8.1 Valence bond Theory

Nothing is perfect! Haven’t you heard it too many times in your life? Yeah, and it’s true! This belief applies to chemistry as well. If you thought that the Lewis theory explained all about compounds and molecules, you are wrong! It failed to explain many concepts and that is why we have the Valence Bond Theory. Here, we will read more about the valence bond theory and also look at its limitations. Yes, even this theory isn’t perfect guys! Let’s learn why.

As useful and appealing as the concept of the shared-electron pair bond is, it raises a somewhat troubling question that we must sooner or later face: what is the nature of the orbitals in which the shared electrons are contained? Up until now, we have been tacitly assuming that each valence electron occupies the same kind of atomic orbital as it did in the isolated atom. As we shall see below, his assumption very quickly leads us into difficulties.

1  Why atomic orbitals don’t work for molecules

Consider how we might explain the bonding in a compound of divalent beryllium, such as beryllium hydride, BeH₂. The beryllium atom, with only four electrons, has a configuration of 1s²2s². Note that the two electrons in the 2s orbital have opposite spins and constitute a stable pair that has no tendency to interact with unpaired electrons on other atoms.

Figure 8.1 Atomic Orbitals in Be

Figure 8.2 Excited energy levels of Be

The only way that we can obtain two unpaired electrons for bonding in beryllium is to promote one of the 2s electrons to the 2p level. However, the energy required to produce this excited-state atom would be sufficiently great to discourage bond formation. It is observed that Be does form reasonably stable bonds with other atoms. Moreover, the two bonds in BeH₂ and similar molecules are completely equivalent; this would not be the case if the electrons in the two bonds shared Be orbitals of different types, as in the “excited state” diagram above.

These facts suggest that it is incorrect to assume that the distribution of valence electrons that are shared with other atoms can be described by atomic-type s, p, and d orbitals at all.

Remember that these different orbitals arise in the first place from the interaction of the electron with the single central electrostatic force field associated with the positive nucleus. An outer-shell electron in a bonded atom will be under the influence of a force field emanating from two positive nuclei, so we would expect the orbitals in the bonded atoms to have a somewhat different character from those in free atoms. In fact, as far as valence electrons are concerned, we can throw out the concept of atomic orbital altogether and reassign the electrons to a new set of molecular orbitals that are characteristic of each molecular configuration. This approach is indeed valid, but we will defer a discussion of it until a later unit.

For now, we will look at a less-radical model that starts out with the familiar valence-shell atomic orbitals, and allows them to combine to form hybrid orbitals whose shapes conform quite well to the bonding geometry that we observe in a wide variety of molecules.

2  What are hybrid orbitals?

About orbitals: a quick review

First, recall that the electron, being a quantum particle, cannot have a distinct location; the most we can do is define the region of space around the nucleus in which the probability of finding the electron exceeds some arbitrary value, such as 90% or 99%. This region of space is the orbital. Because of the wavelike character of matter, the orbital corresponds to a standing wave pattern in 3-dimensional space which we can often represent more clearly in 2-dimensional cross section. The quantity that is varying (“waving”) is a number denoted by ψ (psi) whose value varies from point to point according to the wave function for that particular orbital.

Orbitals of all types are simply mathematical functions that describe particular standing-wave patterns that can be plotted on a graph but have no physical reality of their own. Because of their wavelike nature, two or more orbitals (i.e., two or more functions ψ) can be combined both in-phase and out-of-phase to yield a pair of resultant orbitals which, to be useful, must have squares that describe actual electron distributions in the atom or molecule.

The s,p,d and f orbitals that you are familiar with are the most convenient ones for describing the electron distribution in isolated atoms because assignment of electrons to them according to the usual rules always yields an overall function Ψ² that predicts a spherically symmetric electron distribution, consistent with all physical evidence that atoms are in fact spherical. For atoms having more than one electron, however, the s,p,d, f basis set is only one of many possible ways of arriving at the same observed electron distribution. We use it not because it is unique, but because it is the simplest.

In the case of a molecule such as BeH₂, we know from experimental evidence that the molecule is linear and therefore the electron density surrounding the central atom is no longer spherical, but must be concentrated along two directions 180° apart, and we need to construct a function Ψ² having these geometrical properties. There are any number of ways of doing this, but it is convenient is to use a particular set of functions ψ (which we call hybrid orbitals) that are constructed by combining the atomic s,p,d, and f functions that are already familiar to us.

You should understand that hybridization is not a physical phenomenon; it is merely a mathematical operation that combines the atomic orbitals we are familiar with in such a way that the new (hybrid) orbitals possess the geometric and other properties that are reasonably consistent with what we observe in a wide range (but certainly not in all) molecules. In other words, hybrid orbitals are abstractions that describe reality fairly well in certain classes of molecules (and fortunately, in much of the very large class of organic substances) and are therefore a useful means of organizing a large body of chemical knowledge… but they are far from infallible.

This approach, which assumes that the orbitals remain more or less localized on one central atom, is the basis of the theory which was developed in the early 1930s, mainly by Linus Pauling.

Figure 8.3 Linus Pauling

Linus Pauling (1901-1994) was the most famous American chemist of the 20th century and the author of the classic book The Nature of the Chemical Bond. His early work pioneered the application of X-ray diffraction to determine the structure of complex molecules; he then went on to apply quantum theory to explain these observations and predict the bonding patterns and energies of new molecules.

(His short and lucid 1928 article updating Lewis’ theory of the shared-electron covalent bond can be seen here.) Pauling, who spent most of his career at Cal Tech, won the Nobel Prize for Chemistry in 1954 and the Peace Prize in 1962.

“In December 1930 Pauling had his famous ‘breakthrough’ where, in a rush of inspiration, he ‘stayed up all night, making, writing out, solving the equations, which were so simple that I could solve them in a few minutes‘. This flurry of calculations would eventually become the first of Pauling’s germinal series of papers on the nature of the chemical bond. ‘I just kept getting more and more euphorious as time went by‘, Pauling would recall. ” [source]

Although the hybrid orbital approach has proven very powerful (especially in organic chemistry), it does have its limitations. For example, it predicts that both H₂O and H₂S will be tetrahedrally coordinated bent molecules with bond angles slightly smaller than the tetrahedral angle of 109.5° owing to greater repulsion by the nonbonding pair. This description fits water (104.5°) quite well, but the bond angle in hydrogen sulfide is only 92°, suggesting that atomic p orbitals (which are 90° apart) provide a better description of the electron distribution about the sulfur atom than do sp³ hybrid orbitals.

The hybrid orbital model is simple to apply and understand, but it is best regarded as one special way of looking at a molecule that can often be misleading. Another viewpoint, called the molecular orbital theory, offers us a complementary perspective that it is important to have if we wish to develop a thorough understanding of chemical bonding in a wider range of molecules.

Constructing hybrid orbitals

Below: “Constructive” and “destructive” combinations of 2p and 2s wave functions (line plots) give rise to the sp hybrid function shown at the right.
The solid figures depict the corresponding probability functions ψ².

 Figure 8.4 Combination of Atomic Orbitals

Hybrid orbitals are constructed by combining the ψ functions for atomic orbitals. Because wave patterns can combine both constructively and destructively, a pair of atomic wave functions such as the s– and p– orbitals shown at the left can combine in two ways, yielding the sp hybrids shown.

 Two central theme of VB theory:

1. Opposing spins of the electron pair: According to the exclusion principle, the space formed by the overlapping orbitals has a maximum capacity of two electrons that must have opposite spins. When the molecule of H₂ forms for instance, electrons of two H atoms occupy the overlapping 1s orbitals and have opposite spins.

Figure 8.5 Overlap of H-atomic orbitals

Ref: Commons.wikimedia.org/

2. Maximum overlap of bonding orbitals: The greater the orbital overlap, the stronger the bond. The extent of overlap depends on the shape and energy of the orbitals.  In the HF bond, for example, the 1s orbital of H overlaps the half-filled 2p orbital of F along the long axis of the orbital. Bond formed in any other direction would be weaker.

In this theory, Molecules are visualized as a group of atoms sharing electron pairs between atomic orbitals. Hybrid orbitals which are combinations of the native atomic orbitals, are required to explain molecular structure.