Chemical bonds shape representations

Figure 3.11 Conventional representations of the shapes of the p orbitals. They are used as approximate representations of both ip and tp2. The sign of tp is indicated by the shading. (Reproduced with permission from and M. J. Winter, Chemical Bonding, 1994, Oxford University Press, Oxford.)...

Graphical representations of the electron density will be provided in Chapter 4, and connections drawn between electron density and both chemical bonding and overall molecular size and shape. 

Formal chemical bonds as lines in space represent only a drastically oversimplified representation of chemical bonding, a mere skeletal model, introduced and in use since the early days of chemistry when there was no hope yet to detect, model, visualize, and understand the intricate, fuzzy, three-dimensional features and the wealth of shape information of molecular electron densities. 

The two concepts have on occasion been brought together Coulson and Duncanson[4] gave an explicit formula for sp-orbitals based on Slater type orbitals (STO s). Rozendaal and Baerends used hybrids to describe chemical bonding in a momentum representation [5], and more recently, Cooper considered the shape of sp hybrids in momentum space, and their impact on momentum densities [6], We would like to have a closer look at them, in terms of their functional behavior, their nodal structure and their topology. We will do... 

Chemists have historically employed various means of representating molecular structure. Two-dimensional drawings of atoms connected by lines are some of the most common molecular representations. Each line represents a chemical bond that, in the simplest case, is a pair of electrons shared between the connected atoms, resulting in a very strong attractive interatomic force. The various interatomic forces define the structure or shape of a molecule, while its chemistry is dependent on the distribution of electrons. A chemical reaction involves a change in the electron distribution, i.e., a change in bonding. 

The intimate relation between the nuclear distribution and the electronic density distribution is a natural bridge that connects the more conventional, essentially classical, ball-and-stick models, and the more accurate, quantum-chemical electronic density descriptors of molecular shape. It is somewhat surprising that relatively little effort has been devoted to the natural relation between the purely nuclear interactions and the electronic density. In this contribution this connection will be discussed from a specific viewpoint, leading to a 3D representation of molecular shape and to an interpretation of chemical bonding. 

A structural formula uses lines to represent chemical bonds and shows how the atoms in a molecule are connected to each other. The structural formula for hydrogen peroxide is H—O—O—H. In addition to formulas, we also use molecular models—fhree-dimensional representations of molecules—to represent compounds. In fhis book, we use two types of molecular models balTand-stick and space-filling. In ball-and-stick models, we represent atoms as balls and chemical bonds as sticks. The balls and sticks are connected to represent the molecule s shape. The balls are color coded, and each element is assigned a color as shown in the margin. 

Classical shape representations of molecules are based on assumed analogies between quantum mechanical molecules and macroscopic, classical objects. Since most of the mass of molecules is concentrated in the nuclei, it has appeared natural to place emphasis on nuclear arrangements, and the chemically more relevant shapes of electron densities have become the focus of molecular shapes analysis only recently. It is important to distinguish stereochemistry and molecular shape analysis. The term stereochemistry is commonly used for the 3D pattern of formal bonds, whereas molecular shape often refers to the shape of the fuzzy electron density cloud, or to simpler representations of large-scale molecular features, such as an a-helix or a -sheet of a protein. Several alternative shape representations are also used, such as fused sphere van der Waals (VDW) surfaces, Connolly surfaces, solvent accessibility surfaces, or molecular electrostatic potential (MEP) surfaces. 

As implied by the representations of the water molecule in Figure 1.6, the atoms and bonds in F120 form an angle somewhat greater than 90°. The shapes of molecules are referred to as their molecular geometry, which is crucial in determining the chemical and toxicological activity of a compound and structure-activity relationships. 

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