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Tables of Contents for Atomic Clusters and Nanoparticles/Agregats Atomiques Et Nanoparticules
Experimental Aspects of Metal Clusters
T.P. Martin1
28
Subshells, shells and Supershells
4
3
Observation of electronic shell structure
8
4
Density Functional calculation
12
3
Observation of supershells
15
5
Melting of Clusters
H. Haberland29
28
The bulk limit33
1
Calorimetry for free clusters34
2
The source for thermalized cluster ions38
1
Melting temperatures40
2
Latent heats42
1
Other experiments measuring thermal properties of free clusters43
1
A closer look at the experiment
44
6
Beam Preparation44
1
Reminder: Canonical versus microcanonical ensemble44
1
A canonical distribution of initial energies44
1
Free clusters in vacuum, a microcanonical ensemble45
2
Analysis of the fragmentation process47
1
Photo-excitation and energy relaxation47
1
Mapping of the energy on the mass scale47
1
Broadening of the mass spectra due to the statistics of evaporation48
1
Canonical or microcanonical data evaluation49
1
Results obtained from a closer look
50
2
Negative heat capacity50
2
Entropy52
1
Excitations in Clusters
G.F. Bertsch57
48
Statistical reaction theory
63
8
Cluster evaporation rates66
3
Electron emission69
1
Radiative Cooling70
1
Optical Properties of small particles
71
6
Connections to the bulk72
1
Linear response and short-time behavior73
3
Collective excitations76
1
Calculating the electron wave function
77
7
Time-dependentdensity functional theory82
2
Linear response of simple metal clusters
84
5
Alkali metal clusters84
2
Silver clusters86
3
Chains90
4
Polyenes94
1
Benzene95
3
C6098
1
Carbon nanotubes99
3
Quantized conductance102
3
Density Functional Theory, Methods, Techniques, and Applications
S. Chretien and
D.R. Salahub105
56
Density functional theory
108
5
Hohenberg and Kohn theorems110
1
Levy's constrained search111
1
Kohn-Sham method112
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 functionals130
1
The Optimized effective Potential method (OEP)131
1
Comparison between various approximate functionals132
1
LAP correlation functional
132
2
Solving the Kohn--Sham equations
134
7
The Kohn--Sham orbitals136
2
Coulomb potential138
1
Exchange-correlation potential139
1
Core potential139
1
Other choices and sources of error140
1
Functionality140
1
Ab initio molecular dynamics for an alanine dipeptide model142
2
Transition metal clusters: The ecstasy, and the agony144
1
Vanadium trimer144
1
Nickel clusters145
4
The conversion of acetylene to benzene on Fe clusters149
5
Semiclassical Approaches to Mesoscopic Systems
M. Brack161
60
Extended Thomas-Fermi model for average properties
165
15
Thomas-Fermi approximation165
1
Wigner-Kirkwood expansion166
2
Gradient expansion of density functionals168
1
Density variational method169
4
Applications to metal clusters173
1
Restricted spherical density variation173
4
Unrestricted spherical density variation177
1
Liquid drop model for charged spherical metal clusters178
2
Periodic orbit theory for quantum shell effects
180
22
Semiclassical expansion of the Green function181
1
Trace formulae for level density and total energy182
5
Calculation of periodic orbits and their stability187
3
Uniform approximations190
2
Applications to metal clusters192
1
Supershell structure of spherical alkali clusters192
2
Ground-state deformations194
1
Applications to two-dimensional electronic systems195
2
Conductance oscillations in a circular quantum dot197
3
Integer quantum Hall effect in the two-dimensional electron gas200
1
Conductance oscillations in a channel with antidots200
2
Local-current approximation for linear response
202
19
Quantum-mechanical equations of motion203
2
Variational equation for the local current density205
2
Secular equation using a finite basis207
3
Applications to metal clusters210
1
Optic response in the Jellium model211
1
Optic response with ionic structure211
10
Pairing Correlations in Finite Fermionic Systems
H. Flocard221
76
Basic mechanism: Cooper pair and condensation
227
5
Condensed matter perspective: Electron pairs228
2
Nuclear Physics perspective: Two nucleons in a shell230
1
Condensation of Cooper's pairs231
1
Mean-field approach at finite temperature
232
12
Family of basic operators233
1
Duplicated representation233
1
Basic operators234
1
BCS coefficients; quasi-particles235
1
Wick theorem236
2
BCS finite temperature equations238
1
Density operator, entropy, average particle number238
1
BCS equations239
1
Discussion; problems for finite systems240
1
Discussion; size of a Cooper pair241
1
Discussion; low temperature BCS properties242
2
First attempt at particle number restoration
244
7
Particle number projection244
1
Projected density operator245
1
Expectation values246
1
Projected BCS at T = 0, expectation values247
1
Projected BCS at T = 0, equations248
1
Projected BCS at T = 0, generalized gaps and single particle shifts249
2
Stationary variational principle for thermodynamics
251
4
General method for constructing stationary principles251
1
Stationary action252
1
Characteristic function252
1
Transposition of the general procedure253
1
General properties254
1
Variational principle applied to extended BCS
255
7
Variational spaces and group properties256
1
Extended BCS functional257
1
Extended BCS equations258
1
Properties of the extended BCS equations259
1
Recovering the BCS solution260
1
Beyond the BCS solution261
1
Particle number projection at finite temperature
262
2
Particle number projected action262
1
Number projected stationary equations: sketch of the method263
1
Number parity projected BCS at finite temperature
264
11
Projection and action264
2
Variational equations266
3
Average Values and thermodynamic potentials269
1
Small temperatures270
1
Even number systems270
1
Odd number systems271
2
Numerical illustration273
2
Number parity projected free energy differences275
3
Nuclear odd--even energy differences278
6
Extensions to very small systems
284
8
Zero temperature284
4
Finite temperatures288
4
Conclusions and perspectives
292
5
Models of Metal Clusters and Quantum Dots
M. Manninen297
38
Jellium model and the density functional theory
299
3
Spherical jellium clusters
302
3
Effect of the lattice
305
3
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
Theory of Cluster Magnetism
G.M. Pastor335
66
Background on atomic and solid-state properties
338
10
Localized electron magnetism338
1
Magnetic configurations of atoms: Hund's rules339
2
Magnetic susceptibility of open-shell ions in insulators341
2
Interaction between local moments: Heisenberg model343
2
Stonger model of itinerant magnetism345
2
Localized and itinerant aspects of magnetism in solids347
1
Experiments on magnetic clusters
348
4
Ground-state magnetic properties of transition-metal clusters
352
21
Model Hamiltonians352
2
Mean-field approximation354
2
Second-moment approximation356
2
Spin magnetic moments and magnetic order358
1
Free clusters: Surface effects358
3
Embedded clusters: Interface effects361
3
Magnetic anisotropy and orbital magnetism364
1
Relativistic corrections364
2
Magnetic anisotropy of small clusters366
3
Enhancement of orbital magnetism369
4
Electron-correlation effects on cluster magnetism
373
11
The Hubbard model373
1
Geometry optimizationin graph space374
1
Ground-state structure and total spin375
3
Comparison with non-collinear Hartree-Fock378
6
Finite-Temperature magnetic properties of clusters
384
12
Spin-fluctuation theory of cluster magnetism385
3
Environment dependence of spin fluctuation energies388
3
Role of electron correlations and structural fluctuation391
5
Electron Scattering on Metal Clusters and Fullerenes
A.V. Solov'yov401
36
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
Energy Landscapes
D. J. Wales437
72
Levinthal's paradox440
3
``Strong'' and ``fragile'' liquids443
3
The Born--Oppenheimer approximation
446
5
Normal modes447
1
Orthogonal transformation447
2
The normal mode transformation449
2
Describing the potential energy landscape
451
2
Introduction451
2
Stationary points and pathways
453
24
Zero Hessian eigenvalues454
2
Classification of stationary points456
1
Pathways457
1
Properties of steepest-descent pathways458
1
Uniqueness458
1
Steepest-descent paths from a transition state458
3
Principal directions461
1
Birth and death of symmetry elements462
3
Classification of rearrangements465
2
The Mclver-Stanton rules467
1
Coordinate transformations468
3
``Mass-weighted'' steepest-descent paths471
1
Sylvester's law of inertia472
2
Branch points474
3
Tunnelling in (HF)2480
1
Tunnelling in (H2O)3480
1
Global thermodynamics
481
12
The superposition approximation481
4
Sample incompleteness485
1
Thermodynamics and cluster simulation486
5
Example: Isomerisation dynamics of LJ7491
2
Finite size phase transitions
493
6
Stability and van der Waals loops494
5
Basin-hopping global optimisation500
9
Confinement Technique for Simulating Finite Many-Body Systems
S. F. Chekmarev509
56
Key points and advantages of the confinement simulations: General remarks
517
2
Methods for generating phase trajectories
519
2
Conventional molecular dynamics519
1
Stochastic molecular dynamics520
1
Identification of atomic structures
521
2
Quenching procedure521
1
Characterization of a minimum522
1
Confinement procedures
523
10
Reversal of the trajectory at the boundary of the basin. Microcanonical ensemble523
7
Initiating the trajectory at the point of the last quenching within the basin. Microcanonical and canonical ensembles530
3
Confinement to a selected catchment area. Some applications
533
8
Fractional caloric curves and densities of states of the isomers533
4
Rates of the transitions between catchment basins. Estimation of the rate of a complex transition by successive confinement537
2
Creating a subsystem of a complex system. Self-diffusion in the subsystem of permutational isomers539
2
Complex study of a system by successive confinement
541
19
Surveying a potential energy surface. Strategies542
1
Strategies to survey a surface542
1
A taboo search strategy. Fermi-like distribution over the minima542
9
Kinetics551
2
Equilibrium properties553
1
Study of the alanine tetrapeptide554
6
Molecular Clusters: Potential Energy and Free Energy Surfaces. Quantum Chemical ab initio and Computer Simulation Studies
P. Hobza565
20
The hierarchy of interactions between elementary particles, atoms and molecules567
1
The origin and phenomenological description of vdW interactions568
2
Calculation of interaction energy
570
3
Vibrational frequencies
573
1
Potential energy surface
574
2
Benzene... Arn clusters577
1
Aromatic system dimers and oligomers578
2
Nucleic acid-base pairs580
5
Seminars by participants
585
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