Course „Atomistic simulations of solids and nanostructures” is dedicated to the introduction in modern methods aimed at the simulations of the properties of solids at the macro- and nanoscales. The course includes lecture part in which the basics of theoretical methods of atomistic simulations are covered, as well as the practical part, which consists of a number of problems dealing with the simulation of various properties of solids.
Approximate topics of the graduation thesis
- Theoretical investigation of the atomic structure and properties of nanostructures of (chosen composition)
- Simulation of properties of crystals of (specific) symmetry and (chosen composition)
- Investigation of features of mechanical properties of nanostructures of (chosen composition)
- Investigation of features of electronic properties of nanostructures of (chosen composition)
- Comparison of simulation methods of various levels for the investigation of solids of (chosen composition)
- Comparison of simulation methods of various levels for the investigation of nanostructures of (chosen composition)
|Hours of lecture||Hours of discussion||Hours in laboratory||Hours of independent study||Total numbers of hours|
The student acquire the general scientific (GSC), instrumental (IС) and professional (PC) competencies.
- GSC-1: Ready to use methods of atomistic simulations in condensed matter physics and materials science.
- GSC-2: Ability to actively and purposefully apply the knowledge, skills and abilities to perform the research work and complete undergraduate’s thesis;
- IC-1: Ready for the solution of practical problems in simulation the atomic structure and physical properties of various materials;
- IC-2: Active user skills for the use of specialized software packages in atomistic simulations of solids and nanostructures;
- IC-3: Willingness to work with information in the field of atomistic modeling of solids and nanostructures of scientific papers, monographs and textbooks, Internet;
- PC-1: Ready to use atomistic simulation methods in further career as a researcher, university lecturer, engineer;
- PC-2. Ready for a creative approach in the implementation of scientific and technical problems, based on a systematic updating of acquired knowledge and skills and the use them in simulation of properties of solids and nanostructures.
- Basics of the atomistic simulations (6 hours)
- Review of the basics of quantum mechanics.
- The Born-Oppenheimer approximation.
- Many-electron systems.
- The nature of chemical bonding.
- Basics of the solid state physics
- Reciprocal space.
- Band structure
- The Fermi surface.
- Band energy and bond energy.
- The density of states: total and local.
- Outline of empirical, semi-empirical and ab initio methods.
- Molecular dynamics and other methods of equilibrium/metastable configuration calculations.
- Ab initio methods (8 hours)
- Hartree and Hartree-Fock approximations.
- Self-consistent field method.
- Density-functional theory.
- Local density approximation (LDA).
- Beyond LDA.
- Gaussian- and Slater basis functions.
- Plane wave formalism.
- Semi-empirical methods (5 hours)
- Tight-binding approximation
- Orthogonal, non-orthogonal tight-binding.
- The Slater-Koster method.
- The Mulliken charges, orbital population.
- Vibration analysis.
- Linear scaling algorithms.
- Empirical methods (4 hours)
- Pair potentials: Lennard-Jones, Morse
- Many body potentials: Stillinger-Weber, Ziegler-Biersack-Littmark.
- Bond order potentials: Tersoff, Brenner, ReaxFF
- Molecular dynamics (4 hours)
- Molecular dynamics algorithms
- Classical molecular dynamics
- Ab initio molecular dynamics
- Methods of crystal structure prediction (3 hours)
- Simulated annealing
- Genetic algorithm
Primary text books:
- Charles Kittel. Introduction to Solid State Physics. Wiley, New York, 8 edition, November 2004.
- Richard M. Martin. Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, Cambridge, 1 edition, October 2008.
- R.G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules, Oxford University Press, New York, May 1994.
- D. Marx and J. Hutter, Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods, Cambridge University Press, Cambridge, October 2012.
- R. McWeeny and B. T. Sutcliffe, Methods of Molecular Quantum Mechanics, Academic Press, London, 2 edition, May 1992.
- W. A. Harrison, Elementary Electronic Structure, World Scientific Publishing, Singapore, March 2004
Problems and solutions textbooks:
- D. Frenkel and B. Smith, Understanding Molecular Simulation, Second Edition: From Algorithms to Applications (Computational Science), Academic Press, London, 2 edition, November 2001