Syllabus

Introduction to computational modeling and simulation for Materials Science. Molecular mechanics, Density functional theory (DFT), Molecular dynamics (MD), Monte Carlo (MC) methods, introduction to quantum MC methods, analysis exercises using softwares, Materials genomics, High through-put combinatorial algorithms for materials design.

Detailed version

Introduction to computational modeling and simulation for Materials Science, First principle methods: the beginnings of Quantum mechanics, Schrodinger wave equation, time-independent wave equation,  Molecular mechanics- Force Field Methods, Postulates of quantum mechanics, Energy Hamiltonian, early first principles calculation, Born-Oppenheimer approximation, Hartree method (one electron), Hartree- Fock molecular orbital theory, Self-consistent-field (SCF) procedure;

Density functional theory (DFT): electron density in DFT, Hohenberg-Kohn theorems, Kohn-Sham approach, exchange correlation functionals, solving Kohn-Sham equations, DFT extensions and limitations. DFT exercises using software (VASP/Gaussian).

Molecular dynamics (MD): Atomic model in MD, Molecular mechanics, potentials, solutions for newton’s equation of motion, running MD: initialization, pre-set ups, periodic boundary condition, positions and velocity, time steps, ensembles, integration equilibration, minimisation in static MD run – steepest descent method, conjugate gradients method, run analysis. MD analysis exercises using software (LAMMPS/ XMD)

Monte Carlo (MC) methods: Basis of MC methods, stochastic processes, Markov’s process, ergodicity; Algorithms for MC simulations, random numbers, sampling techniques. Applications of MC methods: System of classical particles, percolation, polymer systems, nucleation, crystal growth, fractal systems. Limitations of MC methods, introduction to quantum MC methods.

Materials genomics: High through-put combinatorial algorithms for materials design.