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E-grāmata: Relativistic Electronic Structure Theory: Part 2. Applications

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The field of relativistic electronic structure theory is generally not part of theoretical chemistry education, and is therefore not covered in most quantum chemistry textbooks. This is due to the fact that only in the last two decades have we learned about the importance of relativistic effects in the chemistry of heavy and superheavy elements. Developments in computer hardware together with sophisticated computer algorithms make it now possible to perform four-component relativistic calculations for larger molecules. Two-component and scalar all-electron relativistic schemes are also becoming part of standard ab-initio and density functional program packages for molecules and the solid state. The second volume of this two-part book series is therefore devoted to applications in this area of quantum chemistry and physics of atoms, molecules and the solid state. Part 1 was devoted to fundamental aspects of relativistic electronic structure theory whereas Part 2 covers more of the applications side. This volume opens with a section on the Chemistry of the Superheavy Elements and contains chapters dealing with Accurate Relativistic Fock-Space Calculations for Many-Electron Atoms, Accurate Relativistic Calculations Including QED, Parity-Violation Effects in Molecules, Accurate Determination of Electric Field Gradients for Heavy Atoms and Molecules, Two-Component Relativistic Effective Core Potential Calculations for Molecules, Relativistic Ab-Initio Model Potential Calculations for Molecules and Embedded Clusters, Relativistic Pseudopotential Calculations for Electronic Excited States, Relativistic Effects on NMR Chemical Shifts, Relativistic Density Functional Calculations on Small Molecules, Quantum Chemistry with the Douglas-Kroll-Hess Approach to Relativistic Density Functional Theory, and Relativistic Solid State Calculations.

- Comprehensive publication which focuses on new developments in relativistic quantum electronic structure theory
- Many leaders from the field of theoretical chemistry have contributed to the TCC series
- Will no doubt become a standard text for scientists in this field.

Recenzijas

"Together, these two volumes give both deep and broad coverage of the field of relativistic electronic structure theory." --Russell M. Pitzer. The Ohio State University, Ohio, Ohio, USA, JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, Vol. 126, 2004

Papildus informācija

The second book in this two-part series, which is part of the Theoretical and Computational Chemistry series.
The Chemistry of the Superheavy Elements and Relativistic Effects
1(81)
Valeria Pershina
Introduction
1(9)
Production and identification of the heaviest elements
2(4)
Role of chemical studies
6(1)
Experimental studies. ``One-atom-at-a-time'' techniques
6(4)
Theoretical studies
10(1)
Relativistic Effects in the Chemistry of the Heaviest Elements
10(37)
Relativistic effects on atomic electronic shells
10(5)
Relativistic methods used for calculations of the electronic structures of the heaviest element atoms and molecules
15(5)
Relativistic effects on atomic properties of the heaviest elements
20(1)
Electronic configurations
20(3)
Ionization potentials, electron affinities and stabilities of oxidation states
23(4)
Ionic/atomic radii and polarizability
27(3)
Relativistic effects on molecular properties of the heaviest elements
30(1)
Elements 104 through 108
30(8)
Element 111
38(2)
Element 112
40(1)
Elements 113 through 117
41(4)
Element 118
45(2)
Elements with Z> 118
47(1)
Predictions of Experimental Behaviour of the Superheavy Elements and Experimental Results
47(23)
Gas-phase chemistry
47(1)
Volatility of atoms
47(5)
Volatility of molecules
52(5)
Aqueous chemistry
57(1)
Redox potentials and reduction experiments
57(1)
Complex formation and extraction by liquid chromatography
58(12)
Summary and Outlook
70(11)
References
72(9)
Accurate Relativistic Fock-Space Calculations for Many-Electron Atoms
81(39)
Uzi Kaldor
Ephraim Eliav
Arie Landau
Introduction
82(1)
Basic Formulation
83(4)
The relativistic Hamiltonian
83(1)
The one-electron equation
84(2)
SCF calculations
86(1)
Electron Correlation: The Fock-Space Coupled Cluster Method
87(3)
The Intermediate Hamiltonian CC Method
90(5)
Formulation
90(2)
Selection of Pm and Pi model spaces
92(1)
Atomic excitation energies not accessible by FSCC
93(1)
Excitation energies of Ba
93(2)
Excitation energies of Xe and Rn
95(1)
Applications: Heavy Elements
95(9)
When is an atom ``heavy''? Ionization potentials of alkali atoms
98(1)
Gold atom: Local maximum of relativistic effects
99(1)
The f2 level of Pr3+ : Importance of dynamic correlation
100(2)
Electron affinities of alkali atoms -- accuracy at the 5 me V level
102(2)
Applications: Superheavy Elements
104(11)
The ground state configuration of eka-gold (element 111)
104(1)
Ground state of rutherfordium -- relativity vs. correlation
105(3)
Eka-lead (element 114) -- an island of stability?
108(4)
Electron affinity of the rare-gas E118 -- how important is QED?
112(1)
Eka-actinium (E121) -- when is the Breit term important?
113(2)
Summary and Conclusion
115(5)
References
116(4)
Accurate Relativistic Calculations Including QED Contributions for Few-Electron Systems
120(68)
Walter R. Johnson
Kwok-Tsang Cheng
Mau Hsiung Chen
Introduction
120(1)
Central-Field Dirac Equation
121(12)
Spherical spinors
122(1)
Separation of Dirac equation
123(1)
Bound-state Coulomb wave functions
124(3)
QED corrections to one-electron energy levels
127(3)
Reduced mass and relativistic recoil
130(1)
Finite nuclear size
131(2)
Summary for radiative corrections in hydrogenic ions
133(1)
Many-Body Perturbation Theory
133(30)
Breit interaction
136(1)
Second- and third-order MBPT for closed-shell atoms
137(1)
Angular reduction of the Coulomb interaction
138(1)
Angular reduction of the Breit interaction
139(2)
B-spline basis sets
141(3)
Ground-state of He-like ions
144(2)
Breit interaction for the helium ground state
146(2)
Single-double (SD) equations
148(2)
Three-electron atoms
150(3)
Angular Reduction
153(1)
Breit interaction for the lithium-like ions
153(2)
Reduced mass and mass polarization
155(3)
Lithium-like uranium and the 2s1/2-2p1/2 Lamb shift
158(2)
Single-double (SD) equations for lithium-like ions
160(1)
Triple excitations and perturbation theory
161(2)
Applications to Li and Be+
163(1)
Relativistic Configuration-Interaction (RCI) Method
163(25)
Finite basis functions
168(1)
RCI equation
169(1)
Two-electron systems
170(4)
Many-electron systems
174(4)
QED corrections in many-electron system
178(4)
Appendix
182(1)
References
183(5)
Parity-Violation Effects in Molecules
188(101)
Robert Berger
Introduction
188(5)
Effects from Parity Violation in Molecules
193(7)
From the Standard Model of Physics to Molecular Parity Violation
200(31)
Elementary particles and their interactions
201(1)
Field theories and global phase transformations
202(1)
Local phase transformations
202(1)
Non-Abelian gauge theories
203(2)
Gauge group of the standard model
205(1)
Spontaneous symmetry breaking in gauche theories
206(6)
Fermionic masses
212(1)
Inclusion of all fermions
212(1)
Quark mixing
213(1)
Symmetry broken electroweak Lagrangian
214(1)
Interactions between fermions and gauge bosons
215(2)
Scattering matrix and equivalent potentials
217(2)
Scattering of two fermions due to Z0 exchange
219(12)
Computational Methods
231(20)
One-component methods
232(2)
Uncoupled Hartree-Fock
234(2)
Configuration interaction singles and Tamm-Dancoff approximation
236(1)
Multi-configuration linear response approach and random phase approximation
237(6)
Four-component methods
243(3)
Relativistically parametrised extended Huckel theory
246(2)
Dirac Hartree-Fock method
248(1)
Four-component coupled cluster method
249(1)
Two-component methods
250(1)
Applications
251(20)
Benchmark, test and model systems
253(6)
Spectroscopically relevant molecules
259(1)
Diatomic molecules
259(3)
Chiral molecules
262(4)
Biologically relevant molecules
266(3)
Chemical reactions
269(2)
Concluding Remarks
271(18)
Appendix
272(2)
References
274(15)
Accurate Determination of Electric Field Gradients for Heavy Atoms and Molecules
289(63)
Markus Pernpointner
Introduction
289(2)
Theoretical considerations
291(6)
Classical treatment
292(3)
Quantum mechanical treatment
295(2)
Experimental methods
297(6)
Measurements of atomic quadrupole coupling constants
298(3)
Measurements of molecular quadrupole coupling constants
301(2)
Methodology of relativistic atomic hyperfine structure calculations
303(16)
Early four-component calculations of hfs constants in atoms
304(2)
Many-body perturbation theory for hyperfine effects
306(8)
Current level of atomic hfs calculations
314(1)
Multi-configuration Dirac-Hartree-Fock calculations
315(3)
Relativistic configuration interaction (CI)
318(1)
Relativistic molecular NQM calculations
319(33)
Perturbative corrections for molecular relativistic EFG contributions
320(1)
Picture change effects in approximate relativistic theories
321(6)
Douglas-Kroll calculations of EFGs excluding the PCE
327(3)
Molecular density functional ZORA EFG calculations
330(3)
First-principles molecular Dirac-Hartree-Fock EFG calculations
333(8)
Conclusions and outlook
341(1)
References
342(10)
Two- component Relativistic Effective Core Potential Calculations for Molecules
352(65)
Yoon Sup Lee
Introduction
352(3)
Theory and Method
355(12)
The Hamiltonian and relativistic effective core potentials
356(1)
Shape consistent relativistic effective core potentials
357(2)
Kramers' restricted Hartree-Fock method
359(3)
Correlated REP methods with two-component spinors
362(1)
Spin-orbit effects on total energies and properties
362(5)
Assessment of two-component REP Calculations
367(14)
Comparison of two-component REP with all-electron DC results
367(9)
Geometries of simple polyatomic molecules from KRHF calculations
376(5)
Diatomic Molecules
381(17)
MH molecules
382(6)
Group 13 and 17 monofluorides
388(4)
The van der Waals molecule Rn2
392(3)
The diatomic thallium
395(3)
Polyatomic Molecules of Superheavy Elements
398(12)
The rare-gas fluorides RgF2 and RgF4 (Rg = Xe, Rn, and element 118)
398(6)
Halides and oxides of the transactinide elements Rf, Db, and Sg
404(6)
Conclusions
410(7)
References
411(6)
Relativistic Ab-Initio Model Potential Calculations for Molecules and Embedded Clusters
417(59)
Luis Seijo
Zoila Barandiaran
Introduction
417(2)
The Ab-Initio Model Potential Method
419(14)
AIMPs as relativistic effective core potentials
420(2)
Cowan-Griffin-Wood-Boring AIMP molecular Hamiltonian
422(4)
Douglas-Kroll-Hess AIMP molecular Hamiltonian
426(1)
Two-step treatment of electron correlation and spin-orbit coupling
427(2)
Heavy element impurities in solids: AIMPs as embedding Potentials
429(2)
Relaxation and polarisation of the crystalline environment
431(2)
Relativistic Ab-Initio Model Potential Calculations
433(39)
Atoms and molecules
434(1)
5f2 manifold of U4+
435(5)
5f3 and 5f2 6d1 manifolds of U3+
440(2)
Structure and spectroscopy of actinide ion impurities in crystals
442(2)
5f1 and 6d1 manifolds of Pa4+ -doped Cs2ZrCl6
444(8)
5f2 and 5f1 6d1 manifolds of U4+ -doped Cs2ZrCl6
452(13)
5f2 6d1 manifold of U3+ -doped Cs2NaYCl6
465(7)
Conclusions and prospects
472(4)
References
472(4)
Relativistic Pseudopotential Calculations for Electronic Excited States
476(76)
Christian Teichteil
Laurent Maron
Valerie Vallet
Introduction
477(4)
Methods
481(28)
Spin-orbit integrals and spin-orbit pseudopotentials
481(1)
Spin-orbit integrals
481(4)
Spin-orbit pseudopotentials
485(4)
Correlation effects on spin-orbit splitting
489(4)
SOCI methods
493(1)
Spin-orbit CI methods versus the full two-component treatments
493(2)
Contracted SOCI methods (CI/SO)
495(3)
Effective Hamiltonian-based contracted SOCI methods (CIeff/SO)
498(4)
Uncontracted SOCI methods (DGCI)
502(2)
Effective Hamiltonian-based uncontracted SOCI methods (DGCIeff)
504(5)
Molecular Applications
509(32)
Molecules in the gas phase
509(1)
Excited states for molecules containing main group elements
509(7)
Excited states for molecules containing d elements
516(6)
Excited states for molecules containing f elements
522(7)
Spin-orbit effects and reactivity on the ground state
529(2)
Spectroscopy of embedded molecules
531(1)
Modelling the spectroscopy of ionic impurities in crystal
531(2)
Spectroscopy of main group element impurities
533(1)
Spectroscopy of lanthanide and actinide impurities
534(5)
Zero-electron pseudopotentials
539(2)
Concluding Remarks
541(2)
Acronyms of methods
543(9)
References
546(6)
Relativistic Effects on NMR Chemical Shifts
552(46)
Martin Kaupp
Introduction
553(1)
Theoretical Background
554(12)
Nonrelativistic theory
554(2)
Relativistic four-component methodology
556(2)
Relativistic two-component Hamiltonians
558(2)
Perturbational treatment of relativistic effects
560(6)
SO Effects on Nuclear Shieldings of Neighbor Atoms
566(17)
Spin-Free Relativistic (SFR) Effects on Nuclear Shieldings of Neighbour Atoms
583(4)
Relativistic Heavy-Atom Effects at the Heavy-Atom Center (``HAHA Effect'')
587(4)
Concluding Remarks
591(7)
References
593(5)
Relativistic Density Functional Calculations on Small Molecules
598(58)
Christoph van Wullen
Introduction
598(2)
Methods
600(28)
The Dirac-Kohn-Sham scheme
600(6)
The exchange-correlation functional
606(8)
Quasi-relativistic approximations
614(12)
Energy derivatives in quasi-relativistic approaches
626(2)
Applications
628(20)
Gold compounds
631(4)
Thallium, lead and bismuth compounds
635(10)
Compounds of superheavy elements
645(3)
Conclusions
648(8)
References
650(6)
Quantum Chemistry with the Douglas-Kroll-Hess Approach to Relativistic Density Functional Theory: Efficient Methods for Molecules and Materials
656(67)
Notker Rosch
Alexei Matveev
Vladimir A. Nasluzov
Konstantin M. Neyman
Lyudmila Moskaleva
Sven Kruger
Introduction
657(1)
The Douglas-Kroll-Hess Formalism in Density Functional Theory
658(22)
Relativistic density functional theory
658(3)
Two-component Douglas-Kroll Hamiltonians
661(3)
Two-electron contributions
664(5)
Douglas-Kroll transformations of higher order
669(2)
Other two-component Hamiltonians
671(2)
Non-collinear spin density functional theory
673(2)
Magnetic properties in DKH: calculations of electronic g values
675(5)
Comparison of Methods
680(6)
Atoms
680(2)
Small molecules
682(4)
Applications
686(24)
Gold complexes
686(4)
Transition metal clusters
690(4)
Actinide complexes
694(1)
Benchmark calculations on actinyls and AcF6 (Ac = U, Np)
695(1)
Four-coordinated actinyl complexes: a comment on the rigidity of the uranyl moiety
696(1)
Effects of solvation
697(2)
From benchmark studies to real chemical systems
699(2)
Adsorption at surfaces and in zeolites
701(1)
Single d-metal atoms on the MgO(001) surface
702(1)
Pd3 and Pt3 species on the α-Al2O3(0001) surface
703(1)
Oxide support as a polydentate ligand: Re(CO)3/MgO
704(2)
Ir4 clusters in zeolite cavities
706(1)
Metal adsorption at metal surfaces
707(2)
Metal nanoclusters as models of single crystal surfaces: CO/Pd(111)
709(1)
Summary and Outlook
710(2)
List of Abbreviations and Notations
712(11)
References
714(9)
Relativistic Solid State Calculations
723(54)
Helmut Eschrig
Manuel Richter
Ingo Opahle
Introduction
723(3)
A Brief Introduction to Four-Current Density Functional Theory
726(6)
The relativistic ground state energy
726(2)
Four-current density functional theory
728(2)
Kohn-Sham-Dirac equations
730(2)
Solution of the Kohn-Sham-Dirac Equations
732(24)
General aspects of the relativistic FPLO method
735(6)
Local basis states
741(4)
Calculation of matrix elements
745(1)
One-center intergrals
746(2)
Multi-center integrals
748(5)
Density calculation
753(1)
Scalar-relativistic approximation
754(2)
Applications
756(16)
Electronic structure
756(4)
Atomic volumes and structural properties
760(3)
Magnetic ground state properties
763(6)
Magneto-optical effects
769(3)
Summary
772(5)
References
773(4)
Index 777