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Heidelberg ; Dordrecht ; London ; New York : Springer, [2011]

xv, 531 stran : ilustrace (některé barevné) ; 25 cm

ISBN 978-3-642-14089-1 (vázáno)

Theoretical and mathematical physics, ISSN 1864-5879

Obsahuje bibliografické odkazy a rejstřík

002002536

1 Introduction I // 2 Foundations of Density Functional Theory: Existence Theorems 11 // 2.1 Hohenberg-Kohn Theorem II // 2.2 Degenerate Ground States 18 // 2.3 Variational Equation, Interacting i>-Representability, Functional // Differentiability 21 // 2.4 Fractional Particle Numbers, Derivative Discontinuity 37 // 2.5 Spin-Polarized Systems 40 // 2.6 Current Density Functional Theory 46 // 2.7 Excited States: Part 1 55 // 3 Effective Single-Particle Equations 57 // 3.1 Kohn-Sham Equations 57 // 3.2 Nonintcracting v-Rcprcscntability 70 // 3.3 Degenerate Kohn-Sham Ground States 73 // 3.4 Janak’s Theorem. Fractional Particle Numbers 76 // 3.5 Kohn-Sham Equations for Spin-Polarized Systems 80 // 3.6 Interpretation of Kohn-Sham Eigenvalues: // Relation to Ionization Potential, Fermi Surface and Band Gap 84 // 3.6.1 Ionization Potential 84 // 3.6.2 Fermi Surface 88 // 3.6.3 Band Gap 99 // 3.7 Kohn-Sham Equations of Current Density Functional Theory 101 // 4 Exchange-Correlation Energy Functional 109 // 4.1 Definition of Exact Exchange within DFT 109 // 4.2 Exact Representations of Exc[/i I 115 // 4.2.1 Variant (a): Kohn-Sham Perturbation Theory 115 // 4.2.2 Variant (b): Adiabatic Connection 126 // 4.3 Local Density Approximation (LDA) 129 // 4.3.1 Exchange 131 // 4.3.2 Correlation: High-Density Limit 132 // 4.3.3 Correlation: Low-Density Limit 135 // 4.3.4 Correlation: Interpolation Between High- and Low-Density Regime 135 // 4.3.5 Density Functional: Local Density Approximation (LDA) 137 // 4.3.6 Spin-Polari7.ed Electron Gas: Local Spin-Dcnsity // Approximation (L.SDA) 142 // 4.4 Nonlocal Corrections to the LDA 145 // 4.4.1 Weakly Inhomogeneous Electron Gas 145 // 4.4.2 Complete Linear Response 152 // 4.4.3 Gradient Expansion 153 // 4.5 Generalized Gradient Approximation (GGA) 169 // 4.5.1 Momentum Space Variant 170 // 4.5.2 Real Space Variant 175 //

4.5.3 Combination of Momentum and Real Space Variants 179 // 4.5.4 Semi-Empirical Construction ofGGAs 182 // 4.5.5 Merits and Limitations of GGAs 185 // 4.6 Weighted Density Approximation (WDA) 201 // 4.7 Self-Interaction Corrections (SIC) 202 // 4.8 Mcla-GGA (MGGA) 204 // 4.9 LDA+Ü 211 // 5 Virial Theorems 219 // 5.1 Scaling Behavior of Energy Contributions 219 // 5.2 Conventional Virial Theorem 221 // 5.3 DFT Virial Theorem 222 // 5.4 Hellmann-Feynman Theorem 224 // 6 Orbital Functionals: Optimized Potential Method 227 // 6.1 Motivation 227 // 6.1.1 Atomic Negative Ions 227 // 6.1.2 Dispersion Forces 228 // 6.1.3 Strongly Correlated Systems 230 // 6.1.4 Third Generation of DFT 232 // 6.2 Derivation of OPM Integral Equation 233 // 6.2.1 Compact Notation 233 // 6.2.2 Direct Functional Derivative 234 // 6.2.3 Total Energy Minimization 239 // 6.2.4 Invariance of Density 241 // 6.2.5 Exact Relations Based on OPM Integral Equation 244 // 6.2.6 Kriegcr-Li-Iafralc Approximation (KL1) 248 // 6.2.7 OPM in Case of Degeneracy 250 // 6.3 Exchange-Only Results 254 // 6.4 First-Principles Implicit Correlation Functionals 271 // Contents х’ // 6.4.1 Kohn-Sham Perturbation Theory 272 // 6.4.2 Kohn-Sham-Basetl Random Phase Approximation 276 // 6.4.3 Interaction Strength Interpolation (ISI) 278 // 6.5 Model-Based Orbital-Dependent Exchange-Correlation Functionals 279 // 6.5.1 Self-Interaction Corrected LDA 280 // 6.5.2 Colle-Salvetti Functional 280 // 6.5.3 Meta-GGA 281 // 6.5.4 Global. Screened and Local Hybrid Functionals 281 // 6.6 Analysis of Orbital-Dependent Correlation Functionals 288 // 6.6.1 Dispersion Force 288 // 6.6.2 Correlation Energy 294 // 6.6.3 Correlation Potential 298 // 6.7 Orbital-Dependent Representation of 2-Particle Density 304 // 7 Time-Dependent Density Functional Theory 307 // 7.1 Runge-Gross Theorem 307 // 7.2 Time-Dependent Kohn-Sham Equations 325 //

7.3 Exchange-Correlation Action: Adiabatic Local Density Approximation and Beyond 329 // 7.4 Time-Dependent Linear Response 331 // 7.5 Spin-Polarized Time-Dependent Density Functional Theory 335 // 7.6 Excited Slates: Part II 336 // 8 Relativistic Density Functional Theory t 351 // 8.1 Notation 352 // 8.2 Field Theoretical Background 353 // 8.3 Existence Theorem 361 // 8.4 Rclativistic Kohn-Sham Equations 367 // 8.5 Towards a Workable RDFT Scheme: No-pair Approximation 371 // 8.6 No-pair RDFT 373 // 8.7 Variants of RDFT 376 // 8.8 Rclativistic Exchange-Correlation Functional: Concepts and // Illustrative Results 384 // 8.8.1 Relativistic Implicit Functionals: Optimized Potential // Method 384 // 8.8.2 Role of Relativistic Corrections in £xc: I. Prototype // Results for Atoms 388 // 8.8.3 Relativistic Local Density Approximation 393 // 8.8.4 Relativistic Generalized Gradient Approximation 397 // 8.8.5 Role of Rclativistic Corrections in £xc: II. Prototype // Results for Molecules and Solids 398 // 9 Further Reading 401 // Contents // Erratum El // Erratum E3 // Л Functionals and the Functional Derivative 403 // Л. I Definition of the Functional 403 // A.2 Functional Derivative 405 // A.3 Calculaliona! Rules 409 // A.4 Variational Principle 411 // В Second Quantization in Many-Body Theory 413 // B.l A’-Particle Hilbert Space 413 // B.1.1 Realization in First Quantized Form 413 // В. 1.2 Formal Representation 417 // B.2 Fock Space 421 // B.2.1 Creation and Annihilation Operators 421 // B.2.2 I-Particle Operators 425 // B.2.3 2-Particlc Operators 428 // С Scaling Behavior of Many-Body Methods 433 // D Explicit Density Functionals for the Kinetic Energy: Thomas-Fermi // Models and Beyond 437 // E Asymptotic Behavior of Quasi-Particle Amplitudes 445 // F Quantization of Noninteracting Fermions in Relativistic Quantum // Field Theory 449 //

G Renormalization Scheme of Vacuum QED 457 // H Relativistic Homogeneous Electron Gas 467 // H.l Basic Propagators 467 // H.2 Response Functions 468 // H.3 Ground State Energy 473 // H.4 Ground State Four Current 478 // I Renormalization of Inhomogeneous Electron Gas 481 // J Gradient Corrections to the Rclativistic I.DA 485 // К Gordon Decomposition 489 // I, Some Useful Formulae 493 // References 499 // Index // 517