Torsional potential plot

Figure 7-10. Two examples of torsional potentials plotted using Eq, (24) with the parameters rt = 2, V = 5.0, y = Fi (solid line), and n = 3. = 3.0, y = 0 (broken line). All other V, ...

Figure 12-1 Fundamental characteristics of the phenylacetylene monomer unit. In this chapter the three basic phenylacetylene valence angles will be represented with a dot ( ) and line (—) convention, as shown in the structure key. The phenylacetylene linkage is characterized by a flexible bending force constant, F(S) [5], and an sp -sp bond order of 1.18. The indicated bond distances are taken from the crystal structure of tolane [6]. The bottom plot shows the torsional potential energy curve in tolane as determine by supersonic jet spectroscopy (adapted from [8]). The outer edges of van der Waals spheres for the two ortho hydrogens on one side of tolane are separated by nearly 2 A in the planar conformation. The result is a virtually barrierless rotation.

Figure 3 plots the torsional angle potential for dihedral d in PCH5, It shows behaviour which is generic for alkyl chain dihedrals. The gauche conformers... 

Fig. 7. Plots of the peak potentials (Ep, ) and decomposition potentials (Ed, ) for the oxidation of silyl substituted ethers in which rotation around Si-C bond is restricted vs. torsion angle of Si-C-O C [13]...

Nelsen and coworkers [562] detected conformational equilibria in eq, eq- and ax, eq-N, A -disubstituted cyclic hydrazines from their oxidation potentials. The anodic oxidation reactions of trans- and cw-l,3-diisopropy-l-2,4-bis(diisopropylamino)-cyclodiphospha(III)azanes are quite different [563] The trans isomer is reversibly oxidized at 0.53 V (SCE) forming a stable cation radical the c/5-isomer undergoes a completely irreversible oxidation at a more positive potential because an unstable radical cation is formed. Evans and coworkers studied structural changes associated with electron transfer reactions of W(// -C5(CH3)5)(CH3)4 and related compounds [564,565]. Yoshida and coworkers found a linear correlation on plotting the oxidation potentials of a-silylated ethers, where the rotation around the C-0 bond is restricted, against the HOMO energy-torsion angle (Si-C-O-C) curve estimated by MO calculation [566]. 

A potential energy plot for rotation about the C2-C3 bond in butane shows unique maxima and minima. There are two kinds of staggered conformations, gauche (steric strain) and anti, and two distinct eclipsed conformations (torsional and steric strain). 

An approach to elucidate new empirical restraints from PDB coordinates and chemical shift in the Biological Magnetic Resonance Data Bank was applied by Kuszewski et al.89,90 for a structure determination automation program. The relation between the chemical shift and coordinates can be used for an NMR assignment validation.91 The torsion angle ranges of (j) and ijj that are favorable in Ramachandran plot and their mean values in PDB are also useful as pseudo-potentials.92,93... 

If we plot some property of the ethane molecule, say, its potential energy, as a function of the torsion angle, we obtain a curve with threefold periodicity. In crystallographic parlance we have a repeating one-dimensional pattern with the line group pm and periodicity t = 120°. The special positions (fixed points) at a = 0° and 60° (modulo 120°) correspond to structures with special symmetry at 0° the eclipsed conformations with D31, symmetry, at 60° the staggered conformations with >3d symmetry. A general position corresponds to a chiral conformation with Z>3 symmetry only. Note that the order of D3 is half that of or 3d but the number of isometric Dj conformations is double the number of isometric 1)31, or conformations. 

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