Hauptseminar Porous Media SS 2021/ab initio MD

Date

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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 ABC of DFT, K. Burke et al., https://dft.uci.edu/doc/g1.pdf

• A. D. Becke.
  "Perspective: Fifty years of density-functional theory in chemical physics".
  The Journal of Chemical Physics 140(18)(18A301), 2014.
  [DOI]
• Segall, M D and Lindan, P J D and Probert, M J and Pickard, Christopher James and Hasnip, P J and Clark, S J and Payne, M C.
  "First-principles simulation:ideas, illustrations and the CASTEP code".
  Journal of Physics: Condensed Matter 14(2717–2744), 2002.
  This paper marks the development of the new CASTEP code. MDS, MJP, CJP, PJH, and SJC made equal contributions to the design and development of this code. PJDL and MCP played supervisory roles. The author list is arbitary, although PJDL contributed the text.
  [DOI]
• Argaman, Nathan and Makov, Guy.
  "Density functional theory: An introduction".
  American Journal of Physics 68(1)(69-79), 2000.
  [DOI]
• Mark E Tuckerman.
  "Ab initio molecular dynamics: basic concepts, current trends and novel applications".
  Journal of Physics: Condensed Matter 14(50)(R1297–R1355), 2002.
  [DOI]
• Capelle, Klaus.
  "A bird's-eye view of density-functional theory".
  Brazilian Journal of Physics 36(1318–1343), 2006.
  [PDF] (371 KB) [DOI]
• Rappoport, Dmitrij and Crawford, Nathan R. M. and Furche, Filipp and Burke, Kieron.
  "Approximate Density Functionals: Which Should I Choose?".
  In Encyclopedia of Inorganic Chemistry.
  American Cancer Society, 2009.
  [URL]
• Frank Jensen.
  "Introduction to Computational Chemistry, 2nd Edition".
  WILEY-V C H VERLAG GMBH, 2006.