Valence Bond Theory

hybridized orbitals of valence bond theory

Core Concepts

In this article, you will learn about Valence Bond Theory, an important component of quantum mechanics, as well as its application in understanding hybridization and bond order.

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Fundamentals of Valence Bond Theory

Valence bond theory is 1 of 2 fundamental bonding theories, along with molecular orbital theory, that help explain the formation of bonds between atoms. Valence bond theory is particularly useful in explaining the nature of covalent bonds between atoms.

 The essence behind valence bond theory lies in denoting covalent bonds as the overlap of atomic orbitals. This differs from Lewis structure theory in that bonds aren’t treated as shared particles, but rather as electron clouds.

We will mostly focus on the overlapping of hybridized S, P, and D orbitals.

Orbital Overlap in Valence Bond Theory

Essentially, a chemical bond involves the nuclei of two atoms attracted to one another’s valence electrons. As two nuclei approach one another, this attractive force increases. However, the two atoms also increasingly repel each other at shorter distances, due to the like charges of the nuclei and electrons. Ultimately, there exists some distance where the atoms are most attracted to each other before the repulsive forces dominate the interaction. When two atoms reach this perfect attractive distance, they are considered chemically bonded.

internuclear distance of bonding atoms

Under valence bond theory, interactions like this only occur under half-filled chemical orbitals, with each atom providing one electron. When a chemical bond forms, the paired bond-forming electrons fill the orbital of both atoms, which “share” the electron pair. Spatially, this involves the bond forming valence electrons occupying the overlap between the orbitals of the two atoms.

Importantly, though these electrons are shared, they’re still considered to occupy the same atomic orbitals as before. For instance, if two hydrogen atoms form a sigma bond, the two electrons involved in the bond still occupy the s orbitals of the hydrogens. This contrasts with Molecular Bond Theory, which involves the electrons occupying a newly-formed molecular orbital.

overlapping orbitals of valence bond theory

Bond order in Valence Bond Theory

Additionally, this anti-bond orbital can determine whether a bond will form or whether it will break. A tool known as the bond order formula allows us to predict how many bonds will form:

Bond Order = [Bonding orbitals’ sum of electrons – anti-bonding orbitals’ sum of electrons]

As an example, neon can’t bond with itself. Because its molecular orbitals are filled up, the intermediary bond between 2 neon atoms would have 4 electrons. And because the sigma bond orbital will be filled up by 2 electrons, the remaining 2 electrons will go into the sigma anti-bonding orbital, thus preventing the bond from forming.

Hybridization in Valence Bond Theory

How does valence bond theory explain the existence of molecules such as sulfur hexafluoride? The central atom (sulfur) has to bond 6 times, yet only has 2 lone valence electrons). To discuss, we must discuss the topic of hybridization.

Hybridization is the process of combining 2 or more atomic orbitals to form a completely new orbital to hold additional electron groups (lone pairs of electrons and bonds). Additionally, the hybrid orbital serves as a useful indicator of relative energy levels as hybrid orbitals with more s character (less p and d hybridization) have much lower energy levels, meaning the bonding orbital is a better electron acceptor.

Why Hybridization Is Energetically Favorable

It is important to note that orbital count is conserved by introducing electrons from a full orbital to an orbital without any electrons. The newly created orbital is allowed to form because it allows for additional electron groups at a collectively lower energy level.

molecular orbital hybridization and their relative energies

In general, the number of bonds and lone pairs required will denote the number of orbitals which will be hybridized. Thus, one of 6 hybrid orbitals will form in the event a molecule will need to hold more electron groups; the molecule will create either sp, sp2, sp3, sp3d, or sp3d2. It’s also important to note that filled p orbitals are what form pi bonds (double and triple bonds). If any double bonds are present, it’s a clear indicator that the hybridization is sp2 or of greater s character.

Referring back to sulfur hexafluoride, the central sulfur will hybridize its orbitals to create an sp3d2 hybrid orbital. This satisfies the number of orbitals needed to house the 6 bonds with each respective fluorine. Any filled orbitals that aren’t used for hybridizing will continue to exist at the higher energy level.

variations of hybrid orbitals, excluding d orbital hybridization

In addition, the bonds created by the hybrid atomic orbitals should align with their shapes predicted by implementing the VSEPR model. This creates a problem within valence bond theory; the shape of the 3-p orbitals and 5-d orbitals won’t align with the VSEPR model. If we are to take into account the nature of the 3-p orbitals, each lying perpendicular to one of the x-y, x-z, or y-z planes, it would predict a 90-degree angle between all additional bonds after the first bond. This is impossible in the VSEPR model. Thus, when hybridization occurs, the shapes of the newly formed orbitals are different from the originals.

shape of singular hybrid orbitals along the x axis of the x-y-z space

Hybridization and resonance in Valence Bond Theory

The hybrid orbitals must remain constant when handling molecules with resonance structures. Thus, we first consider all possible resonance structures of a molecule before we determine its hybridization. If a specific atom within a molecule forms a double bond in 1 resonance structure but holds a lone pair in another resonance structure, its hybridization will be the one with a higher s character. Meaning that even if the atom looks like it’s sp3 in 1 resonance structure, and sp2 in another resonance structure, the molecule must be sp2 across both resonance structures

Sigma and Pi Bonding in Valence Bond Theory

While hybridization can explain how atoms form bonds beyond their number of lone valence electrons, it does explain how double and triple bonds form.

First, we must explain the 2 types of bonds: Sigma and Pi. Sigma bonds form when the highest available orbital of each atom overlaps one another. The constructive interaction will thus lead to the formation of a sigma bond between the two atoms with a higher electron density sharing between the two nuclei.

depiction of overlap needed to form sigma and pi bonding orbitals, important example for valence bond theory

Any additional bonds between two atoms are explained with the formation of pi bonds. This occurs when the un-hybridized (filled) p orbitals of each respective atom overlap to form a higher electron density between the two atoms outside of the established sigma bond. Once again, it is also important to note that this bonding will also create an anti-bonding orbital. Once this orbital fills, the bond between the 2 reactions breaks. Thus to conclude, single bonds between atoms have a sigma bond, while any additional bonds between the two atoms are pi bonds; double bonds have 1 sigma and 1 pi bond and triple bonds have 1 sigma and 2 pi bonds. Referring to a molecule like diatomic nitrogen, the formation of N2 would need 1 sigma and 2 pi bonds between the two nitrogen atoms to satisfy the triple bond.

Quadruple bonds?

The overlap of p orbitals is what form pi bonds. Since there are 3 p orbitals of every atom, this would naturally beg the question: Why can’t a molecule form 1 sigma bond and 3 pi bonds to form a quadruple bond?

Pi bonds form by overlapping p orbitals which are orthogonal (perpendicular) to the initial sigma bond. However, only 2 of the 3 p orbitals can be perpendicular to the sigma bond. The third of the p orbitals is parallel to a given sigma bond. Thus the atom would require invoking the d orbital to form quadruple bonds.

Review Questions:

Try the following review questions out on your own. When you complete the questions, scroll to find the answers further down on the page.

1:How many sigma and pi bonds are in Ethyne?

depiction of the molecule acetylene, important example for valence bond theory

2: How many sigma and pi bonds are in H20?

lewis structure of water, important example for valence bond theory

3: How many sigma and pi bonds are in fructose?

skeletal structure of fructose, important example for valence bond theory

4: What hybrid orbital does the carbon atom on methane form?

depiction of methane, important example for valence bond theory

5: What hybrid orbital does the nitrogen atom on ammonia molecule form?

depiction of ammonia, important example for valence bond theory


1: Ethyne forms 3 sigma and 2 pi bonds

2: H2O forms 2 sigma bonds.

3: fructose forms 24 sigma and 2 pi bonds.

4: the carbon in methane forms an sp3 hybrid orbital because it contains 4 electron groups(4 bonds, 0 lone pairs) and has no resonance structure.

5: the nitrogen in ammonia forms an sp3 hybrid orbital because it contains 4 electron groups(3 bonds, 1 lone pair) and has no resonance structure.