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| Home > Publications database > Quantum Theory of Materials: an Introduction to Density Functional Theory and its Computational Challenges |
| Talk (non conference) | PreJuSER-17998 |
2011
Abstract: Density Functional Theory (DFT) is one of the most used ab initio theoretical frameworks in materials science. DFT-based methods are growing as the standard tools for simulating new materials. Simulations aim at recovering and predicting physical properties (electronic structure, total energy differences, magnetic properties, etc.) of large molecules as well as systems made of many hundreds of atoms. DFT reaches this result by solving self-consistently a rather complex set of quantum mechanical equations leading to the computation of the one-particle density n(r), from which physical properties are derived. In order to preserve self-consistency, numerical implementations of DFT methods consist of a series of iterative cycles; at the end of each cycle a new density is computed and compared to the one calculated in the previous cycle. The end result is a series of successive densities converging to a n(r) approximating the exact density within the desired level of accuracy. The course is divided in two parts. The first part is concerned with theoretical and conceptual foundations of DFT: we will introduce basic concepts of many-body quantum mechanics, proceed to illustrate the fundamental building blocks of DFT, and finally present a broad overview of the three most used ab initio methods. In the second part we will focus on one specific method, FLAPW, and analyze its computational aspects in details; the material will be presented paying special attention on the interrelation between the physics and the numerics of the problem. In order to facilitate the exposition, numerous examples will be presented and discussed in class. A basic knowledge of quantum mechanics concepts is assumed.
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