Computer simulation

Background and personal history

In research on the properties of materials, it is possible to simulate materials at the level of the atom and molecule. From the laws of physics – mechanics and thermodynamics in the first instance, but also quantum mechanics for some simulations –

I did my very first simulation in my PhD. In those days you could not download software from the web, but you had to write your own programs. I write a program to find the minimum of the potential energy of a crystal composed of molecules interacting through simple potentials, but including the Coulomb potential which required incorporating the Ewald method into my program.

DAP and MD on orientational disorder.

Simulations with interatomic potentials

The earliest atomic-scale simulations of materials used simple empirical functions to describe the energy between pairs of atoms. These included a representation of the repulsion experience by neighbouring atoms if they get too close, sometimes a long-range dispersion interaction associated with the effects of fluctuations of the atomic electron density, and Coulomb interactions. These models are still used today, although the are frequently augmented by terms that account for bending of bonds and ionic polarisation. The parameters of these models can be tuned by fitting calculations to experimental data, or to the results of more-exact quantum mechanical simulations.

Nowadays many applications do better by direct applications of quantum mechanical methods, whether using the popular Density Functional Theory approach or methods developed in molecular chemistry. We make use of such methods where we feel that empirical methods may not work so well. However, there is one application where we believe that empirical models will dominate for many years yet, and that is in dynamic simulations of large samples over long periods of time. Quantum mechanical methods are simply too slow in such cases.

Lattice dynamics calculations

To a good first approximation, the motions of atoms within a crystal can be represented as harmonic waves.

Molecular dynamics simulations

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Monte Carlo method

The Monte Carlo (MC) method is a statistical approach to study the thermodynamics of a collection of atoms. The name comes from the use of random numbers (like the roll of the dice) to change the system. In short, the MC method proposes a series of random changes to the sample (like a random displacement of an atom, or swapping the positions of two atoms selected a random, or flipping of a magnetic moment). If each change lowers the energy, it is automatically accepted. If not, it is accepted with a probability based on the relative size of the energy change and a given value of the temperature. After many steps the system reaches a state of thermodynamic equilibrium, and from many calculations it is possible to calculate quantities such as the average energy and its variance (from which we can get properties such as the heat capaci

Reverse Monte Carlo method