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E-grāmata: Relativistic Methods for Chemists

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Relativistic Methods for Chemists, written by a highly qualified team of authors, is targeted at both experimentalists and theoreticians interested in the area of relativistic effects in atomic and molecular systems and processes and in their consequences for the interpretation of the heavy element's chemistry.

The theoretical part of the book focuses on the relativistic methods for molecular calculations discussing problems such as relativistic two-component theory, density functional theory, pseudopotentials and correlations. These chapters are mostly addressed to experimentalists with only general background in theory an to the computational chemists without training in relativistic methods. Teh experimentally oriented chapters describe the use of relativistic methods in different applications focusing on the design of new materials based on heavy element compounds, the role of the spin-orbit coupling in photochemistry and photobiology, and its relations to relativistic description of matter and radiation. This part of the book includes subjects of interest to theoreticians and experimentalists working in different areas of chemistry.

Relativistic Methods for Chemistis is written at an intermediate level in order to appeal to a broader audience than just experts working in the field of relativistic theory, The book is alimeded at individuals not highly versed in these methods who want to acquire theh rudiments of relativistic computing and the associated problems of importance for the heavy element chemistry.

Relativistic Methods for Chemists is written for graduates students, academics, and researchers in theeoretical chemistry as well as experimentalists in materiasl chemistry, inorganic chemistry, and physical chemistry.

1 An Introduction to Relativistic Quantum Chemistry
1(62)
W.H. Eugen Schwarz
1.1 Motivation
2(10)
1.1 Quantization
3(1)
1.1.2 Relativity
4(1)
1.1.3 Relativistic Q3uantum Field Theory for Electrons
5(1)
1.1.4 Quantum Chemistry
6(1)
1.1.5 Relativistic Quantum Chemistry
7(5)
1.1.6 Units and Numbers
12(1)
1.2 From Three Basic Concepts to the Dirac Equation
12(14)
1.2.1 Principle of Invariance: The Lorentz Transformation
12(2)
1.2.2 Reelativity and the Natural Laws for Mechanics and Electrodynamics
14(3)
1.2.3 Relativistic and Non-relativistic Wave Equations
17(1)
1.2.4 The Natural Occurrence of Spin
18(4)
1.2.5 Picture Changes
22(3)
1.2.6 Summary
25(1)
1.3 Dirac Solutions for Hydrogen and Other Atoms
26(21)
1.3..1 Relativistic Orbital Energies of the Simplified H-Atom Model
27(1)
1.3.2 Relativistici Atomic Spinors
28(3)
1.3.3 Relativistic Changes of Orbital Radii
31(1)
1.3.4 Paradoxical Relations
31(3)
1.3.5 Orpitals in Many-Electron Atoms: Small Angular Momenta
34(6)
1.3.6 Orbitals in Many Electron Atoms: Higher Angular Momenta
40(2)
1.3.7 Orbitals in Many-Electron Atoms: The p3/2 Valence Orbital
42(1)
1.3.8 The Relativistic Two-Electron Interaction
43(2)
1.3.9 Smaller Effects: Nuclear Size, QED and Weak Interaction
45(2)
1.4 Relativistic Changes of Molecules
47(11)
1.4.1 Always Two Different Relativistic Contributions
49(2)
1.4.2 Multiple Perturbation Theory
51(2)
1.4.3 Atomic Spionors and Molecular Quaternions
53(2)
1.4.4 The Periodic System of Elements and its Natural End
55(3)
Acknowledgements
58(1)
References
58(5)
2 Relativistic Effects and the Chemistry of the Heavier Main Group Elements
63(36)
John S. Thayer
2.1 Background
63(3)
2.1.1 Introduction to Relativistic Effects
63(2)
2.1.2 Intraatomic Changes
65(1)
2.1.3 Chemical Effects
66(1)
2.2 Sixth Period Elements
66(14)
2.2.1 s-Block Elements
66(1)
2.2.2 d-Block Elements
67(5)
2.2.3 p-Block Elements
72(8)
2.3 Seventh and Eighth Period Elements
80(4)
2.3.1 General
80(1)
2.3.2 s-Block Elements
81(1)
2.3.3 Superheavy Elements
81(3)
2.4 Conclusions
84(1)
Acknowledgments
85(1)
References
85(14)
3 Why do we Need Relativistic Computational Methods?
99(66)
Jacek Styszynski
3.1 Introduction
99(2)
3.2 Energetic Sturcture and Spectroscopic Constants
101(50)
3.2.1 Diatomic Molecules
101(46)
3.2.2 Polyatomic Molecules
147(4)
3.3 Electric Properties of Molecules
151(7)
3.3.1 Electric Properties of Interhalogens
152(2)
3.3.2 Electric Field Gradient and Quadrupole Moments
154(4)
3.4 Conclusions
158(1)
Appendix
159(3)
References
162(3)
4 Two-Component Relativistic Theories
165(26)
Maria Barysz
4.1 Introduction
165(4)
4.2 The Two-Component Methodology
169(17)
4.2.1 Elimination of the Small Component and the Pauli Expansion
169(2)
4.2.2 Regular Approximations (RA)
171(1)
4.2.3 Unitary Transformations of the Dirac Hamiltonian
172(4)
4.2.4 Infinite Order Two-Component (IOTC) Method
176(10)
4.3 Interactions
186(2)
4.4 Summary and Conclusion
188(1)
Acknowledgments
189(1)
References
189(2)
5 Relativistic Density Functional Theory
191(24)
Christoph van Wiillen
5.1 Nonrelativistic Density Functional Theory Basics
191(3)
5.2 Relativistic Extension of DFT
194(4)
5.3 Relativistic Spin Density Functional Theory: Collinear and Noncollinear Approximation
198(3)
5.4 Relativistic Exchange-Correlation Functionals
201(3)
5.5 Dirac-Kohn-Sham Implemetations
204(1)
5.6 Quasirelativistic Methods
205(4)
5.7 The Presence, and the Future
209(1)
References
210(5)
6 Relativistic Pseudopotentials
215(64)
Xiaoyan Cao
Michael Dolg
6.1 Introduction
215(2)
6.2 Theoretical Considerations
217(10)
6.2.1 Phillips-Kleinman Equation
217(3)
6.2.2 Valence Electron Model Hamiltonian for an Atom
220(1)
6.2.3 Analytical Form of Non-relativistic Pseudopotentials
221(2)
6.2.4 Analytical Form of Scalar-Relativistic Pseudopotentials
223(1)
6.2.5 Analytical Form of Relativistic Pseudopotentials
223(2)
6.2.6 Molecular Pseudopotentials
225(1)
6.2.7 Core-Polarization Potentials
225(2)
6.2.8 Core-Core/Nucleus Repulsion Corrections
227(1)
6.3 Energy-Consistent Pseudopotentials
227(10)
6.3.1 Some Historical Aspects
228(2)
6.3.2 Method of Parametrization
230(3)
6.3.3 Availability of Pseudopotentials and Valence Basic Sets
233(4)
6.4 Other Effective Core Potential Methods
237(7)
6.4.1 Shape-Consistent Pseudopotentials
237(2)
6.4.2 Model Potential Method
239(3)
6.4.3 DFT-Based Effective Core Potentials
242(2)
6.5 Example: Uranium
244(25)
6.5.1 Choice of the Reference Data
245(2)
6.5.2 Choice of the Core
247(5)
6.5.3 Pseudopotential Adjustment
252(9)
6.5.4 Valence Basis Set Optimization
261(1)
6.5.5 Calibration and Application
262(7)
6.6 Conclusions
269(1)
Acknowledgements
270(1)
References
270(9)
7 Four-Component Electronic Structure Methods
279(72)
Ephraim Eliav
Uzi Kaldor
7.1 Introduction
279(1)
7.2 Four-Component Methodology
280(22)
7.2.1 Dirac Equation - Historical Overview
280(4)
7.2.2 QED Hamiltonian
284(6)
7.2.3 Particle-Particle Interaction and the No-Virtual-Pair approximation
290(6)
7.2.4 The NVPA Hamiltonian and Benchmarking of Four-Component Methods
296(3)
7.2.5 Standard Four-Component SCF Procedure for Atoms and Molecules
299(3)
7.3 The NVPA Multi-Root Multi-Reference Fock-Space Coupled Cluster Method
302(9)
7.3.1 Basic FSCC Method
302(3)
7.3.2 The Intermediate Hamiltonian CC Method
305(6)
7.4 Applications: Heavy Elements
311(9)
7.4.1 When is an Atom "Heavy"? Ionization Potentials of Alkali Atoms
312(1)
7.4.2 Gold Atom: Local Maximum of Relativistic Effects
313(1)
7.4.3 The f2 Levels of Pr3+ : Importance of Dynamic Correlation
314(1)
7.4.4 Electron Affinities of Alkali Atoms - Accuracy at the 1 me V Level
315(2)
7.4.5 Electron Afinities in Group 13
317(1)
7.4.6 Properties Other Than Energy: Nuclear Quadrupole Moments
318(2)
7.5 Applications: Superheavy Elements
320(13)
7.5.1 Ground State Configuration of Roentgenium (Elll)
320(2)
7.5.2 Ground State of Rutherfordium - Relativity vs. Correlation
322(1)
7.5.3 Eka-Lead (Element 114) - How Inert is it?
323(4)
7.5.4 Electronic Spectrum of Nobelium (Z = 102) and Lawrencium (Z = 103)
327(3)
7.5.5 Can a Rare Gas Atom Bind an Electron?
330(1)
7.5.6 Adsorption of Superheavy Atoms on Surfaces-Identifying and Characterizing New Elements
331(2)
7.6 Directions for Future Development
333(8)
7.6.1 Beyond Standard Four-Component Hartree-Fock Method: the QED-SCF Procedure
333(2)
7.6.2 Beyond NVPA: QED Many-Body Description and the Covariant Evolution Operator Approach
335(3)
7.6.3 Generalized Fock Space. Double Fock-Space CC
338(3)
7.7 Summary and Conclusion
341(1)
Acknowledgments
342(1)
References
342(9)
8 The Effects of Relativity in Materials Science: Core Electron Spectra
351(22)
R. Broer
8.1 Intoduction
351(3)
8.2 Computational Methods
354(4)
8.3 X-Ray Photoelectron Spectra
358(5)
8.4 X-Ray Absorption and Electron Energy Loss Spectra
363(6)
8.5 Summary
369(1)
Acknowledgments
370(1)
References
370(3)
9 Relativistic Symmetries in the Electronic Structure and Properties of Molecules
373(34)
Devashis Majumdar
Szczepan Roszak
Jerzy Lesczynski
9.1 Introduction
375(1)
9.2 Spin-Orbit Interaction and Double Group
375(2)
9.3 Double Groups and Relativistici Treatment of Molecules
377(6)
9.3.1 Diatomic Systems
377(3)
9.3.2 Polyatomic Systems
380(3)
9.4 Applications of Double Group Symmetry in Calculating Molecular Properties
383(12)
9.4.1 Diatomics
383(6)
9.4.2 Polyatomic Systems
389(6)
9.5 Time Reversal
395(5)
9.5.1 Parity
395(2)
9.5.2 Charge Conjugation
397(1)
9.5.3 CPT Theorem and Concept of Time Reversal
397(1)
9.5.4 Properties of T and its Implication in Molecular Properties
398(1)
9.5.5 Time Reversal in Group Theory
399(1)
9.6 Concluding Remarks
400(1)
Acknowledgements
401(1)
Appendix
401(2)
References
403(4)
10 Relativistic Sring-Based Electron Correlation Methods
407(44)
Timo Fleig
10.1 Introduction
407(2)
10.2 General Principles
409(7)
10.2.1 Time-Reversal Symmetry
409(1)
10.2.2 Kramers-Paired Spinors
410(2)
10.2.3 Integrals Over Kramers-Paired Spinors
412(1)
10.2.4 Double Group Symmetry
413(1)
10.2.5 Generalized Active Spaces
414(2)
10.3 Many-Particle Wavefunctions
416(3)
10.3.1 Spinor Strings
416(2)
10.3.2 Relativistic Excitation Classes
418(1)
10.4 Wavefunction-Based Electron Correlation Methods
419(19)
10.4.1 Hamiltonian Operators
419(4)
10.4.2 Configuration Interaction
423(6)
10.4.3 Multi-Configuration SCF
429(4)
10.4.4 Coupled Cluster
433(5)
10.5 Sample Applications
438(5)
10.5.1 Tl2 Ground and Excited States
438(2)
10.5.2 Br2/2+
440(1)
10.5.3 I3 and I3
441(2)
10.6 Concluding Remarks
443(1)
Acknowledgements
444(1)
References
445(6)
11 Electronic Structure and Chemistry of the Heaviest Elements
451(70)
V. Pershina
11.1 Introduction
451(1)
11.2 Production and Identification of the Heaviest Elements
452(3)
11.3 Experimentla Chemical Studies
455(3)
11.3.1 Gas-Phase Chemistry
456(1)
11.3.2 Liquid-Phase Chemistry
457(1)
11.4 Theoretical Studies
458(3)
11.4.1 Role of Theoretical Studies
458(1)
11.4.2 Relativistic and QED Effects on Atomic Electronic Shells of the Heaviest Elements
458(3)
11.5 Relativistic Quantum Chemical Methods
461(6)
11.5.1 Atomic Codes
462(1)
11.5.2 Moledcular Methods
463(4)
11.6 Atomic Properties of the Heaviest Elements and Relativistic Effects
467(6)
11.6.1 Electronic Configurations
467(1)
11.6.2 Ionization Potentials, Electron Affinities and Stable Oxidation States
468(3)
11.6.3 Atomic/Ionic/Covalent Radii and Polarizability
471(2)
11.7 GAS-Phase Chemistry
473(34)
11.7.1 Rf Through HS
473(7)
11.7.2 Rg
480(2)
11.7.3 Element 112
482(11)
11.7.4 Element 113
493(3)
11.7.5 Element 114
496(7)
11.7.6 Element 115-118
503(1)
11.7.7 Elements with Z > 118
503(4)
11.7.8 Summary of Predictions of Volatility of the Heaviest Elements and Their Compounds
507(1)
11.8 Aqueous Chemistry
507(5)
11.8.1 Redox Potentials and Reduction Experiments
507(1)
11.8.2 Complex Formation and Extraction by Liquid Chromatography
508(3)
11.8.3 Summary of Predictions of the Complex Formation
511(1)
11.9 Summary and Outlook
512(1)
Acknowledgements
513(1)
Refernces
513(8)
12 Relativistic Effects on Magnetic Resonance Parameters and Other Properties of Inorganic Molecules and Metal Complexes
521(78)
Jachen Autschbach
12.1 Introduction
521(2)
12.2 Computing Molecular Properties
523(37)
12.2.1 Relativistic Methods in Quantum Chemistry
525(7)
12.2.2 Molecular Response Properties: A Brief Survey. Energy and Quasi-Energy Perturbations
532(7)
12.2.3 Resonance: Computation of Excitation Spectra
539(3)
12.2.4 Examples of Response Properties
542(1)
12.2.5 Perturbation Operators
543(11)
12.2.6 Hyperfine Operators: from Four to Two to One Component and the Nonrelativistic Limit
554(3)
12.2.7 Where in the Molecule Do the Properties "Originate" from?
557(3)
12.3 Benchmark Data and Case Studies
560(30)
12.3.1 NMR Parameters
561(12)
12.3.2 Electron Paramagnetic Resonance
573(7)
12.3.3 Electric Field Gradients (EFGs)
580(4)
12.3.4 Dipole Moments, Polarizabilities, and Linear-Response Based Computations of Excitation Energies
584(6)
12.4 Concluding Remarks
590(1)
Acknowledgements
591(1)
References
591(8)
Index 599