Quantum chemistry
Graduate · Chemistry
Syllabus focus
Theoretical / proof-based
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
Topics typically covered
Theoretical / proof-based
Formal quantum mechanics
- Hilbert spaces, operators, and observables
- Postulates of quantum mechanics in Dirac notation
- Commutation relations and uncertainty principles
- Angular momentum: raising and lowering operators
- Addition of angular momenta and Clebsch–Gordan coefficients
- Identical particles, symmetry, and Pauli principle
- Variational principle and Ritz method
- Time-independent and time-dependent perturbation theory
- WKB approximation and semiclassical methods
- Scattering theory and cross sections (introduction)
Many-electron systems
- Hartree–Fock theory: SCF procedure and Fock operator
- Roothaan–Hall equations and basis sets
- Electron correlation: configuration interaction, MPn, CCSD(T)
- Basis set convergence and extrapolation
- Density functional theory: Hohenberg–Kohn and Kohn–Sham theorems
- Exchange-correlation functionals and Jacob's ladder
- Multireference methods: CASSCF, CASPT2 (overview)
- Relativistic effects: Douglas–Kroll–Hess, ZORA
- Spin-orbit coupling in heavy elements
- Basis set superposition error and counterpoise corrections
Molecular electronic structure
- Born–Oppenheimer approximation and corrections
- Molecular orbital theory: LCAO-MO and symmetry adaptation
- Walsh diagrams and photoelectron spectroscopy interpretation
- Hückel theory and perturbation treatments of π systems
- Valence bond theory and resonance structures
- Natural bond orbital analysis (conceptual)
- Electron density, ESP, and non-covalent interaction analysis
- Excited states: CIS, TD-DFT, EOM-CCSD (overview)
- Conical intersections and photochemistry
- Vibronic coupling and Jahn–Teller effects in molecules
Advanced applications
- Reaction path following and transition state optimization
- Intrinsic reaction coordinate (IRC) calculations
- Thermochemistry from quantum chemical energies
- Solvation models: PCM, SMD, explicit solvent clusters
- QM/MM methods for biomolecular systems
- Periodic boundary conditions and solid-state calculations
- Wannier functions and band structure analysis
- Machine learning for potential energy surfaces
- Validation benchmarks: GMTKN, S66, ionization potentials
- Software ecosystems: Gaussian, ORCA, Psi4, Q-Chem, VASP
Notes
Graduate-level quantum chemistry for PhD and advanced MS students. Topics reflect common quantum chemistry syllabi at US research universities. Prior physical chemistry and linear algebra essential.