First Principles Energy Methods: The Many-Body Problem

Lecture Description

Course Description

This course uses the theory and application of atomistic computer simulations to model, understand, and predict the properties of real materials. Specific topics include: energy models from classical potentials to first-principles approaches; density functional theory and the total-energy pseudopotential method; errors and accuracy of quantitative predictions: thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations; free energy and phase transitions; fluctuations and transport properties; and coarse-graining approaches and mesoscale models. The course employs case studies from industrial applications of advanced materials to nanotechnology. Several laboratories will give students direct experience with simulations of classical force fields, electronic-structure approaches, molecular dynamics, and Monte Carlo.

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Lecture Notes

Course Index

1. Introduction and Case Studies
2. Potentials, Supercells, Relaxation, Methodology
3. Potentials 2: Potentials for Organic Materials and Oxides - It's a Quantum World!
4. First Principles Energy Methods: The Many-Body Problem
5. First Principles Energy Methods: Hartree-Fock and DFT
6. Technical Aspects of Density Functional Theory
7. Case Studies of DFT
8. Advanced DFT: Success and FailureDFT Applications and Performance
9. Finite Temperature: Excitations in Materials and How to Sample Them
10. Molecular Dynamics I
11. Molecular Dynamics II
12. Molecular Dynamics III: First Principles
13. Monte Carlo Simulations: Application to Lattice Models, Sampling Errors, Metastability
14. Monte Carlo Simulation II and Free Energies
15. Free Energies and Physical Coarse-Graining
16. Model Hamiltonions
17. Ab-Initio Thermodynamics and Structure Prediction
18. Accelerated Molecular Dynamics, Kinetic Monte Carlo, and Inhomogeneous Spatial Coarse Graining
19. Case Studies: High PressureConclusions