# News

### Filtering Down – New Tools for Atomic Scale Simulations

**Within the NanoTP action, Prof. Briddon and Dr Rayson have now developed a new “filtration algorithm” based version of their code, AIMPRO, which other scientists within the project from across Europe are using to model and predict a diverse range of new nanomaterials and their properties...**

**Filtering Down – New Tools for Atomic Scale Simulations**

Back in the last millennium (well, quite near the end), computing was not for everyone, and computers were slower than they are now. Computing was mainly reserved for “important issues” rather than entertainment. I had surfed the early waves of the computer revolution, used the first pre-PC at school (I think it had 8kB memory), the first UNIX workstations at the university for my PhD research and in early 1995 became the proud owner of a cutting-edge Silicon Graphics workstation which could deliver about 300MFlops (300 million floating point operations per second – today a good laptop can deliver 10 times that).

I used all this raw computer power (which back then cost around £25,000) to carry out a certain type of quantum-mechanical calculation, called local density functional (LDF) calculations. Compared to some other theoretical approaches in quantum mechanics which tried to capture all the interactions between nuclei and electrons to glean insights into the behaviour of the modelled molecule, and which quickly exceeded the available computer power, the LDF approach cut down significantly the amount of equations which needed to be solved. Even so, calculations of moderate systems with maybe 30 atoms took weeks or months to run. A lot of waiting (and thinking) was involved.

Many innovations in computer hardware have come along since, as have massively parallel machines which can split the problem into many smaller parts and solve them simultaneously. This allowed quicker turn-around times and enabled researchers to tackle larger systems, which started to resemble real-life situations. One such system was a “bucky-onion”, which contained concentric spherical carbon shells similar to the now famous “buckyball” molecule (C_{60}, buckminsterfullerene).

However, there was still a feature in the LDF calculation which limited significant progress, a quantum-leap was needed, so to speak. The number of equations to solve for a system with *n* atoms grew approximately proportionally to *n ^{3}* – which means that doubling the number of atoms will make the calculation about 8 times more complicated & time consuming.

Seriously large systems of interest to solid state physicists were still out of reach until recently, when Prof Patrick Briddon from University of Newcastle and Dr Mark Rayson from Surrey University came up with an ingenious way to speed up LDF calculations of such systems, using a new “filter-algorithm”. The work was published in 2009, entitled “*Highly efficient method for Kohn-Sham density functional calculations of 500–10,000 atom systems*”.

“*The idea is that for an element such as carbon or silicon, one can produce four functions to describe each atom which are given by a combination of Gaussians on the atom and on neighbouring atoms. The use of 4 functions per atom gives calculations with almost the same precision as a conventional basis which uses 20-40 functions.*” says Prof Briddon.

“*The construction [of functions] is automatic - it is done independently for every atom in the system so, for example C atoms near a surface will have functions that describe this environment, functions for a charged or under-coordinated atom are likewise automatically optimised for that environment.*” he continues.

The construction of these functions for one atom takes a time which is independent of the size of system. The construction of functions for all atoms in a unit cell is thus linear scaling with the atoms in the cell. Once these functions are constructed, because of the *n ^{3}* rule, the result is a speed-up of 20

^{3}/4

^{3}

_{ }

_{à}

_{ }40

^{3}/4

^{3}

_{ }i.e. 125 to 1000 times faster.

The use of only 4 functions per atom is the same as what is used in much simpler (and less accurate calculations, e.g. “tight binding” or “semi-empirical” calculations), however, for the largest systems the researchers can now do full LDF at the computational “cost” of tight-binding. High speed calculations with high accuracy !

Within the NanoTP action, Prof. Briddon and Dr Rayson have now developed a new “filtration algorithm” based version of their code, AIMPRO, which other scientists within the project from across Europe are using to model and predict a diverse range of new nanomaterials and their properties.

** What does the future hold?**

We are now nearly at the point where we can simulate how a single, very small silicon-based transistor behaves at the level of its individual atoms (and electrons), and what may happen if we try to miniaturise it even further. We can model other novel exotic materials, such as graphene and nanoribbons, which may in future replace conventional semiconductor chips and which are tipped to have a wide range of other advanced applications, such as advanced solar-cells or for scanning devices (e.g. for airport security).

Bernd Eggen

Associated outreach writer, NanoTP

*The author would like to thank Prof Patrick Briddon, Dr Mark Rayson and Dr Chris Ewels for additional material & advice. Article reference: ***Phys. Rev. B 80, 205104 (2009 )**

* 3 July 2014*