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.
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Notes
- 1.
Note: It is interesting to compare the calculation above based on measured interatomic distances and Van der Waals radii with an estimate using thermodynamic data. Using tabulated densities for C6 H 6 and CH4 of 0.8765 and 0. 4256 g∕cm3, respectively, we find volumes per condensed phase benzene or methane molecule of 148 and 62 \r{A}3. Setting the thickness of the benzene disk to d = 1. 2 \r{A}, (the Van der Waals radius of the hydrogen atom), we find a disk radius of \(\mathrm{r} = {(\mathrm{Vf}/\pi \mathrm{d})}^{1/2} = 5.0\ \mathrm{\r{A}}\). Here f is the packing fraction which we take to be that for randomly close packed spheres, 0.64. Other estimates might be 10 or 15% lower. For methane, approximated as spherical, \((4/3)\pi {\mathrm{r}}^{3} = \mathrm{Vf}\), so r = 2. 1 \r{A}. As for benzene, the disk approximation was used for ethylene. Summarizing
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Wolfsberg, M., Van Hook, W.A., Paneth, P. (2009). Isotope Effects on Dipole Moments, Polarizability, NMR Shielding, and Molar Volume. In: Isotope Effects. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2265-3_12
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DOI: https://doi.org/10.1007/978-90-481-2265-3_12
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