Courses

Instructor:

Arkady V. Krasheninnikov

Pavel B. Sorokin

Course Summary

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)

Course Format

Hours of lectureHours of discussionHours in laboratoryHours of independent studyTotal numbers of hours
301575120

Learning Outcomes

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.

Course Content

  1. 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.
  2. 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.
    • Pseudopotentials.
  3. 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.
  4. Empirical methods (4 hours)
    • Pair potentials: Lennard-Jones, Morse
    • Many body potentials: Stillinger-Weber, Ziegler-Biersack-Littmark.
    • Bond order potentials: Tersoff, Brenner, ReaxFF
  1. Molecular dynamics (4 hours)
    • Molecular dynamics algorithms
    • Classical molecular dynamics
    • Ab initio molecular dynamics
  2. Methods of crystal structure prediction (3 hours)
    • Simulated annealing
    • Metadynamics
    • Genetic algorithm

Reading List

Primary text books:

  1. Charles Kittel. Introduction to Solid State Physics. Wiley, New York, 8 edition, November 2004.
  2. Richard M. Martin. Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, Cambridge, 1 edition, October 2008.
  3. R.G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules, Oxford University Press, New York, May 1994.

Additional textbooks:

  1. D. Marx and J. Hutter, Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods, Cambridge University Press, Cambridge, October 2012.
  2. R. McWeeny and B. T. Sutcliffe, Methods of Molecular Quantum Mechanics, Academic Press, London, 2 edition, May 1992.
  3. W. A. Harrison, Elementary Electronic Structure, World Scientific Publishing, Singapore, March 2004

Problems and solutions textbooks:

  1. D. Frenkel and B. Smith, Understanding Molecular Simulation, Second Edition: From Algorithms to Applications (Computational Science), Academic Press, London, 2 edition, November 2001

Grading

Class participation10%
Homework assignments20%
Midterm exam20%
Final exam50%