🥼Organic Chemistry Unit 1 Review

Molecular orbital (MO) theory explains covalent bonding by describing how atomic orbitals combine to form new orbitals that belong to the entire molecule. Where valence bond theory focuses on localized bonds between two atoms, MO theory gives you a fuller picture of why some molecules are stable, why others don't form at all, and why certain bonds have the reactivity they do.

Molecular orbital theory for covalent bonds

The core idea: when two atomic orbitals of similar energy and symmetry come close together, they combine to form molecular orbitals that span both atoms. Electrons shared in these molecular orbitals are what hold the molecule together.

Two types of molecular orbitals result from this combination:

Bonding molecular orbitals form through constructive interference of atomic orbitals. Electron density concentrates between the two nuclei, pulling them together and stabilizing the molecule. These orbitals sit lower in energy than the original atomic orbitals.
Antibonding molecular orbitals form through destructive interference. Electron density is depleted between the nuclei (there's a node), which destabilizes the molecule. These orbitals sit higher in energy than the original atomic orbitals.

A few key rules govern how electrons fill molecular orbitals:

The number of molecular orbitals formed always equals the number of atomic orbitals that combined. Two atomic orbitals in, two molecular orbitals out.
Electrons fill molecular orbitals from lowest to highest energy (the Aufbau principle).
Each molecular orbital holds a maximum of two electrons with opposite spins (the Pauli exclusion principle).

The mathematical framework behind this is called linear combination of atomic orbitals (LCAO). You won't need to do the math in most organic chemistry courses, but knowing the name helps when you encounter MO diagrams.

Bonding vs. antibonding molecular orbitals

These two types of orbitals differ in energy, shape, and their effect on molecular stability:

Energy levels

Bonding orbitals are lower in energy than the parent atomic orbitals.
Antibonding orbitals are higher in energy than the parent atomic orbitals.

Shape and electron density

Bonding orbitals have increased electron density between the nuclei, which is exactly where it needs to be to hold the atoms together.
Antibonding orbitals have a node between the nuclei, meaning electron density is pushed away from the internuclear region.

Effect on stability

Electrons in bonding orbitals attract the nuclei toward each other, stabilizing the molecule.
Electrons in antibonding orbitals push the nuclei apart, destabilizing the molecule.

Notation

$\sigma$ and $\sigma^*$ refer to bonding and antibonding orbitals formed from head-on overlap (typically s orbitals or p orbitals aligned along the bond axis).
$\pi$ and $\pi^*$ refer to bonding and antibonding orbitals formed from sideways (lateral) overlap of p orbitals.

The asterisk ( $*$ ) always signals an antibonding orbital.

Bond order tells you the net bonding in a molecule. Calculate it as:

$\text{Bond order} = \frac{(\text{electrons in bonding MOs}) - (\text{electrons in antibonding MOs})}{2}$

A bond order of zero means no stable bond forms. Higher bond orders mean stronger, shorter bonds. For example, $H_2$ has two electrons in its $\sigma$ bonding orbital and zero in $\sigma^*$ , giving a bond order of 1.

Molecular orbital theory for covalent bonds, Molecular Orbital Theory | General Chemistry

Pi molecular orbitals in ethylene

Ethylene ( $C_2H_4$ ) is a planar molecule with a carbon-carbon double bond. That double bond consists of one $\sigma$ bond and one $\pi$ bond. The $\pi$ bond is where MO theory becomes especially useful.

Here's how the $\pi$ molecular orbitals form:

Each carbon in ethylene is $sp^2$ hybridized, which leaves one unhybridized 2p orbital on each carbon. These 2p orbitals point perpendicular to the molecular plane.
The two 2p orbitals overlap laterally (sideways), combining to produce two $\pi$ molecular orbitals: one bonding ( $\pi$ ) and one antibonding ( $\pi^*$ ).
The two electrons (one from each carbon's 2p orbital) both go into the lower-energy bonding $\pi$ orbital.

Energy: The bonding $\pi$ orbital is lower in energy than the isolated 2p orbitals; the antibonding $\pi^*$ orbital is higher.

Shape: The bonding $\pi$ orbital has electron density concentrated above and below the molecular plane, with constructive overlap between the carbons. The antibonding $\pi^*$ orbital has a node along the internuclear axis and destructive overlap, meaning electron density is pushed away from the region between the two carbons.

Because both electrons occupy the bonding $\pi$ orbital, the $\pi$ bond strengthens the connection between the carbons beyond what the $\sigma$ bond alone provides. This is also why the $\pi$ bond is the reactive site in ethylene: the electron density sitting above and below the plane is more exposed and accessible to electrophiles than the $\sigma$ electrons tucked between the nuclei.

Atomic and Molecular Properties

The wave function describes the quantum state of an electron. Squaring the wave function gives you the probability of finding the electron at a given point in space. Molecular orbitals are wave functions that extend over the whole molecule.
Hybridization is the mixing of atomic orbitals on a single atom (e.g., one s and two p orbitals forming three $sp^2$ hybrids). This is a valence bond concept, but it complements MO theory by explaining the geometry around individual atoms.
Electron configuration in MO theory works the same way as in atoms: fill orbitals from lowest to highest energy, two electrons per orbital, following Hund's rule for degenerate (equal-energy) orbitals.

🥼Organic Chemistry Unit 1 Review