Polarizability of electrons

Fig. 4.7 Van der Walls bonding as originating from the polarizibility of electron density on hydrogen molecule and carbon atom...

However, one cannot say that the nucleophilic properties, in a philosophical sense, are explained by, for instance, the refractive index. There is not a cause-effect relation between these properties. The measured properties are related to nucleophilicity because they depend on the same intrinsic molecular property, viz. the polarizability of electrons. 

The relative polarizability of electrons of the atoms involved. By polarizability we mean how easily the electrons respond to a chanpng electric field. The electrons of large atoms such as iodine are loosely held and are easily polarized, while the electrons of small atoms such as fluorine are more tightly held and are much less polarizable. 

High polarizability of electrons in Ceo is one of the reasons for which ions and polar molecules are stabilized when trapped in endohedral complexes [3,30]. The dipole polarizability (a) measures the electronic response to a static electric field of a constant strength. Experimental data on polarizability of Ceo or other fullerenes are currently lacking however, a lower bound to a equal to 442.1 au was established by Fowler et al. [31] with the help of ab initio electronic structure calculations carried out at the HF/6-3lG(d) level. Based on this result, one may conclude that, atom for atom, Ceo is at least as polarizable as benzene. A similar (but with a much worse basis set) estimate was obtained for the C70 cluster [32], which was found to be more polarizable than Ceo ... 

There are two contributions to the polarizability of a molecule the distortion of the electronic wave function and the distortion of the nuclear framework. The major contribution is from the electrons, and can be considered to be the sum of contributions from the individual electrons. The contributions of the inner-shell electrons are nearly independent of orientation and these contributions can be ignored. The polarizability of electrons in a bond parallel to the bond direction is different from the polarizability perpendicular to that bond. As a diatomic molecule or linear polyatomic molecule rotates, the components of the polarizability in fixed directions are modulated (fluctuate periodically) as the ellipsoid of polarizability rotates. The rotation of a diatomic or linear polyatomic molecule will be Raman active (produce a Raman spectram). In a nonlinear polyatomic molecule, the polarizabilities of the individual bonds add vectorially to make up the total polarizability. If the molecule is a symmetric top, the total polarizability is the same in all directions and the ellipsoid of polarizability is a sphere. A spherical top molecule has no rotational Raman spectmm. Symmetric tops and asymmetric tops have anisotropic polarizabilities and produce rotational Raman spectra. 

The long-range interactions between a pair of molecules are detemiined by electric multipole moments and polarizabilities of the individual molecules. MuJtipoJe moments are measures that describe the non-sphericity of the charge distribution of a molecule. The zeroth-order moment is the total charge of the molecule Q = Yfi- where q- is the charge of particle and the sum is over all electrons and nuclei in tlie molecule. The first-order moment is the dipole moment vector with Cartesian components given by... 

These moments are related to many physical properties. The Thomas-Kulm-Reiche sum rule says that. S (0) equals the number of electrons in the molecule. Other sum rules [36] relate S(2),, S (1) and. S (-l) to ground state expectation values. The mean static dipole polarizability is md = e-S(-2)/m,.J Q Cauchy expansion... 

This modification of the charge interaction is responsible for shifts in the electron density as permitted by the polarizability of the molecule. 

In order for dipole—dipole and dipole-iaduced dipole iateractioas to be effective, the molecule must coataia polar groups and/or be highly polarizable. Ease of electronic distortion is favored by the presence of aromatic groups and double or triple bonds. These groups frequently are found ia the molecular stmcture of Hquid crystal compouads. The most common nematogenic and smectogenic molecules are of the type shown ia Table 2. 

The importance of solvent participation in the borderline mechanisms should be noted. Nucleophilic participation is minimized by high electronegativity, which reduces the Lewis basicity and polarizability of the solvent molecules. Trifluoroacetic acid and perfiuoro alcohols are among the least nucleophilic of the solvents used in solvolysis studies. These solvents are used to define the characteristics of reactions proceeding without nucleophilic solvent participation. Solvent nucleophilicity increases with the electron-donating capacity of the molecule. The order trifluoroacetic acid < trifluoroetha-nol <acetic acid < water < ethanol gives a qualitative indication of the trend in solvent nucleophilicity. More will be said about solvent nucleophilicity in Section 5.5. 

Another way of obtaining information about the distribution of electrons is by computing the polarizability. This property depends on the second derivative of the energy with respect to an electric field. We ll examine the polarizability of formaldehyde in Chapter 4. 

All the elements have stable electronic configurations (Is or ns np ) and, under normal circumstances are colourless, odourless and tasteless monatomic gases. The non-polar, spherical nature of the atoms which this implies, leads to physical properties which vary regularly with atomic number. The only interatomic interactions are weak van der Waals forces. These increase in magnitude as the polarizabilities of the atoms increase and the ionization energies decrease, the effect of both factors therefore being to increase the interactions as the sizes of the atoms increase. This is shown most directly by the enthalpy of vaporization, which is a measure of the energy required to overcome the... 

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