Bulk parameters polarizability

We have noted that all bulk parameters are a linear function of polarizability Their Introduction Into the correlation equation Is most easily rationalized as a means of correcting T to obtain the appropriate composition of Imf. 

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. 

Polarizability (of a molecule) — There are numerous different mechanisms that contribute to the total polarizability of a molecule. The three most important of these are termed electron polarizability, molecular-distortion polarizability, and orientation polarizability. All these parameters are measured as statistical averages over large numbers of molecules present in the bulk phase. (1) -> Electron polarizability a is a measure of the ease with which electrons tend to be displaced from their zero-field positions by the applied -> electric field. Thus, the electron polarizability of a molecule is defined as the ratio of induced dipole moment pincj (coulomb meters) to the inducing electric field E (volts per meter) ... 

The LSER approach relates a bulk property, P, to molecular parameters thought to account for cavity formation, dipole moment/polarizability, and hydrogen-bonding effects at the molecular level. The cavity term models the energy needed to provide a solute molecule-sized cavity in the solvent. The dipole moment/polarizability terms model dipole and induced dipole interactions between solute and solvent these can be viewed as related to dispersion interactions. The hydrogen-bonding terms model HBA basicity and EIBD acidity interactions. 

One of the most widely used steric parameters is molar refraction (MR), which has been aptly described as a "chameleon" parameter by Tute (160). Although it is generally considered to be a crude measure of overall bulk, it does incorporate a polarizability component that may describe cohesion and is related to London dispersion forces as follows MR = 4TrNa/By where N is Avogadro s number and a is the polarizability of the molecule. It contains no information on shape. MR is also defined by the Lorentz-Lorenz equation ... 

One such methodology is the Kamlet-Taft Solvatochromic parameter approach. In this methodology, a solvent can be characterized by three parameters, tt, a measure of the polarity and polarizability of the fluid, a, the acidity or hydrogen bond donor capability and P, the hydrogen bond acceptor capability or basicity. Each of these parameters is determined from the shift in UV-visible absorbance of a series of select indicator species dissolved in the solvent. Rather than depending on the bulk properties of the fluid, as is the case with the cohesive energy approaches, the solvatochromic parameters are derived from the interactions between the indicator solute and the immediate solvent shell, in effect they are a measure of how a solute sees the solvent. In each case, the scale of values has been normalized to between 0.0 for cyclohexane... 

MR still is the chameleon [91] amongst the physicochemical parameters, despite its broad application in QSAR studies. It has been correlated with lipophilicity, molar volume, and steric bulk. Of course, due to its MW/q component it is indeed related to volume and size of a substituent. But two recent statements that MR is only based on these properties [91, 291] cannot be accepted. The refractive index-related correction term in MR accounts for the polarizability and thus for the size and the polarity of a certain group [158, 173, 286]. The larger the polar part of a molecule is, the larger its MR value will be. Even hydrophobic substituents have a weak enthalpic interaction due to dispersion forces, in addition to their entropic... 

Polarizability-related parameters such as molar refractivity are mostly described as steric descriptors with the acknowledgement of some extra electronic information. Their dual character combines elements that account for the general steric bulk as well as for the polarizability, which refers to the displacement of charges within molecules influenced by an electric field (i.e. induced dipoles). Evidently, molar polarizability influences various global properties of compounds, such as their hydrophobicity, by contributing to the solvation energies in different solvents (Lewis, 1989 Schuiirmann, 1990b). The polarizability factor a corresponds to the dipole induced by the electric field E ... 

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