Recent Progress In Orbital-free Density Functional Theory

Tomasz A Wesolowski, Yan Alexander Wang

• Publisher: WSPC
• Year: 2013
• Print ISBN: 9789814436724
• eBook ISBN: 9789814436748
• Topic: Physical Sciences
• Subtopic: Atomic & Molecular Physics

This is a comprehensive overview of state-of-the-art computational methods based on orbital-free formulation of density functional theory completed by the most recent developments concerning the exact properties, approximations, and interpretations of the relevant quantities in density functional theory.

The book is a compilation of contributions stemming from a series of workshops which had been taking place since 2002. It not only chronicles many of the latest developments but also summarises some of the more significant ones. The chapters are mainly reviews of sub-domains but also include original research.

Contents:

• Part 1: Density Functional for the Kinetic Energy and Its Applications in Orbital-Free DFT Simulations:
  • From the Hohenberg-Kohn Theory to the Kohn-Sham Equations (Y A Wang & P Xiang)
  • Accurate Computation of the Non-Interacting Kinetic Energy from Electron Densities (F A Bulat & W Yang)
  • The Single-Particle Kinetic Energy of Many-Fermion Systems: Transcending the Thomas-Fermi plus Von Weizsäcker Method (G G N Angilella & N H March)
  • An Orbital Free ab initio Method: Applications to Liquid Metals and Clusters (A Aguado, D J González, L E González, J M López, S Núñez & M J Stott)
  • Electronic Structure Calculations at Macroscopic Scales Using Orbital-Free DFT (B G Radhakrishnan & V Gavini)
  • Properties of Hot and Dense Matter by Orbital-Free Molecular Dynamics (F Lambert, J Clérouin, J-F Danel, L Kazandjian & S Mazevet)
  • Shell-Correction and Orbital-Free Density-Functional Methods for Finite Systems (C Yannouleas & U Landman)
  • Finite Element Approximations in Orbital-Free Density Functional Theory (H Chen & A Zhou)
• Part 2: The Functional for the Non-Additive Kinetic Energy and Its Applications in Numerical Simulations:
  • Non-Additive Kinetic Energy and Potential in Analytically Solvable Systems and Their Approximated Counterparts (T A Wesolowski & A Savin)
  • Towards the Description of Covalent Bonds in Subsystem Density-Functional Theory (Ch R Jacob & L Visscher)
  • Orbital-Free Embedding Calculations of Electronic Spectra (J Neugebauer)
  • On the Principal Difference Between the Exact and Approximate Frozen-Density Embedding Theory (O V Gritsenko)
• Part 3: Kinetic Energy Functional and Information Theory:
  • Analytic Approach and Monte Carlo Sampling for Electron Correlations (L M Ghiringhelli & L Delle Site)
  • Kinetic Energy and Fisher Information (Á Nagy)
  • Quantum Fluctuations, Dequantization, Information Theory and Kinetic-Energy Functionals (I P Hamilton, R A Mosna & L Delle Site)
• Part 4: Appendix:
  • Semilocal Approximations for the Kinetic Energy (F Tran & T A Wesolowski)

Readership: Graduate students, academics and researchers in computational chemistry. Atomic & molecular physicists, theoretical physicists, theoretical chemists, physical chemists and chemical physicists.

PART 1

Density Functional for the Kinetic Energy and Its Applications in Orbital-Free DFT Simulations

Chapter 1

From the Hohenberg-Kohn Theory to the Kohn-Sham Equations

Yan Alexander Wang* and Ping Xiang

Department of Chemistry, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1

[email protected]

Two existing ways of deriving the Kohn-Sham equations were analyzed in great details. It turns out that both are incomplete in principle because they will lead to a paradox. It was further shown that the paradox can be resolved by introducing some arbitrary constants in the total Kohn-Sham effective potential. As a result, the functional derivative of the kinetic-energy density functional of the auxiliary non-interacting system within the Kohn-Sham method can be exactly calculated only from the highest occupied Kohn-Sham orbital

where I and

are the first (lowest) ionization energy and the canonical representative of the total Kohn-Sham effective potential, respectively.

Contents

1.1 Introduction

1.2 Routes to the Kohn-Sham equations

1.3 A paradox and its resolution

1.3.1 The Wang paradox

1.3.2 The Wang-Parr resolution

1.4 Direct inclusion of the constraints

1.5 Functional derivative of the kinetic-energy density functional

1.6 Conclusions

References

1.1. Introduction

Two papers published over 45 years ago by Hohenberg, Kohn, and Sham (HKS)^{1, 2} laid the foundation for modern density-functional theory.^3–14 The two Hohenberg-Kohn (HK) theorems¹ first legitimatized the ground-state (GS) electron density ρ₀(r) as the basic variable of the GS quantum chemistry and the Kohn-Sham (KS) method² then offered a specific numerical implementation for this theory. Later, the HKS theory was recasted in the constrained-search formulation. ^{3–5, 15–20}

The first HK theorem¹ guarantees that, for an N-electron quantum chemical system, its total GS electronic energy is a functional of ρ₀(r):

where

is the GS wave function. The second HK theorem¹ insures that, for a fixed external potential v(r), any trial density ρ(r) coming from N-electron wave functions in Hilbert space (HS) corresponds to a higher energy than the GS energy:

If E_v[ρ] is differentiable in the vicinity of ρ₀(r),^{3–9, 12–14} this variational principle can be reexpressed as^{9, 14}

with the normalization condition,

According to a theorem by Gelfand and Fo...

Table of contents

• Cover
• Title Page
• Front Page
• Title Page1
• Copyright Page
• Preface
• Table of Contents
• Part 1: Density Functional for the Kinetic Energy and Its Applications in Orbital-Free DFT Simulations
• 1.   From the Hohenberg-Kohn Theory to the Kohn-Sham Equations
• 2.   Accurate Computation of the Non-Interacting Kinetic Energy from Electron Densities
• 3.   The Single-Particle Kinetic Energy of Many-Fermion Systems: Transcending the Thomas-Fermi plus Von Weizsäcker Method
• 4.   An Orbital Free ab initio Method: Applications to Liquid Metals and Clusters
• 5.   Electronic Structure Calculations at Macroscopic Scales using Orbital-Free DFT
• 6.   Properties of Hot and Dense Matter by Orbital-Free Molecular Dynamics
• 7.   Shell-Correction and Orbital-Free Density-Functional Methods for Finite Systems
• 8.   Finite Element Approximations in Orbital-Free Density Functional Theory
• Part 2: The Functional for the Non-Additive Kinetic Energy and Its Applications in Numerical Simulations
• 9.   Non-Additive Kinetic Energy and Potential in Analytically Solvable Systems and Their Approximated Counterparts
• 10.  Towards the Description of Covalent Bonds in Subsystem Density- Functional Theory
• 11.  Orbital-Free Embedding Calculations of Electronic Spectra
• 12.  On the Principal Difference Between the Exact and Approximate Frozen-Density Embedding Theory
• Part 3: Kinetic Energy Functional and Information Theory
• 13.  Analytic Approach and Monte Carlo Sampling for Electron Correlations
• 14.  Kinetic Energy and Fisher Information
• 15.  Quantum Fluctuations, Dequantization, Information Theory and Kinetic-Energy Functionals
• Part 4: Appendix
• 16.  Semilocal Approximations for the Kinetic Energy
• Author Index
• Subject Index