Modeling Molecular Shapes

A molecule consists of two or more atoms held together by 

Balloons containing latex may cause allergic reactions. 

How does a covalent bond differ from an ionic bond  

How does the VSEPR model take into account the repulsion of electron pairs in predicting molecular shape  

What effect do lone pairs of electrons have on shared bonding orbitals Why  

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Using Soap Bubbles to Model Molecular Shape... 

MultiCASE) (Dearden et al., 1997 Klopman and Rosenkranz, 1994). A further system is Computerized Optimized Parametric Analysis of Chemical Toxicity (COMPACT) (Lewis et al., 1994). The latter analyses the ability of a molecule to fit into the active site of the CYP1A1 isozyme of cytochrome P450 (CYP) (and some other CYP isozymes), by modeling molecular shape (planarity or area/depth) and chemical reactivity (covalent bond formation). The use of COMPACT is limited to molecules that are activated by these CYP enzymes. 

Kier, L.B. and Hall, L.H. (1999d) The kappa indices for modeling molecular shape and flexibility, in Topological Indices and Rdated Descriptors in QSAR and QSPR (eds J. Devillers and A.T. Balaban), Gordon and Breach Science Publishers, Amsterdam, The Netherlands, pp. 455-489. 

Hopfinger et al. [53, 54] have constructed 3D-QSAR models with the 4D-QSAR analysis formahsm. This formalism allows both conformational flexibility and freedom of alignment by ensemble averaging, i.e., the fourth dimension is the dimension of ensemble sampling. The 4D-QSAR analysis can be seen as the evolution of Molecular Shape Analysis [55, 56]. 

J. K. Burdett, Molecular Shape.s Theoretical Models of Inorganic Stereochemistry John Wiley Sons, New York (1980). 

Compound Structural Formula Repulsive Electron Pairs of Electron Pairs Molecular Shape Molecular Model... 

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. 

The connection between a molecule s electron density surface, an electrostatic potential surface, and the molecule s electrostatic potential map can be illustrated for benzene. The electron density surface defines molecular shape and size. It performs the same function as a conventional space-filling model by indicating how close two benzenes can get in a liquid or crystalline state. 

Given the diversity of different SCRF models, and the fact that solvation energies in water may range from a few kcal/mol for say ethane to perhaps 100 kcal/mol for an ion, it is difficult to evaluate just how accurately continuum methods may in principle be able to represent solvation. It seems clear, however, that molecular shaped cavities must be employed, the electiostatic polarization needs a description either in terms of atomic charges or quite high-order multipoles, and cavity and dispersion terms must be included. Properly parameterized, such models appear to be able to give absolute values with an accuracy of a few kcal/mol." Molecular properties are in many cases also sensitive to the environment, but a detailed discussion of this is outside the scope of this book. ... 

No written formula is quite as effective as a molecular model to help us visualize molecular shape. Since chemists find that the shape of a molecule strongly influences its chemical behavior, pictures and models of molecules are important aids. A variety of types of models are... 

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. 

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. 

In this section, we construct a model of molecular shape empirically, which means that we base it on rules suggested by experimental observations rather than on more fundamental principles. We proceed in three steps. First, we set up the basic nodel for simple molecules without lone pairs on the central atom. Then, we elude the effects of lone pairs. Finally, we explore some of the consequences of ecular shape. 

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 ... 

STRATEGY For the electron arrangement, draw the Fewis structure and then use the VSEPR model to decide how the bonding pairs and lone pairs are arranged around the central (nitrogen) atom (consult Fig. 3.2 if necessary). Identify the molecular shape from the layout of atoms, as in Fig. 3.1. 

Having introduced methane and the tetrahedron, we now begin a systematic coverage of the VSEPR model and molecular shapes. The valence shell electron pair repulsion model assumes that electron-electron repulsion determines the arrangement of valence electrons around each inner atom. This is accomplished by positioning electron pairs as far apart as possible. Figure 9-12 shows the optimal arrangements for two electron pairs (linear),... 

Tetrahedral geometry may be the most common shape in chemistry, but several other shapes also occur frequently. This section applies the VSEPR model to four additional electron group geometries and their associated molecular shapes. 

The carbon atom in CO2 has two groups of electrons. Recall from our definition of a group that a double bond counts as one group of four electrons. Although each double bond includes four electrons, all four are concentrated between the nuclei. Remember also that the VSEPR model applies to electron groups, not specifically to electron pairs (despite the name of the model). It is the number of ligands and lone pairs, not the number of shared eiectrons, that determines the steric number and hence the molecular shape of an inner atom. 

In this chapter, we develop a model of bonding that can be applied to molecules as simple as H2 or as complex as chlorophyll. We begin with a description of bonding based on the idea of overlapping atomic orbitals. We then extend the model to include the molecular shapes described in Chapter 9. Next we apply the model to molecules with double and triple bonds. Then we present variations on the orbital overlap model that encompass electrons distributed across three, four, or more atoms, including the extended systems of molecules such as chlorophyll. Finally, we show how to generalize the model to describe the electronic structures of metals and semiconductors. 

We cannot generate a tetrahedron by simple overlap of atomic orbitals, because atomic orbitals do not point toward the comers of a tetrahedron. In this section, we present a modification of the localized bond model that accounts for tetrahedral geometry and several other common molecular shapes. 

Existing SEC retention theories have been independently developed for each of the molecular-shape models shown in Figure 1. The deep hollow cyclin-drical pore in the figure (A, B, and C) illustrates the SEC exclusion effect on three types of solute molecules, hard-sphere, rigid-rod, and random-coil, respectively. The individual theories and their bases of commonality are now reviewed briefly. 

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