First-Principles Materials Modelling

Modelling materials from `first principles', i.e. by solving the quantum mechanical equations for the material, has become the approach of choice for many materials scientists. The most popular and widely successful framework for doing first-principles calculations is density functional theory, which is a Nobel prize-winning reformulation of quantum mechanics. Within this framework, the complicated many-electron Schroedinger equation for the material is transformed into a set of simpler single-particle Schroedinger-like equations.

In this Graduate module, we introduce density functional theory and the ubiquitous `plane-wave pseudopotential' method, building up the theory step-by-step. The course not only covers the theoretical foundations, but also many practical considerations (e.g. convergence of calculations), and how to use density functional to predict a wide range of experimental spectra and observables. The practical sessions use the CASTEP density functional program. CASTEP is a high-performance implementation of the plane-wave pseudopotential method, which has many academic and industrial users worldwide. The main course web pages may be found here.

The animated image below illustrates CASTEP's iterative approach to solving the quantum equations (the Kohn-Sham equations) for the case of a sodium phenoxide molecule. An initial random cloud of electrons is successively improved by CASTEP, by adjusting the electron density to minimise its energy until it reaches the ground state (the lowest possible energy for this system). As the calculation proceeds the electron cloud `condenses' rapidly onto the molecule, and the atomic orbitals and bonds can be seen. Sodium phenoxide has covalent C-C and C-H bonds, a delocalised metallic-like pi-cloud, a polar C-O bond and an ionic O^- Na⁺ bond, none of which are input into CASTEP; these different chemical interactions all emerge spontaneously during the CASTEP calculation.