Rotational potentials

Huller and Baetz [1988] have undertaken a numerical study of the role played by shaking vibrations. The vibration was supposed to change the phase of the rotational potential V (p — a(t)). The phase a(t) was a stochastic classical variable subject to the Langevin equation... 

Palla, P., C. Petrongolo, and J. Tomasi. 1980. Internal Rotation Potential Energy for the Glycine Molecule in Its Zwitterionic and Neutral Forms. A Comparison among Several Methods. J. Phys. Chem. 84, 435-442. 

For an adsorption lattice of the C2 symmetry, the angular part of the adsorption potential selects n preferable molecular orientations. It can be approximated by the hindered-rotation potential... 

Expanding the sum of interactions UCj in r (see Eq. (1.56)) yielded, with the nearest n atoms positioned symmetrically, the hindered rotation potential... 

Fig. 3.5 The plots of steric and conjugative constituents of C,N-rotation potential for CH2=CHN(OSiH3)2 (426)...

FIGURE 8. MM2-85 calculated lp—N—C—H rotational potential curve (C in the tricyclic ring system) for 68, with a pseudoequatorial piperazine ring. The conformations A (dashed line) and B (solid line) are defined in Scheme 6. Reproduced with permission from Reference 108... 

The essential simplification of the model is to replace the alkyl substituents, from mediyl to tert-butyl, by Lennard-Jones spheres of increasing diameters. In this model we cannot calculate the exact values of k and 2 (in fact, these cannot be calculated even if we had the true rotational potential the main missing information is the solvation Gibbs energies of the molecules involved). Nevertheless, we can demonstrate with this simplified model the two major experimental findings regarding the proton-proton correlation in these series of molecules, as shown in Table 4.6. 

PF and A for the pure solvent) and will be cancelled out when computing the binding constants or the correlation function. The quantity Eq( ) is essentially the rotational potential energy of the empty molecule, i.e., the doubly ionized acid, as given in Eqs. (4.8.26) V ,(< >) in Eq. (4.8.26) is the rotational potential energy of ethane (Eliel and Wilen, 1994) and is given by... 

Figure 4.31 shows the total rotational potential for the meso (a) and racemic (b) forms of a-a di-tert-butyl succinic acid, where the tert-butyl is replaced by... 

Figure 4.31. The total rotational potential, in kcal/mol, as a function of the dihedral angle

In the case of dialkylated succinic acid, we have seen that, due to the occurrence of two barriers in the rotational potential of the racemic form (and not of the meso form) with the bulkier alkyl groups (and not the smaller ones), it is likely that the system will freeze-in into a mixture of two components. This is exactly where we observed very large negative cooperativity in the experimental data shown in Table 4.6. One cannot avoid the conclusion that at least a substantial part of the observed cooperativity is spurious. 

The description of the chain dynamics in terms of the Rouse model is not only limited by local stiffness effects but also by local dissipative relaxation processes like jumps over the barrier in the rotational potential. Thus, in order to extend the range of description, a combination of the modified Rouse model with a simple description of the rotational jump processes is asked for. Allegra et al. [213,214] introduced an internal viscosity as a force which arises due to a transient departure from configurational equilibrium, that relaxes by reorientational jumps. Thereby, the rotational relaxation processes are described by one single relaxation rate Tj. From an expression for the difference in free energy due to small excursions from equilibrium an explicit expression for the internal viscosity force in terms of a memory function is derived. The internal viscosity force acting on the k-th backbone atom becomes ... 

All the above compounds yield excimer fluorescence when excited in room-temperature solution. However, because the rotational potential of the C—X bond and the nonbonded interactions of the substituents of the X atom differ from those of the C—C bond 126), the amount of excimer fluorescence from R(C—X—C)R differs from that of R(C—C—C)R. The heteroatom X can also influence the rotational state of the side groups R, as illustrated by the formation of the anti-photodimer in bis(l-naphthylmethyl)ether u2), but not in l,3-bis(l-naphthyl)propane 10). Finally, compounds having n 3 may exhibit excimer fluorescence, if the linkage contains one or more heteroatoms. For example, the—C—O—C—C— linkage in a,to-bis(2-naphthyl) compound allows excimer fluorescence to be observed in room-temperature solution39). 

Calculations of the characteristic ratio and its temperature dependence for PE and isotactic PP have been performed using a RIS model that takes account of non-staggered conformations and the interdependence of the rotational potentials in sequences of four chain bonds. The experimental values are shown to be reproducible satisfactorily by a set of energy parameters consistent with the similarity between steric interactions in the two polymers. 

The intrinsic viscosity of poly(L-proline) is studied as a function of molecular weight and temperature In five commonly used solvents water, trifluoroethanol, acetic acid, propionic acid, and benzyl alcohol. The characteristic ratio is 14 in water and 18-20 in the organic solvents at 303 K, and d (in 0) / d T is negative. The theoretical rotational potential function obtained by Hopfinger and Walton for u-prolyl-L-prolyl-t-prolyl-t-proline J. Macromol. Scl. Phys. 1969, 3, 171 correctly predicts the characteristic ratio at 303 K but predicts the wrong sign for tfiln < >0) IdT. 

The most famous rotational barrier is that in ethane, but because the molecule is nonpolar its barrier is obtained from thermodynamic or infrared data, rather than from microwave spectroscopy. Microwave spectroscopy has provided barrier heights for a few dozen molecules. For molecules with three equivalent potential minima in the internal-rotation potential-energy function, the barriers usually range from 1 to 4 kcal/ mole, except for very bulky substituents, where the barrier is higher. Interestingly, when the potential function has sixfold symmetry, the barrier is extremely low for example, CH3BF2 has a barrier of 14 cal/mole.14... 

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