Atomic polarizability volumes

Apart from the factor of 4rreo, the polarizability of an atom is determined in this model by the volume. If we had been working in cgs (old-fashioned electromagnetic quantities) rather than SI (modem ones), we would have found a = a and for this reason people speak of the polarizability volume. 

From Eq, (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the P-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory" or Lorentz field sums of dipole lattices" static, atomic level modeling of the intrinsic bond polarity" atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. " The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

Various reactivity indices have been derived for benzenoid hydrocarbons from the following purely topological approaches the Huckel model (HMO), first-order perturbation theory (PMO), the free electron MO model (FEMO), and valence-bond structure resonance theory (VBSRT). Since many of the indices that have been known for a long time (index of free valence Fr, self-atom polarizability ir , superdelocalizability Sr, Brown s index Z, cation localization energy Lr+, Dewar reactivity number Nt, Brown s para-localization energy Lp) have been described in detail by Streitwieser in his well-known volume [23] we will refer here only to some more recent developments. 

Molecular polarizability can also be approximated by simply summing atomic polarizabilities over all the molecule atoms. Moreover, molecular polarizability a expressed as polarizability volume is called polarizability volume and is defined as ... 

Both indices can be extended to any other atomic property different from atomic mass, such as -+ atomic polarizability, atomic - van der Waals volume, etc. 

Six different weighting schemes are proposed (1) the unweighted case u (yvi = 1 i —, n, where A is the number of atoms for each compound), (2) atomic mass m, (3) the - van der Waals volume v, (4) the Sanderson - atomic electronegativity e, (5) the - atomic polarizability p and (6) the - electrotopological state indices of Kier and Hall 5. All the weights are also scaled with respect to the carbon atom, and their values are shown in Table W-5 moreover, as all the weights must be positive, the electrotopological indices are scaled thus ... 

Z, atomic number L, principal quantum number Z , number of valence electrons , van der Waals atomic radius covalent radius m, atomic mass , van der Waals volume Sanderson electronegativity a, atomic polarizability (10 " cm ) IP, ionization potential (eV) EA, electron affinity (eV). 

For atomic mass, van der Waals volume, Sanderson electronegativity, and atom polarizability, the scaled values with respect to the carbon atom are listed in Table A3. 

The atomic weighting schemes applied for G ETAWAYdescriptor calculation are those proposed for the WHfM descriptors, that is, atomic mass (m), —> atomic polarizability p), Sanderson atomic electronegativity (e), atomic van der Waals volume (v), and the unit weighting scheme (u). 

Hosoya266 has discussed implications of graph-theoretical techniques and the Coulson-Longuet-Higgins atom-atom polarizability in an analysis of -electron networks. The internal energy as a state function of the polarizability volume and the diamagnetic susceptibility has been discussed by deVisser.265... 

In this notation, the elements of the polarizability tensor are only proportional to the particle volume, similar to the atomic polarizability. is the dielectric constant of the surrounding medium. A dipole with linear response oscillates with the same frequency as the applied electric field and, hence, emits an electric field Es asymptotically given in the far field as... 

We now present a heuristic extension of this relationship between the van der Waals energy and the atomic polarizability to the case of two atoms or molecules interacting in a dielectric medium. For the case just treated, namely a vacuum, the polarizability is related to the dielectric constant by a, = i — l)/pf, where 1 /pi is the molecular volume of species i. In a medium... 

From the dependence of atomic polarizability by the cubic atomic radii rises immediately the correspondence with the atomic volume also. Therefore, atomic polarizability states as a fully atomic related property and have to closely follow the periodicity of atomic volumes, the Lothar Meyer s periodic curve. 

The fraction a = a/ 47tso) has the dimension (length) and is referred to as the polarizability volume. This is the parameter that is normally listed in reference works. The polarizabilities atoms or monatomic ions in the gas phase are not accurately known, but recommended values for polarizability volumes of neutral alkali metal and halogen atoms and ions are listed in Table 3.4. 

Table 3A. Recommended values for the polarizability volumes a (in 10 m ) of some atoms and monatomic ions in the gas phase [5].

Table 3.4 also contains the polarizability volumes of some common monatomic ions. It is seen that removal of the most loosely held electron in an alkali metal atom leads to a dramatic reduction of the polarizability. Similarly, addition of an electron to a halogen atom to form an anion leads to an increase of the polarizability. Comparing cations and anion, we see that halogen anions have considerably higher polarizabilities than alkali metal cations. 

Recommended values for the polarizability volumes of gaseous atoms have been taken from T. M. MiUer and B. Bederson, Adv. At. Mol. Phys, 1977, 13, 1 polarizabUity volumes for alkali metal cations and halide anions from S. Hati, B. Datta and D. Datta, J. Phys. Chem., 1996,100,... 

Sometimes polarizability is referred to as polarizability volume. Note that the units of polarizability given above have the units of volume. Thus, polarizability provides a measure of the atomic or molecular volume. Polarizability values are from the CRC Handbook of Chemistry and Physics, 93rd edition. 

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