Question

How does each of the three major bonding theories (the Lewis model, valence bond theory, and MO theory) define a single chemical bond? A double bond? A triple bond? How are these definitions similar? How are they different?

Short answer

All three bonding theories define single, double, and triple bonds as the sharing of one, two, and three pairs of electrons, respectively. The Lewis model depicts them as shared electron dots between atoms, while valence bond and MO theory involve overlapping orbitals, but MO theory uniquely considers the global distribution of electrons in molecular orbitals.

Step-by-step solution

Defining a Single Chemical Bond

The Lewis model represents a single chemical bond as a pair of electrons shared between two atoms. Valence bond theory describes a single bond as the overlap of two atomic orbitals, each containing one electron, leading to a shared electron density between the atoms. Molecular orbital (MO) theory considers a single bond as a pair of electrons in a molecular orbital that is spread over several atoms but with a concentration between two specific atoms.

Defining a Double Bond

In the Lewis model, a double bond is represented by two pairs of shared electrons between two atoms. Valence bond theory explains a double bond as the overlap of two atomic orbitals to form a sigma bond plus the side-by-side overlap of two parallel p orbitals to create a pi bond. MO theory describes a double bond as one bonding molecular orbital formed by adding the wave functions of the atomic orbitals and a second bonding molecular orbital formed by the side-to-side overlap of p orbitals, resulting in two pairs of electrons in bonding molecular orbitals.

Defining a Triple Bond

The Lewis model depicts a triple bond as three pairs of shared electrons between two atoms. According to valence bond theory, a triple bond consists of one sigma bond and two pi bonds, resulting from the overlap of one sp hybrid orbital with another sp hybrid orbital, and the side-by-side overlaps of two pairs of p orbitals. MO theory defines a triple bond as one sigma bond molecular orbital and two pi bond molecular orbitals, involving three pairs of electrons in bonding molecular orbitals.

Similarities and Differences

All three theories agree that chemical bonds involve the sharing of electrons between atoms, and the number of bonds between atoms corresponds to the number of shared electron pairs. The primary difference is that while the Lewis model focuses on the local aspect of electron sharing, valence bond and MO theories incorporate the concept of orbitals. Additionally, MO theory is unique in its treatment of molecular orbitals, which can extend over multiple atoms, providing a more global view of electron distribution.

Key concepts

Lewis Model of Chemical Bonds

Understanding the Lewis model of chemical bonds is key to grasping the basics of chemical structures. It illustrates chemical bonds through Lewis dot structures, where dots represent valence electrons. In a single bond, two atoms share a pair of electrons, represented by two dots (or a line) between the symbols for the two atoms.
For example, in a hydrogen molecule (H₂), the Lewis structure is H:H or H—H, showing a single shared pair of electrons. In the context of double and triple bonds, the Lewis model simply doubles or triples the shared electron pairs. This visualization helps express the connectivity of atoms in molecules but doesn't delve into the nature of the electron sharing or the spatial orientation of the bonds.

Valence Bond Theory

The valence bond theory takes the concept of Lewis structures further by considering the quantum nature of atoms and their electrons. This theory describes a single bond as the overlap of two half-filled atomic orbitals from two different atoms, leading to a shared electron density between them known as a sigma bond.

Sigma and Pi Bonds

In a double bond, there's an additional component—pi bonds. A double bond consists of one sigma bond (direct orbital overlap) and one pi bond (side-by-side overlap of p orbitals). The triple bond adds yet another pi bond, resulting in one sigma and two pi bonds. This model provides insights into molecular shapes and bond angles but is limited by its localized perspective, assuming electrons are shared only between two atoms.

Molecular Orbital Theory

Molecular orbital (MO) theory is a sophisticated approach that depicts a single bond by a pair of electrons occupying a molecular orbital. This theory doesn't just consider the simple electron pair sharing but uses linear combinations of atomic orbitals to form molecular orbitals that can extend over the entire molecule.
Double bonds are described by MO theory as having one sigma bonding molecular orbital and one pi bonding molecular orbital. Meanwhile, triple bonds consist of one sigma and two pi bonding molecular orbitals. Through this theory, we gain a global perspective on electron distribution, understanding that electrons in a molecule are not confined to the space between two atoms but can be delocalized over the entire molecule.

Sigma and Pi Bonds

Both sigma and pi bonds are fundamental to understanding molecular geometry and stability. Sigma bonds are characterized by head-to-head orbital overlap, creating a single shared electron density along the axis connecting two nuclei. They are the strongest type of covalent bonds and allow for free rotation of the bonded atoms.
On the other hand, pi bonds result from the side-to-side overlap of p orbitals and occur in addition to sigma bonds in double and triple bonds. They are less strong than sigma bonds and restrict the rotation of bonded atoms, leading to fixed geometries like the planarity in alkenes. Together, sigma and pi bonds shape the structural framework of molecules and are crucial in chemical reactivity and physical properties of compounds.