Molecular Shape in

A variety of methodologies have been implemented for the reaction field. The basic equation for the dielectric continuum model is the Poisson-Laplace equation, by which the electrostatic field in a cavity with an arbitrary shape and size is calculated, although some methods do not satisfy the equation. Because the solute s electronic strucmre and the reaction field depend on each other, a nonlinear equation (modified Schrddinger equation) has to be solved in an iterative manner. In practice this is achieved by modifying the electronic Hamiltonian or Fock operator, which is defined through the shape and size of the cavity and the description of the solute s electronic distribution. If one takes a dipole moment approximation for the solute s electronic distribution and a spherical cavity (Onsager s reaction field), the interaction can be derived rather easily and an analytical expression of theFock operator is obtained. However, such an expression is not feasible for an arbitrary electronic distribution in an arbitrary cavity fitted to the molecular shape. In this case the Fock operator is very complicated and has to be prepared by a numerical procedure. 

In this chapter we meet three increasingly sophisticated models of molecular shape. The first considers molecular shape to be a consequence merely of the electrostatic (coulombic) interaction between pairs of electrons. The other two models are theories that describe the distribution of electrons and molecular shape in terms of the occupation of orbitals. 

The Lewis stmcture of a molecule shows how the valence electrons are distributed among the atoms. This gives a useful qualitative picture, but a more thorough understanding of chemistry requires more detailed descriptions of molecular bonding and molecular shapes. In particular, the three-dimensional structure of a molecule, which plays an essential role in determining chemical reactivity, is not shown directly by a Lewis structure. 

Many elements of the periodic table, from titanium and tin to carbon and chlorine, exhibit tetrahedral electron group geometry and tetrahedral molecular shapes. In particular, silicon displays tetrahedral shapes in virtually all of its stable compounds. 

Potschka, M., Universal calibration of gel permeation chromatography and determination of molecular shape in solution, Anal. Biochem., 162, 47, 1987. 

For symmetry-based qualitative molecular-orbital analyses of molecular shapes in the limit of strong metal s- and d-orbital participation in bonding, see R. B. King, Inorg. Chem. 37 (1998), 3057 and C. A. Bayse and M. B. Hall, J. Am. Chem. Soc. 121 (1999), 1348. 

Table 1.1 Common Molecular Shapes in Organic Molecules... 

The general shape of a macromolecule is sometimes referred to as macroconformation—in contrast to microconformation, which concerns the succession of torsion angles about a limited number of consecutive bonds. The random coil, rigid rod, and rigid helix represent examples of macroconformations. The same term is used to specify the molecular shape in semicrystalline polymers, one of the most important and still open problems in the field of polymer morphology. 

Let us consider the case of molecules with Nwn small (Mon typically less than 100) and where there is no long range order in the sense that any eventual periodicity would be of the order of the molecular shape. In the case of molecules, the one-electron wave functions represent MOs and can be simply expressed as a linear combination of Mt atomic orbitals 1(LCAO) of different atoms forming the molecule ... 

Thus the mobility of an ion can be influenced by its pFa value the more it is ionised the greater its mobility and its molecular shape in solution. Since its degree of ionisation may have a bearing on its shape in solution, it can be seen that the behaviour of analytes in solution has the potential to be complex. For many drugs... 

Allocate the following species to their appropriate point group i (you may wish to postpone this exercise until you have read the sections about molecular shapes in Chapters 5 and 6) ... 

J. K. Burdett, Molecular Shapes, Wiley, New York, 1980. This book covers all aspects of molecular shapes in a very readable and thorough manner. 

Figure 6.18 Examples of VSEPR theory predictions of molecular shapes in a series of hypothetical dehydration reactions. The element E is covalently saturated...

The VSEPR theory has its roots in the observation prior to 1940 that isoelectronic molecules or polyatomic ions usually adopt the same shape. Thus BF3, B03 C03, COF2 and NO3 are ail isoelectronic, and they all have planar triangular structures. As developed in more recent years, the VSEPR theory rationalises molecular shapes in terms of repulsions between electron pairs, bonding and nonbonding. It is assumed that the reader is familiar with the rudiments of the theory excellent expositions are to be found in most inorganic texts. 

The VSEPR approach is largely restricted to Main Group species (as is Lewis theory). It can be applied to compounds of the transition elements where the nd subshell is either empty or filled, but a partly-filled nd subshell exerts an influence on stereochemistry which can often be interpreted satisfactorily by means of crystal field theory. Even in Main Group chemistry, VSEPR is by no means infallible. It remains, however, the simplest means of rationalising molecular shapes. In the absence of experimental data, it makes a reasonably reliable prediction of molecular geometry, an essential preliminary to a detailed description of bonding within a more elaborate, quantum-mechanical model such as valence bond or molecular orbital theory. 

As we come to understand the role of molecular shape in determining physical properties of polymers, we may wish to try to impose on a molecule a previously unobserved shape that was indicated in the allowed zones of an n-h map. 

The dendrimer type with a stilbene scaffold and long-chain end groups mentioned in Section 4.1.5.3 was shown to have a disc-like flattened molecular shape in solution by SAXS and SANS studies performed by Ballauff et al. [51]. 

Krukowski et al. [24] studied the effect of molecular shape in details by performing exact enumerations on lattice models of different molecular shapes. They calculated the entropic component of the chemical potential, i.e.,... 

Several points concerning the above prescription should be emphasized. First of all, it is an arbitrary construction that is not derivable from the postulates of quantum mechanics. Second, since the presence of a sufficient number of the aforementioned maxima cannot be guaranteed in general, this prescription is by no means universal. Third, since atoms and molecules have infinite extends, similar considerations cannot be employed in a definition of molecular shape. In summary, although isolated molecules possess neither classical structures nor shapes [3], their geometries can be defined under certain conditions. 

Longer cellulose oligomers have been modeled with MD as well. Two studies have attempted to discuss the molecular shapes in aqueous solution as well as the solvent llo-dextrin and cellodextrin llodextrin interactions [191,192]. The first of these studies showed that chains were heavily solvated and not fully extended or in contact with other cellulose fragments. The simulation was proposed as a model for freshly prepared cellophane. The latter study was more in agreement regarding chain shapes with the results in Figure 5.16. In addition, that work showed, unlike the simulated cellotetraose molecules in the same study. 

In these equations the indicator variable I4" has been defined for the 4"-substituent of the 3-(pyridin-2-yl) moiety (zero for hydrogen and one otherwise) of thiazolidinones (Fig. 26). Also, in these compounds the HIV-1 RT inhibitory activity has been finked to their ability to assume a butterfly-like shape in the receptor. Collectively, the substituents of 2- and 3-aryl moieties of these compounds promote this molecular shape. In this connection, the indicator parameter 12,3 has been introduced to address the collective steric features of the 2- and 3-aryl moieties of these compoimds. In this, 12,3 has been defined to take a value of one if any one substituent at 1 - or 6 - of the 2-phenyl moiety or at the 3"- or 5"- positions of the 3-(pyridin-2yl) moiety is larger than hydrogen and zero otherwise. These equations, while favor-... 

This approach allows the pharmacophore to be defined as 3- or 4-centers, thus forming a triangle or a tetrahedron. The shape probe is optional, but when selected, it allows a precise depiction of molecular shape in a protein cavity, or around ligand molecule(s). 

Phase diagrams for strongly polar molecules in adsorbed films are still in the process of development even for the films on the basal plane of graphite [35]. These systems are made more complex because of the interplay of dipolar forces and molecular shape in determining preferred orientations relative to the surface and to neighboring molecules. A simulation of Stockmayer molecules (Lennard-Jones atoms with ideal dipoles attached) adsorbed on a featureless slit pore at low temperature [46] has shown that the dipoles tend to lie parallel to the surface in... 

P. G. Mezey, Descriptors of Molecular Shape in 3D, in From Chemical Topology to Three-Dimensional Geometry (A. T. Balaban, ed.). Plenum, in press. 

---