Quantum Chemistry

Approximation Methods

Variational Principle

• Trial function gives upper bound to ground state energy
• Better trial function → better energy

Perturbation Theory

• Divide problem into solvable + small perturbation
• Møller-Plesset (MP2, MP3, MP4)

# Example: Hydrogen atom energy levels
def hydrogen_energy(n):
    """
    Calculate hydrogen atom energy.
    n: Principal quantum number
    """
    E0 = -13.6  # eV (ground state)
    return E0 / (n**2)

# Quantum numbers
quantum_numbers = {
    'n': 'Principal (energy level)',
    'l': 'Orbital (0=s, 1=p, 2=d, 3=f)',
    'm_l': 'Magnetic (-l to +l)',
    'm_s': 'Spin (-1/2 or +1/2)'
}

Electronic Structure Methods

Ab Initio

• Hartree-Fock (SCF)
• Configuration Interaction
• Coupled Cluster (CCSD, CCSD(T))
• Møller-Plesset perturbation theory

Density Functional

• LDA, GGA, hybrid functionals
• B3LYP, PBE0, ωB97X

Chemical Bonding

• MO theory: Linear combination of atomic orbitals
• Bonding, antibonding, nonbonding orbitals
• Hückel theory: π-electron systems
• Valence bond theory: Resonance