Polarizability isotope effects

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. 

Induced Moments, Polarizability Isotope Effects 12.3.1 The Polarizability... 

Using Equation 12.12 one obtains (AA/A — Av /v 2) = (Aao/ao). We see that precise refractive index differences measured over a reasonable range of wavelengths allow the recovery of the polarizability isotope effect (i.e. the isotope effect on the electric field induced dipole moment), provided the molar volume and its isotope effect are available. 

Isotope Effects on Dipole Moments, Polarizability, NMR Shielding, and Molar Volume... 

Abstract Although the electronic structure and the electrical properties of molecules in first approximation are independent of isotope substitution, small differences do exist. These are usually due to the isotopic differences which occur on vibrational averaging. Vibrational amplitude effects are important when considering isotope effects on dipole moments, polarizability, NMR chemical shifts, molar volumes, and fine structure in electron spin resonance, all properties which must be averaged over vibrational motion. 

Table 12.1 Dipole moments, polarizabilities, and isotope effects for some diatomic and simple polyatomic molecules (ground vibrational state values)...

Methods for determining permanent dipole moments and polarizabilities can be arbitrarily divided into two groups. The first is based on measuring bulk phase electrical properties of vapors, liquids, or solutions as functions of field strength, temperature, concentration, etc. following methods proposed by Debye and elaborated by Onsager. In the older Debye approach the isotope effects on the dielectric constant and thence the bulk polarization, AP, are plotted vs. reciprocal temperature and the isotope effect on the polarizability and permanent dipole moment recovered from the intercept and slope, respectively, using Equation 12.5. 

Here, A and v 2 are fitting parameters amenable to physical interpretation using Equation 12.11. The point of present concern is that the isotope effect on polarizability can now be expressed in terms of isotopic differences in refractive index. It follows from Equation 12.14 that a plot of AR/R = [6n2/((n2—l)(n2 + 2))][An/n] vs. v2 gives an approximately straight line,... 

Van Hook, W. A. and Wolfsberg, M., Comments on H/D isotope effects on polarizabilities. Correlation with virial coefficient, molar volume and electronic second moment isotope effects. Z Naturforsch. 49A, 563 (1994)... 

Vibrational Raman Scattering of radiation with changed frequency due lo polarizability change during a vibration (A = visible usually) Qualitative for large molecules 10-Ms 10 Pa (100 ion) (v dependent) Useful for characterization. Some structural information from number of bands, position, depolarization ratios, and possibly Isotope effects. All... 

C02 band intensities, which vary by a factor of 1.8 in UP, probe the polarizability of the environment. In several cases, high intensities for C02 v3 bands indicate contacts between the oxygens of C02 and the free radicals, in agreement with the isotope effects on frequencies and linewidths mentioned above. 

OH2 19-22 anharmonicity 15 decomposition 33, 35 energetics 78-79 geometry 77-78, 215-23 isotope effects 119-21 polarizability 162-3 superposition error 25-26, 27 total energy 24... 

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