Valence Bond Theory — Overview & Importance

Molecule Modeling

When describing molecules there are a few types of models used:

• Electron-dot structures - this type of model shows a prediction of the location of electrons in a molecule.

• VSEPR model - this model shows the ideal shape of a molecule based on the repulsion between bonding and lone electron pairs.

The problem with both of these models is that they are simplified models. They do not take into account the details associated with the electronics of covalent bonds. A model which includes quantum mechanics to describe bonding in molecules is called the valence bond theory (VBT).

How Does VBT Work?

VBT allows for the electrons in covalent bonds to be visually depicted. A covalent bond is made up of two electrons shared between two atoms. These electrons exist in atomic orbitals. For the orbitals the electrons to be shared, the orbitals must overlap.

VBT And Bond Strength

A key feature of VBT models is that the more orbital overlap that exists, the stronger the bond. When considering orbital overlap, the direction of the orbitals matters when examining orbitals other than s. The better the orbitals line up, the more overlap, the stronger the bond.

Notice in the image below that the two p orbitals add to each other head-on. This creates optimum overlap and a strong bond.

We understand the basics of quantum mechanics. Electrons behave as both waves and particles. Because of their wave nature, we can't know their exact location and momentum. That's the uncertainty principle. Instead, we use probability. We're 90 percent confident we'll find our electron within a specific region. We call that region an atomic orbital.

Erwin Schrodinger was the first person to solve the equations for a hydrogen atom. Electron-electron repulsion creates too many complications. So, he based everything on hydrogen. We describe every orbital with three quantum numbers. Let's start with the principal number. It conveys the energy level and the atomic radius. Remember, electrostatic interactions mean that [distance]( and energy are connected. The second depicts the shape of the orbitals ( s, p, d, and f). The third expresses the orbital's spacial orientation. Remember, there is also a fourth. But it just catalogs the electron spin. So, the electrons obey the Pauli exclusion principle.

What did Schrodinger's work accomplish? We finally had a working model of the atom! Unfortunately, we still had a problem. We couldn't explain chemical bonding. Thankfully, Walter Heitler determined how to overlap two hydrogen wavefunctions. Suddenly, we had a quantum mechanical model for diatomic hydrogen. We could explain bonding!

In modern computational chemistry, there are two prototypes of bonding. The first model derives from Heitler's work. We call it valence bond theory. That's what we'll study in this explanation. As a side note, the other model is the molecular orbital theory. We'll look at it in a later lesson.

What is Valence Bond Theory?

In valence bond theory, two orbitals overlap to form a bond. But we only care about half-filled valence shells. Why? They are the only ones that can bond. In half-filled orbitals, the electrons can pair. So, they can share electrons by forming a covalent bond. How do we know which orbitals overlap? The easiest way is to write out the electron configuration.

What about the quantum mechanical model? In quantum mechanics, bonding results from constructive interference between the two orbitals. So, we will most likely find our electrons between the bonding atoms. Walter Heitler's work combined the Shrodinger equation for two hydrogen atoms. So, he modeled the interference of orbitals. What was the result? The attraction between the nuclei and the electrons outweighed any repulsion. So, forming a covalent bond lowered the energy. The molecule was more stable.

Valence Bond Theory Complications

Sometimes, the overlapping orbitals are equivalent. For example, in diatomic hydrogen, two s-orbitals come together. Another example is diatomic fluorine. Two $p_{z}$ orbitals overlap. Valence bond theory explains why fluorine's bond is more substantial than hydrogen's. The p-orbitals overlap more than the s-orbitals. So, diatomic hydrogen and fluorine both have a single bond. But, diatomic fluorine has a significantly larger bond energy.

Unfortunately, valence bond theory has some complications. Let's start with the most basic intricacy. There are two types of bonds: sigma and pi bonds. A sigma bond occurs when two orbitals have a direct overlap. A pi bond arises from the indirect overlap of two p-orbitals. Sigma bonds are more robust than pi bonds. But, all molecules have a sigma bond. Double and triple bonds always get formed by pi-bonds. It's the extra bonding that creates stronger bonds.

The more complex difficulty arises when different orbitals overlap. The quintessential example is carbon. Its valence shell has two 2s-orbital and two 2p-orbital electrons. To illustrate the problem, let's consider methane ($CH_{4}$). In methane, carbon is the central atom. It forms four single bonds to the four hydrogen atoms. What's its VSEPR geometry? Tetrahedral. So, all the bond angles and lengths are identical. But we know p-orbitals have more energy than s-orbitals. So, how can the p-orbital and s-orbital bonds be equal? Carbon must have formed hybrid orbitals. A hybrid orbital is a mixture of the s and p orbitals. So, carbon used its 2s-orbital and three 2p-orbitals to create four $sp^{3}$-orbitals. What happens to its valence electrons? Each one half-fills an $sp^{3}$-orbital. The orbitals get filled when carbon bonds with the hydrogens.

The other difficulty is resonance. In valence bond theory, the orbital overlap stays localized. So, the electrons get stuck between the bonding atoms. Why is that a problem? Because some molecules have delocalized electrons. To account for delocalization, we have to consider multiple structures. So, we are limited to molecules with only a few possible configurations.

Advantages of Valence Bond Theory

Valence bond theory has two distinct advantages. One, it provides a more intuitive illustration of bonding. When two atoms bond, we would expect the electrons to become localized. The localized nature of the bonds provides a better understanding of chemical reactions. It's easier to see how electrons move and bonds break. In molecular orbital theory, the electrons become entirely delocalized. That has some advantages. But it's hard to comprehend.

Modern Valence Bond Theory

So far, we've described the historical development of the valence bond theory. Today, it falls under the purview of computational chemists. As chemists began to study more complex molecules, the calculation became impossible. Today, we use advanced computer programs to reach the wavefunctions of interacting particles. Chemists developed these methodologies in the 1950s with the evolution of computers. Modern software has increased our ability to do more advanced calculations.

(Video) Valence Bond Theory

By chemistNATE

In this video, you will learn that valence bond theory states that atomic orbitals containing unpaired electrons overlap to form covalent bonds. The video visualizes the energy diagram associated with bond length to explain the further application of valence bond theory.

This video also includes examples demonstrating the overlap between unpaired electrons forming a covalent bond. And how hybridization plays a vital role in valence bond theory.

Valence Bond Theory: Valence Bond Theory to Explain Bond Types

You can use valence bond theory to explain single bond, double bond, and triple bond. However, hybridization plays a crucial role in creating unpaired electron orbitals in the valence bond theory.