Conducted in
term:
2024/25L
ISCED code: 0533
ECTS credits:
3
Language:
English
Organized by:
Faculty of Physics, Astronomy and Informatics
(in Polish) Density-functional theory for solids 0800-M-DEFUNTSO
This course will cover the following fundamental topics.
- Recapitulation of the basic concepts of density-functional theory: Hohenberg-Kohn theorems, Kohn-Sham equations, exchange-correlation functionals, and interpretation via effective action formalism.
- Operative implementation of density-functional theory: self-consistent cycle, combination with the Bloch theorem, three major families of methods for the solution of the Kohn-Sham equations.
- Pseudopotential methods: treating the core states, orthogonalized plane waves, projector augmented waves, scalability, in-situ pseudopotentials.
- Localized orbital methods: localized atom-centered orbitals, Slater-Koster two-center approximation, Gaussian orbitals and numerical orbitals.
- Augmented methods: muffin-tin spheres, augmented plane waves, Korringa-Kohn-Rostoker method, muffin-tin orbitals, canonical bands, linearization, atomic-sphere approximation versus full-potential methods.
- Hands-on exercises with state-of-the-art codes.
- Selected applications: constrained density-functional theory, linear response formalism, phonon and magnon spectra.
- Basic concepts of multi-scale simulations: from interatomic potentials to ab-initio molecular dynamics; mapping the magnetic excitations onto an effective Heisenberg Hamiltonian; from Bloch waves to localized orbitals.
- Basic notions of strong correlation effects in solids: Fermi-liquid theory, mass renormalization and quasi-particle lifetimes.
Total student workload
- Contact hours with teacher:
- participation in lectures - 30 hrs,
- participation in the discussion of the final projects – 2 hrs,
- consultations - 6 hrs.
- Self-study hours:
- studying lectures materials - 10 hrs,
- reading literature - 10 hrs,
- preparation of the final project - 17 hrs. Altogether: 75 hrs ( 3 ECTS).
Learning outcomes - knowledge
Student:
W1: has advanced knowledge of the density-functional theory and its operating cycle in modern codes (Physics: K_W04, K_W05),
W2: knows the theoretical foundations of the major methods used to solve the Kohn-Sham problem in solids (Physics: K_W02, K_W03),
W3: is familiar with the galaxy of multi-scale approaches available for more advanced material simulations (Physics: K_W01, K_W02, K_W05),
W4: is acquainted with the most important limitations of density functional theory, with a focus on strongly correlated materials (Physics:K_U03, K_W04, K_W05).
Learning outcomes - skills
Student:
U1: is able to use selected software packages to calculate the electronic structure of solids and other basic output (Physics: K_U01, K_U02),
U2: is capable of choosing the best electronic structure method to model different systems for a variety of purposes (Physics: K_U02, K_U04),
U3: has basic skills in connecting the output of electronic structure calculations to data accessible in experiment (Physics: K_U03),
U4: can identify basic conceptual problems in modeling materials (Physics: K_U03).
Learning outcomes - social competencies
Student:
K1: understands the central importance of the electronic problem in modern physics, chemistry and materials science,
K2: understands the need for ab-initio methods in physics,
K3:is aware of the societal relevance of materials optimization,
K4: recognizes the challenge of materials discovery and engineering,
K5: understand how machine learning may revolutionize these tasks,
K6: can communicate the potential outcome of materials modeling for the most pressing societal problems of our time, from clean energy to nanotechnology.
(Physics: otucomes K1-K6 correspond to K_K03)
Expository teaching methods
- problem-based lecture
- informative (conventional) lecture
- informative (conventional) lecture
Exploratory teaching methods
- project work
Type of course
elective course
Prerequisites
- Mandatory:
- Basic knowledge of quantum mechanics,
- Basic knowledge of solid-state theory (e.g. Bloch theorem, crystals),
- Basic knowledge of linux/unix shell for the hands-on sessions. Preferred:
- Introductory knowledge of density-functional theory.
Course coordinators
Assessment criteria
Assessment methods:
- activity during the hands-on sessions: U1-U4.
To pass the class the students are required to prepare a written project (assessment of learning outcomes: U1, U3, U4) and participate in the discussion of all students’ projects during the last lecture (assessment of learning outcomes: W1-W4; U2).
Assessment criteria
Percentage of the achievement of the expected learning outcomes and respective grades:
| Percentage | Grade |
| Less than 50% | 2 (fail) |
| [50% - 60%) | 3 (satisfactory) |
| [60% - 70%) | 3+ (satisfactory plus) |
| [70% - 80%) | 4 (good) |
| [80% - 90%) | 4+ (good plus) |
| [90% - 100%] | 5 (very good) |
Practical placement
Not applicable
Bibliography
Richard M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, 2008
Notes
|
Term 2024/25L:
The class schedule will be established in consultation with the students who will sign up for the course. The lecturer will contact the students via e-mail. The first lecture will be given in the first week of March (02.03.2025 - 07.03.2025). |
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: