Quantum Chemistry: Core Concepts

• Quantum chemistry applies quantum mechanics to chemical systems.

Core Concepts

• It studies the electronic structure and properties of molecules.
• It uses quantum mechanics to describe the behavior of electrons in molecules.
• The Schrödinger equation is central, describing the energy and behavior of quantum systems.
• Approximations are necessary to solve the Schrödinger equation for molecules.
• Born-Oppenheimer approximation separates nuclear and electronic motion.
• Hartree-Fock method approximates electron-electron interactions.
• Electron correlation methods account for the correlation of electron motion.
• Density functional theory (DFT) uses electron density instead of wavefunction.

Molecular Orbitals

• Molecular orbitals (MOs) are formed by combining atomic orbitals (AOs).
• Linear combination of atomic orbitals (LCAO) is a common method.
• MOs can be bonding, antibonding, or nonbonding.
• Bonding MOs are lower in energy and increase stability.
• Antibonding MOs are higher in energy and decrease stability.
• Nonbonding MOs have little effect on stability.
• Sigma (σ) orbitals: electron density along the internuclear axis.
• Pi (π) orbitals: electron density above and below the internuclear axis.
• MO diagrams show the relative energies of MOs.
• Aufbau principle fills MOs in order of increasing energy.
• Hund's rule maximizes unpaired electrons in degenerate MOs.

LCAO Approximation

• Molecular orbitals are expressed as linear combinations of atomic orbitals.
• Ψ = c₁φ₁ + c₂φ₂ +... + cnφn, where Ψ is the molecular orbital, φ are atomic orbitals, and c are coefficients.
• Coefficients determine the contribution of each AO to the MO.
• Variational principle: The best coefficients minimize the energy.
• The number of MOs formed equals the number of AOs combined.

Bonding and Antibonding Orbitals

• Bonding orbitals result from constructive interference of AOs.
• Electron density is concentrated between the nuclei.
• Lower energy than the original AOs, stabilizing the molecule.
• Antibonding orbitals result from destructive interference of AOs.
• Electron density is reduced between the nuclei.
• Higher energy than the original AOs, destabilizing the molecule.
• Nodes exist between the nuclei in antibonding orbitals.

Sigma (σ) Orbitals

• Formed by head-on overlap of atomic orbitals.
• Electron density is concentrated along the internuclear axis.
• Can be bonding (σ) or antibonding (σ*).
• Commonly formed from s and pz atomic orbitals.

Pi (π) Orbitals

• Formed by sideways overlap of atomic orbitals.
• Electron density is concentrated above and below the internuclear axis.
• Can be bonding (π) or antibonding (π*).
• Commonly formed from px and py atomic orbitals.

MO Diagrams

• Visual representation of the energy levels of molecular orbitals.
• Atomic orbital energies are shown on either side of the diagram.
• Molecular orbital energies are shown in the middle.
• Electrons are filled into MOs according to the Aufbau principle and Hund's rule.
• The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are important for chemical reactivity.
• Bond order can be calculated from MO diagrams.
• Bond order = (number of electrons in bonding orbitals - number of electrons in antibonding orbitals) / 2.
• Positive bond order indicates a stable molecule.
• Bond order correlates with bond strength and bond length.

Homonuclear Diatomic Molecules

• Molecules composed of two identical atoms.
• Examples: H₂, O₂, N₂.
• MO diagrams are symmetrical.
• Atomic orbitals of similar energy combine effectively.
• MOs are labeled with σ or π symmetry.
• Filling MOs determines the electronic configuration and bond order.

Heteronuclear Diatomic Molecules

• Molecules composed of two different atoms.
• Examples: CO, HF.
• MO diagrams are asymmetrical.
• Atomic orbitals contribute unequally to MOs.
• More electronegative atom's AOs are lower in energy.
• Bonding MOs have more character from the more electronegative atom.
• Ionic character arises from unequal sharing of electrons.

Polyatomic Molecules

• Molecules composed of more than two atoms.
• MO theory can be extended to polyatomic molecules.
• Symmetry considerations are crucial.
• Linear combinations of atomic orbitals form symmetry-adapted linear combinations (SALCs).
• SALCs transform according to irreducible representations of the molecular point group.
• MO diagrams are more complex than diatomic molecules.
• Delocalization of electrons over multiple atoms.

Hybridization

• Mixing of atomic orbitals to form new hybrid orbitals.
• Hybrid orbitals have different shapes and energies than original AOs.
• sp, sp², sp³ hybridization are common examples.
• Hybrid orbitals explain molecular geometry according to VSEPR theory.
• Hybridization affects bonding and molecular properties.

Computational Methods

• Hartree-Fock (HF) method: Approximates electron-electron interactions.
• Configuration interaction (CI): Accounts for electron correlation.
• Møller-Plesset perturbation theory (MPn): Another method for electron correlation.
• Density functional theory (DFT): Uses electron density instead of wavefunction.
• Gaussian, GAMESS, and other software packages are used for quantum chemical calculations.
• Geometry optimization, frequency calculations, and property calculations are common applications.

Applications

• Predicting molecular geometry and properties.
• Understanding chemical bonding and reactivity.
• Designing new molecules and materials.
• Simulating chemical reactions.
• Spectroscopy and other experimental techniques.
• Quantum computing and quantum information science.