Computational electronic structure
Sangeeta Sharma
Zusätzl. Angaben / Voraussetzungen
Lecture format: 2 hours classroom lecture with interactive computational exercises, optional
online teaching on request by registered students, 2 hours problems class mixed analytical and
computational.
Kommentar
Lecture outline
Matter is made up of the order of 10^23 interacting electrons and nuclei. Even to store the many-body
wave-function of an atom of oxygen would require yottabytes of data: the wave-function is an
inappropriate concept to describe solid matter. Modern solid-state computational descriptions of
matter are thus founded on a radically different notion, known as density functional theory (DFT),
that all quantum mechanical observables can be obtained from the ground state electron density.
This profoundly simpler object – that can be stored and computed with on present-day laptops – has
allowed rich predictive investigation of the cornucopia of quantum materials that the 118 elements
of the periodic table can create. Underpinning the present-day drive to create new materials that will
obviate the environmental cost of present-day information technology, quantum materials science
offers both insight into the nature of quantum matter as well as a practical tool of profound
importance.
This lecture course will cover both the theorems that underpin DFT and its usage, as well as employ
“computer lab” lectures in which the quantum mechanics of materials will be explored at a practical
level. Students will learn both the modern theory of electronic structure as well as computational
skill in running the Elk computer code (elk.sourceforge.io), used by more than 2500 scientists
worldwide.
Lecture plan
[Blue – blackboard lectures, green – “computer lab” lectures]
Lecture 1: Why DFT? Many body wave-function is an inappropriate concept for solids. Hartree-Fock fails.
Lecture 2: Hohenberg-Kohn: all observables can be calculated from the ground state density alone.
Lecture 3: Kohn-Sham and approximating the exchange-correlation function.
Lecture 4: Solving the Kohn-Sham equations for real materials: Al and Si.
Lecture 5: Functional development: what they can and can’t do.
Lecture 6: Response functions: talking to experiments.
Lecture 7: Calculating response functions: Why is copper red-orange and LiF transparent?
Lecture 8: Magnetism in density functional theory.
Lecture 9: Magnetism in solids: Why is Iron magnetic and Copper not?
Lecture 10: Forces and crystal structures.
Lecture 11: Structure optimization: Why is Iron a bcc crystal structure and Nickle a fcc crystal structure?
Lecture 12-13: Student seminars.
20 Termine
Regelmäßige Termine der Lehrveranstaltung