| Description |
1 online resource (243 pages) |
| Contents |
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 |
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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 |
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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 |
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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 |
| Notes |
Description based on publisher supplied metadata and other sources |
| Form |
Electronic book
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| Author |
Jiang, Xiao-Ming
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| ISBN |
3527842330 |
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9783527842339 |
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3527842314 |
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9783527842315 |
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