Atoms spatial arrangements

Loss of two hydrogen atoms from adjaccnl carbon atoms. Addition of two hydrogen atoms. Spatial arrangement of two . ... 

The spatial arrangement of atoms in two-dimensional protein arrays can be detennined using high-resolution transmission electron microscopy [20]. The measurements have to be carried out in high vacuum, but since tire metliod is used above all for investigating membrane proteins, it may be supposed tliat tire presence of tire lipid bilayer ensures tliat tire protein remains essentially in its native configuration. 

If the spatial arrangement of atoms is required this can be deduced from the basic structure by neglecting the positions occupied by lone pairs of electrons. Water, for example, can be described as a V shape whilst ammonia is a trigonal pyramid. 

To code the configuration of a molecule various methods are described in Section 2.8. In particular, the use of wedge symbols clearly demonstrates the value added if stereodescriptors are included in the chemical structure information. The inclusion of stereochemical information gives a more realistic view of the actual spatial arrangement of the atoms of the molecule imder consideration, and can therefore be regarded as between the 2D (topological) and the 3D representation of a chemical structure. 

Basically, two different methods arc commonly used for representing a chemical struchiive in 3D space. Both methods utilize different coordinate systems to describe the spatial arrangement of the atoms of a molecule under con.sidcration. The most common way is to choose a Cartesian coordinate system, i.e., to code the X-, y-, and z-coordinates of each atom, usually as floating point numbers, For each atom the Cartesian coordinates can be listed in a single row. giving consecutively the X-, )> , and z-valnc.s. Figure 2-90 illustrates this method for methane. 

The second method for representing a molecule in 3D space is to use internal coordinates such as bond lengths, bond angles, and torsion angles. Internal coordinates describe the spatial arrangement of the atoms relative to each other. Figure 2-91 illustratc.s thi.s for 1,2-dichlorocthanc. 

Z-matriccs arc commonly used as input to quantum mechanical ab initio and serai-empirical) calculations as they properly describe the spatial arrangement of the atoms of a molecule. Note that there is no explicit information on the connectivity present in the Z-matrix, as there is, c.g., in a connection table, but quantum mechanics derives the bonding and non-bonding intramolecular interactions from the molecular electronic wavefunction, starting from atomic wavefiinctions and a crude 3D structure. In contrast to that, most of the molecular mechanics packages require the initial molecular geometry as 3D Cartesian coordinates plus the connection table, as they have to assign appropriate force constants and potentials to each atom and each bond in order to relax and optimi-/e the molecular structure. Furthermore, Cartesian coordinates are preferable to internal coordinates if the spatial situations of ensembles of different molecules have to be compared. Of course, both representations are interconvertible. 

A.s mentioned above, most molecules ean adopt more than one conformation, or molecular geometry, simply by rotation around rotatable bonds. Thus, the different conformations of a molecule can be regarded as different spatial arrangements of the atoms, but with an identical constitution and configuration, They are interconvertible and mo.stly they cannot be i.solatcd separately. Figure 2-101 show-s a. super-imposition of a set of conformations of 2R-benzylsuccinatc (cf. Figure 2-89). 

Molecules are usually represented as 2D formulas or 3D molecular models. WhOe the 3D coordinates of atoms in a molecule are sufficient to describe the spatial arrangement of atoms, they exhibit two major disadvantages as molecular descriptors they depend on the size of a molecule and they do not describe additional properties (e.g., atomic properties). The first feature is most important for computational analysis of data. Even a simple statistical function, e.g., a correlation, requires the information to be represented in equally sized vectors of a fixed dimension. The solution to this problem is a mathematical transformation of the Cartesian coordinates of a molecule into a vector of fixed length. The second point can... 

Stereochemistry refers to chemistry in three dimensions Its foundations were laid by Jacobus van t Hoff and Joseph Achille Le Bel m 1874 Van t Hoff and Le Bel mde pendently proposed that the four bonds to carbon were directed toward the corners of a tetrahedron One consequence of a tetrahedral arrangement of bonds to carbon is that two compounds may be different because the arrangement of their atoms m space IS different Isomers that have the same constitution but differ m the spatial arrangement of their atoms are called stereoisomers We have already had considerable experience with certain types of stereoisomers—those involving cis and trans substitution patterns m alkenes and m cycloalkanes... 

Stereochemistry (Chapter 7) Chemistry in three dimensions the relationship of physical and chemical properties to the spatial arrangement of the atoms in a molecule Stereoelectron ic effect (Section 5 16) An electronic effect that depends on the spatial arrangement between the or bitals of the electron donor and acceptor Stereoisomers (Section 3 11) Isomers with the same constitu tion but that differ in respect to the arrangement of their atoms in space Stereoisomers may be either enantiomers or diastereomers... 

The medium-size rings (7 to 12 ring atoms) are relatively free of angle strain and can easily take a variety of spatial arrangements. They are not large enough to avoid all nonbonded interactions between atoms. 

Structural Formula and Prefixes. In the structural formula the sequence and spatial arrangement of the atoms in a molecule are indicated. 

The geometries of the phosphoms atom are related to the hybridization and the coordination number. Some of the more commonly encountered hybridizations and their corresponding spatial arrangements iaclude the following. 

The classical approach for determining the structures of crystalline materials is through diflfiaction methods, i.e.. X-ray, neutron-beam, and electron-beam techniques. Difiiaction data can be analyzed to yield the spatial arrangement of all the atoms in the crystal lattice. EXAFS provides a different approach to the analysis of atomic structure, based not on the diffraction of X rays by an array of atoms but rather upon the absorption of X rays by individual atoms in such an array. Herein lie the capabilities and limitations of EXAFS. 

Computing the energy of a particular molecular structure (spatial arrangement of atoms or nuclei and electrons). Properties related to the energy may also be predicted by some methods. 

Spatial congruence of C-H graphs is applied essentially only in chemical formulas which represent a compound of carbon atoms and atoms of valence 1 (or radicals of valence 1). In this case condition (IV), besides (I), (II), (III), adds another restriction not only the relationships are important but also the spatial arrangement of the bonds. The spatial interpretation of the congruence of C-H graphs coincides with the interpretation of the chemical formula as stereoformula. I use stereoisomers in this sense. For example, the number of different stereoisomers is equal to the number of spati-... 

Up to this point, we ve viewed molecules primarily in a two-dimensional way and have given little thought to any consequences that might arise from the spatial arrangement of atoms in molecules. Now it s time to add a third dimension to our study. Stereochemistry is the branch of chemistry concerned with the three-dimensional aspects of molecules. We ll see on many occasions in future chapters that the exact three-dimensional structure of a molecule is often crucial to determining its properties and biological behavior. 

One further point needs to be mentioned—the matter of absolute configuration. How do we know that our assignments of R,S configuration are correct in an absolute, rather than a relative, sense Since we can t see the molecules themselves, how do we know that the R configuration belongs to the dextrorotatory enantiomer of lactic acid This difficult question was finally solved in 1951, when J. M. Bijvoet of the University of Utrecht reported an X-ray spectroscopic method for determining the absolute spatial arrangement of atoms in a molecule. Based on his results, we can say with certainty that the R,S conventions are correct. 

Remember the spatial arrangement of the p or- atom has partially filled valence orbitals. Elec-bitals Each one protrudes along one of the tron sharing can occur, placing electrons close three cartesian axes (as shown in Figure 15-9). to two nuclei simultaneously. Hence a stable If the electrons have the orbital occupancy of bond can occur. This is shown in representations 20), then two electrons occupy the p orbital (22) and (23). 

In NH and NFS, three p orbitals are involved in the bonding [see representation (30)]. Figure 16-10 shows the spatial arrangement implied by assuming persistence of the hydrogen atom orbitals after bonding. We expect, then, that ant-... 

Although they are built from the same numbers and kinds of atoms, structural isomers have different chemical formulas, because the formulas show how the atoms are grouped in or outside the coordination sphere. Stereoisomers, on the other hand, have the same formulas, because their atoms have the same partners in the coordination spheres only the spatial arrangement of the ligands differs. There are two types of stereoisomerism, geometrical and optical. 

We shall use the word configuration in this paper to represent the approximate relative spatial arrangement of the nuclei of the atoms in the system under consideration (neglecting the effect of the vibrational motion on the nuclear positions). 

The conformation, i.e. the (approximate) spatial arrangement of the ring atoms of a monosaccharide in the cyclic form, may be indicated by an italic capital letter designating the type of ring shape, and numerals, distinguishing the variants. The... 

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