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Tables of Contents for Metal Clusters
Chapter/Section Title
Page #
Page Count
Contributors
xi
2
Series Preface
xiii
1 Application of the Jellium Model and its Refinements to the Study of the Electronic-Properties of Metal Clusters
1
28
Walter Ekardt
W.-D. Schone
J. M. Pacheco
1.1 Introduction
1
3
1.2 Properties of the Ground State
4
10
1.3 The Optical Properties
14
4
1.4 Pseudopotential Perturbation Theory
18
4
1.5 The Effect of Temperature
22
2
1.6 Summary and Conclusions
24
2
1.7 References
26
3
2 The Quantum-Chemical Approach
29
42
Vlasta Bonacic-Koutecky
Jiri Pittner
Detlef Reichardt
Piercarlo Fantucci
Jaroslav Koutecky
2.0 Abbreviations
29
1
2.1 Introduction
30
1
2.2 Computational Methods
31
5
2.2.1 Gradient-based Methods for Determination of Cluster Structures at Zero Temperature
31
1
2.2.2 Ab Initio Molecular Dynamics for Determination of Structures and their Temperature Behavior
32
1
2.2.3 Ab Initio Methods for the Calculation of Excited States
33
3
2.3 Structures and Absorption Spectra of Na(n) + and Na(n) Clusters
36
8
2.3.1 Zero Temperature
36
6
2.3.2 Temperature Line-Broadening
42
2
2.4 Structural and Temperature Behavior of Metallic Clusters
44
9
2.5 Structures and Absorption Spectra of Nonstoichiometric Alkali Halide And Alkali Hydride Clusters
53
6
2.5.1 Na(n)F(m) (n is greater than m)
53
3
2.5.2 Na(6)F(3)
56
1
2.5.3 Li(n)H(n-1) and Li(n)H(n-2)
56
3
2.6 Applicability of the Plasmon Theory to Clusters
59
8
2.6.1 Derivation of the Expression for the Plasmon Energy
59
3
2.6.2 Two Models of Periodic Systems
62
1
2.6.3 Oscillatory Behavior of Plasmons
63
2
2.6.4 Classical Limit for Plasmon Energy and Conditions for Existence of Plasmons
65
2
2.7 Concluding Remarks
67
1
2.8 Appendix
68
1
2.9 Acknowledgments
68
1
2.10 References
68
3
3 Density Functional Theory and Car-Parrinello Molecular Dynamics for Metal Clusters
71
74
Pietro Ballone
Wanda Andreoni
3.1 Introduction
71
2
3.2 Density Functional Theory
73
6
3.3 Computational Schemes for DFT Applications: the Electronic Problem
79
7
3.3.1 Kohn--Sham Equations
79
1
3.3.2 Basis Sets for Electronic Wave Functions
80
1
3.3.2.1 Localized Basis Sets
80
1
3.3.2.2 Plane-Waves
81
1
3.3.3 Pseudopotentials
82
3
3.3.4 Diagonalization Techniques
85
1
3.4 Computational Schemes for DFT Applications: Structure and Dynamics
86
5
3.4.1 Computation of Forces on the Ions
86
1
3.4.2 Car--Parrinello Molecular Dynamics
87
2
3.4.3 Optimization Strategies
89
1
3.4.3.1 Simulated Annealing
89
1
3.4.3.2 Genetic Algorithms
90
1
3.4.4 Additional Remarks
90
1
3.5 Computation of Properties
91
7
3.5.1 Vibrational Analysis
91
1
3.5.2 Optical Properties
92
3
3.5.3 Static Dipole Polarizability
95
1
3.5.4 Photoelectron Spectroscopy
95
2
3.5.5 Electron Spin Resonance
97
1
3.6 Alkali Metals
98
7
3.7 Clusters of the IIA and IIB Elements
105
5
3.8 IIIB Metals
110
3
3.9 Magnetism in Transition-Metal and Rare-Earth-Metal Clusters
113
8
3.10 Noble and Nonmagnetic Transition-Metal Clusters
121
5
3.11 Heteroatom and Alloy Clusters
126
3
3.12 Conclusions
129
1
3.13 Appendices
130
5
3.13.1 Appendix A: DFT-related Methods
130
1
3.13.2 Appendix B: Details of CP Molecular Dynamics
131
2
3.13.3 Appendix C: Computational Details
133
2
3.14 Acknowledgments
135
1
3.15 References and Notes
136
9
4 Dissociation, Fragmentation and Fission of Simple Metal Clusters
145
36
Constantine Yannouleas
Uzi Landman
Robert N. Barnett
4.1 Introduction
145
3
4.1.1 Metal Cluster Fission and Nuclear Fission: Similarities and Differences
146
1
4.1.2 Other Decay Modes in Atomic and Molecular Clusters
147
1
4.1.3 Organization of the Chapter
148
1
4.2 Theory of Shape Deformations
148
11
4.2.1 Microscopic Foundation of Shell-Correction Methods--the LDA-SCM
150
1
4.2.2 Semiempirical Shell-Correction Method (SE-SCM)
151
1
4.2.2.1 Methodology
151
1
4.2.2.2 Liquid-Drop Model for Neutral and Charged Deformed Clusters
152
2
4.2.2.3 The Modified Nilsson Potential for Ellipsoidal Shapes
154
1
4.2.2.4 Shell-Correction and Averaging of Single-Particle Spectra for the Modified Nilsson Potential
155
1
4.2.2.5 Overall Procedure
156
1
4.2.2.6 Asymmetric Two-Center Oscillator Model for Fission
157
2
4.3 Experimental Trends and Theoretical Interpretation
159
14
4.3.1 Electronic Shell Effects in Monomer and Dimer Separation Energies
159
1
4.3.2 Electronic Shell Effects in Fission Energetics
160
2
4.3.3 Electronic Shell Effects in Fission Barriers and Fission Dynamics of Metal Clusters
162
1
4.3.3.1 Molecular-Dynamics Studies of Fission
162
2
4.3.3.2 SE-SCM Interpretation of Fissioning Processes
164
9
4.4 Influence of Electronic Entropy on Shell Effects
173
3
4.5 Summary
176
1
4.6 Acknowledgments
176
1
4.7 References and Notes
177
4
5 Optical and Thermal Properties of Sodium Clusters
181
30
Hellmut Haberland
5.1 History and Motivation
181
1
5.2 Experiment
182
4
5.2.1 Variable-Temperature Cluster Source
183
1
5.2.2 Temperature Distributions
184
2
5.3 Temperature Dependence of the Optical Response
186
5
5.3.1 Low-Temperature Spectra
188
2
5.3.2 High-Temperature Spectra
190
1
5.4 Size Dependence of the Optical Response
191
10
5.4.1 Peak Positions
192
5
5.4.2 Asymptotic Limit
197
1
5.4.3 Sum Rules and Moments l
198
1
5.4.3.1 Oscillator Strength
198
1
5.4.3.2 Mean Transition Energy
199
1
5.4.3.3 Polarizability
199
1
5.4.3.4 Temperature Dependence
200
1
5.5 Charge Dependence of the Optical Response
201
2
5.6 Line Shape
203
2
5.6.1 Width of the Bulk Mie Plasmon
203
1
5.6.2 Single Line Width and Lifetime of the Resonance
203
1
5.6.3 Total Width and Scaling Laws
204
1
5.7 Thermodynamic Properties
205
3
5.7.1 Caloric Curve of a Free Cluster
205
1
5.7.2 Size Dependence of the Melting Point
206
2
5.8 Unsolved Problems and Future Directions
208
1
5.9 Summary
208
1
5.10 Acknowledgments
208
1
5.11 References and Notes
209
2
6 Magnetic Properties of Transition-Metal Clusters
211
38
G. M. Pastor
K. H. Bennemann
6.1 Introduction
211
4
6.2 Theory
215
8
6.2.1 Ground-State Properties
216
2
6.2.2 Finite-Temperature Properties: Spin Fluctuations
218
2
6.2.3 Exact Treatment of Electron Correlations
220
3
6.3 Results
223
22
6.3.1 Magnetic Moments and their Order
223
5
6.3.2 Magnetic Anisotropy Effects
228
8
6.3.3 Magnetic Properties at Finite Temperatures: Spin-Fluctuation Effects
236
3
6.3.4 Effects of Electron Correlations and Structure on Cluster Magnetism
239
6
6.4 Discussion
245
1
6.5 Acknowledgments
246
1
6.6 References
246
3
7 Comparison of Resonance Dynamics in Metal Clusters and Nuclei
249
32
P.-G. Reinhard
E. Suraud
7.1 Introduction
249
1
7.2 Theoretical Framework
250
5
7.2.1 Energy Functional for Clusters
250
2
7.2.2 Energy Functional for Nuclei
252
1
7.2.3 Equations of Motion and their Solution
253
1
7.2.4 Linearized Equations of Motion
254
1
7.3 Dynamics in the Linear Response Domain
255
11
7.3.1 Typical Observables
255
1
7.3.2 General Spectral Properties
256
3
7.3.3 Higher Multipolarities
259
1
7.3.4 Dipole Resonance and Deformation
260
2
7 3.5 Widths
262
2
7.3.6 Effect of Ions
264
2
7.4 Resonance Dynamics beyond the Linear Regime
266
10
7.4.1 On Excitation Mechanisms
266
1
7.4.2 Typical Observables
267
1
7.4.3 From Small- to Large-Amplitude Dynamics
268
2
7.4.4 Deeper into Reaction Mechanisms
270
1
7.4.4.1 Coulomb Excitation in Clusters and Nuclei
270
2
7.4.4.2 Heavy-Ion Collisions
272
2
7.4.4.3 Cluster Response to an Intense Femtosecond Laser
274
1
7.4.5 Semiclassical Approximations to TDLDA
274
2
7.5 Conclusion
276
1
7.6 Acknowledgments
277
1
7.7 References
277
4
Index
281