Hindered rotations

Hindered Rotation (kT to) With hindered rotation, the potential energy of the internal rotation is restricted by a potential barrier, Vq, whose magnitude varies as the two parts of the molecules rotate past each other in a cyclic fashion. For example, in the molecule H3C-CCI3, the potential varies as the hydrogen atoms on one carbon move past the chlorine atoms on the other. 

In order to obtain the partition function for systems of this type (where the thermal energy and potential barrier are of the same magnitude), it is necessary to have the quantum mechanical energy levels associated with the barrier. Pitzer5 has used a potential of the form 

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Molecules larger than those considered so far are fonned by linking together several smaller components. A new kind of dynamics typical of these systems is already seen in a molecule such as C2Hg, in which there is hindered rotation of the two methyl groups. Systems with hindered internal rotation have been studied in great... 

Wagner A F, Kiefer J H and Kumaran S S 1992 The importance of hindered rotation and other... 

Kiefer J H, Mudipalli P S, Wagner A F and Harding L 1996 Importance of hindered rotations in the thermal dissociation of small unsaturated molecules classical formulation and application to hen and hcch J. Chem. Phys. 105 1-22... 

The quantum numbers tliat are appropriate to describe tire vibrational levels of a quasilinear complex such as Ar-HCl are tluis tire monomer vibrational quantum number v, an intennolecular stretching quantum number n and two quantum numbers j and K to describe tire hindered rotational motion. For more rigid complexes, it becomes appropriate to replace j and K witli nonnal-mode vibrational quantum numbers, tliough tliere is an awkw ard intennediate regime in which neitlier description is satisfactory see [3] for a discussion of tire transition between tire two cases. In addition, tliere is always a quantum number J for tire total angular momentum (excluding nuclear spin). The total parity (symmetry under space-fixed inversion of all coordinates) is also a conserved quantity tliat is spectroscopically important. 

Ha T, Glass J, Enderle T, Chemla D S and Weiss S 1998 Hindered rotational diffusion and rotational ]umps of single molecules Phys. Rev. Lett. 80 2093-7... 

The treatment of conjugated systems in terms of electron systems that extend smoothly over all atoms allows the treatment of a variety of structural phenomena, as may be explained with a spedes that shows hindered rotation and with the nitro group. 

The formalism that we have set up to describe chain flexibility readily lends itself to the problem of hindered rotation. Figure 1.8a shows a sawhorse representation of an ethane molecule in which the angle of rotation around the bond is designated by electron repulsion between the atoms bonded to... 

Figure 1.8 Hindered rotation around a carbon-carbon bond, (a) The definition of (p (from 0 = 0) in terms of the ethane molecule, (b) The potential energy as a function of (p. (c) Here (p is shown (from (p = 0) for a carbon-carbon bond along a polyethylene backbone, (d) The potential energy for case (c) shown as a function of (p. [Panels (b) and (d) reprinted with permission from W. J. Taylor, J.Chem.Phys. 16 257 (1948).]...

Chiral separations are concerned with separating molecules that can exist as nonsupetimposable mirror images. Examples of these types of molecules, called enantiomers or optical isomers are illustrated in Figure 1. Although chirahty is often associated with compounds containing a tetrahedral carbon with four different substituents, other atoms, such as phosphoms or sulfur, may also be chiral. In addition, molecules containing a center of asymmetry, such as hexahehcene, tetrasubstituted adamantanes, and substituted aHenes or molecules with hindered rotation, such as some 2,2 disubstituted binaphthyls, may also be chiral. Compounds exhibiting a center of asymmetry are called atropisomers. An extensive review of stereochemistry may be found under Pharmaceuticals, Chiral. 

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

As seen from this table, the WKB approximation is reasonably accurate even for very shallow potentials. At 7 = 0 the hindered rotation is a coherent tunneling process like that studied in section 2.3 for the double well. If, for instance, the system is initially prepared in one of the wells, say, with cp = 0, then the probability to find it in one of the other wells is P( jn, t) = 5sin (2Ar), while the survival probability equals 1 — sin ( Ar). The transition amplitude A t), defined as P( + t) = A t), is connected with the tunneling frequency by... 

Fig. 55. The potential of hindered rotation of the CH3 group in nitromethane (CH3NO2) crystal, (a) calculated from INS data, Vi = 0.586 kcal/mol, V = 0.356 kcal/mol, S = 30°, and (b) calculated with the atom-atom potential method [Cavagnat and Pesquer 1986]. The barrier height is 0.768 kcal/mol.

Fig. 56. Contour plots of (a) shaking and (b) breathing vibrations coupled to hindered rotation around the three-fold axis. The MEP is shown.

Propane, the next higher member in the alkane series., also has a torsional barrier that results in hindered rotation around the carbon-carbon bonds. The barrier is slightly higher in propane than in ethane—a total of 14 kj/mol (3.4 kcal/mol) versus 12 kj/mol. 

Apparently, the 1H NMR spectra of 1 //-azepines are invariant over substantial temperature ranges.61 However, temperature dependence has been noted69 in the 13CNMR spectra of some 1 -acyl-1 //-azepines, and is attributed to hindered rotation about the N-CO bond rather than to ring-inversion phenomena AG free enthalpies of activation for hindered rotation of 62-66 kJ moP1 have been calculated. E/Z-rotamcr ratios for l-aroyl-l//-azepines have been assessed and show a slight preference for the -rotamer 22 however, an X-ray structural analysis of l-(4-bromobenzoyl)-2-methyl-3.5,7-triphenyl-l//-azepine demonstrates that in the crystal state it is exclusively in the E configuration.22... 

The fact that both heats of formation and equilibrium pressures of the hydrates of spherical molecules correctly follow from one model must mean that the L-J-D theory gives a good account of the entropy associated with the motions of these solutes in the cavities of a clathrate. That the heat of formation of ethane hydrate is predicted correctly, whereas the theoretical value of its vapor pressure is too low, is a further indication that the latter discrepancy must be ascribed to hindered rotation of the ethane molecules in their cavities. 

Although these potential barriers are only of the order of a few thousand calories in most circumstances, there are a number of properties which are markedly influenced by them. Thus the heat capacity, entropy, and equilibrium constants contain an appreciable contribution from the hindered rotation. Since statistical mechanics combined with molecular structural data has provided such a highly successful method of calculating heat capacities and entropies for simpler molecules, it is natural to try to extend the method to molecules containing the possibility of hindered rotation. Much effort has been expended in this direction, with the result that a wide class of molecules can be dealt with, provided that the height of the potential barrier is known from empirical sources. A great many molecules of considerable industrial importance are included in this category, notably the simpler hydrocarbons. 

Hindered rotation, 33, 34 internal, 367 Homopolymer, 168, 183 Hot bands, 374 Hot lattice, 4, 11, 21 Hydrates, 7, 9, 21, 31, 41 crystallization, 44 Hydrochloric acid clathrates, 2 in hydroquinone, 7 Hydrogen, bound, 4, 175 bromine hydrate, 35 4- carbon dioxide system, 110 4 carbon monoxide system, 96, 108 chloride hydrate, 35 clathrates, 2 chloride, 30... 

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