# Hauptseminar Porous Media SS 2021/ab initio MD

- 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

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. Due to its complexities, 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, Ehrenfest dynamics, and the Car-Parrinello 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
- The electronic structure and Schrödinger's equation
- The Hohenberg-Kohn density functional theory
- The Kohn-Sham ansatz
- The Born-Oppenheimer approximation

## Literature

- THE JOURNAL OF CHEMICAL PHYSICS 140, 18A301 (2014), Perspective: Fifty years of density-functional theory in chemical physics, Axel D. Beckea)
- The ABC of DFT, K. Burke et al., https://dft.uci.edu/doc/g1.pdf
- J. Phys.: Condens. Matter 14 (2002) 2717–2744 PII: S0953-8984(02)32831-5, First-principles simulation: ideas, illustrations and the CASTEP code, M D Segall1,2, Philip J D Lindan3,7, M J Probert4, C J Pickard1, P J Hasnip5, S J Clark6 and M C Payne1
- Density functional theory: An introduction, Nathan Argaman, and Guy Makov, : American Journal of Physics 68, 69 (2000); doi: 10.1119/1.19375
- Ab initio molecular dynamics: basic concepts, current trends and novel applications, Mark E Tuckerman 2002 J. Phys.: Condens. Matter 14 R1297
- A bird's-eye view of density-functional theory, K. Capelle, 2002
- 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
- Molecular Modelling: Principles and Applications, A. Leach
- Introduction to Computational Chemistry, F. Jensen, Wiley & Sons Ltd