Molecular orbital theory

Molecular orbital theory (MOT) is a fundamental theory in chemistry that explains how atoms combine together to form molecules. It provides a more sophisticated understanding of chemical bonding than other models such as valence bond theory (VBT). In this comprehensive explanation, we will take a deep look at the basic concepts, the formation of a molecular orbital, and the application of molecular orbital theory to explain bonding in molecules.

Basic concepts

Molecular orbital theory describes the behavior of electrons in molecules. Unlike VBT, which assumes that bonds are formed by the overlap of atomic orbitals of different atoms, MOT proposes molecular orbitals that belong to the entire molecule.

Formation of molecular orbitals

Molecular orbitals are formed when atomic orbitals in a molecule combine. Let's consider the simplest diatomic molecule: H 2. Each hydrogen atom contributes a 1s atomic orbital, and these orbitals can combine in two different ways:

• Constructive combination: When atomic orbitals combine constructively, they form a molecular orbital called a bonding molecular orbital. It is characterized by an increase in electron density between the two nuclei and is lower in energy than the original atomic orbitals.
• Destructive combination: When atomic orbitals combine destructively, they form an antibonding molecular orbital. It is characterized by a node (a region of zero electron density) between the nuclei and is high in energy.

Visual example of molecular orbital combination

        H --(1s)-- + H --(1s)-- | | VV Bonding Antibonding Orbital Orbital
        H --(1s)-- + H --(1s)-- | | VV Bonding Antibonding Orbital Orbital
    

Molecular orbital diagram

The arrangement of bonding and restricting molecular orbitals can be shown in a molecular orbital diagram. Here is an example for molecular hydrogen:

        Energy ↑ | σ* 1s (Antibonding) |----------------------------- | σ 1s (Bonding) |----------------------------- |
        Energy ↑ | σ* 1s (Antibonding) |----------------------------- | σ 1s (Bonding) |----------------------------- |
    

In this diagram, σ 1s bonding molecular orbital and σ* 1s antibonding molecular orbital. The electrons will first fill the lower energy bonding orbital, followed by the antibonding orbital if there are more electrons.

Bond order

Molecular orbital theory introduces the concept of bond order to predict the stability of a molecule. The bond order is calculated as follows:

        Bond Order = (Number of electrons in bonding orbitals - Number of electrons in antibonding orbitals) / 2
        Bond Order = (Number of electrons in bonding orbitals - Number of electrons in antibonding orbitals) / 2
    

Higher bond order indicates more stable bonds. For example, in _{H 2}:

        Bonding Electrons = 2 Antibonding Electrons = 0 Bond Order = (2 - 0) / 2 = 1
        Bonding Electrons = 2 Antibonding Electrons = 0 Bond Order = (2 - 0) / 2 = 1
    

Applications of molecular orbital theory

MOT can be applied to more complex molecules such as O 2 and N 2 Let's explore these examples:

Oxygen molecule _{O 2}

The oxygen molecule has 16 valence electrons. Its molecular orbital diagram looks like this:

        Energy ↑ | σ* 2p |------------------------- | π* 2p π* 2p |------------------------- | π 2p π 2p |------------------------- | σ 2p |------------------------- | σ* 2s |------------------------- | σ 2s
        Energy ↑ | σ* 2p |------------------------- | π* 2p π* 2p |------------------------- | π 2p π 2p |------------------------- | σ 2p |------------------------- | σ* 2s |------------------------- | σ 2s
    

        Bonding Electrons: 10 Antibonding Electrons: 6 Bond Order: (10 - 6) / 2 = 2
        Bonding Electrons: 10 Antibonding Electrons: 6 Bond Order: (10 - 6) / 2 = 2
    

The bond order 2 explains why _{O 2} has a double bond.

Nitrogen molecule N 2

The nitrogen molecule has 14 valence electrons. Its molecular orbital diagram looks like this:

        Energy ↑ | σ* 2p |------------------------- | π* 2p π* 2p |------------------------- | π 2p π 2p |------------------------- | σ 2p |------------------------- | σ* 2s |------------------------- | σ 2s
        Energy ↑ | σ* 2p |------------------------- | π* 2p π* 2p |------------------------- | π 2p π 2p |------------------------- | σ 2p |------------------------- | σ* 2s |------------------------- | σ 2s
    

        Bonding Electrons: 10 Antibonding Electrons: 4 Bond Order: (10 - 4) / 2 = 3
        Bonding Electrons: 10 Antibonding Electrons: 4 Bond Order: (10 - 4) / 2 = 3
    

The bond order 3 for N 2 correlates with its observed triple bond.

Advantages of molecular orbital theory

• Mott gives a more detailed picture of the electronic structure of molecules.
• It is responsible for the magnetic properties of molecules (e.g., paramagnetism in _{O 2}).
• Provides a method for calculating molecular properties such as bond order and bond length.

Limitations of molecular orbital theory

• For larger molecules this can be complex and mathematically intensive.
• Empirical data are still needed for some predictions and confirmations.

Conclusion

Molecular orbital theory is an essential concept in chemistry that provides a more complete understanding of chemical bonding and molecular structure. By considering the molecule as a whole, it allows chemists to predict and explain molecular behavior that is essential to advances in chemical research and industry.

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