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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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