# Method enables bigger models

of minuscule molecular systems

*Posted January 9, 2009*

Lin-Wang Wang |

Imagine that the only way to appreciate the beauty of a Ming vase was to shatter it into a thousand pieces, examine the shape and color of each piece, then glue it back together – here’s the hard part – so it’s impossible to detect the seams.

This is much like the challenge that faced physicist Lin-Wang Wang and his colleagues at Lawrence Berkeley National Laboratory (LBNL) when they set out to develop physics algorithms to model the nanomaterials equivalent of a Ming vase. The next generation of materials for solar cells and a wide range of electronic components will depend on such solutions.

Wang and his LBNL team – Byounghak Lee, Hongzhang Shan, Zhengji Zhao, Juan Meza, Erich Strohmaier and David Bailey – needed new algorithms to simulate the electronic structure of semiconductor nanomaterials. It is a class of systems so intricate and complex that physicists continue to puzzle over the materials’ unique properties. Because nanomaterials are so tiny – approaching electron wavelengths – they behave very differently from the same material in bulk forms.

Those who study nanostructures are interested mainly in the location and energy level of electrons in the system – information that determines a material’s properties. Unlike uniform systems such as graphite and diamond, Wang’s structures can’t be represented by just a few atoms. Because it is a coordinated system, any attempt to understand the materials’ properties must simulate the system as a whole, Wang says.

A reliable method called density functional theory (DFT) allows physicists to simulate the electronic properties of materials. But DFT calculations are time-consuming and any system with more than 1,000 atoms quickly overwhelms computing resources. The challenge for Wang became to find a way of retaining DFT’s accuracy while performing calculations with tens of thousands of atoms.

Petascale computing, which can distribute calculations over thousands of processor cores, presented a new way to solve large systems like nanostructure calculations. But even at the petascale, calculating a system with tens of thousands of atoms will be extremely challenging because the computational cost of the conventional DFT method scales as the third power of the size of the system. Thus, when a nanostructure size increases 10 times, computing power must increase 1,000 times. Making up that power gap would take the hardware community more than a decade of development. Wang had to find a way to make computational cost scale linearly to the size of nanostructure systems. He settled on a method he calls “divide and conquer,” and it worked like a charm.