Introduction to Computational Studies of Electronic Structure of Nanosystems

Timetable

Module aim (aims)

The purpose of the course is to introduce the students to the fundamentals of the methods of

computations of electronic structure of matter, including the density functional theory as well

as other first principle approaches. A particular emphasis will be given to specific aspects of

the computational methods in applications to nanostructures. A practical introduction to a few commonly used computational packages will be given. To get the credit for the course the students will be required to conceive a specific problem relevant to the field of nanoscience, study it with one of the computational packages and provide the detailed report of the solution.

Pre-requisites in terms of knowledge, skills and social competences (where relevant)

Knowledge of basics of quantum mechanics or quantum chemistry is necessary.

Acquaintance with solid state physics, statistical physics will also be useful. Ability of

independent reading with understanding of original publications and review papers (in

english) from leading journals will be important. Familiarity with UNIX-like operational system

will be also helpful.

Syllabus

Week 1: Introduction: examples of nanosystems investigated using first-principles methods

Week 2: Interactions in the condensed systems

Week 3: The concept of electronic correlations

Week 4: Hartree-Fock approximation and the Thomas-Fermi method

Week 5: Density functional theory: basic concepts

Week 6: Hohemberg-Kohn theorems and exchange-correlation energy

Week 7: Kohn-Sham equations

Week 8: Adiabatic transitions and testing of models of exchange correlation potentials

Week 9: Local density approximation and generalized gradient approximation

Week 10: Beyond the pseudolocal approximation of the density functional theory

Week 11: Effectiveness of approximations of the density functional theory in condensate systems

Week 12: Various choices of the basis functions

Week 13: Introduction to the theory of the pseudopotential

Week 14: Overview of functionalities of computational packages: SIESTA

Week 15: Overview of functionalities of computational packages: Quantum Espresso

Reading list

[1] Parr, R. G.; Yang, W. (1989). Density-Functional Theory of Atoms and Molecules.

New York: Oxford University Press.

[2] Axel D. Becke. Perspective: Fifty years of density-functional theory in chemical physics.

J. Chem.Phys. 140, 18A301 (2014).

[3] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias and J.D. Joannopoulos. Iterative minimization

techniques for ab initio total-energy calculations: molecular dynamics and conjugate

gradients. Rev. Mod. Phys. 64, 1045 (1992).

[4] J. M. Soler et al. The SIESTA method for ab initio order-N materials simulation.

J. Phys.: Cond. Mat. 14, 2745 (2002).

[5] P. Giannozzi et al. Advanced capabilities for materials modelling with Quantum ESPRESSO.

J. Phys.: Condens. Matter 29 465901 (2017).