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First-principles simulation

First-principles simulation has grown to become one of the most influential and important techniques for modelling at the atomic level. With nuclei and electrons as the basic ingredients the system is modelled at a deeper level of physics than with atoms and interatomic potentials. By explicitly including the electrons in the model and treating their interactions using quantum-mechanical laws, chemical bonding arises as an emergent phenomenon of the model. All kinds of bonding - ionic, covalent, metallic, hydrogen can be treated using the same method. The price of this accurate Hamiltonian is a computational cost orders of magnitude higher than atomic potential models. Nevertheless it is possible and convenient with modern parallel computers to simulate systems of hundreds of atoms, and perform optimization and molecular dynamics in a variety of ensembles.

In this advanced course I will provide a rapid introduction to the "nuts and bolts" of first-principles simulation. In accordance with the philosophy of the CCP5 Summer School, the aim is to attempt to open up the "black box" and explain the concepts and algorithms used. The presentation will assume a familiarity with wave mechanics at the undergraduate level and Dirac notation.

In the practicals you will be able to try for yourself using an advanced density functional code. You should be capable of running realistic calculations by the end of the course, and aware of the major aspects of setup and testing that are vital ingredients for success. The practicals will consist of a series of guided exercises with the CASTEP and CRYSTAL codes.

Synopsis

An Introduction to First-Principles Simulation

  • Motivation
  • Quantum-Mechanical approaches
  • Density-Functional Theory
  • Excited states: TD-DFT
  • Electronic Structure of Condensed Phases
  • Total-energy calculations
  • Basis sets
  • Plane waves and pseudopotentials
  • How to solve the equations
  • Ab-initio simulations

Practical calculations using first-principles QM: Convergence, convergence, convergence

  • Convergence
  • Structural Calculations
  • Lattice Dynamics
  • Exchange and Correlation Functionals
  • Summary

Further Study

The lecture notes from the CASTEP workshop held in 2007 are available from http://www.castep.org. Links to a number of ab-initio methods and resources are available at http://electronicstructure.org/.