Mutual polarizability

Attractive forces (sometimes also referred to as dispersion forces) between apolar molecules arising from the mutual polarizability of the interacting molecules. London forces also contribute to the interactive forces between polar molecules. See also van der Waals Forces Noncovalent Interactions... 

To complete the picture, calculating mutual polarizabilities relevant to the EHCF/ MM context can be found in [77]. The atom-atom mutual polarizability matrix II has a block-diagonal form ... 

Finally, according to the general formulae given, say, in [27], the matrix element of the bare orbital mutual polarizability entering eq. (4.111) is given by ... 

London forces (or "dispersion forces") — are forces attracting apolar molecules due to their mutual polarizability. London forces are also components of the forces between polar molecules. The London equation approximately describes respective energy of interactions, Vi = -C/r6, where C is constant dependent on energy of ionization and polarizabilities of both molecules and r is the distance between the molecules. See also - van der Waals forces, and - Casimirforce. 

The mutual polarizability is important because, through the alternating positive and negative sign of 7T according as there is an even or an odd number of bonds present betweeni and A ,[the well-known alternating polarity on introduction of a substituent is explained theoretically and can also be calculated quantitatively in a simple way. 

An analytical expression for that contribution can be obtained by using molecular orbital theory at the independent electron level. This was shown by Pople and co-workers (ref. 152) to be directly related (through a constant for each pair of coupled nuclei) to a quantity whose origin lies in the Hiickel theory of tt systems and named the mutual polarizability for the two valence-shell s orbitals centred on the coupled nuclei N and N, tTss ... 

Protic and dipolar aprotic solvents are very different in their ability to solvate anions (Parker, 1962 1965a). The differences arise because protic solvents have a general hydrogen-bonding interaction with small anions (Parker, 1963 Parker and Brody, 1963), whereas dipolar aprotic solvents, which are highly polarizable, have a mutual polarizability... 

Fig. 1. Qualitative representation of the effect of electrostatic, hydrogen-bonding, and mutual polarizability interactions on the free energy of solvation of anions in methanol and in DMF. (cf. Table 26).

London forces Attractive forces between apolar molecules due to their mutual polarizability. They are also components of the forces between polar molecules. Also called dispersion forces. 

Solvent induced shifts of absorption and emission spectra of dissolved symmetric conjugated linear chains as a function of solvent refractive index can provide experimental evidence of the relative state ordering (28,29). The frequency shift Au is approximated by the mutual polarizability expression... 

Anions are less solvated in dipolar aprotic solvents than in water. In water and protic solvents, the anions solvate by ion-dipole interactions on which strong hydrogen bonding is superimposed. In the cases of the dipolar aprotic solvents, the anions solvate also by ion-dipole interactions, but without the influence of hydrogen bonding. Instead, solvation is aided by less energetic interactions arising from the mutual polarizability of the anions and the solvent molecules (Parker, 1962). 

Scalar couplings to metal nuclei are dominated by the Fermi contact term, and approximation on a similar level as for the chemical shifts leads to the expression in Eq. (5), with A being the mean triplet excitation energy, S(0) x the s-electron density at the nucleus X, and ttml the mutual polarizability of the orbital connecting the metal and the ligating atom L. ... 

Soft-soft pertubation is large. Mutual polarizability factors are dominant. Orbital stabilization Is large. 

The identiheation of the coulomb integrals with the electronegativity has some very interesting implications. It allows to redefine the reactivity indices, introduced earlier [45] through the parameters of Hiickel theory, in terms of density functional theory [40]. Indeed, the self and mutual polarizabilities, defined [45] respectively as ... 

The greater magnitude of Up-m-co (trans) was attributed to the larger mutual polarizability of two ligands trans rather than cis" (27). The dependence of Jp-M-co on L is probably due to the varying electronegativities and the resulting difference in the s electron density in the bonds. 

Van der Waals interactions are due to forces between molecules that are not bonded together by chemical bonds. Most important are the interactions between charges, charges and dipole moments, and quadrupole moments, and interaction between dipole moments and quadrupole moments. A particular kind of van der Waals force is London interactions, which decrease with distance as 1/R , where R is the distance between the molecules or atoms (for example, inert gas atoms). In a way, this interaction is a correlation effect between electrons on different atoms. The physical picture is that a momentary charge deviation of the electrons in one atom causes a reaction of the same kind in the other atom. The interaction between these two deviations leads to a small energy lowering, which is responsible for condensation of the inert gas at low temperature. One may also talk about attractions due to mutual polarizability. 

In some papers [27-29] an improved expression for Eg was obtained, which takes into account the effect of mutual polarizability of reactants and the effect of a finite size of reactants in calculating the integral in Eq. (12). Both the above effects give rise to additional terms of the order of a /R" and b /R in the geometric factor in Eq, (45). Energies Vi and Vf in Eq. (44) can be expressed as... 

Some quantities related to the self-polarizability, 7Tr, r are of practical utility in connection with heteroaromatic molecules. They are the mutual polarizabilities of atoms r and s and the polarizability of atom r by the bond s-t defined, respectively, as... 

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