Hindered rotors

Variational RRKM theory is particularly important for imimolecular dissociation reactions, in which vibrational modes of the reactant molecule become translations and rotations in the products [22]. For CH —> CHg+H dissociation there are tlnee vibrational modes of this type, i.e. the C—H stretch which is the reaction coordinate and the two degenerate H—CH bends, which first transfomi from high-frequency to low-frequency vibrations and then hindered rotors as the H—C bond ruptures. These latter two degrees of freedom are called transitional modes [24,25]. C2Hg 2CH3 dissociation has five transitional modes, i.e. two pairs of degenerate CH rocking/rotational motions and the CH torsion. 

The above treatment has made some assumptions, such as harmonic frequencies and sufficiently small energy spacing between the rotational levels. If a more elaborate treatment is required, the summation for the partition functions must be carried out explicitly. Many molecules also have internal rotations with quite small barriers, hi the above they are assumed to be described by simple harmonic vibrations, which may be a poor approximation. Calculating the energy levels for a hindered rotor is somewhat complicated, and is rarely done. If the barrier is very low, the motion may be treated as a free rotor, in which case it contributes a constant factor of RT to the enthalpy and R/2 to the entropy. 

The higher energy features can indeed be associated with transitions of He lCl(K,v" = 0) ground-state complexes with rigid He I—Cl linear geometries. In contrast to the T-shaped band that is associated with transitions to the most strongly bound intermolecular vibrational level in the excited state without intermolecular vibrational excitation, n = 0, the transitions of the linear conformer access numerous excited intermolecular vibrational levels, n > 1. These levels are delocalized in the angular coordinate and resemble hindered rotor levels with the He atom delocalized about the l Cl molecule. 

He2 ICl complex will access excited-state levels that have one He atom locahzed in the T-shaped well and the other in bending or hindered-rotor levels. Our group is currently undertaking dynamical studies on He2 ICl. As mentioned above, we have already measured the binding energy of the... 

Strictly speaking, / is the reduced moment of inertia for the relative rotational motion of the system. For the case of a relatively light rotor such as CH3 it is the moment of inertia of the hindered rotor that appears in Eq. (143). 

Pitzer and Gwinn have also provided tables to determine the thermodynamic contributions of hindered rotors (those having torsional barriers on the order of ksT) when such rotors are well described by the torsional potential... 

S. E. Stein and B. S. Rabinovitch. Accurate Evaluation of Internal Energy Level Sums and Densities Including Anharmonic Oscillators and Hindered Rotors. J. Chem. Phys., 58 2438-2445,1973. 

The dynamics of tunneling rotation of hindered rotors interacting with intra- and intermolecular vibrations has received much less attention than structural studies. Such interactions shift and broaden tunneling spectral lines and, when temperature is raised, lead to transitions from coherent tunneling to thermally activated hopping. 

Due to recurring problems with the treatment of methyl rotations in calculations of vibrational averages of optical rotations, Mort and Autschbach [149] have proposed a computational protocol for a separate treatment of hindered rotations. In a nutshell, in this approach a quasi-free rotation of a functional group is treated separately from the vibrational average, with numerically calculated hindered-rotor wavefunctions. With regards to optical activity, the authors studied their protocol on three molecules (R)-methyloxirane, (lS)-norbomanone, and... 

More complex mathematical treatment is necessary when the thermal motion is very large, as for hydrogen atoms in a room-temperature neutron structure analysis, or when it is curvilinear as in a hindered-rotor. The Uy second-rank tensor does not adequately describe the nuclear or electron-scattering density when the motion is far from harmonic or when it deviates from the familiar ellipsoidal probability form. Tb deal with such examples, more complex mathematic expressions using Gram Charlier or Edgeworth expansions are available [210]. 

Disconnected, in coupled cluster theory, 133 Exchange integral, 61, 67 General contraction of basis sets, 157 Hindered rotor, partition function for, 306... 

In some instances, a quantitative understanding of anharmonic effects may be required to acheive a priori accuracies of better than a factor of two. Procedures for incorporating one-dimensional corrections, particularly for hindered rotors are well developed and commonly employed. Increased quantum chemical and computational capabilities should now allow for studies of the fully coupled nonrigid anharmonic state densities and/or partition functions via direct Monte Carlo sampling. Such accurate state density studies are a necessary prerequisite to furthering our understanding of the accuracy limits of both quantum chemical estimates and of RRKM theory itself. 

The temperature and stress dependences of the piy2 spectra of the (Be, 1H), (Be, 2H), and (Be, Li) complexes have also been investigated [137]. They confirm that the (Be, 1H) and (Be, 2H) complexes undergo either tunnelling or hindered rotor motion. 

A summary of the energies for the hindered rotors obtained by these... 

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