- Elements of Statistical Mechanics and Thermodynamics
– Relationship between macroscopic and microscopic quantities
– Dynamical systems: phase space and trajectories
– The microcanonical ensemble (NVE)
– Axiomatic definition of Entropy
– The canonical ensemble (NVT)
– Axiomatic definition of Helmholtz free energy
– Fluctuations of the Energy in the NVT ensemble
- Molecular modelling of systems in the condensed phase
– Time-evolution: from quantum to classical dynamics
– The Born-Oppenheimer approximation / BO dynamics
– Hellmann-Feynman theorem for the calculation of quantum mechanical forces
– Sampling the phase space: ergodic hypothesis
– Molecular dynamics algorithms (Verlet, Leapfrog, velocity Verlet)
– Ab initio MD
– Mechanical models – force fields
– time-step and thermostats, Shake algorithm
– Calculation of non-bonded forces - truncation methods
– Ewald summation for electrostatic interactions
- Enhanced sampling methods
– Conformational sampling and convergence
– Slow events: activated vs. diffusional phenomena
– One dimensional methods: Thermodynamic integration, Free-energy perturbation, Umbrella sampling
– Metadynamics
- Large-scale simulations: Coarse graining
– Data vs. Information, emergent properties
– Coarse grained mapping - representations
– Coarse grained Hamiltonians - force matching, Iterative Boltzmann Inversion
– A Simple CG representation: the Elastic Network Model
- Mixing the scales
– Hybrid QM/MM
– All-atom/CG models
– Hybrid particle/density-field approach
- Lab experiences
– Kac model of molecular chaos
– Writing a simple MD code
– Investigating coupled harmonic oscillators
– Coupled penduli: Ljapunov instability
– thermostats and barostats
– A simple van de Waals gas
– GROMACS: example of a professional MD package - Water models
– Simulations of a peptide in water