Recent progress in orbital-free density functional theory / edited by Tomasz A. Wesolowski & Yan Alexander Wang.

Format:

Book

Contributor:

Wesolowski, Tomasz A.

Wang, Yan Alexander.

Series:

Recent Advances In Computational Chemistry

Recent advances in computational chemistry ; vol. 6

Language:

English

Subjects (All):

Computational biology.

Molecular biology.

Physical Description:

1 online resource (464 pages)

Edition:

1st ed.

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific Pub., c2013.

New Jersey : World Scientific, [2013]

Language Note:

English

Summary:

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 or

Contents:

Intro

Contents

Preface

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 Y. A. Wang &amp

P. Xiang

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

Acknowledgement

References

2. Accurate Computation of the Non-Interacting Kinetic Energy from Electron Densities F. A. Bulat &amp

W. Yang

2.1. Introduction

2.2. Theory

2.2.1. Direct optimization method for the Kohn-Sham kinetic energy functional Ts and the exact exchange-correlation potential vxc

2.2.2. Exchange vx and correlation vc components of the exchange-correlation potential vxc

2.3. Regularization of the WY functional

2.4. Results and discussion

2.4.1. Exchange-correlation vxc(r) potentials

2.4.2. Kohn-Sham kinetic energy

2.4.3. Exchange vx(r) and correlation vc(r) potentials

2.5. Conclusions

Acknowledgements

3. The Single-Particle Kinetic Energy of Many-Fermion Systems: Transcending the Thomas-Fermi plus Von Weizs¨acker Method G. G. N. Angilella &amp

N. H. March

3.1. Background and outline

3.2. Fermions in surface regimes: nuclei and simple liquid metals

3.2.1. The nucleon surface density

3.2.2. Brief background on surface energies

3.2.2.1. Nucleon surface energies

3.2.2.2. Application to a liquid metal planar surface

3.3. Variational principle for the TF plus von Weizsacker (TFvW) method

3.4. Differential virial theorem and the Dirac density matrix

3.4.1. Relation of the exact DVT to the semiclassical Thomas-Fermi method.

3.5. Perturbative expansion of Dirac density matrix (r, r') in powers of the given one-body potential V (r)

3.5.1. Stoddart-March series for the kinetic energy density t(r) in three dimensions

3.6. Complete DFT for harmonically confined Fermions in D dimensions, for an arbitrary number of closed shells

3.6.1. Current experimental focus on many Fermions that are harmonically confined

3.6.2. Differential equation for Fermion density

3.6.3. Kinetic energy density functional t[ ] for arbitrary number of Fermions moving independently in one-dimensional harmonic oscillator potential

3.6.4. Summary of complete DFT for many closed shells of Fermions which are (isotropically) harmonically confined in D dimensions

3.7. The Pauli potential in relation to the functional derivative of the single-particle kinetic energy density

3.7.1. Relation to the differential virial theorem

3.7.2. Example of harmonic confinement

3.8. Non-local potential theory: V (r) V (r, r')

3.8.1. Fine-tuning of Hartree-Fock (HF) density for spherical atoms like neon

3.8.2. Scaling approach to obtain a correlated density (r) from HF densities for Ne and Ar

3.9. Summary and directions for future studies

A.1. Exact correlated kinetic energy related to Fermion density in model two-electron atom with harmonic confinement and arbitrary interparticle interaction

A.1.1. Correlated relative motion kinetic energy density, in terms of relative motion wave function R(r)

A.1.2. Some specific results for correlated kinetic energy of model two-electron ground states

A.1.2.1. The Hookean atom with Vext = 1 8 r2 and u(r12) = e2/r12

A.2. Transcending the von Weizsacker single-particle kinetic energy in an artificial two-electron atom

References.

4. An Orbital Free ab initio Method: Applications to Liquid Metals and Clusters A. Aguado, D. J. Gonzalez, L. E. Gonzalez, J. M. Lopez, S. Nunez &amp

M. J. Stott

4.1 Introduction

4.2 Theory

4.2.1 Kohn-Sham approach

4.2.2. Orbital free approach

4.2.2.1. The kinetic energy functional

4.2.2.2. Known limiting cases

4.2.2.3. Approximate functionals

4.2.3. Pseudopotentials

4.2.3.1. Local pseudopotentials

4.2.4. Future prospects

4.3. OF-AIMD simulation of liquid metal systems

4.3.1. Bulk liquid simple metals and alloys

4.3.1.1. Dynamic properties of liquids

4.3.2. Liquid Mg

4.3.3. Liquid Ga

4.3.4. Liquid Si

4.3.5. Liquid Ga-In

4.4. OF-AIMD studies of the liquid-vapor interface in simple liquid metallic systems

4.4.1. Liquid Ga

4.4.2. Liquid In

4.4.3. Liquid Ga-In

4.5. OF-AIMD studies of solid-liquid interfaces

4.5.1. Surface relaxation and its temperature variation. Al(110) and Mg(1010)

4.5.1.1. Al(110)

4.5.1.2. Mg(1010)

4.5.2. Liquid Al on pinned solid Al

4.5.3. Liquid Li on solid Ca

4.6. OF-AIMD study of the melting-like transition in alkali clusters

4.6.1. Background

4.6.2. Analysis of the molecular dynamics

4.6.3. OF-AIMD simulations of melting in Na clusters

4.6.3.1. Irregular variation of the melting point in a broad size range

4.6.3.2. Variation of the melting point in a narrow size range: N = 135 - 147

4.6.3.3. Small sodium clusters that melt gradually: melting mechanisms

4.7. Conclusion

Appendix A. The kinetic energy functional

Appendix B. Position-dependent chemical potential

5. Electronic Structure Calculations at Macroscopic Scales using Orbital-Free DFT B. G. Radhakrishnan &amp

V. Gavini

5.1. Introduction

5.2. Overview of quasi-continuum orbital-free density functional theory.

5.2.1. Real-space formulation of OFDFT

5.2.2. Finite-element discretization

5.2.3. Quasi-continuum reduction

5.3. Vacancies in aluminum

5.4. Outlook

6. Properties of Hot and Dense Matter by Orbital-Free Molecular Dynamics F. Lambert, J. Clerouin, J.-F. Danel, L. Kazandjian &amp

S. Mazevet

6.1. Introduction

6.2. What kind of matter are we dealing with?

6.3. From quantum to orbital-free molecular dynamics

6.3.1. Quantum molecular dynamics

6.3.1.1. Kohn-Sham scheme

6.3.1.2. Pseudo-potential and the problem of delocalization

6.3.2. Orbital-free molecular dynamics

6.4. Numerical features of the orbital-free treatment

6.4.1. Description of the energy contributions

6.4.2. Free energy minimization

6.4.3. Parallelization

6.4.4. Regularization of the electron-nucleus interaction

6.4.4.1. Orbital-free average atom model

6.4.4.2. Regularization of the Coulomb potential

6.4.4.3. Convergence with the cut-off radius

6.4.4.4. Other convergence issues

6.5. Thermodynamics: towards high-density plasmas

6.6. Structural and dynamic properties: the quest for ionization

6.6.1. Ionization choice

6.6.2. Comparison of results

6.7. Inside the mixture: the plasma as a soup of electrons and nuclei

6.7.1. Eos mixing rule

6.7.2. Transport coefficients and partial ionization

6.8. Conclusion

Acknowledgments

7. Shell-Correction and Orbital-Free Density-Functional Methods for Finite Systems C. Yannouleas &amp

U. Landman

7.1. Introduction

7.1.1. Preamble

7.1.2. Motivation for finite systems

7.1.3. Plan of the chapter

7.2. Methodology and derivation of microscopic DFT-SCM

7.2.1. Historical review of SCM

7.2.2. DFT-SCM

7.3. Applications of DFT-SCM

7.3.1. Metal clusters

7.3.1.1. Charging of metal clusters.

7.3.1.2. Electron affinities and borders of stability

7.3.1.3. Critical sizes for potassium and aluminum

7.3.1.4. Metastability against electron autodetachment

7.3.2. Neutral and multiply charged fullerenes

7.3.2.1. Stabilized jellium approximation - The generalized DFT-SCM

7.3.2.2. ETF electron-density profile

7.3.2.3. Shell correction and icosahedral splitting

7.3.2.4. Ionization potentials and electron affinities

7.3.2.5. Charging energies and capacitance of fullerenes

7.3.2.6. Lifetimes of metastable anions, C x- 60

7.3.3. On mesoscopic forces and quantized conductance in model metallic nanowires

7.3.3.1. Background and motivation

7.3.3.2. The jellium model for metallic nanowires: Theoretical method and results

7.4. Summary

Appendix A. Semiempirical shell-correction method (SE-SCM)

A.1. Semiempirical shell-correction method for triaxially deformed clusters

A.1.1. Liquid-drop model for neutral and charged deformed clusters

A.1.2. The modified Nilsson potential

A.1.3. Averaging of single-particle spectra and semi-empirical shell correction

A.1.4. Overall procedure

A.2. Applications of SE-SCM to metal clusters

8. Finite Element Approximations in Orbital-Free Density Functional Theory H. Chen &amp

A. Zhou

8.1. Introduction

8.2. Finite element discretizations for linear eigenvalue problems

8.2.1. Standard finite element discretization

8.2.2. Multi-scale based finite element discretizations

8.3. Finite element approximations of TF-HK equation

8.3.1. SCF iteration for TF-HK equation

8.3.2. Adaptive finite element calculation

8.4. Finite element methods for direct minimization

8.5. Numerical examples

Part 2: The Functional for the Non-Additive Kinetic Energy and Its Applications in Numerical Simulations.

Notes:

Description based on publisher supplied metadata and other sources.

Includes bibliographical references and index.

Description based upon print version of record.

Other Format:

Print version: Wang, Yan Alexander Recent Progress In Orbital-free Density Functional Theory

ISBN:

9789814436731

9814436739

OCLC:

842882091