4.7. MOLECULAR ORBITAL THEORY

Molecular orbital (MO) theory was developed by F. Hund and R.S. Mulliken in 1932. The salient features of this theory are: (i) The electrons in a molecule are present in the various molecular orbitals as the electrons of atoms are present in the various atomic orbitals. (ii) The atomic orbitals of comparable energies and proper symmetry combine to form molecular orbitals.

Molecular Orbital Theory provides insights into how atomic orbitals combine to form molecular orbitals. Unlike the earlier models that focused solely on bonds being a simple overlap of atomic orbitals, this theory recognizes that atomic orbitals can combine in ways that result in more complex interactions. The electrons in a molecule occupy these molecular orbitals, which can encompass contributions from multiple nuclei, leading to a more stable configuration.

Think of molecular orbitals like a shared workspace where multiple people (electrons) can come together to collaborate on projects (bonding). Just as different workspaces allow for different kinds of collaboration, atomic orbitals combine in various ways to form molecular orbitals, creating stronger teams—or bonds.

According to wave mechanics, the atomic orbitals can be expressed by wave functions (ψ’s) which represent the amplitude of the electron waves. These are obtained from the solution of Schrödinger wave equation. To overcome the difficulty of directly obtaining molecular orbitals, an approximate method known as linear combination of atomic orbitals (LCAO) has been adopted.

The Linear Combination of Atomic Orbitals (LCAO) is a critical method used in Molecular Orbital Theory. It allows for the formation of molecular orbitals by expressing atomic orbitals as wave functions. By adding or subtracting these wave functions, bonding and antibonding molecular orbitals are formed. This method highlights the importance of atomic orbital overlap in determining the properties of molecules.

Imagine blending two different colors of paint. When you mix them together (adding the wave functions), you create a new color (molecular orbital). Sometimes, you might have a color that is more vibrant (bonding orbital) and sometimes a color that is dull (antibonding orbital), depending on how you mixed the paints.

The bonding molecular orbital has lower energy and hence greater stability than the corresponding antibonding molecular orbital. The molecular orbitals like atomic orbitals are filled in accordance with the aufbau principle obeying the Pauli’s exclusion principle and the Hund’s rule.

The stability and energy of molecular orbitals are fundamental concepts in molecular orbital theory. Bonding molecular orbitals, formed from the constructive overlap of atomic orbitals, have lower energy levels compared to antibonding orbitals, which form from destructive interference. This difference in energy levels explains why molecules tend to adopt configurations that maximize occupancy of bonding orbitals for stability.

Think of bonding and antibonding orbitals like different levels in a swimming pool. The shallow end (bonding) is where everyone wants to be because it feels safe and comfortable. Conversely, the deep end (antibonding) is less stable and a bit more challenging, just like how filling antibonding orbitals leads to instability in molecules.

Molecular orbitals of diatomic molecules are designated as σ (sigma), π (pi), δ (delta), etc. In this nomenclature, the sigma (σ) molecular orbitals are symmetrical around the bond-axis while pi (π) molecular orbitals are not symmetrical.

In molecular orbital theory, different types of molecular orbitals are described based on their geometric orientation. Sigma orbitals (σ) arise from end-to-end overlapping of atomic orbitals and are positioned symmetrically around the bond axis. Pi orbitals (π) arise from side-to-side overlaps and have different characteristics. This classification helps in understanding the bonding and shapes of various molecules.

Consider the way bicycles are built. The main frame (σ bond) provides the crucial support and symmetry needed for stability in motion, while the extra wheels (π bonds) add character and support but are not as crucial for the core structure. This distinction helps in visualizing how different bonds can shape the stability and properties of a molecule.

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