Shape, molecular

The VSEPR model is used to determine molecular shape. It assumes arrangements that minimize repulsion of electron pairs around the central atom. The presence of four bonding pairs produces a tetrahedral arrangement. Three such pairs produce a trigonal planar shape, unless there also is a lone pair on the central atom, in which case the shape is trigonal pyramidal. Two bonding pairs produce a linear shape, but if there also are two lone pairs on the central atom, the shape will be bent. 

Use the VSEPR model and the concept of hybridization to describe the hybrid orbitals and the shape of each of the following molecules. 

The shape of a molecule deteraiines many of its physical and chemical properties. Molecular shape, in turn, is determined by the overlap of orbitals that share electrons. Theories have been developed to explain the overlap of bonding orbitals and are used to predict the shape of the molecule. 

Many chemical reactions, especially those in living things, depend on the ability of two compounds to contact each other. The shape of the molecule determines whether or not molecules can get close enough to react. 

Once a Lewis structure is drawn, you can determine the molecular geometry, or shape, of the molecule. The model used to determine the molecular shape is referred to as the Valence Shell Electron Pair Repulsion model, or VSEPR model. This model is based on an arrangement that minimizes the repulsion of shared and unshared pairs of electrons around the central atom. 

Now consider a water molecule (H2O), which has two single covalent bonds and two lone pairs according to its Lewis structure. Although a water molecule has four electron pairs off the central atom, it is not tetrahedral because the two lone pairs occupy more space than do the paired electrons. The water molecule has a bent shape with a bond angle of 104.5°. 

Electrons in a molecule are located as far apart as they can be, just as these balloons are arranged. 

There is no simple demonstration of how molecular shape, like spin or the atomic valence state, emerges as a consequence of environmental pressure, but there is the compelling argument that it never features in molecular physics, unless it is introduced by hand. 

Apart from subtle exceptions, an isolated molecule differs from a molecule in a crystal in that the isolated molecule has no shape, whereas in a crystal it acquires shape, but loses its identity as an independent entity. This paradoxical situation is best understood through the famous Goldstone theorem, which for the present purpose is interpreted to state that any phase transition, or symmetry broken, is induced by a special interaction. When a molecule is introduced into an environment of other molecules of its own kind, a phase transition occurs as the molecule changes its ideal (gas) behaviour to suit the non-ideal conditions, created by the van der Waals interaction with its neighbours. An applied electric or magnetic field may induce another type of transformation due to polarization of the molecular charge density, which may cause alignment of the nuclei. When the field is switched off the inverse transformation happens and the structure disappears. The Faraday effect (6.2.3) is one example. 

Transition from the liquid to the solid state happens as the vibrational motion of individual molecules spreads through the bulk of the material to reappear as lattice modes. The molecules are now coupled into a periodic 

This general scheme of events, although valid for all materials, does not predict the same effects under the same conditions for all species. It depends quite critically on the complexity of the molecule. Large biomolecules or polymers have no gas-phase existence and even in solution, or the liquid state, may have a well-defined molecular shape, while small molecules like ammonia settle into a classical structure only at very low temperatures. 

the spherical index, is equal to 1 for a sphere Fq, the cylindrical index, is large for a cylindrical object, but small for a disk-shaped object. Neither index takes indentations into account, and Fg would be equal to 1 also for a sea urchin, while Fq is very high also for a camshaft. 

The molecular radius, is defined as the radius of a sphere of volume V. The volume-to-surface ratio is high for a convex object, and small for a concave one. This ratio is equal to F/3 for a sphere of radius F, hence the asphericity index [7]  

Further, it is not at all strange that we can use number of carbon atoms to express the structure relation for many different properties. It is not being said that number of carbon atoms is in any way synonymous with solubility or boiling point or, in fact, that number of carbon atoms stands for solubility or boiling point. The structure-activity model essentially represents the relationship between structure and property in a quantitative mathematical form suitable for further use. 

The molecular connectivity indexes represent molecular structure in a manner analogous to the count of carbon atoms, but in a much more general way. That is, chi indexes are weighted counts of structure features with the same mathematical qualities as counts, but with much more structure information. 

Further complications in quantitating molecular shape arise from the variable nature of atom relationships across space. This conformational variability presents uncertainty in depicting a reliable shape, although quantum mechanics addresses the problem of energy-preferred structures. A molecule, as 

Bearing these considerations in mind, nonetheless, shape quantitation presents a challenge well worth the effort. The potential value of shape quantitation is clearly demonstrable in physical and biological studies where this attribute is influential. Accordingly, we have addressed this problem and have contributed one possible approach to its solution. 

BioKoster in Medicinal Oiemi ry, First Edition. Edited by Nathan Brown 

Methods for molecular shape similarity can be roughly divided into two categories those that require finding the optimal superposition of the molecules being compared (superposition-based) and those that, by contrast, are independent of molecular orientation and position (superposition-free). Here we are restricting our focused review to those techniques that have demonstrated to perform shape similarity and its suitability to bioisosteric replacement in small molecules. 

Sodium carbonate has both ionic and covalent bonds. Ionic bonds exist between each of the sodium ions and the carbonate ion. Covalent bonds are present between the carbon and oxygen atoms within the carbonate ion. One important difference between the ionic and covalent bonds in this compound can be demonstrated by dissolving sodium carbonate in water. It dissolves in water, forming three charged particles— two sodium ions and one carbonate ion—per formula unit of Na2C03  

The col ion remains as a unit, held together by covalent bonds but where the bonds are ionic, dissociation of the ions takes place. Do not think, however, that polyatomic ions are so stable that they cannot be altered. Chemical reactions by which polyatomic ions can be changed to other substances do exist. 

Water is known to have the geometric shape known as bent or V-shaped. Carbon dioxide exhibits a linear shape. BF3 forms a third molecular shape called trigonal planar since all the atoms lie in one plane in a triangular arrangement. One of the more common molecular shapes is the tetrahedron, illustrated by the molecule methane (CH4). 

How do we predict the geometric shape of a molecule We will now study a model developed to assist in making predictions from the Lewis structure. 

Geometric shapes of common molecules. Each molecule is shown as a ball-and-stick model (showing the bonds) and as a spacefilling model (showing the shape). 

Some of the mechanical and thermal characteristics of polymers are a function of the ability of chain segments to experience rotation in response to applied stresses or thermal vibrations. Rotational flexibility is dependent on repeat unit structure and chemistry. For example, the region of a chain segment that has a double bond (C=C) is rotationaUy rigid. Also, introduction of a bulky or large side group of atoms restricts rotational movement. For example, polystyrene molecules, which have a phenyl side group (Table 14.3), are more resistant to rotational motion than are polyethylene chains. 

2nd edition, by Treloar (1958), Fig. 3.3, p. 47. By permission of Oxford University Press.) 

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Another important application of perturbation theory is to molecules with anisotropic interactions. Examples are dipolar hard spheres, in which the anisotropy is due to the polarity of tlie molecule, and liquid crystals in which the anisotropy is due also to the shape of the molecules. The use of an anisotropic reference system is more natural in accounting for molecular shape, but presents difficulties. Hence, we will consider only... 

Weisz P B 1981 Molecular shape selective catalysis Proc. 7th Int. Congr. on Catalysis (Tokyo) 1 1... 

Apart from tliese mainstream metliods enabling one to gain a comprehensive and detailed stmctural picture of proteins, which may or may not be in tlieir native state, tliere is a wide variety of otlier metliods capable of yielding detailed infonnation on one particular stmctural aspect, or comprehensive but lower resolution infonnation while keeping tlie protein in its native environment. One of tlie earliest of such metliods, which has recently undergone a notable renaissance, is analytical ultracentrifugation [24], which can yield infonnation on molecular mass and hence subunit composition and their association/dissociation equilibria (via sedimentation equilibrium experiments), and on molecular shape (via sedimentation velocity experiments), albeit only at solution concentrations of at least a few tentlis of a gram per litre. 

Besides the aforementioned descriptors, grid-based methods are frequently used in the field of QSAR quantitative structure-activity relationships) [50]. A molecule is placed in a box and for an orthogonal grid of points the interaction energy values between this molecule and another small molecule, such as water, are calculated. The grid map thus obtained characterizes the molecular shape, charge distribution, and hydrophobicity. 

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]. 

Rhyn K-B, H C Patel and A J Hopfinger 1995. A 3D-QSAR Study of Anticoccidal Triazlnes Usir Molecular Shape Analysis. Journal of Chemical Information and Computer Science 35 771-778. 

Terms in the energy expression that describe a single aspect of the molecular shape, such as bond stretching, angle bending, ring inversion, or torsional motion, are called valence terms. All force fields have at least one valence term and most have three or more. 

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... 

On the assumption that the pairs of electrons in the valency shell of a bonded atom in a molecule are arranged in a definite way which depends on the number of electron pairs (coordination number), the geometrical arrangement or shape of molecules may be predicted. A multiple bond is regarded as equivalent to a single bond as far as molecular shape is concerned. 

It would clearly be desirable to extend the scope of the Kelvin method to include a range of adsorptives having varied physical properties, especially surface tension, molar volume, molecular shape and size. This would enable the validity of the method and its attendant assumptions to be tested more adequately, and would also allow a variation in experimental technique, for example by permitting measurements at 298 K rather than 77 K. 

In discussing molecular symmetry it is essential that the molecular shape is accurately known, commonly by spectroscopic methods or by X-ray, electron or neutron diffraction. 

In the main, the physical and chemical properties of saturated and partially unsaturated alicyclic compounds closely resemble those of the analogous acyclic compounds formally derived by cleavage of the carbon ring at a point remote from any functionality. Relatively small, but often significant, differences in properties arise from conformational effects, and from strain effects in small rings, and these differences can be striking in properties which are particularly sensitive to molecular shape. 

The term endocrine disrupter (ED) has tended to be used for those chemicals which act specifically at the level of the hormone receptor present in the target cells of various organs. Such chemicals may either mimic the action of the natural hormone (agonistic activity) or are sufficiently similar in molecular shape to the naturally produced hormone to interfere with the interaction between the hormone and receptor, thus blocking or impeding the activation of the receptor (antagonsitic activity). Such effects may occur at very low concentrations (as with the endogenous hormone), compared with the concentrations normally required to elicit the more traditional toxic effects attributed to chemicals. Recently,... 

As the temperature is decreased, free-volume is lost. If the molecular shape or cross-linking prevent crystallisation, then the liquid structure is retained, and free-volume is not all lost immediately (Fig. 22.8c). As with the melt, flow can still occur, though naturally it is more difficult, so the viscosity increases. As the polymer is cooled further, more free volume is lost. There comes a point at which the volume, though sufficient to contain the molecules, is too small to allow them to move and rearrange. All the free volume is gone, and the curve of specific volume flattens out (Fig. 22.8c). This is the glass transition temperature, T . Below this temperature the polymer is a glass. 

With the development of accurate computational methods for generating 3D conformations of chemical structures, QSAR approaches that employ 3D descriptors have been developed to address the problems of 2D QSAR techniques, e.g., their inability to distinguish stereoisomers. The examples of 3D QSAR include molecular shape analysis (MSA) [34], distance geometry [35,36], and Voronoi techniques [37]. 

AJ Hopfinger. A QSAR investigation of dihydrofolate reductase inhibition by Baker triazmes based upon molecular shape analysis. I Am Chem Soc 102 7196-7206, 1980. 

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. 

Of the various geometric parameters associated with molecular shape, the one most nearly constant from molecule to molecule and most nearly independent of substituent effects is bond length. Bond lengths to carbon depend strongly on the hybridization of the carbon involved but are little influenced by other factors. Table 1.2 lists the interatomic distances for some of the most common bonds in organic molecules. The near constancy of bond lengths from molecule to molecule reflects the fact that the properties of individual bonds are, to a good approximation, independent of the remainder of the molecule. 

Up to this point, we have emphasized the stereochemical properties of molecules as objects, without concern for processes which affect the molecular shape. The term dynamic stereochemistry applies to die topology of processes which effect a structural change. The cases that are most important in organic chemistry are chemical reactions, conformational changes, and noncovalent complex formation. In order to understand the stereochemical aspects of a dynamic process, it is essential not only that the stereochemical relationship between starting and product states be established, but also that the spatial features of proposed intermediates and transition states must account for the observed stereochemical transformations. 

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