Polarizability, molecular effect

In the equation s is the measured dielectric constant and e0 the permittivity of the vacuum, M is the molar mass and p the molecular density, while Aa and A (po2) are the isotope effects on the polarizability and the square of the permanent dipole moment respectively. Unfortunately, because the isotope effects under discussion are small, and high precision in measurements of bulk phase polarization is difficult to achieve, this approach has fallen into disfavor and now is only rarely used. Polarizability isotope effects, Aa, are better determined by measuring the frequency dependence of the refractive index (see below), and isotope effects on permanent dipole moments with spectroscopic experiments. 

This approach is based on the introduction of molecular effective polarizabilities, i.e. molecular properties which have been modified by the combination of the two different environment effects represented in terms of cavity and reaction fields. In terms of these properties the outcome of quantum mechanical calculations can be directly compared with the outcome of the experimental measurements of the various NLO processes. The explicit expressions reported here refer to the first-order refractometric measurements and to the third-order EFISH processes, but the PCM methodology maps all the other NLO processes such as the electro-optical Kerr effect (OKE), intensity-dependent refractive index (IDRI), and others. More recently, the approach has been extended to the case of linear birefringences such as the Cotton-Mouton [21] and the Kerr effects [22] (see also the contribution to this book specifically devoted to birefringences). 

Terms of higher order in the field amplitudes or in the multipole expansion are indicated by. . . The other two tensors in (1) are the electric polarizability ax and the magnetizability The linear response tensors in (1) are molecular properties, amenable to ab initio computations, and the tensor elements are functions of the frequency m of the applied fields. Because of the time derivatives of the fields involved with the mixed electric-magnetic polarizabilities, chiroptical effects vanish as a> goes to zero (however, f has a nonzero static limit). Away from resonances, the OR parameter is given by [32]... 

Many-Body Effects in Systems of Peptide Hydrogen- Bonded Networks and Their Gontributions to Ligand Binding A Comparison of DFT and Polarizable Molecular... 

Intramolecular interaction energies in model alanine and glycine tetrapep-tides. Evaluation of anisotropy, polarization, and correlation effects. A parallel ab initio HF/MP2, DFT, and polarizable molecular mechanics study113... 

In small, weakly polarizable molecules, having strong, easily accessible moments—H2O, SO2, HF—the directional effect may be so promineni that it causes the formation of double molecules. Particularly intense interactions always take place if strong dipoles are present on the one hand and easily polarizable molecular components are available, on the other. In such cases it may be anticipated that well defined portions ol larger molecules interact and give rise to stable, stoichiometrically constructed complex compounds. 

Many-body effects in systems of peptide hydrogen-bonded networks and their contributions to ligand binding A comparison of the performances of DFT and polarizable molecular mechanics ... 

Conformational Adjustments The conformations of protein and ligand in the free state may differ from those in the complex. The conformation in the complex may be different from the most stable conformation in solution, and/or a broader range of conformations may be sampled in solution than in the complex. In the former case, the required adjustment raises the energy, in the latter it lowers the entropy in either case this effect favors the dissociated state (although exceptional instances in which the flexibility increases as a result of complex formation seem possible). With current models based on two-body potentials (but not with force fields based on polarizable atoms, currently under development), separate intra-molecular energies of protein and ligand in the complex are, in fact, definable. However, it is impossible to assign separate entropies to the two parts of the complex. 

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. 

This is not an SCRF model, as the dipole moment and stabilization are not calculated in a self-consistent way. When the back-polarization of the medium is taken into account, the dipole moment changes, depending on how polarizable the molecule is. Taking only the first-order effect into account, the stabilization becomes (a is the molecular polarizability, the first-order change in the dipole moment with respect to an electric field, Section 10.1.1). 

The n values were high for all of the ionic liquids investigated (0.97-1.28) when compared to molecular solvents. The n values result from measuring the ability of the solvent to induce a dipole in a variety of solute species, and they will incorporate the Coulombic interactions from the ions as well as dipole-dipole and polarizability effects. This explains the consistently high values for all of the salts in the studies. The values for quaternary ammonium salts are lower than those for the monoalkylammonium salts. This probably arises from the ability of the charge center on the cation to approach the solute more closely for the monoalkylammonium salts. The values for the imidazolium salts are lower still, probably reflecting the delocalization of the charge in the cation. 

Dispersive forces are more difficult to describe. Although electric in nature, they result from charge fluctuations rather than permanent electrical charges on the molecule. Examples of purely dispersive interactions are the molecular forces that exist between saturated aliphatic hydrocarbon molecules. Saturated aliphatic hydrocarbons are not ionic, have no permanent dipoles and are not polarizable. Yet molecular forces between hydrocarbons are strong and consequently, n-heptane is not a gas, but a liquid that boils at 100°C. This is a result of the collective effect of all the dispersive interactions that hold the molecules together as a liquid. 

---