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Overview of Molecular Orbital Theory

Molecular orbital theory describes the distribution of electrons in molecules in the same way as the distribution of electrons in atoms is described using atomic orbitals. Quantum mechanics describes the behavior of an electron in a molecule by a wave function, Ψ, analogous to the behavior in an atom. Just like electrons around isolated atoms, electrons around atoms in molecules are limited to discrete (quantized) energies. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital (Ψ2). Like an atomic orbital, a molecular orbital is full when it contains two electrons with opposite spin.

Linear Combination of Atomic Orbitals

The mathematical process of combining atomic orbitals to generate molecular orbitals is called the linear combination of atomic orbitals (LCAO). Quantum mechanics describes molecular orbitals as combinations of atomic orbital wave functions. Combining waves can lead to constructive or destructive interference. In orbitals, the waves can combine with in-phase waves producing regions with a higher probability of electron density and out-of-phase waves producing nodes, or regions of no electron density.

Bonding and Antibonding Molecular Orbitals

There are two types of molecular orbitals that can form from the overlap of two atomic s orbitals on adjacent atoms. The in-phase combination produces a lower energy σs molecular orbital (read as "sigma-s") in which most of the electron density is directly between the nuclei. The out-of-phase addition (or subtracting the wave functions) produces a higher energy σs* molecular orbital (read as "sigma-s-star"), in which there is a node between the nuclei. The asterisk signifies that the orbital is an antibonding orbital. Electrons in a σs orbital are attracted by both nuclei at the same time and are more stable (of lower energy) than they would be in the isolated atoms. Adding electrons to these orbitals creates a force that holds the two nuclei together, so these orbitals are called bonding orbitals. Electrons in the σs* orbitals are located well away from the region between the two nuclei. The attractive force between the nuclei and these electrons pulls the two nuclei apart. Hence, these orbitals are called antibonding orbitals. Electrons fill the lower-energy bonding orbital before the higher-energy antibonding orbital. 

In p orbitals, the wave function gives rise to two lobes with opposite phases. When orbital lobes of the same phase overlap, constructive wave interference increases the electron density. When regions of opposite phase overlap, the destructive wave interference decreases electron density and creates nodes. When p orbitals overlap end to end, they create σ and σ* orbitals. The side-by-side overlap of two p orbitals gives rise to a pi (π) bonding molecular orbital and a π* antibonding molecular orbital. Electrons in the π orbital interact with both nuclei and help hold the two atoms together, making it a bonding orbital. For the out-of-phase combination, there are two nodal planes created, one along the internuclear axis and a perpendicular one between the nuclei. 

This text has been adapted from Openstax, Chemistry 2e, Section 8.4: Molecular Orbital Theory.

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