Electron Waves and Chemical Bonds

Before we describe these theories in the context of organic molecules, let s first think about bonding between two hydrogen atoms in the most fundamental terms. We ll begin with two hydrogen atoms that are far apart and see what happens as the distance 

Hydrocarbons are divided into two main classes aliphatic and aromatic. This classihcation dates from the nineteenth century, when organic chemistry was devoted almost entirely to the study of materials from natural soiuces, and terms were coined that reflected a substance s origin. Two sources were fats and oils, and the word aliphatic was derived from the Greek word aleiphar meaning fat. Aromatic hydrocarbons, irrespective of their own odor, were typically obtained by chemical treatment of pleasant-smelling plant extracts. 

Aliphatic hydrocarbons include three major groups alkanes, alkenes, and alkynes. Alkanes are hydrocarbons in which all the bonds are single bonds, alkenes contain at least one carbon-carbon double bond, and alkynes contain at least one carbon-carbon triple bond. Examples of the three classes of aliphatic hydrocarbons are the two-carbon compounds ethane, ethylene, and acetylene. 

Another name for aromatic hydrocarbons is arenes. The most important aromatic hydrocarbon is benzene. 

Different properties in these hydrocarbons are the result of the different types of bonding involving carbon. The shared electron pair, or Lewis model of chemical bonding described in Section 1.3, does not account for all of the differences. In the following sections, we will consider two additional bonding theories the valence bond model and molecular orbital theory. 

Before we describe these theories in the context of organic molecules, let s first think about bonding between two hydrogen atoms in the most fundamental terms. We ll begin with two hydrogen atoms that are far apart and see what happens as the distance between them decreases. The forces involved are electron-electron (—) repulsions, nucleus-nucleus (+ + ) repulsions, and electron-nucleus (—h) attractions. All of these forces increase as the distance between the two hydrogens decreases. Because the electrons are so mobile, however, they can choreograph their motions so as to minimize their 

PROBLEM 1.19 Which of the following compounds would you expect to have a dipole moment If the molecule has a dipole moment, specify its direction. 

SAMPLE SOLUTION (a) Boron trifluoride is planar with 120° bond angles. Although each boron-fluorine bond is polar, their combined effects cancel and the molecule has no dipole moment. 

All of the forces In chemistry, except for nuclear chemistry, are electrical. Opposite charges attract like charges repel. This simple fact can take you a long way. 

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FIGURE 1.14 Plot of potential energy versus distance for two hydrogen atoms. At long distances, there is a weak attractive force. As the distance decreases, the potential energy decreases, and the system becomes more stable because each electron now feels the attractive force of two protons rather than one. The optimum distance of separation (74 pm) corresponds to the normal bond distance of an H2 molecule. At shorter distances, nucleus-nucleus and electron-electron repulsions are greater than electron-nucleus attractions, and the system becomes less stable. 

FIGURE 1.15 Interference between waves, (a) Constructive interference occurs when two waves combine in phase with each other. The amplitude of the resulting wave at each point is the sum of the amplitudes of the original waves. (6) Destructive interference in the case of two phases out of phase with each other causes a mutual cancellation. 

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Classes of Hydrocarbons S3 Electron Waves and Chemical Bonds... 

Analysis of the total electron density distribution p(r) of a molecule is useful since p(r), contrary to MOs and wave functions, is an observable quantity that can be determined both experimentally and theoretically. As shown by Hohenberg and Kohn, the energy of a molecule in a non-degenerate ground state is a function of p(r). All physical and chemical properties of a molecule depend in some way on the electron density distribution. Accordingly, it is plausible that analysis of p(r) should lead to primary information of electronic structure and chemical bonding of 1. 

The ubiquitous electron was discoveied by J. J. Thompson in 1897 some 25 y after the original work on chemical periodicity by D. I. Mendeleev and Lothar Meyer however, a further 20 y were to pass before G. N. Lewis and then I. Langmuir connected the electron with valency and chemical bonding. Refinements continued via wave mechanics and molecular Orbital theory, and the symbiotic relation between experiment and theory still continues... 

PHYSICAL CHEMISTRY. Application of the concepts and laws of physics to chemical phenomena in order to describe in quantitative (mathematical) terms a vast amount of empirical (observational) information. A selection of only the most important concepts of physical chemistiy would include the electron wave equation and the quantum mechanical interpretation of atomic and molecular structure, the study of the subatomic fundamental particles of matter. Application of thermodynamics to heats of formation of compounds and the heats of chemical reaction, the theory of rate processes and chemical equilibria, orbital theory and chemical bonding. surface chemistry (including catalysis and finely divided particles) die principles of electrochemistry and ionization. Although physical chemistry is closely related to both inorganic and organic chemistry, it is considered a separate discipline. See also Inorganic Chemistry and Organic Chemistry. 

The main result that emerges from the discussions of particular eases is that it has proved possible to give a description of a molecule in terms of equivalent orbitals which are approximately localised, but which can be-transformed into delocalised molecular orbitals without any change in the value of the total wave function. The equivalent orbitals are closely associated with the interpretation of a chemical bond in the theory, for, in a saturated molecule, the equivalent orbitals are mainly localised about two atoms, or correspond to lone-pair electrons. Double and triple bonds in molecules such as ethylene and acetylene are represented as bent single bonds, although the rather less localised o-n description is equally valid. 

The first term in the product is associated with the spatial part and the second with the spin labels. The letters ua and b stand for atomic orbitals centered in hydrogen atoms Ha and H respectively. To account for the indistinguishability of the electrons, spatial and spin factors appear in two products (configurations). Consequently, the VB approach is multideterminantal from the outset. This superposition of determinants causes the VB wave function, even in its most simple form, to maintain the indistinguishability of the electrons within the chemical bond. This effect is called exclusion correlation , a non-dynamical correlation effect. 

The first attempt to clarify the physical basis of the Jahn-Teller theorem was due to Ruch, [3] in an introductory presentation to the 1957 annual meeting of the Bunsen-Gesellschaft in Kiel, which was organised by H. Hartmann. Ruch discussed the general connection between symmetry and chemical bonding, and also touched upon the Jahn-Teller effect in transition-metal complexes. He explained that degeneracy can always be related to the existence of a higher than twofold rotational axis and a wave function which is not totally symmetric under a rotation around this axis. Provided that the wave function is real the electron densities for such a wave function are bound to be anisotropic. The combination of an anisotropic distribution of the electron cloud and a symmetric nuclear frame leads to electrostatic distortion forces where the nuclear frame adapts itself to the anisotropic attraction force. 

As attractive as it appears, a plane-wave basis also carries with it its own disadvantages. Generally, we are interested in the behaviour of the valence electrons of a material it is these electrons that form chemical bonds which break and reform during the process of chemical reactions. However, near the atomic cores, the valence electron wavefunctions undergo rapid oscillations, due... 

The valence-bond treatment of polyatomic molecules is closely tied to chemical ideas of structure. One begins with the atoms that form the molecule and pairs up the unpaired electrons to form chemical bonds. There are usually several ways of pairing up (coupling) the electrons. Each pairing scheme gives a VB structure. A Heitler-London-type function (called a bond eigenfunction) is written for each structure i, and the molecular wave function is taken as a linear combination 2, c,4>, of the bond eigenfunctions. The variation principle is then applied to determine the coefficients c,. The VB wave function is said to be a resonance hybrid of the various structures. 

The full explanation of these facts is based on wave mechanics and the modern theories of electron distribution in chemical bonds. A simplified explanation is that the carbon atoms in benzene are held together by valencies (3 electrons). Two valency electrons are firmly located in a bond directly between each pair of carbon atoms, but the remaining electrons are pooled between all six atoms and are free to move to particular atoms when the molecule is influenced by some outside reagent... 

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