Symmetry of molecular motions

An instructive illustration of the effect of molecular motion in solids is the proton resonance from solid cyclohexane, studied by Andrew and Eades 101). Figure 10 illustrates their results on the variation of the second moment of the resonance with temperature. The second moment below 150°K is consistent with a Dsi molecular symmetry, tetrahedral bond angles, a C—C bond distance of 1.54 A and C—H bond distance of 1.10 A. This is ascertained by application of Van Vleck s formula, Equation (17), to calculate the inter- and intramolecular contribution to the second moment. Calculation of the intermolecular contribution was made on the basis of the x-ray determined structure of the solid. 

Dynamic properties, on the other hand, may change under symmetry operations. Molecular motion itself is a most common dynamic property. In our previous discussions of molecular structure, the molecules were mostly assumed to be motionless, and only the symmetry of their nuclear arrangement was considered. However, real molecules are never motionless, and their chemical behavior is influenced by their motion to a great extent. 

There are analogous phenomena for all kinds of molecular motion which may be symmetric and antisymmetric with respect to the various symmetry operations of the molecular point group. The two main kinds of motion in a molecule are nuclear and electronic. The nuclear motion may be translational, rotational and vibrational (Chapter 5). The electronic motion is basically the changes in the electron density distribution (Chapter 6). 

Temperature dependent lineshape variation of the Pake doublet represents then an experimental evidence of a motion occurring in the solid state. 2H NMR investigations on selectively deuterated compounds, therefore, are important tools for the recognition of molecular motions in solids. This method has been applied to the characterization of molecular motions in molecular solids [8] and inclusion compounds [9]. As an example in Fig. 3.2.4 is reported the effect of the motion about the molecular symmetry axis, either by two-fold or n-fold (n>3) flips, on the deuterium spectrum of a deuterated para-substituted benzene [10]. 

There are two important time scales. The one we shall call the NMR time scale it has a characteristic time that is the reciprocal of the spectrum width in hertz, typically about 10"3 s. The other is the time scale of molecular tumbling, with a characteristic time of the order of 10"11 s. The rate of molecular motions relative to these time scales determines major features of the symmetry and structure of the observed spectra. 

The chemical shift anisotropies for the carbonyl and aromatic carbons of Hytrel were reconstructed from a Herzfeld-Beiger analysis (24) of the intensities of the sidebands from NMR magic angle spinning experiments. The results in Table III indicate that the carbonyl carbon chemical shift anisotropy is axially symmetric for each terephthalate ester. We attribute this axial symmetry to a general property of terephthalate esters, rather than as a consequence of molecular motion, as the highly crystalline dimethyl terephthalate also has an axially symmetric carbonyl carbon chemical shift tensor. 

Because of their two-fold symmetry, the phenolic side-chains of Tyr can execute a 7r-flip motion about the Cp-Cy bond between two orientations of locally equal energy. Generally, the effect of molecular motion reduces the quadrupole coupling to a time-averaged value which is smaller than the rigid lattice constant. Thus, the small inner doublet with a splitting of 30 kHz, which is observed both for B. mori and S.c. ricini silk fibroin, is attributed to a fast... 

Another aspect of high chain symmetry is the possibility of molecular motion within the crystal lattice contributing to higher T. For example, polyethylene and polytetrafluoroethylene are both sufficiently symmetrical to be considered as smooth, stiff cylindrical rods. In the crystal, these rods tend to roll over each other and change position when thermally agitated. This motion within the crystal lattice, called premelting, effectively stabilizes the lattice. Consequently, more thermal energy is required to break down... 

Pulsed NQR measurements of the spin-lattice relaxation time, T, also give detailed information on the mechanisms and dynamics of molecular motion in solids. For example, quadrupole relaxation times for solid triethylenediamine show a Ti minimum at a temperature close to 260 K. when 7j equals 0.048 On either side of the minimum, 7j depends exponentially on temperature, according to an Arrhenius-type equation with an activation energy of 34 kJ moP . The mechanism of the relaxation is shown to be hindered rotation of the triethylenediamine molecule about its threefold symmetry axis, which modulates the dipolar coupling between N and the adjacent CH2 protons. 

The current application of NMR methods to the study of polymeric materials falls essentially into two categories. Of initial interest is its potential for characterising molecular orientation rather more precisely than has hitherto been possible in the past, using other methods. At present, experimental inaccuracies and mathematical complexities pose a limitation to its application to those polymer systems involving low symmetries. Set against this, is its well established success in characterising orientation in uniaxially drawn semi-crystalline polymers and perhaps even more impressively its application to non-crystalline polymers. Secondly, we have seen that the anisotropy of the second moment can also be quantitatively analysed in the case of various forms of molecular motion. Providing the firequency of molecular motion is comparable to the NMR line width it will have a predictable effect on the second moment anisotropy and this has already been studied in a number of oriented polymer systems. The implications for a molecular interpretation of mechanical relaxations are clear. 

The older literature (131) suggested two relationships between Tg and Tf TJTf i for symmetrical polymers, and TJTf — for nonsymmetrical polymers. Definitions of symmetry differ, however. One method uses the appearance of atoms down the chain if a central portion of the chain appears the same when viewed from both ends, it is symmetrical. However, even from the beginning, there were many exceptions to the above. Tlie only rule obeyed in this regard is that Tg is always lower than Tf for homopolymers. This is because (a) the same kinds of molecular motion should occur at Tg and 7), and (b) short-range order exists at Tg, but long-range order exists at Tf. 

CONTEXT Phosphorus pentachloride, PF5, is a popular molecule in general chemistry classes for exemplifying the trigonal bipyramidal shape in VSEPR theory The structure is highly symmetric, having two equivalent axial fluorines (so-called because they lie on the principal rotational axis of the molecule) and three equivalent equatorial fluorines. However, studies of the molecular symmetry led to the discovery of an unexpected type of molecular motion. 

Combination bands arise from sums and differences of fundamental stretching and bending vibrations. The combination bands of molecules are dependent on molecular symmetry and thus are unique [13]. As a result, absorbance due to sums and differences of molecular motion can be used to resolve closely absorbing species. For example, consider a sample matrix containing the O—H bands of alcohol, carboxylic acid, and water. The overtones of all three O—H bands fall within tens of nanometers away Irom each other whereas the combination bands fall approximately 100 nm apart (Figure 27.3). 

This type of analysis can also give some information on the dynamics of molecular motion. Figure 1.24 shows the structure of Al2(CH3)6. The symmetry axes and mirror... 

As shown by Table 4, N linewidths vary widely, depending on two factors, the nitrogen bond type and the molecular or ionic mobility. High-resolution work is possible if the local electronic symmetry, and the mobility, are both high and N is a useful probe nucleus for studies of molecular motions. 

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