1) APPLIED MATHEMATICAL METHODS
- First- and second-order ordinary differential equations.
- Representation theory.
- Group theory.
- Variational Calculus
2) ADVANCED PROGRAMMING
- Advanced programming in high-level languages
- Parallel programming
- Programming complex scripts
3) ELECTRONIC STRUCTURE
- Hartee Fock method
- Post-Hartree Fock methods to account for the electron correlation. Multiconfigurational methods
- Density Functional Theory
- Semiempirical methods
4) QUANTUM DYNAMICS
- Representation of the wave function. Finite Basis Representation (FBR) methods, Discrete Variable Representation (DVR) methods, Fast Fourier Transform
- Wave Packets: construction and propagation
- The Multi Configurational Time Dependent Hartree (MCTDH) scheme
- Analysis of the wave function
- Applications to chemical reactivity and molecular spectroscopy
5) INTRODUCTION TO EQUILIBRIUM STATISTICAL MECHANICS
- Principle of Maximum Entropy.
- Maxwell-Boltzmann Distribution.
- Thermodynamic potentials.
- Chemical potential.
- Systems in interaction. Mean field.
- Quantum Statistical Mechanics.
- Multidisciplinary applications in physics, chemistry and biology
6) NON-EQUILIBRIUM STATISTICAL PHYSICS
- Non-equilibrium thermodynamics. Entropy production
- Fluctuation phenomena. Brownian motion. Langevin and Fokker-Planck equations. Fluctuation-dissipation theorem. Master equation. Kinetic theory.
- Diffusion processes. Active transport.
- Activated processes. Rate theory.
- Multidisciplinary applications in chemistry and biology.
7) ADVANCED METHODS OF SIMULATION
- Advanced techniques in Monte Carlo. Biased Monte Carlo methods. Calculation of free energies.
- Quantum Monte Carlo
- Advanced Molecular Dynamics. Thermostats and barostats. Calculation of free energies. Event Driven Molecular Dynamics
- “Ab initio” Molecular Dynamics. Car-Parrinello method.
- Introduction to advanced optimization methods in Statistical Physics.
8) MULTISCALE, COARSE-GRAINED METHODS AND MIXED METHODS
- Introduction to multiscale problems
- Classical algorithms in multiscale modeling
- Simulation of rare events. Activated dynamics. Transition State Theory. Transition Path Sampling. Metadynamics
- Mesoscopic dynamics
- Hybrid methods. QM/MM
9) CONDENSED MATTER
- Phases of matter. Structure and symmetry. Phase transitions.
- Statistical field theories
- The Renormalization Group in Condensed Matter.
- Disordered phases of matter.
- Quantum phases of matter
- Bose gases. Fermi Gases.
10) ELECTRONIC STRUCTURE OF SOLIDS
- Free electron model. Electron transport
- Periodic systems. Bloch functions, electronic bands.
- Distortions in one-dimensional systems
- Electronic structure of solids: 2D systems. Symmetry and Brillouin zones. Fermi surface.
- Electronic structure of solids: 3D systems. Chemical bonding and band structure
- Applications
11) SURFACES AND CATALYSIS
- Basic concepts in heterogeneous catalysis
- Types of catalysts and design
- Heterogeneous catalysis in the chemical industry
- Heterogeneous catalysis and computational chemistry: simulation of spectra and STM images, study of reaction mechanisms, periodic models and nanoparticles.
- Applications
12) MOLECULAR STRUCTURE AND CHEMICAL REACTIVITY
- Electron density and quantitative description of the chemical bond
- Born-Oppenheimer approximation. Topological features of potential energy surfaces. Reaction paths.
- Geometry optimization algorithms. Localization of minima and transition states.
- Applications
13) SOFT MATTER
- Interactions and Phase Transitions
- Macromolecules
- Colloids
- Supramolecular self-assembly
- Interfacial phenomena
- Deformation and Flow
14) COMPLEX SYSTEMS
- Introduction to complex systems: dynamical systems and scaling laws
- Spatio-temporal structures. Modelization, linear stability, simulation
- Introduction to complex networks: structure and applications
15) STRUCTURE OF BIOMACROMOLECULES AND BIOPOLYMERS
- Structure and function of DNA and RNA
- Structure and function of proteins
- Protein folding
- Enzymatic reactions
- Protein-ligand recognition; protein-protein recognition
- Computer-aided drug design
16) COMPUTATIONAL SYSTEMS BIOLOGY
- Introduction to the computational systems biology
- Metabolic regulation. Concepts of enzymology, metabolic control analysis, macromolecular crowding
- Flux balance analysis in metabolism
- Processes in cell signaling and genetic regulation