Ring asymmetry parameters from out-of-plane atomic displacements

Abstract

Formulae are given for calculating ring asymmetry parameters and e.s.d.'s from the out-of-plane displacements of the atoms of a ring.The asymmetry parameters have been proposed by Duax, Weeks & Rohrer (1976) to give a quantitative evaluation of how a ring of any size deviates from ideal symmetry and to help in describing its conformation. These parameters are calculated as r.m.s.'s of the sums of mirror-related torsion angles (ACs) or r.m.s.'s of the differences of twofoldaxis-related torsion angles (AC2).Similar parameters, but directly connected with Cremer & Pople's (1975) total puckering amplitude, can be defined using the perpendicular displacements of the atoms from the mean plane through them. These parameters, which could be called displacement asymmetry parameters, are defined, together with their e.s.d.'s, by the following equations, where n is the number of the atoms of the ring, r i is the perpendicular displacement of atom i from the mean plane and R i is its distance from the center of the ring (the nomenclature is that proposed by Duax et al.). all the possible cases are as follows.

Methyl 5-cyano-1-[2-(methoxycarbonyl)phenyl]-4,5-dihydro-3-pyrazolecarboxylate

“…ORTEPII (Johnson, 1976) drawing of molecule A with the numbering scheme of the heavy atoms, the same numbering was applied to molecule B. Displacement ellipsoids are drawn at the 20% probability level; H atoms are not to scale. C14H13N304 Pople, 1975)], while in molecule B it has an envelope conformation [Qt = 0.185 (2) A, minimum displacement asymmetry parameter As(C5B ) = 0.016(1) (Nardelli, 1983b)]. The same difference is also observed for the torsion angles around the rings, which range between +3.5 ° in molecule A and from -17.3 to 18.2 ° in molecule B.…”

Crystal and Molecular Structure Study of the Complex Cd(L) 2Br2.C2H5OH (L=2-(4-Methylsulfanyl phenyl)-1H-benzimidazole)

“…Geometry calculations were performed using PLATON 10 , ORTEP representations were prepared 11 using ORTEP-3 and packing diagrams 12 were made using CAMERON incorporated in the WinGX 11 software packing. The mean plane calculation was done using the program PARST 13 .…”

Enantiomerically pure α-haloketals: structure and conformation of (2'S,4'R,5'R)-dimethyl 2'-halo-1',2',3',4'-tetrahydrospiro[1,3-dioxolane-2,1'-naphthalene]-4,5-dicarboxylates (halo = Cl, Br, I)

“…Qr is the total puckering amplitude (A) (Cremer & Pople, 1975) and ADP denotes asymmetry displacement parameters (Nardelli, 1983b). (8) (6) 1.973 (7) 1.420 (7) 1.421 (7) 1.445 (6) 1.418 (7) 1.201 (7) 1.337 (9) 1.463 (9) 1.323 (8) 1.450 (8) 1.192 (8) 1.406 (9) 1.396 (8) 1.513 (5) (11) 1.379 (7) (12) 1.400 (9) (ll) 1.381 (7) (10) 1.398 (6) (8) 1.499 (5) (9) 1.519 (6) (10) 1.516 (6) (4) (6) 1.384 (10) 1.386 (9) 1.513 (8) 1.513 (4) 1.379 (12) 1.380 (5) 1.411 (15) 1.400 (6) 1.379 (12) 1.382 (5) 1.393 (10) 1.400 (5) 1.507 (9) 1.501 (4) 1.526 (I0) 1.516 (6) 1.507 (10) 1.515 (5) 1.526 (7) 1.524 (3) 1.536 (10) 1.534 (4) 1.515 (9) 1.510 (6) 1.533 (9) 1.527 (4) 109.9 (3) 110.2 (4) ll0.1 (2) 108.0 (3) 107.9 (4) I08.1 (2) 116.1 (4) 114.8 (6) 116.1 (6) 116.6 (3) 117.7 (6) 116.6 (4) 120.4 (3) 120.…”