Advanced physical 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
Classical thermodynamics
- Postulates of thermodynamics and entropy as a state function
- Legendre transforms and thermodynamic potentials
- Maxwell relations and Jacobian methods
- Stability criteria and phase transitions: Clausius–Clapeyron
- Chemical potential in multicomponent systems
- Gibbs–Duhem equation and activity coefficients
- Non-ideal solutions: Margules, van Laar, Wilson equations
- Electrochemical thermodynamics and the Nernst equation derivation
- Surface thermodynamics: Gibbs adsorption isotherm
- Irreversible thermodynamics and entropy production (intro)
Statistical mechanics
- Ensembles: microcanonical, canonical, grand canonical
- Partition functions and connection to thermodynamic quantities
- Ideal gas, ideal crystal, and Einstein model
- Debye model for heat capacity of solids
- Classical and quantum statistics: Maxwell–Boltzmann, Bose–Einstein, Fermi–Dirac
- Fermi energy and electronic contribution to heat capacity
- Configurational entropy and mixing in solutions
- Fluctuation-dissipation theorem (introduction)
- Monte Carlo and molecular dynamics foundations
- Critical phenomena and Ising model (overview)
Chemical kinetics and dynamics
- Potential energy surfaces and reaction dynamics
- Transition state theory: derivation and limitations
- RRKM theory for unimolecular reactions
- Marcus theory for electron transfer reactions
- Kramers theory for reactions in solution
- Femtochemistry and ultrafast spectroscopy
- Molecular beam scattering and crossed-beam experiments
- State-to-state dynamics and steric effects
- Rice–Ramsperger–Kassel theory extensions
- Master equations and stochastic kinetics
Advanced spectroscopy theory
- Time-dependent perturbation theory and Fermi's golden rule
- Selection rules from symmetry and transition dipoles
- Raman and resonance Raman theory
- Multiphoton absorption and nonlinear spectroscopy
- Coherent two-dimensional spectroscopy (overview)
- NMR: density matrix formalism and relaxation
- EPR and ENDOR spectroscopy theory
- X-ray spectroscopy: XAS, XES (introduction)
- Photoelectron spectroscopy and Koopmans' theorem
- Computational spectroscopy: time-dependent DFT
Notes
Graduate-level physical chemistry for PhD and advanced MS students. Topics reflect common advanced physical chemistry syllabi at US research universities. Strong mathematical background in calculus, linear algebra, and differential equations expected.