Applications of Polarizability

B. Applicability of Polarizability Anisotropy to Structural or Conformational Problems... 

Applications of Polarizability Anisotropy to Problems of Molecular Structure or Conformation... 

VL Aspects of Polarizability Requiring Investigation VTL Miscellaneous Applications of Polarizability... 

We have presented a necessarily shortened and simplified overview of hybrid QM/MM methods by focusing on the aspects which are more specific for their applications to photoinduced processes in biosystems. We have tried to show that the QM/MM strategy can be effectively used to describe both specific and bulk effects of the environment as well as to account for dynamic effects which are required to simulate reactive processes involving different electronic states. We have also shown that some important problems are still open and further developments of the model are necessary in order to obtain accurate simulations of photoinduced processes. In the near future, we may expect improvements in the efiiciency and applicability of QM/MM dynamics as well an expansion in the applicability of polarizable MM schemes. 

It is thus seen that the dipole-induced dipole propagation gives an exponential rather than an inverse x cube dependence of U x) with x. As with the dispersion potential, the interaction depends on the polarizability, but unlike the dispersion case, it is only the polarizability of the adsorbed species that is involved. The application of Eq. VI-43 to physical adsoiption is considered in Section XVII-7D. For the moment, the treatment illustrates how a long-range interaction can arise as a propagation of short-range interactions. 

Equations (10.17) and (10.18) show that both the relative dielectric constant and the refractive index of a substance are measurable properties of matter that quantify the interaction between matter and electric fields of whatever origin. The polarizability is the molecular parameter which is pertinent to this interaction. We shall see in the next section that a also plays an important role in the theory of light scattering. The following example illustrates the use of Eq. (10.17) to evaluate a and considers one aspect of the applicability of this quantity to light scattering. 

In the first example of applications of the theory in this chapter, we made a point with respect to the polarizability of molecules and showed how the problem could have been handled by the RISM-SCF/MCSCF theory. However, the current level of our method has a serious limitation in this respect. The method can handle the polarizability of molecules in neat liquids or that of a single molecule in solution in a reasonable manner. But in order to be able to treat the polarizability of both solute and solvent molecules in solution, considerable generalization of the RISM side of the theory is required. When solvent molecules are situated within the influence of solute molecules, the solvent molecules are polarized differently depending on the distance from the solute molecules, and the solvent can no longer be neat. Therefore, the polarizable model developed for neat liquids is not valid. In such a case, solvent-solvent PCF should be treated under the solute... 

The application of these methods to unsaturated hydrocarbons involves certain complications. Unsaturated hydrocarbons show an additional polarizability19 of 0.58 x 10 24 cm3 per double bond and 0.86 x 10 24 cm3 per triple bond in the molecule. Similarly the polarizability of a molecule containing a benzene ring exceeds that computed for the atoms present by about 1.28 x 10 24 cm3. These results are most readily explained on the basis that oscillations of charge from atom to atom are significant when double bonds are present. 

The significance of the values calculated for the effective polarizability was first established with physical data, among them relaxation energies derived from a combination of X-ray photoelectron and Auger spectroscopy, as well as N-ls ESCA data53, 54). From our point of view, however, the most important applications of effective polarizability are to be found in correlating chemical reactivity data. Thus, the proton affinity (PA) of 49 unsubstituted alkylamines comprising primary, secondary and tertiary amines of a variety of skeletal types correlate directly with effective polarizability values (Fig. 22). 

Ab initio electron correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities were reported for oxadiazoles <1996JPC8752>. The various measures of delocalization in the five-membered heteroaromatic compounds were obtained from MO calculations at the HF/6-31G level and the application of natural bond orbital analysis and natural resonance theory. The hydrogen transfer and aromatic energies of these compounds were also calculated. These were compared to the relative ranking of aromaticity reported by J. P. Bean from a principal component analysis of other measures of aromaticity <1998JOC2497>. 

J. L. Rivail and D. Rinaldi, Liquid state quantum chemistry computational applications of the polarizable continuum models, in Computational Chemistry, Review of Current Trends, J. Leszczynski, ed., World Scientific, New York (1996) pp. 139-174. 

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