Syllabus for Computational Chemistry

Other Useful Texts:

See the Book List for a list of other helpful texts. We will be referring most frequently to Frenkel & Smit when the primary text doesn't contain a topic of interest.

Course Outline:

  1. Introduction
  2. Force fields and molecular representations of matter
    1. Intramolecular (bonding) interactions
    2. Non-bonded interactions
      1. Electrostatic (Coulomb, Dipolar) interactions
      2. London (van der Waals) interactions
    3. Hydrogen bonds
    4. Constraints and Restraints
    5. United atom and other coarse-grained approaches
    6. Non-pairwise interactions
    7. Just how accurate are force fields?
  3. Methods for Simulating Large systems
    1. Non-bonded Cutoffs
      1. Shifted potential and shifted force
      2. Switching functions
      3. Neighbor lists
    2. Boundaries
      1. Periodic Boundary conditions
      2. Stochastic forces at spherical boundary
    3. Long-range interactions
      1. The Ewald Sum
      2. The Reaction field method
      3. Real-space methods
  4. Energy Minimization and related analysis techniques
    1. Steepest descent
    2. Conjugate gradient
    3. Newton-Raphson
    4. Comparison of methods
    5. Advanced techniques: Simulated Annealing, Branch-and-bound, simplex
    6. What's the big deal about the minimum anyway?
  5. Introduction to Equilibrium Statistical Mechanics
    1. Phase space, ergodicity, and Liouville's theorem
    2. Ensemble theory, thermodynamic averages
      1. Microcanonical Ensemble
      2. Canonical Ensemble
      3. Other ensembles
    3. Statistical mechanics of fluids
  6. Monte Carlo
    1. MC integration and Markov chains
    2. The Metropolis method
    3. Biased MC
  7. Molecular Dynamics
    1. Classical mechanics: equations of motion
    2. Finite Difference methods
      1. Verlet algorithm
      2. Velocity verlet
      3. The Time step: practical issues
      4. Multiple time-step algorithms
    3. Constraint Dynamics
      1. Fundamental concepts
      2. SHAKE and RATTLE
    4. Temperature: Maxwell-Boltzmann distribution of velocities
    5. Temperature control
      1. Velocity scaling
      2. Andersen's method
      3. Nose-Hoover dynamics
    6. Calculating properties from MD trajectories
    7. Hybrid MC
  8. Free Energy
    1. Perturbation methods
    2. Thermodynamic integration
  9. Brownian dynamics and the Langevin Equation