# Difference between revisions of "Hauptseminar Porous Media SS 2021/ab initio MD"

Line 12: | Line 12: | ||

Due the complexities of the Schrödinger's equation, it can only be analytically solved for very simple systems or with rigorous simplifications, for example, the time-independent solution. DFT, on the other hand, uses the electron density to describe the energy state of the system, and is much simpler to obtain than the wavefunction. | Due the complexities of the Schrödinger's equation, it can only be analytically solved for very simple systems or with rigorous simplifications, for example, the time-independent solution. DFT, on the other hand, uses the electron density to describe the energy state of the system, and is much simpler to obtain than the wavefunction. | ||

− | In this topic, we aim to introduce the fundamentals of Density Functional Theory (DFT), which allow us to understand the electronic structure of matter. We will start by discussing the Schrödinger equation. The underlying schemes such as Hohenberg-Kohn and Kohn-Sham, the Born-Oppenheimer approximation and the development of various exchange-correlation functionals will be presented. | + | In this topic, we aim to introduce the fundamentals of Density Functional Theory (DFT), which allow us to understand the electronic structure of matter. We will start by discussing the Schrödinger's equation. The underlying schemes such as Hohenberg-Kohn and Kohn-Sham, the Born-Oppenheimer approximation and the development of various exchange-correlation functionals will be presented. |

This is the first talk from a three-part series. In order to adhere to a consistent theme, the discussion will mainly revolve around the potential energy surface. | This is the first talk from a three-part series. In order to adhere to a consistent theme, the discussion will mainly revolve around the potential energy surface. |

## Revision as of 12:28, 7 February 2021

- Date
- TBA"TBA" contains an extrinsic dash or other characters that are invalid for a date interpretation.
- Time
- TBA
- Topic
- Density functional theory based MD
- Speaker
- TBD
- Tutor
- Azade Yazdanyar

## Contents

Due the complexities of the Schrödinger's equation, it can only be analytically solved for very simple systems or with rigorous simplifications, for example, the time-independent solution. DFT, on the other hand, uses the electron density to describe the energy state of the system, and is much simpler to obtain than the wavefunction.

In this topic, we aim to introduce the fundamentals of Density Functional Theory (DFT), which allow us to understand the electronic structure of matter. We will start by discussing the Schrödinger's equation. The underlying schemes such as Hohenberg-Kohn and Kohn-Sham, the Born-Oppenheimer approximation and the development of various exchange-correlation functionals will be presented.

This is the first talk from a three-part series. In order to adhere to a consistent theme, the discussion will mainly revolve around the potential energy surface.

## Main points to be discussed

- The many-body problem
- The electronic structure and the Schrödinger equation
- The Hohenberg-Kohn density functional theory
- The Kohn-Sham ansatz
- The Born-Oppenheimer approximation
- Exchange-correlation functionals
- Performance, accuracy and challenges

## Literature

- Understanding Molecular Simulation: From Algorithms to Applications, B. Smit and D. Frenkel
- Computer simulation of liquids, M.P. Allen and D.J. Tildesley, Oxford Science Publications
- Molecular Modelling: Principles and Applications, A. Leach
- A bird's-eye view of density-functional theory, K. Capelle, 2002
- The ABC of DFT, K. Burke et al., https://dft.uci.edu/doc/g1.pdf
- Self-Consistent Equations Including Exchange and Correlation Effects, W. Kohn and L.J. Sham, Phys. Rev. (140), A1133 (1965), DOI:https://doi.org/10.1103/PhysRev.140.A1133
- Approximate Density Functionals: Which Should I Choose?, D. Rappoport, N.R.M. Crawford, F. Furche, K. and Burke, 2009, In Encyclopedia of Inorganic Chemistry (eds R.B. King, R.H. Crabtree, C.M. Lukehart, D.A. Atwood and R.A. Scott), https://doi.org/10.1002/0470862106.ia615
- Introduction to Computational Chemistry, F. Jensen, Wiley & Sons Ltd