Much of chemistry is explainable in terms of the structures of chemical compounds. The understanding of these structures hinges very strongly on understanding the electronic configurations of the elements. The union of atoms, and therefore the formation of compounds from the elements, is associated with interactions among the extranuclear electrons of the individual atoms. Electronic interactions among atoms may occur in two ways: Electrons may be transferred from one atom to another, or they may be shared by two (or more) atoms. The first type of interaction is called electrovalence and results in the formation of electrically charged monatomic ions. The second, covalence, leads to the formation of molecules and complex ions. See also Chemical bonding.
In considering structures more complex than those derived from simple monoatomic ions, the logical step is to consider single polyhedral aggregates of atoms. In its most precise sense, structure is used to denote a knowledge of the bonding distances and angles between atoms in chemical compounds and, in turn, the geometrical arrangements which they form. These atomic arrangements and the associated distances and angles serve uniquely as “fingerprints” of these atom spatial configurations, and depend very much on the electronic configurations around atoms. The chemical combination of neutral atoms to produce uncharged species results in molecule formation, whereas the similar combination of atoms or ions possessing a net charge results in the formation of complex ions. A basic understanding of the species formed involves the concept of the coordination polyhedron, which allows a simple classification of the structures of many polyatomic molecules and ions. This type of classification is particularly useful because it conveniently explains the packing together of simple chemical molecules or ions in terms of highly symmetrical polyhedra. There is an obvious connection between polyhedra and the structures found in crystalline solids formed from them. Crystal formation often involves the linking of convex polyhedra by the sharing of corners, edges, or faces, ultimately forming space-filling assemblies in which all faces of each polyhedron are in contact with faces of other polyhedra. The most important simple polyhedrons are the tetrahedron, the trigonal bipyramid, the octahedron, the pentagonal bipyramid, and the cube. The most commonly observed of these polyhedral configurations are the tetrahedron (four faces) and the octahedron (six faces).
The simplest correlative device which accurately summarizes a very large number of structures and enables the chemist to predict, with a good chance of success, the geometric array of the atoms in a compound of known composition, is based on an extreme electrostatic model. This model, or theory, represents the bonds in a purely formal way. The central atom is considered to be a positive ion having a charge equal to its oxidation state. The groups attached to the central atom (the ligands) are then treated either as negative ions or as neutral dipolar molecules. The principal justification for this approach lies in its successful correlation of a vast amount of information.
A number of significant observations can be made with regard to these formulations. There are series of ions, or ions and molecules, having the same type of composition, differing only in the nature of the central ion and the net charge on the aggregate. Examples are found in the series: NO3−, CO32−, BO33−, CIO3−, SO32−, PO33−; ClO4−, SO42−, PO43−, SiO44−; AlF63−, SiF62−, PF6−. The numbers of atomic nuclei and of electrons are the same for all the members of each series; consequently, these are called isoelectronic series. Not only are the several chemical entities in such series isoelectronic, but they are usually identical in geometrical structure (isostructural).
It may also be observed that corresponding ions from a given vertical family of the periodic table commonly vary in coordination number. A useful example is found in N5+ and P5+ which form NO3− and PO43−, respectively. In addition, some neutral molecules expand their coordination numbers to form stable anionic halo complexes, whereas others do not. Thus, SiF4 reacts with fluoride ion to form SiF62−, whereas CF4 does not form a similar complex ion. The most satisfactory explanation of these and many related observations is conveniently formulated in terms of the electrostatic model chosen here.
The necessary condition for stability of the coordination polyhedron MAn requires that the anions A are each in contact with the central atom M. As a consequence of this condition, the limit of stability of the structure arises in those cases where the anions are also mutually in contact. Larger ligands, or anions, would not be in contact with the central ion. This relationship is usually summarized in terms of the limiting ratio of the radius of the cation, rM, to that of the anion, rA, below which the anions would no longer be in contact with the cation.
According to the valence-bond theory, the principal requirements for the formation of a covalent bond are a pair of electrons and suitably oriented electron orbitals on each of the atoms being bonded. The geometry of the atoms in the resulting coordination polyhedron is correlated with the orientation of the orbitals on the central atom. The orbitals used depend on the energies of the electrons in them. In general, the order of increasing energy of the electron orbitals is (n − 1)d < ns < np < nd. It is concluded that a nontransition atom having one valence electron will form a covalent bond utilizing an s orbital. In those cases where an unshared pair of electrons may be assigned to the ns orbital, as many as three equivalent bonds may be formed by utilizing the three np orbitals of the central atom. Because of the orientation of these p orbitals with respect to each other, the three resulting bonds should be at 90° to each other. This expectation is nearly realized in PH3. In order to account for four or six equivalent bonds, or for that matter in order to account for all the remaining polyhedral and polygonal structures, except the angular structure for a coordination number of 2 (with two unshared pairs of electrons on the central atom), an additional assumption is necessary. It is assumed that s and p, s and d, or s, p, and d orbitals, are replaced by new orbitals, called hybridized orbitals. These hybridized orbitals are derived from the original orbitals (mathematically) in such a way that the required number of equivalent bonds may be formed. In the simplest case, it is shown that s and p may be combined to form two equivalent sp hybridized orbitals directed at 180° to each other. Other sets of hybridized orbitals have been shown to be appropriate to describe the bonding in other structures. See also Ligand field theory.
Among inert-gas ions of the first row of eight elements in the periodic table, there are four orbitals available for covalent bond formation, one 2s and three 2p. Consequently, a maximum of four bonds may be formed. This is in general agreement with the existence of the tetrahedron as the limiting coordination polyhedron among these elements, for example, BeF42−, BF4−, CCl4, NH4+. Although only Li+ deviates from this pattern, having a coordination number of 6 in its crystalline halides, these compounds are best treated as simple electrovalent salts. In keeping with the limitation of only four orbitals, the formation of double or triple bonds between atoms of these elements reduces the coordination number of the central atom. Thus, the highest coordination number of a first-row element forming one double bond is 3. This is illustrated by the structures below.
The formation of a second π bond (a triple bond or two double bonds) reduces the coordination number of the atom in question still further, resulting in the linear sp set of hybridized orbitals being utilized in σ-bond formation. See also Valence.
With regard to the nature of doubly bonded compounds, another problem arises when such structures are viewed from the standpoint of valence-bond theory. In the species BCl3, COCl2, NO2Cl, and many similar substances, nonequivalent bonds are predicted. The doubly bonded oxygen should be closer to the central carbon atom than the singly bonded ones. This is not found to be true experimentally so long as the similar atoms are otherwise equivalent. There is only one observable CO distance in carbonate, one NO distance in nitrate, and so on. To account for such facts as these, the concept of resonance must be introduced. If the π bond exists, it must exist equally between the central atom and all the equivalent oxygen atoms. The resonance method of describing this situation is to say that one of the pictorial structures is inadequate to describe the substance properly, but that enough pictorial structures (resonance structures) should be considered to permute the double bond about all the equivalent bonds. The true structure is assumed to be something intermediate to all the resonance structures and more stable than any of them because it exists in preference to any one of them. The resonance structures for CO32− are the following:
The classic homologous series of compounds in organic chemistry provide useful examples involving the condensation of polyhedrons containing the same central element in the individual units. The general formula, CnH2n + 2, represents a large number of compounds extending from the lowest member, methane, CH4, to polyethylene, a plastic of economic importance in which n is a very large number. Two ways exist for the linking together of these tetrahedrons. This gives rise to two molecular forms, both of which are stable, well-known compounds. It is an essential part of these structures that each C link is linear (because it is merely a σ-bond); however, when two carbon atoms are linked to a third, the CCC angle is essentially determined by the bond angle of the central carbon atom (that is, the other carbons may be treated as ligands to the first (Fig. 1). The other familiar homologous series of organic chemistry differ from the saturated hydrocarbons in having at least one unique coordination polyhedron of a different type. The olefins contain two doubly bonded, or unsaturated, carbon atoms, whose polyhedral structures are trigonal planar, and the remainder of the carbons are tetrahedral. As in the case of the aliphatic hydrocarbons, the olefins exhibit an isomerism which is associated with the branching of the chain structure. In addition, the presence of two linked trigonal planar carbon atoms and the fact that the polyhedrons cannot rotate about the double bond give rise to a different kind of isomerism, called cis-trans isomerism (Fig. 2). See also Bond angle and distance.
Geometric structure of propane.
Cis-trans isomerism among olefins.
The existence of a predicted isomerism provides one of the most important confirmations of the theories of chemical structure. In general, the polyhedral view of molecular structure, as described here, has been thoroughly verified by the discovery of the many types of predicted isomerism. The first really convincing proof of the tetrahedral structures of saturated carbon atoms involved optical isomerism. See also Optical activity.
The aromatic hydrocarbons are characterized by cyclic arrangements of trigonal planar carbon atoms (Fig. 3a). The highly symmetrical nature of the benzene molecule is not fully represented by such a structure. The figure indicates the presence of three double and three single bonds in the ring. It has been shown that the CC bonds are all the same and, consequently, the true structure of the substance must be represented by two resonance structures which interchange the single and double bonds (Fig. 3b). See also Benzene.
Benzene molecule. (a) Structural formula. (b) Two forms in resonance.
