Computer simulations play a growing role in our society e.g. flight simulators allow pilots to be trained more cheaply and safely than in the air. In science and technology, computer simulation is a powerful tool for understanding or even predicting complex processes in real materials. Simulations are often used alongside conventional experiments, but they can also be used in situations where experiments would be expensive or even impossible to perform e.g. when studying materials in extreme conditions such as the high temperatures and pressures in the Earth's core.
The turn of the last century saw the start of a scientific revolution with the discovery of quantum mechanics (QM), an astonishingly accurate theory that underlies all of our science and technology. What attracted me to my field is the prospect of harnessing the power of QM to apply it to contemporary scientific problems. The challenge is that the equations of QM are very complicated. Even on the fastest computers it is only possible to solve them exactly for small molecules, whereas the systems of interest to scientists today contain many thousands. Even the rapid and relentless progress of computer technology cannot overcome this because of the scaling of the problem.
The work needed to complete a task usually increases with its size e.g. the time taken to mow a lawn is proportional to its area: double the size of the garden and it takes twice as long. This is an example of linear scaling, but the effort to do many tasks increases more rapidly. Arranging a hand in a game of cards usually scales as the square of the number of objects involved: triple the number and it takes nine (three squared) times as long. Some are even worse e.g. solving the travelling salesman problem to find the quickest route which visits a given set of locations. Adding one extra location doubles the amount of time to solve the problem. If three locations can be done in one minute, four will take two minutes, and five will take four minutes. Just 22 will take a whole year! Solving QM exactly scales like this.
However in the 1960s a leap forward was made with the discovery of density-functional theory (DFT), for which the Nobel Prize was awarded in 1998. The origin of the unfavourable scaling of QM is that electrons carry charge. Like charges repel, so one electron's trajectory depends on all the others' as it wants to avoid them. So solving the equations which describe these trajectories becomes much harder as more electrons are involved. The remarkable result of DFT is that the physical properties of the whole system (the answers to the questions we want to ask) do not depend upon the details of the individual trajectories, just their average. This means a linear-scaling approach to QM within DFT is a possibility.
My research focuses on developing practical linear-scaling methods, and has resulted in the ONETEP program for QM simulations of up to 30,000 atoms (so far!) of systems from nanorods for solar cells to enzymes. The next challenge is to find new ways of analysing all the data generated to gain greater scientific understanding. One possibility is to create a virtual laboratory which uses ONETEP to simulate the results of real experiments e.g. how a material absorbs light. The virtual lab gives total control: you can change the arrangement of atoms in a material or molecule and see the effect. The virtual lab will never replace the real one, but it promises to be a powerful tool alongside.