March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)
Part I. Introduction
Chapter 1. Localized Chemical Bonding
1.C. Hybridization
Consider the case of mercury. Its electronic structure is
Although it has no half-filled orbitals, it has a valence of 2 and forms two covalent bonds. This result can be explained by imagining that one of the 6s electrons is promoted to a vacant 6p orbital to give the excited configuration
In this state, the atom has two half-filled orbitals, but they are not equivalent. If bonding were to occur by the overlap of these orbitals with the orbitals of external atoms, the two bonds would not be equivalent. The bond formed from the 6p orbital would be more stable than the one formed from the 6s orbital, since a larger amount of overlap is possible with the former. A more stable situation is achieved when, in the course of bond formation, the 6s and 6porbitals combine to form two new orbitals that are equivalent; these are shown in Fig. 1.3.
Fig. 1.3 The two sp orbitals formed by mercury.
The new molecular orbitals are a mixture of the two original orbitals, so they are called hybrid orbitals. Each orbital is a merger of an s and p orbital and is called an sp orbital. The sp orbitals, each of which consists of a large lobe and a very small one, arise only in the bonding process and do not represent a possible structure for the free atom. A mercury atom forms its two bonds by overlapping each of the large lobes shown in Fig. 1.3 with an orbital from an external atom. The orbital of this external atom may be any of the atomic orbitals previously considered (s, p, d, or f), or it may be another hybrid orbital. Note that only lobes of the same sign can overlap. In any of these cases, the molecular orbital that arises is called a σ orbital since it fits the previous definition of a σ orbital.
In general, equivalent orbitals lie as far away from each other as possible because of mutual repulsion, so two sp orbitals form an angle of 180°. In other words, an atom that forms only two σ bonds uses two sp orbitals so HgCl2, for example, should be a linear molecule, and it is. This kind of hybridization is called digonal hybridization. An sp hybrid orbital forms a stronger covalent bond than either an s or a p orbital because it extends out in space in the direction of the other atom's orbital farther than the s or the p and permits greater overlap. Compare HgCl2 with water (OH2). It is known that the shape of HgCl2 is linear, but water is angular. This fact suggests that the hybrid orbitals utilized by oxygen in water is different from those used by mercury in HgCl2.
Many other kinds of hybridization are possible. Consider boron, which has the electronic configuration 1s22s22p1 yet has a valence of 3. To begin, boron has only three valence electrons available to form bonds, hence the valence of three. Any hybridization model must take this into account. As before, imagine promotion of an electron and hybridization:
In this case, there are three equivalent hybrid orbitals, each called sp2 (trigonal hybridization). This method of designating hybrid orbitals is perhaps unfortunate since nonhybrid orbitals are designated by single letters, but keep in mind that each of the three orbitals is called sp2. The key is to understand that the atom forms two σ bonds for sp hybridization and three σ bonds for sp2 hybridization. The sp2 hybrid orbitals just noted are shown in Fig. 1.4. The three axes are all in one plane and point to the corners of an equilateral triangle. This accords with the known structure of BF3, a planar molecule with angles of 120°.
Fig. 1.4 The three sp2 and the four sp3 orbitals.
Another type of hybrid orbital is possible, formed by atoms that can form four σ bonds. Carbon is an important atom that can form four single bonds (four σ bonds). Imagine promotion of an electron and hybridization that leads to
There are four equivalent molecular orbitals, each called sp3, and electron repulsion leads to a shape in which the orbitals point to the corners of a regular tetrahedron (Fig. 1.4). A typical molecule is methane (CH4) and assuming that carbon forms four bonds with sp3 hybrid orbitals, the bond angles of methane would thus be expected to be 109°28′, which is the angle for a regular tetrahedron. In reality, electrons are not “promoted” in atomic orbitals, but atomic orbitals are different from molecular orbitals (e.g., those found in methane). The model of promoting an electron is a mathematical device to describe molecular orbitals using the atomic orbitals.
The hybrid orbitals discussed in this section stem from only one possible approximate solution of the Schrödinger equation. The s and the three p atomic orbitals used to form sp3 orbitals, for example, can be combined in other equally valid ways. As will be seen in Section 1.E, the four C–H bonds of methane do not always behave as if they are equivalent. Bickelhaupt6 has proposed an alternative approach to the bonding in carbon suggesting that the maximum coordination number of carbn cannot exceed four because it is too small to allow more than four substituents approach and form the appropriate bonds.