COMPUTATIONAL STATISTICAL PHYSICS AND APPLICATIONS

Specialization / Direction

Upon successful completion, students will be able to: use the basic methods of statistical computational materials science: Molecular Dynamics (MD), Density Functional Theory (DFT), Monte Carlo Methods

The course opens by situating computational materials science within modern materials research, outlining what problems are solvable on today’s computers and how atomistic/electronic-structure tools complement experiment. It also previews the two pillars that carry the text: molecular dynamics (MD) and first-principles electronic-structure methods (with expanded coverage of DFT beyond LDA/GGA, including GGA+U and hybrid functionals). Foundations of computational methods. Early chapters introduce core concepts common to all simulations: representations of matter (nuclei + electrons vs. atoms/molecules), discretization of time/space, boundary conditions, ensembles, and statistical mechanics links (ergodicity, averaging, fluctuation–dissipation). The discussion also covers practical computing topics—hardware, parallelization, numerical precision, and data handling—to prepare readers for large-scale runs. Molecular Dynamics (MD). A substantial block develops MD from first principles: Interatomic potentials (what they encode; choices and trade-offs). Equations of motion and their numerical integration; stability and timestep selection. Initialization/equilibration strategies; thermostats and barostats for NVT/NPT ensembles. Production runs & analysis: sampling quality, error bars, trajectory post-processing. This sequence takes the reader from model selection to data production in a lab-like workflow. Monte Carlo (MC) & complementary samplers. MC ideas (Metropolis sampling, acceptance criteria, move sets) are presented as complementary to MD—especially for equilibrium properties, phase behavior, or systems where rare-event sampling matters. Hybrid MD/MC strategies and advanced sampling may also be touched on to round out the toolbox. Electronic-structure theory. The next core strand is electronic structure with density functional theory (DFT): Basic formalism and approximations; pseudopotentials and plane-wave vs localized bases. Practical workflows (geometry optimization, band structures, DOS, charge density and bonding analysis). Beyond-GGA improvements (e.g., GGA+U, hybrid functionals) to treat correlated systems or improve band gaps—an area expanded in the second edition. Linking scales & case studies. Worked examples connect MD/DFT outputs to real materials questions: diffusion and transport, defects and surfaces, mechanical response at the nanoscale, thermodynamics of phase stability, or optoelectronic properties relevant to LEDs and photovoltaics. These case-led chapters emphasize how to choose a method, set it up, validate it (often against higher-level theory), and interpret results in a materials-design context. Modern potentials & data. The course introduces the rationale for machine-learning(ML) interatomic potentials alongside classical forms, explaining training datasets, validation against DFT, and when ML trade-offs make sense—bridging accuracy and scale for realistic simulations. Practicalities & resources. Final sections typically consolidate best practices (verification/validation, convergence testing, reproducibility), common pitfalls, and pointers to software, datasets, and further reading—so students can translate theory into robust computational studies.

Statistical Computational Materials Science, Molecular Dynamics (MD), Density Functional Theory (DFT), Monte Carlo Methods, Machine-Learning Interatomic Potentials

03-09-2025