 114 have been determined from all-electron relativistic coupled cluster theory. It is shown that the isotropic and anisotropic components of the polarizability increase monotonically with the nuclear charge, except for the spin-orbit coupled /=0 states, which start to decrease from Sn to Pb and even further to element 114. So, spin-orbit coupling leads to a significant reduction of the polarizability of element 114, i.e., from 47.9 a.u. at the scalar-relativistic Douglas-Kroll level to 31.5 a.u. at the Dirac-Coulomb level of theory, which is below the value of Si. The calculations further demonstrate that relativistic and electron correlation effects are nonadditive. The measured dipole polarizabilities of Sn (42.4 11 a.u.) and Pb (47.1 7) are in reasonable agreement with the theoretical values, 52.9 a.u. and 47.3 a.u., respectively. 

Most of the classes of organometallic compounds which have found extensive use as synthetic reagents are derivatives of the elements considered in this chapter. In most cases their synthetic value is due to the polarity of the metal-carbon bond, e.g. the reactivity of the lithium alkyls and Grignard reagents is largely due to the polar Li(S-l-)—C(8—) and Mg(8-t-)—C(8—) bonds which very readily react with polar (or in some instances particularly polarizable) groups ... 

A detailed discussion of individual halides is given under the chemistry of each particular element. This section deals with more general aspects of the halides as a class of compound and will consider, in turn, general preparative routes, structure and bonding. For reasons outlined on p. 805, fluorides tend to differ from the other halides either in their method of synthesis, their structure or their bond-type. For example, the fluoride ion is the smallest and least polarizable of all anions and fluorides frequently adopt 3D ionic structures typical of oxides. By contrast, chlorides, bromides and iodides are larger and more polarizable and frequently adopt mutually similar layer-lattices or chain structures (cf. sulfides). Numerous examples of this dichotomy can be found in other chapters and in several general references.Because of this it is convenient to discuss fluorides as a group first, and then the other halides. 

All the elements in a main group have in common a characteristic valence electron configuration. The electron configuration controls the valence of the element (the number of bonds that it can form) and affects its chemical and physical properties. Five atomic properties are principally responsible for the characteristic properties of each element atomic radius, ionization energy, electron affinity, electronegativity, and polarizability. All five properties are related to trends in the effective nuclear charge experienced by the valence electrons and their distance from the nucleus. 

It is shown that the stabilities of solids can be related to Parr s physical hardness parameter for solids, and that this is proportional to Pearson s chemical hardness parameter for molecules. For sp-bonded metals, the bulk moduli correlate with the chemical hardness density (CffD), and for covalently bonded crystals, the octahedral shear moduli correlate with CHD. By analogy with molecules, the chemical hardness is related to the gap in the spectrum of bonding energies. This is verified for the Group IV elements and the isoelec-tronic III-V compounds. Since polarization requires excitation of the valence electrons, polarizability is related to band-gaps, and thence to chemical hardness and elastic moduli. Another measure of stability is indentation hardness, and it is shown that this correlates linearly with reciprocal polarizability. Finally, it is shown that theoretical values of critical transformation pressures correlate linearly with indentation hardness numbers, so the latter are a good measure of phase stability. 

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 simple calculation for urea by Spackman is instructive. Urea crystallizes in an acentric space group (it is a well-known nonlinear optical material), in which the symmetry axes of the molecules coincide with the two-fold axes of the space group. All molecules are lined up parallel to the tetragonal c axis. If the electric field is given by E, and the principal element of the diagonalized molecular polarizability tensor along the c axis by oc , the induced moment along the polar c axis is... 

Combining the highest electronegativity (4,0) with a rather small polarizability volume which amounts to not more than 0.5 makes fluorine a unique element. Its incorporation into hydrocarbon frameworks results in different electrostatic effects, which are sometimes rarely predictable. However, the influence of fluorine substituents on the acidity of nearby functional groups such as OH, NH,... 

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