Atomic coordinates conformation

For each combination of atoms i.j, k, and I, c is defined by Eq. (29), where X , y,. and Zj are the coordinates of atom j in Cartesian space defined in such a way that atom i is at position (0, 0, 0), atomj lies on the positive side of the x-axis, and atom k lies on the xy-plaiic and has a positive y-coordinate. On the right-hand side of Eq. (29), the numerator represents the volume of a rectangular prism with edges % , y ., and Zi, while the denominator is proportional to the surface of the same solid. If X . y ., or 2 has a very small absolute value, the set of four atoms is deviating only slightly from an achiral situation. This is reflected in c, which would then take a small absolute value the value of c is conformation-dependent because it is a function of the 3D atomic coordinates. 

There are a number of different ways that the molecular graph can be conununicated between the computer and the end-user. One common representation is the connection table, of which there are various flavours, but most provide information about the atoms present in the molecule and their connectivity. The most basic connection tables simply indicate the atomic number of each atom and which atoms form each bond others may include information about the atom hybridisation state and the bond order. Hydrogens may be included or they may be imphed. In addition, information about the atomic coordinates (for the standard two-dimensional chemical drawing or for the three-dimensional conformation) can be included. The connection table for acetic acid in one of the most popular formats, the Molecular Design mol format [Dalby et al. 1992], is shown in Figure 12.3. 

The first step in the DG calculations is the generation of the holonomic distance matrix for aU pairwise atom distances of a molecule [121]. Holonomic constraints are expressed in terms of equations which restrict the atom coordinates of a molecule. For example, hydrogen atoms bound to neighboring carbon atoms have a maximum distance of 3.1 A. As a result, parts of the coordinates become interdependent and the degrees of freedom of the molecular system are confined. The acquisition of these distance restraints is based on the topology of a model structure with an arbitrary, but energetically optimized conformation. 

P212121 Z = 8 Dx = 1.419 R = 0.068 for 1,373 intensities. The crystal structure contains two symmetry-independent molecules having slightly different conformations. The pyranoside conformations are 1C4 with Q = 57,60 pm, 0=173,177°. The nitro and acetate groups are oriented approximately normal to the mean plane of the pyranoside ring. The atomic coordinates refer to the d enantiomer. The hydrogen-atom positions were not reported. 

P2j Z = 2 D = 1.377 R = 0.12 for 1,858 intensities. This is an unrefined analysis, made for the purpose of confirming the configuration and approximate conformation. No atomic coordinates were reported. 

P212121 Z = 4 D = 1.25 R = 0.069 number of intensities not reported. This analysis was to confirm a configuration derived from n.m.r. data. The pyranoid rings are slightly distorted 4Q, due to fusion to the trioxacyclooctane ring, which has an almost ideal, boat-chair conformation. The overall molecule has a convex, sickle conformation. There is an error in the atomic coordinates reported, which do not correspond to the structure given in the paper. 

P2j Z = 2 D = 1.17 R = 0.080 for 3,888 intensities. This is aconfigu-rational analysis of the macrolide antibiotic 23672RP from Streptomyces chryeus. All three sugar residues are pyranoid the conformation of the a-ketose is CX, with Q = 56 pm, 0 = 9° that of the / -D-mycinose (6-deoxy-2,3-di-0-methyl-D-allose) is 4Clt with Q = 59 pm, 0 = 6° and that of the / -L-mycarose (2,6-dideoxy-3-C-methyl-L-riho-hexose) is 1C4, with Q = 53 pm, 0= 177°. The O-5-C-l-O-l-C glycosidic torsion-angles are —71, —87, —83°. The atomic coordinates reported in the paper refer to the opposite enantiomer. 

Several mathematical techniques have been used to obtain atomic coordinates for nucleic acid structures. They incorporate several different approaches. (a) Systematic rotations about all backbone torsional angles are performed and those conformations which form helicies and have adjacent bases parallel or in a given orientation are selected (59 6o). (b) Least squares techniques are used to re-... 

Comparison of the experimental data with the trends predicted from quantum chemistry ab initio simulations demonstrated that the multiple conductance values of Au-alkanedithiol-Au junctions could be attributed to different Au-sulfur coordination geometries and to different conformations of the alkyl chain. In particular, the medium conductance corresponds to an all-trans conformation of the alkyl chain, with each sulfur atom coordinated in atop position to a single... 

At the end of the process, one obtains a large amount of information regarding the solid-state structure of a compound. Its three-dimensional structure and molecular conformation become known, as do the patterns of molecular packings that enable the assembly of the crystal. In addition, one obtains complete summaries of bond angles and bond lengths for the molecules in the crystal as well as detailed atomic coordinates for all of the atoms present in the solid. One generally finds... 

P2i2i2i Z = 4 Dx = 1.21 R = 0.16 for 2,306 intensities (partially photographic). This is the hydrobromide dihydrate of the aminoglycoside antibiotic P-2536(P). The conformation of the pyranosyl group is 4C1 (8 = 3°, q = 60 pm). The aglycon hexitol moiety has a bent carbon-chain conformation, with C-1-C-2-C-3-C-4 = -75° C-2-C-3-C-4-C-5 = -161°. The results have low accuracy, and the hydrogen atoms were not located. The atomic coordinates reported were for the L enantiomer. 

X-Ray diffraction analyses of vincristine methiodide (39) and vinzoli-dine 1-naphthalene sulfonate (40) provide atomic coordinates of compounds that are either modified in the velbanamine portion (alkylation at N-6, Fig. 3) or in the vindoline portion (a spiro-fused oxazolidinedione at C-3 and C-23, Fig. 4). These structures show a chair-boat conformation for ring C with C-8 exhibiting an endo pucker. Ring D is clearly in a chair conformation, but, in contrast to the conclusions drawn from C-NMR studies, the N-6 -C-7 bond is axial relative to the piperidine ring. 

XRD analysis of (n-BuLi)e (291b) reveals that the cluster of six Li atoms has an approximate symmetry (trigonal antiprismatic), with the six w-Bu groups placed around the axis of rotation. Each Li atom is coordinated to four Li atoms, one a-C and one /3-C atom the conformation of the six n-Bu groups is such that the a-C atom is coordinated to the three Li atoms of a face of the distorted octahedron and the fi-C atom to one of them only ". ... 

Given atomic coordinates for a particular conformation of a molecule and some property value assigned to each atom, one can easily calculate a chirality function that distinguishes enantiomers, is zero for an achiral molecule, and is a continuous function of the coordinates and properties. This is useful as a quantitative measure of chirality for molecular modeling and structure-activity relations. 

It must be independent of rigid translation and (proper) rotation of the given atomic coordinates, although it may depend on conformation. 

X-Ray diffraction data give the atomic coordinates and thereby the conformations of molecules in the crystalline phase. If many structures of a given type are known, which unfortunately is rarely the case for medium rings, it is likely that an excellent picture of the global conformational energy minimum will be obtained as lattice effects should be more or less random. 

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