Electronic Structure Methods for Complex Materials

The orthogonalized linear combination of atomic orbitals

WAI-YIM CHING and PAUL RULIS University of Missouri-Kansas City, USA

OXFORD UNIVERSITY PRESS

Contents

1 Electronic Structure Methods in Materials Theory i 1.1 Introduction 1 1.2 One electron methods 2 1.3 Quantum chemical approaches and solid state methods 3 1.4 The OLCAO method 3

2 Historical Account of the LCAO Method 6 2.1 Early days of the band theory of solids 6 2.2 Origin of the LCAO method 7 2.3 Use of Gaussian orbitals in LCAO calculations 8 2.4 Beginning of the OLCAO method 10 2.5 Current status and future trends of the OLCAO method 11

3 Basic Theory and Techniques of the OLCAO Method 14 3.1 The atomic basis functions 14 3.2 Bloch functions and the Kohn-Sham equation 18 3.3 The site-decomposed potential function 21 3.4 The technique of Gaussian transformation 24 3.5 The technique of core orthogonalization 28 3.6 Brillouin zone integration 31 3.7 Special advantages in the OLCAO method 32

4 Calculation of Physical Properties Using the OLCAO Method 35 4.1 Band structure and band gap 35 4.2 Density of states and its partial components 37 4.3 Effective charges, bond order, and the localization index 38 4.4 Spin-polarized band structures 40 4.5 Scalar relativistic corrections and spin-orbit coupling 41 4.6 Magnetic properties 44 4.7 Linear optical properties and dielectric functions 45 4.8 Conductivity function in metals 47 4.9 Non-linear optical properties of insulators 49

4.10 Bulk properties and geometry optimization 50

Contents

5 Application to Semiconductors and Insulators 5.1 Elemental and binary semiconductors

5.2 Binary insulators

5.3 Oxides

5.3.1 Binary oxides 5.3.2 Ternary oxides 5.3.3 Laser host crystals 5.3.4 Quaternary oxides and other complex oxides

5.4 Nitrides 5.4.1 Binary nitrides 5.4.2 Spinel nitrides 5.4.3 Ternary and quaternary nitrides and oxynitrides 5.4.4 Other complex nitrides

5.5 Carbides

5.5.1 SiC 5.5.2 Other carbides

5.6 Boron and boron compounds 5.6.1 Elemental boron 5.6.2 B4C 5.6.3 Other boron compounds 5.6.4 Other forms of complex boron compounds

5.7 Phosphates

5.7.1 Simple phosphates: AIPO4 5.7.2 Complex phosphates: KTP 5.7.3 Lithium iron phosphate: LiFeP04

6 Application to Crystalline Metals and Alloys 6.1 Elemental metals and alloys

6.1.1 Elemental metals 6.1.2 Fe borides 6.1.3 Fe nitrides 6.1.4 Yttrium iron garnet

6.2 Permanent hard magnets 6.2.1 Application to R^Fe^B crystals 6.2.2 Further applications to Nd2Fej4B 6.2.3 Application to Re2Fe|7 and related phases

6.3 High T c superconductors 6.3.1 YBCO superconductor 6.3.2 Other oxide superconductors 6.3.3 Non-oxide superconductors

6.4 Other recent studies on metals and alloys 6.4.1 Mo-Si-B alloys 6.4.2 MAX phases

7 Application to Complex Crystals 7.1 Carbon-related systems

7.1.1 Bucky-ball (Cgo) and alkali-doped C60 crystals 7.1.2 Negative curvature graphitic carbon structures

Contents

Graphene, graphite, and carbon nanotubes

7.2.1 Graphene and graphite

7.2.2 Carbon nanotubes

Polymeric crystals

Organic crystals

7.4.1 Organic superconductors 7.4.2 Fe-TCNE

7.4.3 Herapathite crystal

Bioceramic crystals 7.5.1 Calcium apatite crystals 7.5.2 a- and ß-tricalcium phosphate

8 Application to Non-Crystalline Solids a Liquids 8.1 Amorphous Si and a-SiÜ2

8.1.1 Amorphous Si and hydrogenated a-Si 8.1.2 Amorphous SiC>2 and a-SiOx glasses 8.1.3 Other glassy systems

8.2 Metallic glasses 8.2.1 CuxZri_x metallic glass 8.2.2 Other metallic glasses 8.2.3 Transport properties in metallic glasses 8.2.4 Recent efforts on metallic glasses

8.3 Intergranular glassy films

8.3.1 The basal model 8.3.2 The prismatic model 8.3.3 Prismatic-basal model (Yoshiya model)

8.4 Model of bulk water

8.5 Models for molten salts: NaCl and KCl

8.6 Models for concrete

9 Application to Impurities, Defects, and Surfaces 9.1 Isolated vacancies and substitutional impurities

9.1.1 Isolated vacancies 9.1.2 Single impurities or dopants

9.2 Vacancies and impurities in MgAl2Ü4 (spinel) 9.2.1 Strategy 9.2.2 Effect of inversion

9.2.3 Effect of isolated vacancies 9.2.4 Effect of Fe substitution

9.3 Impurity vacancy complexes

9.4 Grain boundary models 9.4.1 Grain boundaries in 1X-AI2O3 9.4.2 Passive defects 9.4.3 Grain boundary in SrTi03

9.5 Surfaces

9.6 Interfaces

7.2

7.3 7.4

7.5

Contents

10 Application to Biomolecular Systems 10.1 Vitamin B12 cobalamins

10.2 b-DNA modeis

10.3 Collagen modeis

10.4 Other biomolecular systems

11 Application to Core Level Spectroscopy 11.1 Basic principles of the supercell OLCAO method

11.2 Select examples 11.2.1 Simple crystals 11.2.2 Complex crystals 11.2.3 Y-K edge in different local environments 11.2.4 Boron and boron-rich compounds 11.2.5 Substitutional defects in crystals 11.2.6 Biomolecular systems 11.2.7 Application to grain boundaries and surfaces 11.2.8 Application to intergranular glassy films 11.2.9 Statistical description of O-K edges in bulk water

11.3 Spectral imaging 11.3.1 Introduction 11.3.2 Procedures for SI 11.3.3 Application to a Si defect model

11.4 Further development of the supercell OLCAO method

12 Enhancement and Extension of the OLCAO Method 12.1 Versatility

12.1.1 The OLCAO basis set 12.1.2 The OLCAO potential and charge density representation 12.1.3 Relativistic OLCAO 12.1.4 Exchange-correlation functionals 12.1.5 Magnetism and non-collinear spin polarization 12.1.6 Configuration interaction 12.1.7 Hamaker constants and long-range van der Waals-London

interaction

12.2 Efficiency 12.2.1 The memory hierarchy 12.2.2 Modularization 12.2.3 Parallelization

12.3 Ease of use 12.3.1 User interface and control 12.3.2 Interaction with third party software 12.3.3 Data visualization

Appendices A. Database for Atomic Basis Functions

B. Database for Initial Atomic Potential Functions

Contents XIII

C. Current Implementation of the OLCAO Suite 270 C.l Introduction 270 C.2 Input generation 271 C.3 Program execution 282 C.4 Results analysis 295

D. Examples of Computational Statistics 297

Index 301