Torsional motion rings

Terms in the energy expression that describe a single aspect of the molecular shape, such as bond stretching, angle bending, ring inversion, or torsional motion, are called valence terms. All force fields have at least one valence term and most have three or more. 

The decay of the tetramethylene diradical derived from 2,2,5,5-t/4-cyclopenta-none is much slower than seen for the C4Hg diradical. Both principal decay modes, fragmentation to two ethylenes and ring-closure to cyclobutane, may be dependent dynamically on torsional motions of the terminal methylene groups. 

The barriers restricting the torsional motion of the rings are definitely fairly low in all (CsHs)jM compounds which have hitherto been investigated373. In one case, e. g. ferrocene, (C5Hs)2Fe a barrier of 3.8 13 kJ/mol has been determined by electron diffraction22. Unfortunately, there are no other gas phase quantitative barrier determinations for the ring torsional motion of these sandwich compounds. 

The main difference between these stretched-bipyramidalized conical intersections in rings and substituted ethylenes is the process by which they are reached. As already discussed before (Section 8.4), dynamics calculations [38, 66, 90] showed that an important fraction of trajectories of polar substituted ethylenes undergoes stretching and bipyramidalization in the beginning of the time evolution. Nevertheless, in rings the stretched-bipyramidalized configuration cannot be reached by the direct activation of these modes, but it is obtained indirectly as a consequence of the torsional motion around specific bonds. Despite the fact... 

In an oversimplified picture, nonradiative decay in U and C is controlled by a torsional motion about the C(5)C(6) double bond, while in the canonical G tautomer out-of-plane deformations of the six-membered ring are chiefly responsible for internal conversion. In the case of G, the canonical, biologically relevant, 9H-keto form indeed exhibits photophysical properties which are distinctly different from other tautomers. Its excited state lifetime, for example, is the shortest of all tautomers. This is a consequence of its pronounced out-of-plane distortions absent in other tautomers. 

It is important to note that the proportional relationship between Amax, Amid, and Amin for these couplings is the same for 100% spin density, and for the present case with approximately 50% spin density. When this is so it indicates that there is no rocking motion at the radical site. This is good evidence therefore that the radical site is essentially planar. The best evidence for radical planarity comes from the analysis of the direction cosines associated with each principal values of the hyperfine coupling tensor. The direction of Amin (Table 18-2) is known to be associated with the direction of the >C-H bond, while the direction associated with the Amid indicates the direction of the n-clcctron orbital. These directions are easily calculated from the crystal structure, and are included in Table 18-2. One sees that the direction associated with Amid deviates only 2.0° from the computed perpendicular to the ring plane, while the direction of Amin, deviates only 2.8° from the computed direction of the C6-H bond. The errors listed on these values are at the 95% confidence level. This is very clear evidence that the radical shown here is planar in the solid-state. Any torsional motion of the C6-H would lead to asymmetries of the hyperfine coupling tensor, and would not produce the observed agreement between the direction cosines and the known directions obtained from the crystal structure. 

The torsional potential of mean force (Fig. 24) and the correlation function for the torsional motions of the Tyr-21 ring in BPTI suggest that the time dependence of A can be described by the Langevin equation for a damped harmonic oscillator (see Chapt. IV.C and D). 

The friction constant, 7/3, may be related to an angular diffusion constant by use of the Einstein formula, D = kBT/I. For the Tyr-21 ring torsional motion in BPTI, one obtains D = 2.3 X 1011 s 1 at 308 K, the temperature of the simulation. This value is somewhat larger than experimental diffusion constants for the corresponding rotational motion of small aromatic molecules in organic solvents (e.g., the value for benzene in isopentane is 8 X 10l° s-1). 

Torsional motions around bonds in "floppy" rings are generally more restricted than motions around bonds which are not in rings, but less restricted than motions around bonds in "rigid" (especially aromatic) rings ... 

The two pyridine rings are tilted with respect to each other by 22.7(6) Each rotational transition is spht into two components due to the torsional motion coimecting four equivalent minima. The lower of the two barriers to inversion, corresponding to the planar configuration, was determined to be 45.0(3) cm... 

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