Molecular shape representation

In this chapter some of the physical properties and approximate models used for molecular shape representation will be reviewed. 

The next most important aspect of a molecular compound is its shape. The pictorial representations of molecules that most accurately show their shapes are images based on computation or software that represents atoms by spheres of various sizes. An example is the space-filling model of an ethanol molecule shown in Fig. C.2a. The atoms are represented by colored spheres (they are not the actual colors of the atoms) that fit into one another. Another representation of the same molecule, called a ball-and-stick model, is shown in Fig. C.2b. Each ball represents the location of an atom, and the sticks represent the bonds. Although this kind of model does not represent the actual molecular shape as well as a space-filling model does, it shows bond lengths and angles more clearly. It is also easier to draw and interpret. 

The Lewis structures encountered in Chapter 2 are two-dimensional representations of the links between atoms—their connectivity—and except in the simplest cases do not depict the arrangement of atoms in space. The valence-shell electron-pair repulsion model (VSEPR model) extends Lewis s theory of bonding to account for molecular shapes by adding rules that account for bond angles. The model starts from the idea that because electrons repel one another, the shapes of simple molecules correspond to arrangements in which pairs of bonding electrons lie as far apart as possible. Specifically ... 

FIG. 4 Schematic representation of various lipid phase structures influenced by lipid molecular shape. 

Figure 2-1. Representations of the electron density of the water molecule (a) relief map showing values of p(r) projected onto the plane, which contains the nuclei (large values near the oxygen atom are cut out) (b) three dimensional molecular shape represented by an envelope of constant electron density (0.001 a.u.). 

In more recent years, additional progress and new computational methodologies in macromolecular quantum chemistry have placed further emphasis on studies in transferability. Motivated by studies on molecular similarity [69-115] and electron density representations of molecular shapes [116-130], the transferability, adjustability, and additivity of local density fragments have been analyzed within the framework of an Additive Fuzzy Density Fragmentation (AFDF) approach [114, 131, 132], This AFDF approach, motivated by the early charge assignment approach of Mulliken [1, 2], is the basis of the first technique for the computation of ab initio quality electron densities of macromolecules such as proteins [133-141],... 

The procedure, described in more detail elsewhere [68], is demonstrated well by noting the relationship between molecular shape and the representation of symmetry groups. 

Diagrammatic representation of scattering data on large particles, obtained at different angles but at the same concentration, constructed by plotting sin (.6y2)AR(6) versus sin(0/2), or q AR 9) versus q, and used for the determination of molecular shape. For definitions of symbols, see Definition 3.3.12. 

The new representation is, by the rules, a member of the group, and is also the only possible addition to the set of representations so far deduced for the molecular shape under consideration. There are no other combinations of 1 and -1 that would form a different representation. 

The idea that distortion of a triatomic molecule from a linear to a bent shape occurs if the HOMO and LUMO are of the same symmetry representation, so that electrons in the HOMO are stabilized, was discussed as a tentative general approach to molecular shape. 

In the examples predated in the text, the distortions from high symmetry which lead to stabilization of the molecular shapes are those in which the HOMO and LUMO of the highly symmetric molecules both become the completely symmetric representations of the distorted molecules, i.e. a. There is a general rule which deals wi+h this phenomenon in a detailed way called the second-order Jahn-Teller effect but nt they say. anotlv . ... 

The need to limit the number of parameters becomes especially evident if molecular shape, which decisively influences the biological properties of chemical compounds, must be considered. Principally, shape can be precisely accounted for by the coordinates of all the atoms in the molecule. Even with rather small molecules (e.g. 20 atoms) one would need a prohibitive amount of parameters (e.g. 60) alone for representation of steric properties. Again, simplifying assumptions are made to reduce the number of parameters. Thus, one can for example assume that only the steric bulk in a certain position determines the biological properties, in which case a one-parameter representation may suffice, e.g. MR or van der Waals volume of the respective substituent. 

Whereas furanose rings are almost, but not quite, flat, pyranose rings are not, thus Haworth representations do not show the actual molecular shape. Pyranose rings assume one of two chair forms designated the chair because C-4 is up and C-l is down or the 1C4 form. The 4C1 chair is by far the most... 

Figure 16. Idealized cartoon representation of the molecular shapes and orientations of the major liquid-crystalline phase types. (Reproduced with permission from R. G. Weiss in Photochemistry in organized and constrained media, V. Ramamurthy, ed., VCH, New York, 1991, p. 603).

Previously, the Ramachandran technique (2) was used to learn the range of allowed molecular shapes. We now propose a new representation of the allowed shapes of a polymer. The new... 

Valence-bond representation Molecular-orbital representation it bonding and multicenter it bonds Shapes of molecules Coordination compounds Isomerism Bonding in metals... 

In the following sections, we shah demonstrate that the observed behavior of electro-optic activity with chromophore number density can be quantitatively explained in terms of intermolecular electrostatic interactions treated within a self-consistent framework. We shall consider such interactions at various levels to provide detailed insight into the role of both electronic and nuclear (molecular shape) interactions. Treatments at several levels of mathematical sophistication will be discussed and both analytical and numerical results will be presented. The theoretical approaches presented here also provide a bridge to the fast-developing area of ferro- and antiferroelectric liquid crystals [219-222]. Let us start with the simplest description of our system possible, namely, that of the Ising model [223,224]. This model is a simple two-state representation of the to-... 

Figure 5.18 Molecular shape of the cyclic [8]catenane 14 (Y = methyl, n= 14) in the crystalline state, showing the interlocking of eight rings. Space-filling representation seen along the Sg-axis (a) and perpendicular to it (b). Alkyl residues and hydrogen atoms are omitted for clarity.

Figure 5.19 Molecular shape of rotaxane 23 (n = 6), a hetero-dimeric assembly of a tetraloop tetra-urea 9 (stick representation) and tetra-tosylurea 4 (space filling), based on MD simulations. Ether groups (OY = OC5Hnn,) areomitted in the formula.

Fig. 12 Schematic representation of the self-assembly of dendromesogens into various type of mesophases (smectic, hexagonal and rectangular columnar, micellar cubic, and tetragonal phases) by the control of the molecular shape conformation (from flat tapered to cylindrical to conical and to spherical shape). From [126]...

Appendix B-4 shows electronegativity values for a larger set of elements. Any set can be used for the prediction of bond angles and molecular shape specific sets are more useful for the calculation of properties for which they are designed. A graphic representation of electronegativity is in Figure 8-1. 

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