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Time-Dependent Density Functional Theory 2006 ed. [Kietas viršelis]

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  • Formatas: Hardback, 555 pages, aukštis x plotis: 235x155 mm, weight: 2320 g, XXXIV, 555 p., 1 Hardback
  • Serija: Lecture Notes in Physics 706
  • Išleidimo metai: 14-Aug-2006
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540354220
  • ISBN-13: 9783540354222
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 555 pages, aukštis x plotis: 235x155 mm, weight: 2320 g, XXXIV, 555 p., 1 Hardback
  • Serija: Lecture Notes in Physics 706
  • Išleidimo metai: 14-Aug-2006
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540354220
  • ISBN-13: 9783540354222
Kitos knygos pagal šią temą:
The year 2004 was a remarkable one for the growing ?eld of time-dependent density functional theory (TDDFT). Not only did we celebrate the 40th - niversary of the Hohenberg-Kohn paper, which had laid the foundation for ground-state density functional theory (DFT), but it was also the 20th - niversary of the work by Runge and Gross, establishing a ?rm footing for the time-dependent theory. Because the ?eld has grown to such prominence, and has spread to so many areas of science (from materials to biochemistry), we feel that a volume dedicated to TDDFT is most timely. TDDFT is based on a set of ideas and theorems quite distinct from those governingground-stateDFT,butemployingsimilar techniques.Itisfarmore than just applying ground-state DFT to time-dependent problems, as it - volves its own exact theorems and new and di erent density functionals. Presently,themostpopularapplicationistheextractionofelectronicexcit- state properties, especially transition frequencies. By applying TDDFT after thegroundstateofamoleculehasbeenfound,wecanexploreandunderstand the complexity of its spectrum, thus providing much more information about the species. TDDFT has a especially strong impact in the photochemistry of biological molecules, where the molecules are too large to be handled by t- ditional quantum chemical methods, and are too complex to be understood with simple empirical frontier orbital theory.

Recenzijos

From the reviews:









"Time-Dependent Density Functional Theory represents a concise overview of the field . this is a well-structured text, with a common set of notations and a single comprehensive and up-to-date list of references, rather than just a compilation of research articles. Because of its clear organization, the book can be used by novices (basic knowledge of ground-state DFT is assumed) and experienced users of TD-DFT, as well as developers in the field." (Anna I. Krylov, Journal of the American Chemical Society, Vol. 129 (21), 2007)



"The reviewed book is a broad reflection of the current state of the TD DFT and summary of its achievements since 1984. It is naturally partitioned into the chapters that outline the formal theoretical approach of the TD DFT . To summarize, the book Time-Dependent Density Functional Theory is a valuable book for those, PhD students in particular, who are interested in the whole spectrum of problems related to density functional theory and its broad applications to many-body quantum theory." (Eugene Kryachko, Zentralblatt MATH, Vol. 1110 (12), 2007)

Preface v
User's Guide vii
List of Contributors
xxiii
Abbreviations xxix
Notation xxxiii
Basics
1(16)
E.K.U. Gross
K. Burke
Introduction
1(2)
One-to-One Correspondence
3(3)
Time-Dependent Kohn-Sham Equations
6(2)
Linear Response
8(2)
Adiabatic Connection Formula
10(1)
Adiabatic Approximation
11(1)
Relation to Ground-State DFT
12(5)
Part I Formal Theory
Beyond the Runge-Gross Theorem
17(16)
R. van Leeuwen
Introduction
17(1)
The Extended Runge-Gross Theorem: Different Interactions and Initial States
17(6)
Invertibility of the Linear Density Response Function
23(5)
Consequences of v-Representability for the Quantum Mechanical Action
28(5)
Introduction to the Keldysh Formalism
33(28)
R. van Leeuwen
N.E. Dahlen
G. Stefanucci
C.-O. Almbladh
U. von Barth
Introduction
33(1)
The Keldysh Contour
34(2)
Nonequilibrium Green Functions
36(2)
The Keldysh Book-Keeping
38(4)
The Kadanoff-Baym Equations
42(2)
Example: H2 in An Electric Field
44(2)
Conserving Approximations
46(3)
Noninteracting Electrons
49(4)
Action Functional and TDDFT
53(4)
Example: Time-Dependent OEP
57(4)
Initial-State Dependence and Memory
61(14)
N.T. Maitra
Introduction
61(2)
History Dependence: An Example
63(1)
Initial-State Dependence
64(5)
Memory: An Exact Condition
69(2)
Role of Memory in Quantum Control Phenomena
71(3)
Outlook
74(1)
Current Density Functional Theory
75(18)
G. Vignale
Introduction
75(1)
First Hints of Ultranonlocality: The Harmonic Potential Theorem
76(1)
TDDFT and Hydrodynamics
77(3)
Current Density Functional Theory
80(1)
The xc Vector Potential for The Homogeneous Electron Liquid
81(4)
The xc Vector Potential for the Inhomogeneous Electron Liquid
85(1)
Applications
86(7)
Multicomponent Density-Functional Theory
93(14)
R. van Leeuwen
E.K.U. Gross
Introduction
93(1)
Fundamentals
93(4)
Definition of the Densities
96(1)
The Runge-Gross Theorem for Multicomponent Systems
97(1)
The Kohn-Sham Scheme for Multicomponent Systems
98(1)
The Multicomponent Action
99(3)
Linear Response and Multicomponent Systems
102(1)
Example
103(3)
Conclusions
106(1)
Intermolecular Forces and Generalized Response Functions in Liouville Space
107(16)
S. Mukamel
A.E. Cohen
U. Harbola
Introduction
107(1)
Quantum Dynamics in Liouville Space; Superoperators
108(3)
TDDFT Equations of Motion for the GRFs
111(1)
Collective Electronic Oscillator Representation of the GRF
112(4)
GRF Expressions for Intermolecular Interaction Energies
116(7)
Part II Approximate Functionals
Time-Dependent Deformation Approximation
123(14)
I.V. Tokatly
Introduction
123(2)
DFT as Exact Quantum Continuum Mechanics
125(2)
Conservation Laws and the Hydrodynamic Formulation of DFT
125(1)
Definition of the xc Potentials
126(1)
Geometric Formulation of TDDFT
127(4)
Preliminaries: Static LDA vs. Time-Dependent LDA
127(2)
TDDFT in the Lagrangian Frame
129(2)
Time-Dependent Local Deformation Approximation
131(6)
General Formulation of the TDLDefA
131(1)
Exchange-Only TDLDefA
132(1)
Inclusion of Correlations: Elastic TDLDefA
133(4)
Exact-Exchange Methods and Perturbation Theory along the Adiabatic Connection
137(24)
A. Gorling
Preliminary Remarks
137(3)
Exact Exchange Methods and Static Perturbation Theory
140(9)
Perturbation Theory along the Adiabatic Connection and the Static Exact Exchange Equation
140(3)
Implementations of Static Exact Exchange KS Methods
143(2)
Static Effective Exact Exchange KS Methods
145(4)
Time-Dependent Perturbation Theory and the Exact Exchange Kernel
149(12)
Time-Dependent Perturbation Theory along the Adiabatic Connection and the Time Dependent Exact Exchange Equation
149(4)
The Exact Exchange Kernel
153(8)
Approximate Functionals from Many-Body Perturbation Theory
161(20)
A. Marini
R. Del Sole
A. Rubio
Motivations
161(1)
Hedin's Equations and the Vertex Function
162(4)
The Bethe-Salpeter Equation
164(2)
The xc Kernel: Different Schemes Based on MBPT
166(7)
Static Long-Range Kernels
167(1)
A Perturbative Scheme
168(3)
The fxc Perturbative Series: Convergence and Cancellations
171(2)
The Vertex Function Γ: a TDDFT-Based Approach
173(6)
Including Density-Functional Concepts into MBPT
178(1)
Conclusions and Perspectives
179(2)
Exact Conditions
181(16)
K. Burke
Introduction
181(1)
Review of the Ground State
181(3)
Basic Conditions
181(1)
Finite Systems
182(1)
Uniform and Nearly Uniform Gas
183(1)
Finite Versus Extended Systems
183(1)
Types of Approximations
183(1)
Conditions and Approximations
184(1)
Role of the Energy
184(1)
Approximations
185(1)
General Conditions
185(3)
Adiabatic Limit
185(1)
Equations of Motion
186(1)
Self-Interaction
187(1)
Initial State Dependence
187(1)
Coupling-Constant Dependence
188(1)
Translational Invariance
188(1)
Linear Response
188(3)
Adiabatic Limit
188(1)
Zero Force and Torque
189(1)
Self-Interaction Error
189(1)
Initial-State Dependence
189(1)
Coupling-Constant Dependence
189(1)
Symmetry
190(1)
Kramers-Kronig
190(1)
Adiabatic Connection
191(1)
Finite Versus Extended Systems, and Currents
191(1)
Gradient Expansion in the Current
192(1)
Response to Homogeneous Field
192(1)
Odds and Ends
192(1)
Functional Derivatives
192(1)
Infinite Lifetimes of Eigenstates
192(1)
Single-Pole Approximation for Exchange
193(1)
Memory Correlation Approximations
193(1)
Double Excitations and Branch Cuts
193(1)
Beyond Linear Response
193(1)
Summary
194(3)
Part III Numerical Aspects
12 Propagators for the Time-Dependent Kohn-Sham Equations
197(14)
A. Castro
M.A.L. Marques
Introduction
197(2)
Formulation of the Problem
199(2)
Approximations to the Exponential of an Operator
201(3)
Polynomial Expansions
202(1)
Krylov Subspace Projection
203(1)
Splitting Techniques
204(1)
Analysis of Integrators for the TDSE
204(5)
``Classical'' Propagators
205(1)
Exponential Midpoint Rule
206(1)
Time-Reversal Symmetry Based Propagator
206(1)
Splitting Techniques
206(1)
Magnus Expansions
207(2)
Conclusions
209(2)
Solution of the Linear-Response Equations in a Basis Set
211(6)
P.L. de Boeij
Introduction
211(1)
An Expansion in Orbital Products
211(1)
An Efficient Solution Scheme
212(5)
Excited-State Dynamics in Finite Systems and Biomolecules
217(10)
J. Hutter
Introduction
217(1)
Lagrangian of the Excited State Energy
218(2)
Lagrange Multipliers and Relaxed One-Particle Density Matrix
220(2)
Molecular Dynamics
222(2)
Coupling to Classical Force Fields
224(3)
Time Versus Frequency Space Techniques
227(16)
M.A.L. Marques
A. Rubio
Introduction
227(2)
Notation
228(1)
Time-Evolution Scheme
229(2)
Sternheimer's Approach
231(2)
Casida's Equation
233(1)
Response Equation in Momentum/Frequency Space
234(2)
Space-Time Method for Response Calculations
236(2)
Discussion
238(5)
Part IV Applications: Linear Response
Linear-Response Time-Dependent Density Functional Theory for Open-Shell Molecules
243(16)
M.E. Casida
A. Ipatov
F. Cordova
Introduction
243(2)
Open-Shell Ground States
245(5)
Open-Shell Excitation Spectra from TDDFT
250(5)
Beyond the Adiabatic Approximation
255(2)
Conclusion
257(2)
Atoms and Clusters
259(12)
J.R. Chelikowsky
Y. Saad
I. Vasiliev
Introduction
259(2)
Theoretical Methods
261(2)
Applications to Atoms
263(1)
Applications to Clusters
264(7)
Semiconductor Nanostructures
271(16)
C.A. Ullrich
Introduction
271(1)
Effective-Mass Approximation for Quantum Wells
272(3)
Intersubband Dynamics in Quantum Wells
275(6)
TDDFT Response Theory and Plasmon Dispersions
275(3)
ISB Plasmon Linewidth
278(3)
Quantum Dots
281(6)
Electronic Structure of Quantum Dots
282(1)
Collective Excitations: Kohn's Theorem and Beyond
283(4)
Solids from Time-Dependent Current DFT
287(14)
P.L. de Boeij
Introduction
287(2)
Surface and Macroscopic Bulk Effects
289(3)
The Time-Dependent Current Density Functional Approach
292(4)
Application to Solids
296(3)
Conclusion
299(2)
Optical Properties of Solids and Nanostructures from a Many-Body fxc Kernel
301(16)
A. Marini
R. Del Sole
A. Rubio
Introduction
301(1)
Applications to Solids and Surfaces
302(7)
Applications to One Dimensional Systems and Molecules
309(6)
Summary
315(2)
Linear Response Calculations for Polymers
317(6)
P.L. de Boeij
Introduction
317(1)
The Counteracting Exchange Potential
318(2)
An Alternative to Orbital-Dependent Potentials
320(2)
Conclusion
322(1)
Biochromophores
323(14)
X. Lopez
M.A.L. Marques
Introduction
323(1)
π → π* Transitions and Biochromophores
323(1)
Biochromophores in Proteins
324(4)
Proteins: Aminoacid Polymers
325(1)
Proteins as Chromophores
326(1)
Proteins and Phrosthetic Groups
327(1)
Methods
328(2)
Molecular Dynamics
328(1)
Force Fields
329(1)
QM/MM Techniques
329(1)
Practical Cases
330(6)
Green Fluorescent Protein and its Mutants: Structural Effects
331(4)
Astaxanthin and the Colour of the Lobster's Shell
335(1)
Conclusions
336(1)
Excited States and Photochemistry
337(20)
D. Rappoport
F. Furche
Introduction
337(1)
Excited State Properties from TDDFT
337(5)
Lagrangian Approach
337(1)
Implementation
338(2)
Efficiency
340(2)
Basis Set Requirements
342(1)
Performance
342(4)
Vertical Excitation and CD Spectra
342(2)
Excited State Structure and Dynamics
344(1)
Shortcomings of Present TDDFT
345(1)
Applications
346(7)
Aromatic Compounds and Fullerenes
346(1)
Biological Systems
347(1)
Porphyrins and Related Compounds
348(2)
Transition Metal Compounds
350(1)
Organic Polymers
351(1)
Charge and Proton Transfer
352(1)
Conclusions and Outlook
353(4)
Part V Applications: Beyond Linear Response
Atoms and Molecules in Strong Laser Fields
357(20)
C.A. Ullrich
A.D. Bandrauk
Introduction
357(2)
Atoms in Strong Laser Fields: An Overview
359(4)
Multiphoton Ionization
359(2)
Above-Threshold Ionization
361(1)
Harmonic Generation
361(1)
Theoretical Methods
362(1)
TDDFT for Atoms in Strong Laser Fields
363(5)
Molecules in Strong Fields
368(6)
Overview
368(2)
A 1-D Example: H2 with Fixed Nuclei
370(3)
TDDFT for Molecules in Strong Fields
373(1)
Conclusion and Perspectives
374(3)
Highlights and Challenges in Strong-Field Atomic and Molecular Processes
377(14)
V. Veniard
Introduction
377(2)
Determination of the Spectra
379(1)
One-Photon Double Ionization of Helium
380(4)
Ionization of a Model Lithium Atom
384(2)
Dynamics of an H2 Molecule in a Strong Laser Field
386(3)
Conclusion
389(2)
Cluster Dynamics in Strong Laser Fields
391(16)
P.-G. Reinhard
E. Suraud
Introduction
391(1)
Formalities
392(4)
Coupled Ionic and Electronic Dynamics
392(2)
Self Interaction Correction
394(2)
Distributions of Emitted Electrons
396(7)
Computing Observables from Emission
396(1)
Multi-Plasmon Features in Photo-Electron Spectra
397(2)
Angular Distributions -- Low Intensity Domain
399(3)
Angular Distributions -- High Intensity Domain
402(1)
Pump-Probe Analysis of Ionic Dynamics
403(1)
Conclusion
404(3)
Excited-State Dynamics in Extended Systems
407(16)
O. Sugino
Y. Miyamoto
Introduction
407(3)
Real-Time Evolution of the Kohn-Sham Orbitals
410(2)
Computational Procedures
412(2)
Examples of TDDFT-MD Simulations
414(5)
Semiconductor Bulk and Surfaces
414(2)
Carbon Nanotubes
416(3)
Concluding Remarks
419(4)
Part VI New Frontiers
Back to the Ground-State: Electron Gas
423(12)
M. Lein
E.K.U. Gross
Introduction
423(1)
Adiabatic Connection
424(3)
Scaling Properties
427(1)
Approximations for the xc Kernel
428(6)
Concluding Remarks
434(1)
The Exchange-Correlation Potential in the Adiabatic-Connection Fluctuation-Dissipation Framework
435(8)
Y.M. Niquet
M. Fuchs
Introduction
435(1)
The RPA Exchange-Correlation Potential
436(3)
Asymptotic Behavior of the RPA Potential in Finite Systems
439(1)
The Bandgap Energy of Solids
440(2)
Conclusion
442(1)
Dispersion (Van Der Waals) Forces and TDDFT
443(20)
J.F. Dobson
Introduction
443(1)
Simple Models of the vdW Interaction between Small Systems
443(2)
Coupled-Fluctuation Model
443(1)
Model Based on the Static Correlation Hole: Failure of LDA/GGA at Large Separations
444(1)
Model Based on Small Distortions of the Ground State Density
444(1)
Coupled-Plasmon Model
445(1)
The Simplest Models for vdW Energetics of Larger Systems
445(1)
Formal Perturbation Theory Approaches
446(2)
Second Order Perturbation Theory for Two Finite Nonoverlapping Systems
446(2)
vdW and Higher-Order Perturbation Theory
448(1)
Nonuniversality of vdW Asymptotics in Layered and Striated Systems
448(1)
Correlation Energies from Response Functions: The Fluctuation-Dissipation Theorem
449(4)
Basic Adiabatic Connection Fluctuation-Dissipation Theory
449(3)
Exact Exchange: A Strength of the ACFD Approach
452(1)
The xc Energy in the Random Phase Approximation
453(2)
Testing the RPA Correlation Energy For vdW in the Well-Separated Limit: The Second-Order Perturbation Regime
454(1)
Coupled Plasmons and the ACFD Approach
455(1)
Beyond the RPA: The ACFD with a Nonzero xc Kernel
455(4)
The Case of Two Small Distant Systems in the ACFD with a Nonzero xc Kernel
455(1)
Beyond the RPA in the ACFD: Energy-Optimized fxc Kernels
456(1)
Beyond the RPA in the ACFD: More Realistic Uniform-Gas Based fxc Kernels
457(1)
xc Kernels not Based on the Uniform Electron Gas
458(1)
Is the ACFD Energy Insensitive to fxc in Layered and Striated Systems having Zero Bandgap?
458(1)
Density-based Approximations for the Response Functions in ACFD vdW Theory
459(3)
Density-Based Approximations for the Non-Overlapping Regime
459(1)
``Seamless'' Density-Based vdW Approximations Valid into the Overlapped Regime
460(2)
Summary
462(1)
Kohn-Sham Master Equation Approach to Transport Through Single Molecules
463(16)
R. Gebauer
K. Burke
R. Car
Introduction
463(1)
Modeling a Molecular Junction
464(2)
Periodic Boundary Conditions
464(1)
The Role of Dissipation
465(1)
Master Equations
466(3)
Master Equation
467(1)
TDDFT and a KS Master Equation
468(1)
Practical Aspects
469(2)
Time Propagation
469(1)
Calculating Currents
470(1)
Results
471(5)
Model Calculation
471(3)
Realistic Simulations
474(2)
Comparison with Standard NEGF Treatment
476(1)
Conclusions
477(2)
Time-Dependent Transport Through Single Molecules: Nonequilibrium Green's Functions
479(14)
G. Stefanucci
C.-O. Almbladh
S. Kurth
E.K.U. Gross
A. Rubio
R. van Leeuwen
N.E. Dahlen
U. von Barth
Introduction
479(2)
An Exact Formulation Based on TDDFT
481(2)
Non-Equilibrium Green Functions
483(4)
Steady State
487(1)
A Practical Implementation Scheme
488(3)
Conclusions
491(2)
Scattering Amplitudes
493(14)
A. Wasserman
K. Burke
Introduction
493(1)
Linear Response for the (N + 1)-Electron System
494(1)
One Dimension
495(7)
Transmission Amplitudes from the Susceptibility
495(3)
TDDFT Equation for Transmission Amplitudes
498(1)
A Trivial Example, N = 0
498(1)
A Non-Trivial Example, N = 1
499(3)
Three Dimensions
502(3)
Single-Pole Approximation in the Continuum
502(2)
Partial-Wave Analysis
504(1)
Summary and Outlook
505(2)
Acknowledgements 507(2)
References 509(76)
Index 585