Lecturers |
Preface |
Contents |
Experimental Aspects of Metal Clusters / T.P. MartinCourse 1: |
Introduction / 1: |
Subshells, shells and supershells / 2: |
The experiment / 3: |
Observation of electronic shell structure / 4: |
Density functional calculation / 5: |
Observation of supershells / 6: |
Fission / 7: |
Concluding remarks / 8: |
Melting of Clusters / H. HaberlandCourse 2: |
Cluster calorimetry |
The bulk limit / 2.1: |
Calorimetry for free clusters / 2.2: |
Experiment |
The source for thermalized cluster ions / 3.1: |
Caloric curves |
Melting temperatures / 4.1: |
Latent heats / 4.2: |
Other experiments measuring thermal properties of free clusters / 4.3: |
A closer look at the experiment |
Beam preparation / 5.1: |
Reminder: Canonical versus microcanonical ensemble / 5.1.1: |
A canonical distribution of initial energies / 5.1.2: |
Free clusters in vacuum, a microcanonical ensemble / 5.1.3: |
Analysis of the fragmentation process / 5.2: |
Photo-excitation and energy relaxation / 5.2.1: |
Mapping of the energy on the mass scale / 5.2.2: |
Broadening of the mass spectra due to the statistics of evaporation / 5.2.3: |
Canonical or microcanonical data evaluation / 5.3: |
Results obtained from a closer look |
Negative heat capacity / 6.1: |
Entropy / 6.2: |
Unsolved problems |
Summary and outlook |
Excitations in Clusters / G.F. BertschCourse 3: |
Statistical reaction theory |
Cluster evaporation rates |
Electron emission |
Radiative cooling / 2.3: |
Optical properties of small particles |
Connections to the bulk |
Linear response and short-time behavior / 3.2: |
Collective excitations / 3.3: |
Calculating the electron wave function |
Time-dependent density functional theory |
Linear response of simple metal clusters |
Alkali metal clusters |
Silver clusters |
Carbon structures |
Chains |
Polyenes |
Benzene / 6.3: |
C60 / 6.4: |
Carbon nanotubes / 6.5: |
Quantized conductance / 6.6: |
Density Functional Theory, Methods, Techniques, and Applications / S. Chrétien ; D.R. SalahubCourse 4: |
Density functional theory |
Hohenberg and Kohn theorems |
Levy's constrained search |
Kohn-Sham method |
Density matrices and pair correlation functions |
Adiabatic connection or coupling strength integration |
Comparing and constrasting KS-DFT and HF-CI |
Preparing new functionals |
Approximate exchange and correlation functionals |
The Local Spin Density Approximation (LSDA) / 7.1: |
Gradient Expansion Approximation (GEA) / 7.2: |
Generalized Gradient Approximation (GGA) / 7.3: |
meta-Generalized Gradient Approximation (meta-GGA) / 7.4: |
Hybrid functionals / 7.5: |
The Optimized Effective Potential method (OEP) / 7.6: |
Comparison between various approximate functionals / 7.7: |
LAP correlation functional |
Solving the Kohn-Sham equations / 9: |
The Kohn-Sham orbitals / 9.1: |
Coulomb potential / 9.2: |
Exchange-correlation potential / 9.3: |
Core potential / 9.4: |
Other choices and sources of error / 9.5: |
Functionality / 9.6: |
Applications / 10: |
Ab initio molecular dynamics for an alanine dipeptide model / 10.1: |
Transition metal clusters: The ecstasy, and the agony / 10.2: |
Vanadium trimer / 10.2.1: |
Nickel clusters / 10.2.2: |
The conversion of acetylene to benzene on Fe clusters / 10.3: |
Conclusions / 11: |
Semiclassical Approaches to Mesoscopic Systems / M. BrackCourse 5: |
Extended Thomas-Fermi model for average properties |
Thomas-Fermi approximation |
Wigner-Kirkwood expansion |
Gradient expansion of density functionals |
Density variational method / 2.4: |
Applications to metal clusters / 2.5: |
Restricted spherical density variation / 2.5.1: |
Unrestricted spherical density variation / 2.5.2: |
Liquid drop model for charged spherical metal clusters / 2.5.3: |
Periodic orbit theory for quantum shell effects |
Semiclassical expansion of the Green function |
Trace formulae for level density and total energy |
Calculation of periodic orbits and their stability |
Uniform approximations / 3.4: |
Supershell structure of spherical alkali clusters / 3.5: |
Ground-state deformations / 3.5.2: |
Applications to two-dimensional electronic systems / 3.6: |
Conductance oscillations in a circular quantum dot / 3.6.1: |
Integer quantum Hall effect in the two-dimensional electron gas / 3.6.2: |
Conductance oscillations in a channel with antidots / 3.6.3: |
Local-current approximation for linear response |
Quantum-mechanical equations of motion |
Variational equation for the local current density |
Secular equation using a finite basis |
Optic response in the jellium model / 4.4: |
Optic response with ionic structure / 4.4.2: |
Pairing Correlations in Finite Fermionic Systems / H. FlocardCourse 6: |
Basic mechanism: Cooper pair and condensation |
Condensed matter perspective: Electron pairs |
Nuclear physics perspective: Two nucleons in a shell |
Condensation of Cooper's pairs |
Mean-field approach at finite temperature |
Family of basic operators |
Duplicated representation / 3.1.1: |
Basic operators / 3.1.2: |
BCS coefficients; quasi-particles / 3.1.3: |
Wick theorem |
BCS finite temperature equations |
Density operator, entropy, average particle number / 3.3.1: |
BCS equations / 3.3.2: |
Discussion; problems for finite systems / 3.3.3: |
Discussion; size of a Cooper pair / 3.3.4: |
Discussion; low temperature BCS properties |
First attempt at particle number restoration |
Particle number projection |
Projected density operator |
Expectation values |
Projected BCS at T = 0, expectation values |
Projected BCS at T = 0, equations / 4.5: |
Projected BCS at T = 0, generalized gaps and single particle shifts / 4.6: |
Stationary variational principle for thermodynamics |
General method for constructing stationary principles |
Stationary action |
Characteristic function |
Transposition of the general procedure |
General properties |
Variational principle applied to extended BCS |
Variational spaces and group properties |
Extended BCS functional |
Extended BCS equations |
Properties of the extended BCS equations |
Recovering the BCS solution |
Beyond the BCS solution |
Particle number projection at finite temperature |
Particle number projected action |
Number projected stationary equations: sketch of the method |
Number parity projected BCS at finite temperature |
Projection and action / 8.1: |
Variational equations / 8.2: |
Average values and thermodynamic potentials / 8.3: |
Small temperatures / 8.4: |
Even number systems / 8.4.1: |
Odd number systems / 8.4.2: |
Numerical illustration / 8.5: |
Odd-even effects |
Number parity projected free energy differences |
Nuclear odd-even energy differences |
Extensions to very small systems |
Zero temperature |
Finite temperatures |
Conclusions and perspectives |
Models of Metal Clusters and Quantum Dots / M. ManninenCourse 7: |
Jellium model and the density functional theory |
Spherical jellium clusters |
Effect of the lattice |
Tight-binding model |
Shape deformation |
Tetrahedral and triangular shapes |
Odd-even staggering in metal clusters |
Ab initio electronic structure: Shape and photoabsorption |
Quantum dots: Hund's rule and spin-density waves |
Deformation in quantum dots |
Localization of electrons in a strong magnetic field / 12: |
Theory of Cluster Magnetism / G.M. Pastor13: |
Background on atomic and solid-state properties |
Localized electron magnetism |
Magnetic configurations of atoms: Hund's rules / 2.1.1: |
Magnetic susceptibility of open-shell ions in insulators / 2.1.2: |
Interaction between local moments: Heisenberg model / 2.1.3: |
Stoner model of itinerant magnetism |
Localized and itinerant aspects of magnetism in solids |
Experiments on magnetic clusters |
Ground-state magnetic properties of transition-metal clusters |
Model Hamiltonians |
Mean-field approximation |
Second-moment approximation |
Spin magnetic moments and magnetic order |
Free clusters: Surface effects |
Embedded clusters: Interface effects |
Magnetic anisotropy and orbital magnetism |
Relativistic corrections / 4.5.1: |
Magnetic anisotropy of small clusters / 4.5.2: |
Enhancement of orbital magnetism / 4.5.3: |
Electron-correlation effects on cluster magnetism |
The Hubbard model |
Geometry optimization in graph space |
Ground-state structure and total spin |
Comparison with non-collinear Hartree-Fock / 5.4: |
Finite-temperature magnetic properties of clusters |
Spin-fluctuation theory of cluster magnetism |
Environment dependence of spin fluctuation energies |
Role of electron correlations and structural fluctuations |
Conclusion |
Electron Scattering on Metal Clusters and Fullerenes / A.V. Solov'yovCourse 9: |
Jellium model: Cluster electron wave functions |
Diffraction of fast electrons on clusters: Theory and experiment |
Elements of many-body theory |
Inelastic scattering of fast electrons on metal clusters |
Plasmon resonance approximation: Diffraction phenomena, comparison with experiment and RPAE |
Surface and volume plasmon excitations in the formation of the electron energy loss spectrum |
Polarization effects in low-energy electron cluster collision and the photon emission process |
How electron excitations in a cluster relax |
Energy Landscapes / D.J. WalesCourse 10: |
Levinthal's paradox / 1.1: |
"Strong" and "fragile" liquids / 1.2: |
The Born-Oppenheimer approximation |
Normal modes |
Orthogonal transformations |
The normal mode transformation |
Describing the potential energy landscape |
Stationary points and pathways |
Zero Hessian eigenvalues |
Classification of stationary points |
Pathways |
Properties of steepest-descent pathways |
Uniqueness |
Steepest-descent paths from a transition state |
Principal directions / 4.4.3: |
Birth and death of symmetry elements / 4.4.4: |
Classification of rearrangements |
The Mclver-Stanton rules |
Coordinate transformations / 4.7: |
"Mass-weighted" steepest-descent paths / 4.7.1: |
Sylvester's law of inertia / 4.7.2: |
Branch points / 4.8: |
Tunnelling |
Tunnelling in (HF)(2) |
Tunnelling in (H(2)O)(3) |
Global thermodynamics |
The superposition approximation |
Sample incompleteness |
Thermodynamics and cluster simulation |
Example: Isomerisation dynamics of LJ7 |
Finite size phase transitions |
Stability and van der Waals loops |
Global optimisation |
Basin-hopping global optimisation |
Confinement Technique for Simulating Finite Many-Body Systems / S.F. ChekmarevCourse 11: |
Key points and advantages of the confinement simulations: General remarks |
Methods for generating phase trajectories |
Conventional molecular dynamics |
Stochastic molecular dynamics |
Identification of atomic structures |
Quenching procedure / .1: |
Characterization of a minimum |
Confinement procedures |
Reversal of the trajectory at the boundary of the basin. Microcanonical ensemble |
Initiating the trajectory at the point of the last quenching within the basin. Microcanonical and canonical ensembles |
Confinement to a selected catchment area. Some applications |
Fractional caloric curves and densities of states of the isomers |
Rates of the transitions between catchment basins. Estimation of the rate of a complex transition by successive confinement |
Creating a subsystem of a complex system. Self-diffusion in the subsystem of permutational isomers |
Complex study of a system by successive confinement |
Surveying a potential energy surface. Strategies |
Strategies to survey a surface / 7.1.1: |
A taboo search strategy. Fermi-like distribution over the minima / 7.1.2: |
Kinetics |
Equilibrium properties |
Study of the alanine tetrapeptide |
Molecular Clusters: Potential Energy and Free Energy Surfaces. Quantum Chemical ab initio and Computer Simulation Studies / P. HobzaCourse 12: |
The hierarchy of interactions between elementary particles, atoms and molecules |
The origin and phenomenological description of vdW interactions |
Calculation of interaction energy |
Vibrational frequencies |
Potential energy surface |
Free energy surface |
Benzene .Ar clusters |
Aromatic system dimers and oligomers |
Nucleic acid-base pairs |
Seminars by participants |