Puckering amplitude

Fig. 16.7 Theoretical curves of the CCR rate as a function of the ribose pseudorotation phase angle P for three different pucker amplitudes (i/m = 30, 35 and 40°. A rotational correlation time of 1.5 ns and a C-H distance of 1.07 A has been used for the calculation.

The correlation of the primitive cos and sin forms with established nomenclature for medium-sized rings is summarized in table 2. In practice the procedure is to start from atomic coordinates and to generate puckering displacements, which are converted to puckering amplitudes and phases, and finally decomposed into a linear sum of primitive contributions ... 

A particular ring conformer can be described by two parameters, the puckering amplitude (Xm) and the pseudorotational phase angle (P), which can be illustrated by the pseudorotational wheel shown in Figure 21 for a D-aldofuranose [106]. The radius of the circle is and P, which defines the part of the ring that is most puckered. 

Although four-membered rings are rare in carbohydrate chemistry, they represent the simplest case for the Cremer-Pople treatment, x = 4, so that their conformation is described uniquely by the puckering amplitude, i.e. the amount by which the fourth atom is displaced from the plane defined by the remaining three (Figure 2.3). 

Zi being the displacement coordinate of the /th atom (/ = 1,2,3,4,5) from the mean plane of the nonplanar pentagon. Alternatively, the displacement vector may be expressed in terms of a puckering amplitude q and a phase angle 0 (polar coordinates) with components... 

For any given set of out-of-plane displacements z,-, the values of the puckering amplitude q and the phase angle (p can be calculated from... 

Fig. 9.13. Polar diagram of the puckering phase 0 (°) vs. the puckering amplitude (A) of 181 non-fused furanose rings in fragments of type 11 found in the CSD release July 1991 (no disorder, no error flag, i <0.08). The numbers show the position of some selected ring conformations 1(0°) envelope (e) with mirror plane through C(2 ) endo 2(144°) e C(3 ) endo 3(324°) e C(3 ) exo 4(180°) e C(2 ) exo 5(126°) twist with C2 axis through C(T) 6(72°) e O(l ) endo...

Fig. 9.14. Polar diagram of the puckering phase 0 (°) vs. the puckering amplitude (A) of 376 acyclic substituted furan rings found in the CSD release July 1991 (no disorder, no error flag, J s0.08)...

Fig. 9.15. Top Polar diagram of the puckering phase 0(°) vs. the puckering amplitude q(k) of 52 cyclopenten-2-one fragments with no cyclic substitution and cr(C-C)<0.01 A from the July 1987 release of the CSD. Since coordinates of chiral molecules from racemic crystals refer to an arbitrarily chosen enantiomer, all points were transferred into the range (p = 270 - 90° by adding 180° (corresponding to the enantiomeric structure) if necessary. Bottom Mean bond angles with standard deviations from the 26 fragments from the above structures with (t(C-C)< 0.005 A...

Table 6 Experimental bond lengths, angles, and puckering amplitude q) for tetrahydrofuran (C2).

A statistical survey of crystal structures of nucleic acid constituents has led to the proposal that a full description of nucleoside molecular geometry can be given in terms of four parameters the phase angle of pseudorotation, P, the puckering amplitude, the conformation of the side-chain, 5, and the glycosidic torsional angle, X these allow the variability of bond and torsion angles to be described. ... 

In a study of the conformation of 3,3-dimethyl-3-silatetrahydrothiophene two different twist conformations could fit the electron diffraction data well, with a slight preference for the form in which the S and C(5) atoms lay above and below the plane of the remaining three ring atoms. Ab initio calculations at the HF/6-311++G level indicated that this last form was the potential minimum, and so this conformation was assumed in the analysis of the structure. Differences between some parameters were then computed at the MP2(fc)/6-311++G level and used as constraints in the refinement. Refined parameters (rg, 4) included S-C(mean) 182.9(5), Si-C(mean) 188.3(6), C-C 154.1(7) pm, ZCSC 98.6(8) and ZCSiC(ring) 97.7(6)°. The conformation was described in terms of the ring puckering amplitude, 10.7(6) °, and the pseudorotation phase angle, 168.1(44) °. 

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