Bonding | Research & Encyclopedia Articles

Bonding

A molecule is the smallest unit of a substance capable of independent existence. As early as the 17th century, there were proposals that molecules were made up of atoms of elements held together either by the mutual attraction of the atoms or by the atoms fitting together in a manner similar to a jigsaw puzzle. Well into the 19th century, however, there were continuing disagreements on the molecular nature of chemical compounds. After Edward Frankland proposed in 1866 that molecules are made up of atoms held together by localized directional chemical bonds, the supporting experimental evidence led to general acceptance of the idea. In 1874, August Kekulé and the team of J. H. van't Hoff and J. A. Le Bel independently proposed a tetrahedral structure for carbon in polyatomic molecules. In the methane molecule CH₄, for instance, the carbon atom is located at the center of a tetrahedron with the four hydrogen atoms located at the four apexes of the tetrahedron. The geometry of molecules involving the atoms of a number of other elements was soon proposed.

This new way of thinking of molecules as stable groupings of atoms, with these atoms having a definite arrangement in space relative to one another, revolutionized chemistry. A chemical or molecular bond was now regarded as the combination of forces that holds two atoms in fixed relationship within a molecule. Chemical reactions could now be thought of as the formation and the breaking of bonds, with chemical reactivity dependant on the strength of bonds and on their spatial arrangement. Indeed, the concept of chemical bonds lies at the heart of much of the work with which chemistry is involved.

The exact nature of chemical bonds and the explanation of the source of the attraction between atoms which holds them in such definite spatial relationships remained a mystery. Any significantly useful bonding theory had to explain why bonds form, why some bonds are stronger and some more reactive than others, and why a particular spatial arrangement is the most stable.

In 1902, soon after J. J. Thomson proved, in 1897, that negatively charged electrical units known as electrons exist and are a basic constituent of matter, G. N. Lewis proposed that atoms form ionic bonds by the transfer of one or more electrons from one atom to the other. In 1916, Lewis proposed that non-ionic, or covalent, bonds are formed by the sharing of electrons between the atoms which are held together by such a bond. It remained for quantum mechanics to provide the methods for understanding the chemical bond and the chemical phenomena associated with it on the basis of this shared electron concept.

The two extremes of molecular bonding are ionic bonds and covalent bonds. When one atom comes close to another, the electrons of the two atoms are attracted electostatically to the nuclei of both atoms. Ionic bonds form between atoms with widely different electronegativities, i.e., abilities to hold onto their electrons. When two atoms with large differences in electronegativity come into close proximity, the atom with the greater attraction for electrons not only holds onto its own electrons but may pull one or more electrons away from the other, less electronegative atom. One atom thus becomes a negative ion and the other a positive ion. The two ions of opposite charge attract each other and an ionic bond is formed. The energy of attraction between oppositely charged particles is inversely proportional to the distance between them. At great distances of separation, the attraction between the two ions is essentially zero; as the distance decreases, the attraction increases. The maximum energy of attraction would come when the distance of separation is zero. This does not happen, however, because the electron clouds of the two ions repel each other at very close distance, as do the nuclei of the two ions. Therefore, when an ionic bond forms, the bond length is the equilibrium distance at which the forces of attraction exactly balance the forces of repulsion.

A covalent bond forms when the participant atoms do not differ greatly in electronegativity and, consequently, both have essentially the same hold on their electrons. When two such atoms come close together, the electrons of the two atoms are attracted, as in the case of an ionic bond, to the nuclei of both atoms. Now, however, neither atom is strong enough to pull electrons away from the other, and ions do not form. One or more of the electrons from each of the atoms may, however, be able to move around both nuclei, spending part of the time more closely associated first with one, then the other nucleus. These electrons are shared by the two nuclei, and a covalent bond forms. The bond length is determined by the equilibrium position at which the attraction resulting from sharing an electron is exactly balanced by the repulsion of positive nuclei and negative electrons.

Bonds between atoms of the same element, such as hydrogen, H₂, are purely covalent: the shared bonding electrons are equally attracted to both nuclei. The covalent bonds of atoms with unequal electronegativities, however, are polar covalent bonds. In such a bond the electrons that the two atoms share are attracted more to the atom with the greater electronegativity, and they spend more time near it. Consequently, the more electronegative atom has a partial negative charge. The less electronegative atom has a partial positive charge since the shared electrons spend less time with it. Because there is a separation of charges, with a partial positive charge at one end of the bond and an equal negative partial charge at the other, a polar bond results.

This simplified qualitative discussion of molecular bonding is placed on a much firmer theoretical and quantitative basis through the utilization of quantum mechanics. A number of scientists have contributed to the development of quantum mechanical applications to molecular systems. The work of Linus Pauling was central to this effort. His book The Nature of the Chemical Bond (1960) is a classic and provides an excellent introduction to the field of quantum chemistry.

Attention has been focused on two principal methods for the quantum mechanical treatment of molecular bonding: valence bonding theory and molecular orbital theory. Only a very general introduction, incorporating ideas from both approaches, can be given here.

The solutions of the quantum mechanical wave equation for an atom are a set of wave functions, known as atomic orbitals. Each electron of the atom may be assigned to a wave function, and the region of space where the electron is located can be determined from its wave function. The region occupied by some atomic orbitals is spherical with the nucleus of the atom at the center of the sphere. Other orbitals have directional character with their associated electrons located in a particular direction relative to the nucleus. Since only the electrons that are more distant from the nucleus are shared in bond formation, only the atomic orbitals associated with these electrons, known as valence electrons, need be considered in the discussion of bond formation between atoms.

As atoms approach each other, their orbitals overlap, i.e., they occupy the same region in space. Mathematically, the two atomic orbitals add together, resulting in a molecular orbital associated with both atoms. An electron that was initially associated with only an atomic orbital on its own atom, is now associated with a molecular orbital and may move about in the space corresponding with this new orbital, space that includes both atoms. If the quantum mechanical solution for the energy associated with an orbital indicates that the electrons in the molecular orbital are more stable than in the two isolated atomic orbitals, a bond is formed, and the molecular orbital is a bonding orbital.

The bonds that have been discussed up to this point involve the overlapping of a single atomic orbital on each of the two bonded atoms to form a molecular orbital that contains two shared electrons, one from each of the bonded atoms. This is called a single bond. It is also possible for two orbitals on each atom to overlap, forming two molecular orbitals between the two atoms. The result is a double bond. If three atomic orbitals on each of the two atoms overlap to form three molecular orbitals, a triple bond is formed.

The approaches used above to explain the bonding between two atoms may be generalized to polyatomic molecules. The bonds in many polyatomic molecules can be considered to be localized covalent bonds: the bond between each pair of atoms in the molecule is thought of as being made up of only the overlapping atomic orbitals of those two atoms, and the electrons shared by each pair of atoms are confined to the space between the two atoms. The molecular orbital description for such a polyatomic molecule is simply the collection of the localized molecular orbitals of all its individual bonds. The properties of the polyatomic molecule, such as reactivity and geometry, result from the properties of all the localized molecular orbitals associated with the bonds between the individual pairs of atoms.

In some cases, however, the properties of a polyatomic molecule are quite different from what might be expected from the sum of individual localized bonds making up the molecule. In these cases, nonlocalized molecular orbitals must be considered. Nonlocalized molecular orbitals are made up of the atomic orbitals of more than two atoms; they stretch over more than two atoms and the shared electrons are associated with all of the atoms whose atomic orbitals make up the molecular orbital. A good example of nonlocalized bonds is the benzene molecule. One way of picturing the bonding in the benzene ring is with alternating localized single and double bonds. Bond strength is the energy needed to break apart two bonded atoms. Bond length is the distance between two bonded atoms. The energy needed to break a single bond is significantly different from that needed to break a double bond. A double bond is significantly shorter than a single bond. Experimentally, however, the distance between adjacent carbon atoms in benzene is found to be the same for each pair of carbons. Also, the energy needed to separate any pair of carbon atoms is found to be the same. Molecular orbital theory explains this by using atomic orbitals on all six carbons of the benzene ring to form six nonlocalized molecular orbitals associated with all six atoms. The shared electrons in these molecular orbitals are free to move throughout the ring. This model of benzene predicts that the properties of all six carbon-carbon bonds (e.g., bond distances and bond energies) should be the same, in agreement with the experimental observations. Also, the values predicted for the bond angles (the angle formed by adjacent bonds in a polyatomic molecule) agrees with experiment.

The use of atomic orbitals on each of the six carbon atoms in the benzene ring to form molecular orbitals is an example of one of the most powerful computational methods used in the study of bonding in molecules. In this approach, the wave function of molecular orbitals for a polyatomic molecule are assumed to be made up of contributions from all atoms in the molecule. The molecular orbital is said to be a linear combination of atomic orbitals (LCAO), with the contribution of each atomic orbital to the resulting molecular orbital given an appropriate weight. Sophisticated computer programs are then used to determine the values for the contribution of each atomic orbital which gives the best fit to experimental data. For benzene, the contribution of each of the six atomic orbitals will be the same. In molecules in which there is little interaction between bonds, a set of molecular orbitals will be obtained which correspond to localized bonds involving only two adjacent atoms in each molecular orbital.

The use of quantum mechanical approaches has revolutionized the understanding of chemical bonds and has proved highly successful in explaining the phenomena related to bonds, including chemical reactivity and molecular geometry. The field of quantum chemistry continues to apply, with great success, the methods of quantum mechanics to virtually all areas of concern to chemists.

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