By name: quantum-chemistry description: Quantum mechanics in chemistry license: MIT compatibility: opencode metadata: audience: quantum chemists, researchers, students category: chemistry
What I do
- Apply quantum mechanics to chemical systems
- Calculate molecular electronic structure
- Predict molecular properties
- Analyze spectroscopic transitions
- Develop computational methods
- Study chemical bonding
When to use me
- When calculating molecular orbitals
- When predicting molecular properties
- When studying chemical bonding
- When analyzing spectroscopy
- When designing new molecules
- When simulating molecular behavior
Key Concepts
Schrödinger Equation
Time-independent form
ĤΨ = EΨ
- Ĥ: Hamiltonian operator
- Ψ: Wavefunction
- E: Energy eigenvalue
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