Molecular orbital diagrams and electron configurations are key to understanding how atoms bond in molecules. They show us how atomic orbitals combine to form molecular orbitals, which determine a molecule's properties and behavior.

By applying quantum mechanical principles, we can predict molecular stability, bond strength, and magnetic properties. This knowledge helps us grasp how molecules interact and react, connecting the microscopic world of atoms to the macroscopic world we observe.

Molecular Orbital Theory Principles

Constructing Molecular Orbital Diagrams

• Molecular orbital diagrams visually represent the energy levels and electron configurations of molecules
• Molecular orbitals are formed by the constructive and destructive interference of atomic orbitals
• Bonding orbitals have lower energy than the constituent atomic orbitals and are populated first
• Antibonding orbitals have higher energy than the constituent atomic orbitals and are populated last
• Nonbonding orbitals have energy levels similar to the constituent atomic orbitals and do not significantly contribute to bonding

Applying Quantum Mechanical Principles

• The Aufbau principle states that electrons fill molecular orbitals in order of increasing energy
• Hund's rule states that electrons occupy degenerate orbitals singly before pairing up, maximizing the number of unpaired electrons
• The Pauli exclusion principle states that no two electrons in a molecule can have the same set of four quantum numbers
• Energy level ordering determines the sequence in which molecular orbitals are filled $(\sigma < \pi < \sigma^* < \pi^*)$
• Molecular orbital configurations are written similarly to atomic orbital configurations, using the molecular orbital labels $(\sigma_{1s}^2 \sigma_{1s}^{*2} \sigma_{2s}^2 \sigma_{2s}^{*2} \pi_{2p}^4 \sigma_{2p}^2)$

Molecular Properties

Bond Order and Stability

• Bond order is the number of bonding electron pairs minus the number of antibonding electron pairs, divided by 2
• Higher bond orders indicate stronger bonds and greater stability $(\ce{N2}: \text{bond order} = \frac{1}{2}(10 - 4) = 3)$
• Molecules with bond order 0 are unstable and dissociate into separate atoms $(\ce{He2}: \text{bond order} = \frac{1}{2}(2 - 2) = 0)$
• Bond length decreases as bond order increases due to greater attractive forces between the nuclei

Magnetic Properties

• Paramagnetic molecules have unpaired electrons and are attracted to magnetic fields $(\ce{O2}: \text{unpaired electrons} = 2)$
• Diamagnetic molecules have no unpaired electrons and are weakly repelled by magnetic fields $(\ce{N2}: \text{unpaired electrons} = 0)$
• Degenerate orbitals are orbitals with the same energy level, such as the $\pi_{2p}$ orbitals in homonuclear diatomic molecules
• Molecules with degenerate orbitals containing unpaired electrons are paramagnetic $(\ce{O2}: \pi_{2p}^{2})$

Diatomic Molecules

Homonuclear Diatomic Molecules

• Homonuclear diatomic molecules consist of two atoms of the same element $(\ce{H2}, \ce{N2}, \ce{O2})$
• Molecular orbitals are formed by the combination of atomic orbitals with the same symmetry and energy
• Bonding orbitals are labeled $\sigma$ (s orbital overlap) and $\pi$ (p orbital overlap), while antibonding orbitals are labeled $\sigma^$ and $\pi^$
• The energy level ordering for homonuclear diatomic molecules is $\sigma_{1s} < \sigma_{1s}^* < \sigma_{2s} < \sigma_{2s}^* < \pi_{2p} < \sigma_{2p} < \pi_{2p}^* < \sigma_{2p}^*$

Heteronuclear Diatomic Molecules

• Heteronuclear diatomic molecules consist of two different atoms $(\ce{CO}, \ce{NO}, \ce{HCl})$
• Molecular orbitals are formed by the combination of atomic orbitals with similar energies and symmetries
• The energy level ordering for heteronuclear diatomic molecules depends on the relative energies of the atomic orbitals
• Heteronuclear diatomic molecules often have a non-zero dipole moment due to the unequal distribution of electron density $(\ce{CO}: \text{dipole moment} = 0.112 \text{ D})$