Details

Autor(en) / Beteiligte

• Guo, Guo-Cong
• Jiang, Xiao-Ming

Titel

Electronic Structure Crystallography and Functional Motifs of Materials

Auflage

1st ed

Ort / Verlag

Newark : John Wiley & Sons, Incorporated,

Erscheinungsjahr

2024

Beschreibungen/Notizen

• Cover -- Title Page -- Copyright -- Contents -- About the Authors -- Foreword 1 -- Foreword 2 -- Preface -- Abbreviations -- Introduction -- Chapter 1 Overview of Electronic Structure Crystallography -- 1.1 Introduction -- 1.1.1 History of Electronic Structure Crystallography -- 1.1.2 The Beginnings of X‐ray Crystallography and Quantum Mechanics -- 1.1.3 The Nascent Period of Experimental Electronic Structure Research -- 1.1.4 Developments of Pseudo‐atom Models -- 1.1.5 Developments of Experimental Electron‐density Matrix Models -- 1.1.6 Developments of Experimental Electron Wavefunction Models -- 1.1.7 Developments in Electron Diffraction‐Based Studies of Electronic Structures -- 1.2 Basic Descriptors of Electronic Structure -- 1.2.1 Electron Density -- 1.2.2 Residual Density -- 1.2.3 Deformation Density -- 1.2.4 Electron Wavefunction and Density Matrix -- 1.3 Experimental Characterization of Electronic Structure -- 1.3.1 Experimental Electronic Structure Measurement with X‐ray Single‐crystal Diffractometer -- 1.3.1.1 X‐ray Source -- 1.3.1.2 Goniometer -- 1.3.1.3 X‐ray Detector -- 1.3.1.4 Cryogenic Systems -- 1.3.2 Key Aspects of Experimental Electronic Structure Measurement -- 1.3.2.1 Single‐crystal Samples -- 1.3.2.2 Measurement Process -- 1.3.2.3 Data Correction -- 1.3.2.4 Examination of the Quality of Electronic Structure Refinement -- References -- Chapter 2 First‐Principles Calculations of the Electron Density Functions -- 2.1 Introduction -- 2.2 Basic Framework and Assumptions of the First‐Principles Calculations -- 2.3 Density Matrix and Density Function -- 2.3.1 Basic Definition -- 2.3.2 Electron Density -- 2.3.3 Momentum Density -- 2.4 Hartree-Fock (HF) and Kohn-Sham (KS) Methods -- 2.4.1 Basic Theoretical Framework -- 2.4.2 Periodic Solutions of Hartree-Fock (HF) and Kohn-Sham (KS) Equations.
• 2.4.3 Calculation of Crystal Density Matrix and Density Function -- 2.4.4 Pseudopotentials -- 2.4.5 Basis Set -- References -- Chapter 3 Topological Indices and Properties of Electronic Structures -- 3.1 Introduction -- 3.2 Analysis of Topological Atoms in Molecules -- 3.2.1 Topological Description of the Electron Density -- 3.2.2 Gradient Vector Field and Topological Atoms -- 3.2.3 Bond Path and Molecular Topological Graph -- 3.2.4 Laplacian -- 3.2.5 Topological Properties of Chemical Bonds -- 3.2.5.1 Electron Density at Bond Critical Points -- 3.2.5.2 Bond Radius and Bond Path Length -- 3.2.5.3 Laplacian of Electron Density at the Bond Critical Points -- 3.2.5.4 Ellipticity -- 3.2.5.5 Energy Density of Bond Critical Points -- 3.2.5.6 Delocalization Index and Bond Order -- 3.2.6 Topological Atomic Properties -- 3.2.6.1 Atomic Charges -- 3.2.6.2 Atomic Volume -- 3.2.6.3 Atomic Kinetic Energy -- 3.2.6.4 Laplacian -- 3.2.6.5 Total Atomic Energy -- 3.2.6.6 Atomic Dipole Moment -- 3.2.6.7 Atomic Quadrupole Moment -- 3.2.6.8 Atomic Information Entropy -- 3.3 Chemical Interaction Analysis -- 3.3.1 Source Function -- 3.3.2 Electron Localization Function -- 3.3.3 Reduced Density Gradient -- 3.4 Coarse Graining and Energy Partition of the Density Matrix -- 3.4.1 Partition of the Density Matrix in Real Space -- 3.4.2 Energy Partition -- 3.4.3 Electron Population Statistics -- 3.5 Restricted Space Partition -- 3.5.1 ω‐Restricted Partition -- 3.5.2 Restricted Electron Population Analysis -- 3.5.3 Quasi‐continuous Distribution -- 3.5.4 Electron Localization Indicators (ELI) -- 3.5.4.1 Same‐spin Electron Pairs -- 3.5.4.2 Singlet and Triplet Electron Pairs -- 3.5.4.3 ELI in Momentum Space -- 3.6 Intermolecular Interaction Energy -- 3.6.1 Interaction Energy of Experimental Electron Density -- 3.6.2 Pseudoatomic Representation of Electrostatic Interactions.
• 3.6.2.1 Multipole Expansion Approximation -- 3.6.2.2 Exact Potential and Multipole Moment (EPMM) Model -- 3.6.2.3 Promolecular Approximation -- 3.6.3 Non‐electrostatic Interactions -- 3.6.4 Lattice Energy -- 3.6.5 Interaction Energies Obtained from Experimental Charge Analysis -- References -- Chapter 4 Principles of Electronic Structure Measurement -- 4.1 Introduction -- 4.2 Thermal Vibration Analysis -- 4.2.1 Lattice Dynamics -- 4.2.2 Atomic Displacement Parameters -- 4.2.3 Rigid Fragment Analysis -- 4.2.4 Neutron Diffraction‐assisted Analysis -- 4.2.4.1 Temperature -- 4.2.4.2 Absorption -- 4.2.4.3 Extinction -- 4.2.4.4 Thermal Diffuse Scattering -- 4.2.4.5 Multiple Scattering -- 4.3 Scattering Experiments -- 4.3.1 X‐ray Diffraction -- 4.3.2 Polarized Neutron Diffraction -- 4.3.3 Compton Scattering -- 4.4 Refinement Algorithm for Experimental Electronic Structure -- 4.4.1 Least‐square Method -- 4.4.1.1 Mathematical -- 4.4.1.2 Least‐square Refinement of Structure Factors -- 4.4.1.3 Parameter‐estimated variance and covariance -- 4.4.2 Maximum Entropy Method -- References -- Chapter 5 Pseudo‐atom Models -- 5.1 Introduction -- 5.2 Independent Atom Model -- 5.3 Kappa Model -- 5.4 Multipole Model -- 5.4.1 Multipole Spherical Harmonics -- 5.4.2 Real Spherical Harmonic Density Function -- 5.4.3 Radial Distribution Functions -- 5.4.4 Multipole Model Framework -- 5.4.5 Aspheric Atomic Scattering Factors -- 5.4.6 Multipolar Model of Core Electron Expansion -- 5.5 Spin Density Model -- 5.5.1 Pure Spin Contribution -- 5.5.1.1 Atomic Orbital Model of Spin Density -- 5.5.1.2 Multipole Refinement of Spin Density -- 5.5.2 Spin and Orbital Contributions -- 5.5.3 Non‐collinear Magnetism -- 5.5.4 Combinatorial Refinement of Electron Density and Spin Density -- 5.6 Other Electron Density Models -- 5.6.1 The X‐ray Atomic Orbital (XAO) Model.
• 5.6.1.1 Atomic Single‐electron Orbitals in a Crystal Field -- 5.6.1.2 Electron Density and Structure Factor -- 5.6.2 X‐ray Molecular Orbital Model (XMO) -- 5.6.2.1 Molecular Orbital and Electron Density -- 5.6.2.2 Structure Factors for Monocentric and Bicentric Terms -- 5.6.2.3 Processing of Temperature Factors -- 5.6.3 Molecular Orbitals with Variable Occupation Numbers Model (MOON) -- References -- Chapter 6 Density Matrix Model -- 6.1 Introduction -- 6.2 Density Matrix Model -- 6.2.1 Definition of the Density Matrix -- 6.2.2 Localized Model of the Density Matrix -- 6.3 Correlation of Density Matrix to Scattering Experiments -- 6.3.1 Dynamic Scattering Factor -- 6.3.2 Static Structure Factor -- 6.3.3 Elastic Scattering -- 6.3.4 Inelastic Scattering -- 6.4 Reconstruction and Refinement of the Density Matrix -- 6.4.1 Bayesian Method -- 6.4.2 Combined Refinement of Different Types of Data -- 6.4.3 Refinement of the One‐electron Reduced Density Matrix (1‐RDM) -- 6.4.4 Combinatorial Refinement of Structure Factor and Compton Profile Data -- 6.4.5 Spin‐resolved One‐order Reduced Density Matrix (1‐SRDM) Refinement -- 6.4.5.1 Basic Framework -- 6.4.5.2 Molecular Modeling -- 6.4.5.3 Magnetic Structure Factor and Magnetic Compton Profile -- 6.4.5.4 Variation of the Basis Functions -- 6.4.5.5 Variation of Spin Population Matrices -- References -- Chapter 7 Electron Wavefunction Models -- 7.1 Introduction -- 7.2 X‐ray Constrained Wavefunction (XCW) Model -- 7.2.1 Mathematical Framework -- 7.2.2 Hirshfeld Atom Refinement -- 7.2.2.1 Selection of Wavefunction -- 7.2.2.2 Electron Density -- 7.2.2.3 Hirshfeld Atomic Partitioning Method -- 7.2.2.4 Calculation of the Structure Factor -- 7.2.3 X‐ray Constrained Wavefunction Refinement -- 7.2.3.1 Special Treatment for Thermal Vibrations -- 7.2.3.2 Density Matrix Representation of Structure Factor.
• 7.2.3.3 Experimental Constrained Wavefunction Refinement -- 7.2.4 Open Shell System Method -- 7.2.5 Treatment of Relativistic Effects -- 7.3 The X‐ray‐Constrained Extremely Localized Molecular Orbital Method -- 7.3.1 Theoretical Extremely Localized Molecular Orbitals -- 7.3.2 Refinement of the Experimentally Constrained Extremely Localized Molecular Orbitals -- References -- Chapter 8 Functional Electronic Structures and Functional Motif of Materials -- 8.1 Introduction -- 8.2 Material Functional Motif -- 8.2.1 Crystal Structure -- 8.2.2 Electronic Structure -- 8.2.3 Magnetic Structure -- 8.2.4 Modulated Defects -- 8.2.5 Statistical Defects -- 8.2.6 Local Defects -- 8.3 Functional Electronic Structures -- References -- Index -- EULA.
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