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

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|number=1
 
|number=1
 
|topic=Density functional theory based MD
 
|topic=Density functional theory based MD
|speaker= TBD
+
|speaker= Konstantin Nikolaou
|date=TBA
+
|date=2021-05-14
|time=TBA
+
|time=14:30
 
|tutor=[[Azade Yazdanyar]]
 
|tutor=[[Azade Yazdanyar]]
 
|handout=
 
|handout=
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== Contents ==
 
== Contents ==
Due to the complexities of 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 allows us to understand the electronic structure of matter. We will start by discussing Schrödinger's equation. Due to its complexity, Schrödinger's equation can only be analytically solved for very simple systems or with rigorous simplifications.  
  
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 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.
+
We will then discuss the foundations of DFT, first introduced by Hohenberg, Kohn and Sham. DFT uses the electron density to describe the energy state of the system, and is much simpler to obtain than the many-body wavefunction.
 +
 
 +
A development on DFT was to generalize it further for dynamic systems. Therefore, one can use first-principles electronic structure methods 'on the fly' to obtain the forces, and couple it with a time-step evolution formulation. There exist various approaches to ''ab initio'' MD (AIMD), such as the Born-Oppenheimer MD. These topics will be marginally presented.
  
 
This is the first talk from a three-part series. 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. To adhere to a consistent theme, the discussion will mainly revolve around the potential energy surface.
  
 
== Main points to be discussed ==
 
== Main points to be discussed ==
* The many-body problem
+
* The many-body problem, electronic structure and Schrödinger's equation
* The electronic structure and Schrödinger's equation
 
 
* The Hohenberg-Kohn density functional theory
 
* The Hohenberg-Kohn density functional theory
 
* The Kohn-Sham ansatz
 
* The Kohn-Sham ansatz
* The Born-Oppenheimer approximation
+
* ''Ab initio'' MD
* Exchange-correlation functionals
+
* Strengths and limitations of DFT and AIMD
* Performance, accuracy and challenges
 
  
 
== Literature ==
 
== Literature ==
  
 
+
<bibentry pdflink="yes">
* A bird's-eye view of density-functional theory, K. Capelle, 2002
+
becke14a
* The ABC of DFT, K. Burke et al., https://dft.uci.edu/doc/g1.pdf
+
argaman00a
* 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
+
tuckerman02b
* Molecular Modelling: Principles and Applications, A. Leach
+
jensen06a
* Introduction to Computational Chemistry, F. Jensen, Wiley & Sons Ltd
+
</bibentry>

Latest revision as of 17:16, 15 February 2021

Date
2021-05-14
Time
14:30
Topic
Density functional theory based MD
Speaker
Konstantin Nikolaou
Tutor
Azade Yazdanyar

Contents

In this topic, we aim to introduce the fundamentals of Density Functional Theory (DFT), which allows us to understand the electronic structure of matter. We will start by discussing Schrödinger's equation. Due to its complexity, Schrödinger's equation can only be analytically solved for very simple systems or with rigorous simplifications.

We will then discuss the foundations of DFT, first introduced by Hohenberg, Kohn and Sham. DFT uses the electron density to describe the energy state of the system, and is much simpler to obtain than the many-body wavefunction.

A development on DFT was to generalize it further for dynamic systems. Therefore, one can use first-principles electronic structure methods 'on the fly' to obtain the forces, and couple it with a time-step evolution formulation. There exist various approaches to ab initio MD (AIMD), such as the Born-Oppenheimer MD. These topics will be marginally presented.

This is the first talk from a three-part series. 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, electronic structure and Schrödinger's equation
  • The Hohenberg-Kohn density functional theory
  • The Kohn-Sham ansatz
  • Ab initio MD
  • Strengths and limitations of DFT and AIMD

Literature