From Molecular to Continuum Physics I
Paolo Carloni, Stephan Blügel, Emiliano Ippoliti, Jens Dreyer, Paul Strodel
Scope of the course: To provide key theoretical concepts of atomistic simulation, from first principle quantum mechnical approaches to stochastic dynamics.
Programme
Basic knowledge required for the course - Preparation material
(Regular font = essential, Italics = useful)
Mathematics
• Functions, Taylor expansions, series
• Basic differential and integral calculus
• Vector analysis, matrix algebra
• Differential and integral calculus for several variables
• Fourier series and transformation
• Simple differential equations
Physics
• Basic thermodynamics
• Temperature, ideal gas, kinetic gas theory, laws of thermodynamics
• Statistical thermodynamics
• Canonical ensemble, Boltzmann statistics, partition functions, internal and free energy, entropy
• Basic electrostatics
• Classical mechanics
• Newtonian, Lagrangian, Hamiltonian mechanics
• Quantum mechanics
• Wave mechanics
• Wave function and Born probability interpretation
• Schrödinger equation
• Simple systems for which there is an analytical solution
• Free particle
• Particle in a box, particle on a ring
• Rigid rotator
• Harmonic oscillator
• Basics
• Uncertainty relation
• Operators and expectation values
• Angular momentum
• Hydrogen atom
• Energy values, atomic orbitals
• Electron spin
• Quantum mechanics of several particles (Pauli principle)
• Many electron atoms
• Periodic system: structural principle
• Molecules
• Two-atomic molecules (H2+,H2, X2)
• Many-atomic molecules
Structural Chemistry
• States of matter
• Types of chemical bonding
• Ionic bond, covalent bond, metallic bond
• Hydrogen bonding
• Structure of Hydrocarbons
• Alkanes, alkenes, alkines
• Aromatics
• Alcohols, carbonyl compounds (aldehydes, ketones), carboxylic acids, ester
Computer Science
• Basic working knowledge of linux/unix operating systems
• Basic programming knowledge, e.g. in C, C++, Fortran, Java, Python, Perl, etc.
Scope of the course: To provide key theoretical concepts of atomistic simulation, from first principle quantum mechnical approaches to stochastic dynamics.
Programme
- Ab initio Molecular Dynamics: principle and practical implementation with planewaves and pseudopotentials
- Classical Molecular Dynamics and Hybrid QM/MM Methods - Tutorial
- Simulations in the NVT and NPT ensembles
- Free energy calculations
- Langevin Dynamics. Brownian Dynamics
- Computational Molecular Spectroscopy
- Classical Molecular Dynamics and Hybrid QM/MM Methods - Tutorial
- Simulations in the NVT and NPT ensembles
- Free energy calculations
- Langevin Dynamics. Brownian Dynamics
- Computational Molecular Spectroscopy
Literature:
1. D. Frenkel and B. Smit: Understanding Molecular Simulation (2002)
2. A. Leach: Molecular Modeling - Principle and Applications (2001)
3. D. Marx and J. Hutter: Ab initio Molecular Dynamics: Basic Theory and Advanced Methods (2009)
Lecture notes and slides
1. D. Frenkel and B. Smit: Understanding Molecular Simulation (2002)
2. A. Leach: Molecular Modeling - Principle and Applications (2001)
3. D. Marx and J. Hutter: Ab initio Molecular Dynamics: Basic Theory and Advanced Methods (2009)
Basic knowledge required for the course - Preparation material
(Regular font = essential, Italics = useful)
Mathematics
• Functions, Taylor expansions, series
• Basic differential and integral calculus
• Vector analysis, matrix algebra
• Differential and integral calculus for several variables
• Fourier series and transformation
• Simple differential equations
Physics
• Basic thermodynamics
• Temperature, ideal gas, kinetic gas theory, laws of thermodynamics
• Statistical thermodynamics
• Canonical ensemble, Boltzmann statistics, partition functions, internal and free energy, entropy
• Basic electrostatics
• Classical mechanics
• Newtonian, Lagrangian, Hamiltonian mechanics
• Quantum mechanics
• Wave mechanics
• Wave function and Born probability interpretation
• Schrödinger equation
• Simple systems for which there is an analytical solution
• Free particle
• Particle in a box, particle on a ring
• Rigid rotator
• Harmonic oscillator
• Basics
• Uncertainty relation
• Operators and expectation values
• Angular momentum
• Hydrogen atom
• Energy values, atomic orbitals
• Electron spin
• Quantum mechanics of several particles (Pauli principle)
• Many electron atoms
• Periodic system: structural principle
• Molecules
• Two-atomic molecules (H2+,H2, X2)
• Many-atomic molecules
Structural Chemistry
• States of matter
• Types of chemical bonding
• Ionic bond, covalent bond, metallic bond
• Hydrogen bonding
• Structure of Hydrocarbons
• Alkanes, alkenes, alkines
• Aromatics
• Alcohols, carbonyl compounds (aldehydes, ketones), carboxylic acids, ester
Computer Science
• Basic working knowledge of linux/unix operating systems
• Basic programming knowledge, e.g. in C, C++, Fortran, Java, Python, Perl, etc.