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Tables of Contents for Atomic Clusters and Nanoparticles/Agregats Atomiques Et Nanoparticules
Chapter/Section Title
Page #
Page Count
Lecturers
xi
Preface
xvii
Preface
xxi
Contents
xxv
Experimental Aspects of Metal Clusters
T.P. Martin
1
28
Introduction
3
1
Subshells, shells and Supershells
4
3
The experiment
7
1
Observation of electronic shell structure
8
4
Density Functional calculation
12
3
Observation of supershells
15
5
Fission
20
6
Concluding remarks
26
3
Melting of Clusters
H. Haberland
29
28
Introduction
31
2
Cluster Calorimetry
33
3
The bulk limit
33
1
Calorimetry for free clusters
34
2
Experiment
36
3
The source for thermalized cluster ions
38
1
Caloric curves
39
5
Melting temperatures
40
2
Latent heats
42
1
Other experiments measuring thermal properties of free clusters
43
1
A closer look at the experiment
44
6
Beam Preparation
44
1
Reminder: Canonical versus microcanonical ensemble
44
1
A canonical distribution of initial energies
44
1
Free clusters in vacuum, a microcanonical ensemble
45
2
Analysis of the fragmentation process
47
1
Photo-excitation and energy relaxation
47
1
Mapping of the energy on the mass scale
47
1
Broadening of the mass spectra due to the statistics of evaporation
48
1
Canonical or microcanonical data evaluation
49
1
Results obtained from a closer look
50
2
Negative heat capacity
50
2
Entropy
52
1
Unsolved Problems
52
1
Summary and Outlook
53
4
Excitations in Clusters
G.F. Bertsch
57
48
Introduction
59
4
Statistical reaction theory
63
8
Cluster evaporation rates
66
3
Electron emission
69
1
Radiative Cooling
70
1
Optical Properties of small particles
71
6
Connections to the bulk
72
1
Linear response and short-time behavior
73
3
Collective excitations
76
1
Calculating the electron wave function
77
7
Time-dependentdensity functional theory
82
2
Linear response of simple metal clusters
84
5
Alkali metal clusters
84
2
Silver clusters
86
3
Carbon Structures
89
16
Chains
90
4
Polyenes
94
1
Benzene
95
3
C60
98
1
Carbon nanotubes
99
3
Quantized conductance
102
3
Density Functional Theory, Methods, Techniques, and Applications
S. Chretien and D.R. Salahub
105
56
Introduction
107
1
Density functional theory
108
5
Hohenberg and Kohn theorems
110
1
Levy's constrained search
111
1
Kohn-Sham method
112
1
Density matrices and pair correlation functions
113
2
Adiabatic connection or coupling strength integration
115
3
Comparing and constrasting KS-DFT and HF-CI
118
4
Preparing new functionals
122
1
Approximate exchange and correlation functionals
123
9
The Local Spin Density Approximation (LSDA)
124
2
Gradient Expansion Approximation (GEA)
126
1
Generalized Gradient Approximation (GGA)
127
2
meta-Generalized Gradient Approximation (meta-GGA)
129
1
Hybrid functionals
130
1
The Optimized effective Potential method (OEP)
131
1
Comparison between various approximate functionals
132
1
LAP correlation functional
132
2
Solving the Kohn--Sham equations
134
7
The Kohn--Sham orbitals
136
2
Coulomb potential
138
1
Exchange-correlation potential
139
1
Core potential
139
1
Other choices and sources of error
140
1
Functionality
140
1
Applications
141
13
Ab initio molecular dynamics for an alanine dipeptide model
142
2
Transition metal clusters: The ecstasy, and the agony
144
1
Vanadium trimer
144
1
Nickel clusters
145
4
The conversion of acetylene to benzene on Fe clusters
149
5
Conclusions
154
7
Semiclassical Approaches to Mesoscopic Systems
M. Brack
161
60
Introduction
164
1
Extended Thomas-Fermi model for average properties
165
15
Thomas-Fermi approximation
165
1
Wigner-Kirkwood expansion
166
2
Gradient expansion of density functionals
168
1
Density variational method
169
4
Applications to metal clusters
173
1
Restricted spherical density variation
173
4
Unrestricted spherical density variation
177
1
Liquid drop model for charged spherical metal clusters
178
2
Periodic orbit theory for quantum shell effects
180
22
Semiclassical expansion of the Green function
181
1
Trace formulae for level density and total energy
182
5
Calculation of periodic orbits and their stability
187
3
Uniform approximations
190
2
Applications to metal clusters
192
1
Supershell structure of spherical alkali clusters
192
2
Ground-state deformations
194
1
Applications to two-dimensional electronic systems
195
2
Conductance oscillations in a circular quantum dot
197
3
Integer quantum Hall effect in the two-dimensional electron gas
200
1
Conductance oscillations in a channel with antidots
200
2
Local-current approximation for linear response
202
19
Quantum-mechanical equations of motion
203
2
Variational equation for the local current density
205
2
Secular equation using a finite basis
207
3
Applications to metal clusters
210
1
Optic response in the Jellium model
211
1
Optic response with ionic structure
211
10
Pairing Correlations in Finite Fermionic Systems
H. Flocard
221
76
Introduction
225
2
Basic mechanism: Cooper pair and condensation
227
5
Condensed matter perspective: Electron pairs
228
2
Nuclear Physics perspective: Two nucleons in a shell
230
1
Condensation of Cooper's pairs
231
1
Mean-field approach at finite temperature
232
12
Family of basic operators
233
1
Duplicated representation
233
1
Basic operators
234
1
BCS coefficients; quasi-particles
235
1
Wick theorem
236
2
BCS finite temperature equations
238
1
Density operator, entropy, average particle number
238
1
BCS equations
239
1
Discussion; problems for finite systems
240
1
Discussion; size of a Cooper pair
241
1
Discussion; low temperature BCS properties
242
2
First attempt at particle number restoration
244
7
Particle number projection
244
1
Projected density operator
245
1
Expectation values
246
1
Projected BCS at T = 0, expectation values
247
1
Projected BCS at T = 0, equations
248
1
Projected BCS at T = 0, generalized gaps and single particle shifts
249
2
Stationary variational principle for thermodynamics
251
4
General method for constructing stationary principles
251
1
Stationary action
252
1
Characteristic function
252
1
Transposition of the general procedure
253
1
General properties
254
1
Variational principle applied to extended BCS
255
7
Variational spaces and group properties
256
1
Extended BCS functional
257
1
Extended BCS equations
258
1
Properties of the extended BCS equations
259
1
Recovering the BCS solution
260
1
Beyond the BCS solution
261
1
Particle number projection at finite temperature
262
2
Particle number projected action
262
1
Number projected stationary equations: sketch of the method
263
1
Number parity projected BCS at finite temperature
264
11
Projection and action
264
2
Variational equations
266
3
Average Values and thermodynamic potentials
269
1
Small temperatures
270
1
Even number systems
270
1
Odd number systems
271
2
Numerical illustration
273
2
Odd--even effects
275
9
Number parity projected free energy differences
275
3
Nuclear odd--even energy differences
278
6
Extensions to very small systems
284
8
Zero temperature
284
4
Finite temperatures
288
4
Conclusions and perspectives
292
5
Models of Metal Clusters and Quantum Dots
M. Manninen
297
38
Introduction
299
1
Jellium model and the density functional theory
299
3
Spherical jellium clusters
302
3
Effect of the lattice
305
3
Tight-binding model
308
1
Shape deformation
309
6
Tetrahedral and triangular shapes
315
1
Odd--even staggering in metal clusters
315
2
Ab initio electronic structure: Shape and photoabsorption
317
3
Quantum dots: Hund's rule and spin-density waves
320
4
Deformation in quantum dots
324
2
Localization of electrons in a strong magnetic field
326
4
Conclusions
330
5
Theory of Cluster Magnetism
G.M. Pastor
335
66
Introduction
337
1
Background on atomic and solid-state properties
338
10
Localized electron magnetism
338
1
Magnetic configurations of atoms: Hund's rules
339
2
Magnetic susceptibility of open-shell ions in insulators
341
2
Interaction between local moments: Heisenberg model
343
2
Stonger model of itinerant magnetism
345
2
Localized and itinerant aspects of magnetism in solids
347
1
Experiments on magnetic clusters
348
4
Ground-state magnetic properties of transition-metal clusters
352
21
Model Hamiltonians
352
2
Mean-field approximation
354
2
Second-moment approximation
356
2
Spin magnetic moments and magnetic order
358
1
Free clusters: Surface effects
358
3
Embedded clusters: Interface effects
361
3
Magnetic anisotropy and orbital magnetism
364
1
Relativistic corrections
364
2
Magnetic anisotropy of small clusters
366
3
Enhancement of orbital magnetism
369
4
Electron-correlation effects on cluster magnetism
373
11
The Hubbard model
373
1
Geometry optimizationin graph space
374
1
Ground-state structure and total spin
375
3
Comparison with non-collinear Hartree-Fock
378
6
Finite-Temperature magnetic properties of clusters
384
12
Spin-fluctuation theory of cluster magnetism
385
3
Environment dependence of spin fluctuation energies
388
3
Role of electron correlations and structural fluctuation
391
5
Conclusion
396
5
Electron Scattering on Metal Clusters and Fullerenes
A.V. Solov'yov
401
36
Introduction
403
2
Jellium model: Cluster electron wave functions
405
2
Diffraction of fast electrons on clusters: Theory and experiment
407
2
Elements of many-body theory
409
3
Inelastic scattering of fast electrons on metal clusters
412
3
Plasmon resonance approximation: Diffraction phenomena, comparison with experiment and RPAE
415
6
Surface and volume plasmon excitations in the formation of the electron energy loss spectrum
421
4
Polarization effects in low-energy electron cluster collision and the photon emission process
425
4
How electron excitations in a cluster relax
429
3
Concluding remarks
432
5
Energy Landscapes
D. J. Wales
437
72
Introduction
439
7
Levinthal's paradox
440
3
``Strong'' and ``fragile'' liquids
443
3
The Born--Oppenheimer approximation
446
5
Normal modes
447
1
Orthogonal transformation
447
2
The normal mode transformation
449
2
Describing the potential energy landscape
451
2
Introduction
451
2
Stationary points and pathways
453
24
Zero Hessian eigenvalues
454
2
Classification of stationary points
456
1
Pathways
457
1
Properties of steepest-descent pathways
458
1
Uniqueness
458
1
Steepest-descent paths from a transition state
458
3
Principal directions
461
1
Birth and death of symmetry elements
462
3
Classification of rearrangements
465
2
The Mclver-Stanton rules
467
1
Coordinate transformations
468
3
``Mass-weighted'' steepest-descent paths
471
1
Sylvester's law of inertia
472
2
Branch points
474
3
Tunnelling
477
4
Tunnelling in (HF)2
480
1
Tunnelling in (H2O)3
480
1
Global thermodynamics
481
12
The superposition approximation
481
4
Sample incompleteness
485
1
Thermodynamics and cluster simulation
486
5
Example: Isomerisation dynamics of LJ7
491
2
Finite size phase transitions
493
6
Stability and van der Waals loops
494
5
Global optimisation
499
10
Basin-hopping global optimisation
500
9
Confinement Technique for Simulating Finite Many-Body Systems
S. F. Chekmarev
509
56
Introduction
511
6
Key points and advantages of the confinement simulations: General remarks
517
2
Methods for generating phase trajectories
519
2
Conventional molecular dynamics
519
1
Stochastic molecular dynamics
520
1
Identification of atomic structures
521
2
Quenching procedure
521
1
Characterization of a minimum
522
1
Confinement procedures
523
10
Reversal of the trajectory at the boundary of the basin. Microcanonical ensemble
523
7
Initiating the trajectory at the point of the last quenching within the basin. Microcanonical and canonical ensembles
530
3
Confinement to a selected catchment area. Some applications
533
8
Fractional caloric curves and densities of states of the isomers
533
4
Rates of the transitions between catchment basins. Estimation of the rate of a complex transition by successive confinement
537
2
Creating a subsystem of a complex system. Self-diffusion in the subsystem of permutational isomers
539
2
Complex study of a system by successive confinement
541
19
Surveying a potential energy surface. Strategies
542
1
Strategies to survey a surface
542
1
A taboo search strategy. Fermi-like distribution over the minima
542
9
Kinetics
551
2
Equilibrium properties
553
1
Study of the alanine tetrapeptide
554
6
Concluding remarks
560
5
Molecular Clusters: Potential Energy and Free Energy Surfaces. Quantum Chemical ab initio and Computer Simulation Studies
P. Hobza
565
20
Introduction
567
3
The hierarchy of interactions between elementary particles, atoms and molecules
567
1
The origin and phenomenological description of vdW interactions
568
2
Calculation of interaction energy
570
3
Vibrational frequencies
573
1
Potential energy surface
574
2
Free energy surface
576
1
Applications
577
8
Benzene... Arn clusters
577
1
Aromatic system dimers and oligomers
578
2
Nucleic acid-base pairs
580
5
Seminars by participants
585
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