Rotational potentials threefold

Aspirin. Aspirin, acetyl salicylic acid, is an example of a methylated (CD3) molecule, which has recently been studied by deuterium NMR [76], The spectroscopic measurements were analyzed considering the threefold term of the potential only. Additional information on the rotational potential was obtained from the INS spectra of aspirin with a protonated methyl group [77], the essential difference between the two systems being the moment of inertia of the rotors. The two sets of data can only be reconciled when the V6 term of the potential is included. A numerical calculation of the rotational potential, based on the room temperature crystal structure [78], corroborates this interpretation of the INS data and the published NMR data. 

Threefold rotational potential energy barriers such as in ethane and butane are not always encountered. Twofold potential rotational energy barriers are produced by 1,4-phenylene groups in the main chain, for example. Catena-po y(su uv) also has a twofold rotational potential energy barrier. 

The conformations of aliphatic hydrocarbons are characterized by threefold rotational potentials and a preferred trans conformation. These two characteristics do not always predominate. Twofold rotational potentials are produced by, for example, 1,4-phenylene groups and polymeric sulfur. 

The difference in behavior of the two series of compounds, mesogenic derivatives of m-carborane versus nonmesogenic adamantane analogs, was rationalized by higher conformational mobility of the m-carborane-Ph junction (fivefold symmetry rotational potential) than the adamantane-Ph (threefold symmetry rotational potential), which leads to less ordered phases in the former. 

Next come the dihedral angles (or torsions), and the contribution that each makes to the total intramolecular potential energy depends on the local symmetry. We distinguish between torsion where full internal rotation is chemically possible, and torsion where we would not normally expect full rotation. Full rotation about the C-C bond in ethane is normal behaviour at room temperature (although 1 have yet to tell you why), and the two CH3 groups would clearly need a threefold potential, such as... 

Sixfold barriers to internal rotation occur in molecules such as toluene andp-fluoro-toluene whose molecular frame has C2v symmetry about the rotor axis. The simplest spectroscopic model of internal methyl rotation assumes a rigid, threefold symmetric methyl rotor attached to a rigid molecular frame with the C2 axis coincident with the rotor top axis.25 The effective one-dimensional sixfold torsional potential takes the traditional form,... 

Over the past several years, Gruen and coworkers have examined the SH response from iron electrodes in alkaline solutions [45, 53, 172]. In their work on polycrystalline iron, they concluded that the potential dependent SH response which was observed during surface oxidation could be attributed to two intermediate phases on the electrode surface between the passive film at oxidative potentials and the reduced metal at hydrogen evolution potentials [53]. They have recently extended this work to Fe(110). In this study [172], they examined the SH rotational anisotropy from this crystal under ambient conditions. They found that the experiments reveal the presence of both twofold and threefold symmetric species at the metal/oxide interface. When their data is fit to the theory of Tom et al. [68], they conclude that the measured three-fold symmetric oxide is found to be tilted by 5° from the Fe(110) plane. The two-fold symmetric structure is aligned with the Fe(110) surface. 

Figure 7.1. Correlation between the energy levels of free rotation of a symmetric top and those of torsion vibration in the threefold potential. Quantum numbers J and K are rotational levels n represents vibrational levels. Relative positions of A and E levels in multiplets n = 0, 1,. . . , are shown on the right.

Figure 7.13. Contour plot of the potential for shaking (a) and breathing (b) vibrations (coordinate q along the y axis) coupled to hindered rotation about the threefold axis.

The simplest potential that we can use to interpret the measured tunnelling spectra is a ID torsional potential with threefold symmetry, V3. For this, the principal tunnelling energy between the rotational ground and the first excited state... 

Regardless of the lack of our present knowledge concerning the nature and heights of these two barriers in the polypeptide backbone, two important points seem evident, viz. these barriers are not as high as the barriers to rotation about C—C bonds in hydrocarbons where the barriers are of the order of 3 kcal mole-1 or greater, and the potentials are probably threefold rather than sixfold, because sixfold potentials occur in only a few cases where the symmetry is such that the threefold contribution cancels. 

In order to illustrate the power of the Group Theory for Non-Rigid Molecules, let us consider the double internal rotation problem in acetone, solved in [34]. This motion is described by a restricted Hamiltonian operator such as that of pyrocatechin (32) in which only the threefold periodicity of the potential for acetone (47) has been introduced ... 

The periodicity of the cosine functions creates the multiple potential energy wells that are required. In both CHARMM and MM3, the expansions may include multiple terms. However, the parameter sets for CHARMM generally use just a single term, such as a threefold torsional potential for rotation about a single bond. Although MM3 uses three different periodicities to describe torsional potential energy surfaces, in many cases (e.g., H—C—C—H) one or two of these terms are small or zero. 

CH Si Torsion in PDMS. The torsional potential curve has three degenerate minima because of the threefold symmetry of the methyl group. For this reason. Figure 6 shows only the behavior of one-third of the full rotation. The barrier height is 1.7 kcal/mol when the backbone is allowed to relax and 2.4 kcal/mol when the backbone is frozen. The experimental value is 2.2 kcal/mol (i), but this value is based on results determined at two temperatures above and below Tg. Our results indicate that at least one more experimental measurement, at Tg for the Si-CHa bond, is needed. These calculations predict that the new measured value will set the data... 

FIG. 2. The potential energy for the Cw sitting at (0,0,0) as a function of rotation angle away from its equilibrium orientations. Ill, 110, and 1-10 correspond, respectively, to threefold, fivefold, and twofold rotation axes of the molecule. 

The wave functions describing rotation of a hindered methyl group have A and E symmetry in the threefold symmetric potential and are associated with nuclear spin functions having the same symmetry representations and corresponding to a total spin of the protons of three-halves and one-half,... 

---