Inversion point, adiabatic

The electronic charge distribution of H2 is inversion symmetric and, therefore, H2 is necessarily non-polar. The HD molecule possesses a nearly identical electronic cloud. Nevertheless, HD does feature a (weak) permanent dipole moment. It is of a non-adiabatic nature and arises from the fact that the zero-point motion of the proton takes place with a greater amplitude than that of the deuteron. As a consequence, the side of the proton is slightly more positively charged than that of the deuteron if the HD molecule is in the vibrational ground state. 

The MEP for inversion corresponds to 6 = 0 and is characterized by the barrier height VWhen C/2V, > 1, apart from this MEP, there is a path that includes two segments described by Eq. (8.42) and a second-order saddle point. The barrier along this path is greater than V, and equal to U,(l + 2V0/C). The transverse frequency along the straight-line MEP for inversion has a minimum at the saddle point q = 0, 0 = 0 consequently, the vibrationally adiabatic barrier is lower than the static one. 

Coriolis coupling (p. 906 and 912) critical points (p. 888) cross section (p. 901) curvature coupling (p. 906 and 914) cycloaddition reaction (p. 944) democratic coordinates (p. 898) diabatic and adiabatic states (p. 949) donating mode (p. 914) early and late reaction barriers (p. 895) electrophilic attack (p. 938) entrance and exit channels (p. 895) exo- and endothermic reactions (p. 909) femtosecond spectroscopy (p. 889) Franck-Condon factors (p. 962) intrinsic reaction coordinate (IRC) (p. 902) inverse Marcus region (p. 954) mass-weighted coordinates (p. 903)... 

This rapid adiabatic expansion is sufficient to cool the nitrogen to below its boiling point of 77°K, so this is a way to make liquid nitrogen. There is a temperature for each gas called the Joule-Thomson inversion temperature and cooling occurs if the initial temperature is below that temperature but the gas heats upon expansion if the initial temperature is above the inversion temperature. At room temperature He is above its inversion temperature and will actually heat up upon expansion. Although there is also a pressure effect, there are absolute temperatures for this effect. For He the temperature is 51°K, for H2 202°K, for N2 621°K, and for O2 it is 764°K (see discussion at http //en.citizendium.org/wiki/Joule-Thomson effect). Thus, air (N2 + O2) can be liquefied by adiabatic expansion starting from room temperature and 1 atm, but He and H2 must be precooled to below their Joule-Thomson inversion temperatures. 

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