Stereochemical studies. XXXIV. Quantitative description of ring puckering via torsional angles. The case of six‐membered rings

Abstract

The quantitative description of ring puckering suggested by the authors is compared with that of Cremer and Pople. The applicability of both methods is discussed for the case of six‐membered rings with the use of model calculations simulating various ring distortions and with the analysis and comparison of puckering parameters computed on the basis of x‐ray data for 40 six‐membered rings in different cyclic structures. The 2N times reduction of the field of variation of puckering parameters for the N‐membered ring is suggested and the algorithm for the renumbering of the ring atoms for this purpose is described for six‐membered rings.

Puckering free energy of pyranoses: A NMR and metadynamics-umbrella sampling investigation

“…Alternative generalized coordinates can be in principle employed to characterize the puckered conformers of six-membered rings, such as the three out-of-plane dihedrals introduced by Strauss and Pickett 88 , or other definitions based on three internal dihedral angles [89][90][91] . All these alternative schemes produce good puckering coordinates, in the sense that they allow to uniquely map the complete puckering conformational space.…”

Conformational Pathways of Saturated Six-Membered Rings. A Static and Dynamical Density Functional Study

“…19 Alternatively, spherical polar coordinates can be derived by Fourier transform from the ring torsion angles. 20,21 In the preceding paper, 17 we have derived quantitative expressions for the characterization of the pyranose and other six-membered ring conformations which rely heavily on the definitions of the natural internal coordinates introduced by Pulay et al 22,23 If τ 1 , τ 2 , τ 3 , τ 4 , τ 5 , and τ 6 torsion angles are defined by the C 1 C 2 C 3 C 4 ,C 2 C 3 C 4 C 5 ,C 3 C 4 C 5 O, C 4 C 5 OC 1 ,C 5 -OC 1 C 2 , and OC 1 C 2 C 3 atom sets, respectively, displacement into the 1 C 4 chair conformation is described by the internal coordinate. Displacement into 1,4 B boat (q 2 ) and O S 2 skew-boat (q 3 ) conformations are described by the internal coordinates respectively.…”

(1R,2S,5R)-2-Isopropyl-5-methylcyclohexyl 4-Aminobutyrate Hydrochloride

“…Configuration of chiral centers at C1, C2, and C5 atoms (R, S, and R, respectively) was simultaneously determined by calculating the Flack parameter (−0.04(10)). The saturated cycle adopts the chair conformation (puckering parameters are [7]: S = 1.16, θ = 0.52 • , ψ = 49.2 • ). Under these conditions, atoms C2 and C5 deviate to different sides from mean-square plane of the remaining atoms of this cycle (deviation amounts to 0.67 Å and −0.69 Å, respectively).…”