This is a hands on graduate level course covering current methods for modeling soft matter (polymers, surfactant solutions, colloids, liquid crystals, etc.), nano-structured materials (nanoparticles, nano-composites, nano-porous materials, etc.), and biomolecular systems at the electronic, atomistic, meso-scale and continuum levels. The topics to be covered will include:

1. Ab Initio Quantum Mechanical Methods . The Schrödinger wave equation and wave functions. Solution methods and approximations. Variational Principle. Born-Oppenheimer approximation. Molecular orbital calculations. Hartree-Fock method. Basis sets. Semi-empirical methods. Perturbation methods. Density functional theory. Applications to water, polymers, biopolymers, enzymes, adsorbates on surfaces.

• Statistical Mechanics of Nonspherical Molecules . Introduction and commonly used models (rigid vs non-rigid molecules, when classical treatments are possible, pair additivity of potentials). The partition function and thermodynamic properties (canonical ensemble). Factorization of the partition function and the distribution function. Distribution functions and correlation functions. The grand canonical ensemble. Other ensembles. The Gibbs inequality. The uniqueness theorem. Potential distribution theorem.
• Force Fields . Contributions to intermolecular potentials; non-additivity; H-bonding; bond stretching, bending and torsion. Water. United atom force fields. Class I, II and III force fields for organic substances. Force fields for inorganic molecules; force fields for solid-state systems. Force field parameterization.
• Atomistic (molecular) Simulation . Features common to various simulation methods (initial conditions, periodic boundaries, minimum image, neighbor lists, etc.). Difficult systems. Finite size scaling. Ginzburg parameter.
• Monte Carlo methods . Metropolis sampling. Derivation of acceptance criteria for various ensembles (canonical, grand canonical, isothermal-isobaric, Gibbs). Detailed balance. Specialized methods for free energies and phase equilibria: test particle method; thermodynamic integration; umbrella sampling; histogram reweighting; parallel tempering. Reverse MC. Application of RMC to nano-structured materials.
• Molecular Dynamics methods. Numerical solution of the equations of motion. Finite difference methods. Verlet's algorithm (basic, leapfrog, velocity Verlet). Gear predictor-corrector method. Calculating energy, pressure, heat capacity, structure. Application to water. MD in various ensembles. Non-equilibrium MD. Time correlation functions. Velocity autocorrelation functions and diffusion. Applications to drug design. Pharmacophores and receptor sites.
• Meso - Scale Simulation Methods: Lattice Monte Carlo . Lattice Monte Carlo . Larson's model and applications to polymers and polymer solutions. Applications to surfactant and micellar solutions. Applications to templated nano-porous materials; silica MCM-41, SBA-15 and mesocellular foams Application to protein folding.
• Meso - Scale Simulation Methods: Langevin dynamics . Brownian motion. Langevin' equation. Fluctuation-dissipation theorem. Coarse graining methods. Rigorous coarse graining. More approximate methods. Application to surfactant and micellar solutions. Brownian dynamics. Applications of BD to study nano-particles, tethered nano-particles, ion transport across the potassium channel in cell membranes, counterion condensation. Dissipative particle dynamics. Examples of applications of DPD to soft matter (surfactant solutions, polymers, diblock copolymers, etc.) and nano-structured materials. Application of DPD to liposome formation.
• Continuum Methods: Transport equations, constitutive equations. Finite element and finite difference methods.
• Applications: Several applications will be discussed, in each case indicating the most appropriate methods and their advantages and drawbacks
• Phase equilibria in bulk fluids and solids
• Phase equilibria in confined systems (narrow pores)
• Membrane and micelle structure
• Rational drug design
• Colloidal systems
• Proteins and peptides, protein folding, protein dynamics, DNA dynamics
• Chemical Reactions. Reaction coordinate, potential energy surface, free energy surface. Methods and examples of determination of reaction mechanism and optimal reaction paths. Reaction equilibrium. Reaction rates.

The course material will be covered in two lectures per week (75 minutes each). In addition, a tutorial will be held every two weeks to introduce students to the web site and help get them started early on applications. Illustrations of the use of the methods will be provided via web-based applications. A choice of projects will be provided and independent projects will also be permitted. Students will gain experience of the methods via examples and problems based on the web modules. There will be no formal exams in the course. Students will be expected to complete a term paper project on a topic related to the course. The term paper should include results from a computational project carried out using the web modules or independent study. The web modules can accommodate students with no prior experience on UNIX operating systems.

NCSU has recommended minimum specifications for computers used for classes. Depending on your computer needs, we recommend your computer meet or exceed the following minimum specifications below.

PCs must have an Intel-compatible 800 MHz processor, 256 MB RAM, 8 GB hard drive with 1 GB free space available, 256 Color Display, CD-ROM drive, 800x600 (min.) video adapter, sound card, and speakers. The operating system should be Windows 2000 or XP. Real One Player Basic (available free online) and high speed Internet connection such as cable, DSL, T1 or LAN will be required for EOL courses.

MAC users must have a G3 processor with firewire and USB factory built-in, 256 MB RAM, 10 GB with 1GB free space available, 256 Color Display, CD-ROM drive, 800x600 (min) video adapter, sound card, and speakers. The operating system must be MacOS 10.3 (minimum) along with the above RealOne and Internet specifications above.

For more detailed information on computer specifications and recommendations, please refer to our website at: http://engineeringonline.ncsu.edu/currentstudents/computeraccess.htm

Dr. Keith E. Gubbins, Professor
Dept. of Chemical Engineering
North Carolina State University
2088A Engineering Building 1
Campus Box 7905
Raleigh, NC 27695-7905

Phone: (919) 513-2262
Fax: (919) 515-3465
E-Mail: keg@ncsu.edu
Instructor Website:http://www.che.ncsu.edu/faculty_staff/keg.html