quantum-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) ```python # 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