Variation with torsion angle

By considering the variation with torsion angle of both the mixing coefficient and the component of the charge flow magnetic moment perpendicular to the... 

Figure 8.5 Natural atomic charge (0 variations with torsional angle (p in aminoborane, showing zwitterion-like pattern of charges on B (gg, circles, left scale) and N (0i, crosses, right scale) as the Tig-N coordinate bond is broken by 90° twisting.

For such an asymmetric structure as dimethoxymethane with one torsion angle fixed at 60 °, additional sine terms are necessary, in order to account for the lack of symmetry about 0 = 180° (see Ref. 94). The individual components V,(0), V2(0), and V3(0) of the total potential function V(0) can be identified with specific physical effects of similar periodicity. For example, the onefold term, V,(0) = 0.5 V ( 1 — cos 0), moves from a maximum v ue to a minimum value as 0 changes by 180 °. The same variation with torsion shows dipolar or steric interactions. The twofold term, V2(0), changes from a maximum to a minimum as 0 changes by 90°. This periodicity frequently corresponds to the change of delocalization interactions. Finally, the threefold term, V3(0), moves from a maximum value to a minimum value as it changes by 60°. This is generally attributed to the intrinsic torsion potential. 

Fig. 20.—The Variation of Bond Angles C-5 - 0-5 - C-1 (Curves Denoted by a) and 0-5 -C-1-0-1 (Denoted by b) with Torsional Angle in the Axial Form (Dashed Line) and Equatorial Form (Full Line) of 2-Methoxyoxane.

Figure 4.4. Variation of energy with torsion angle (co) for butane.

The general equation that desalbes the variation of energy with torsion angle is conveniently written as a 3-term Fourier series as in Eq. (4.5) ... 

Even so for the symmetric structures, CUPWAL, DACLUO and DUTBUP, variations in torsion angles of ca 10° are found. The 0...0 distances around the cone average at 2.67A for molecules with = H. Only one structure for calix[5]arene is available in the database [58], BIMXIE, calix[5]arene bis(acetone)clathrate though recently two other structures (called XXXXXX,YYYYYY in Table 1) have been determined viz tetramethylbutylcalix[5]arene and tetramethylbutylcalix[5]arene toluene clathrate [68]. As is apparent from the torsion angles in Table 1, these three structures have relatively similar conformations. The 0...0 distances around the cone average at 2.84A. 

Fig. 4.S Variation in torsional energy (AMBER force field) with O-C-C-0 torsion angle (to) for OCH -CHjO fragment. The minimum energy conformations arise for to = 60° and 300°.

Fig. 5.1 Variation in the energy of pentane with the two torsion angles indicated and represented as a contour diagram and isometric plot. Only the lowest-energy regions are shown.

Table 3.24. Torsionalflexing p/NfECI-EF, showing relaxed R c and Rqf bond lengths and (9 pNC and %cr valence angles with variation of the torsion angle (cf. Fig. 3.64) (0ipnc denotes the angle between the lone pair and ctnc NHOs at N)...

Figure 1. The variation of bond angles C5-05-C1 and 05-C1-01 with the torsion angle < ) for 2-methoxytetrahydropyran. The curves with squares (C5-05-C1) and triangles (05-C1-01) are for the axial form and the rhombuses (C5-05-C1) and stars (05-C1-01) are for the equatorial form. These curves were calculated with PCILO, with full optimization of geometry at each increment.

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