A new record has been set by the Oden Institute’s Center for Computational Materials for calculating the energy distribution function, or “density of states,” for over 100,000 silicon atoms, a first in computational materials science. Calculations of this kind enable greater understanding of both the optical and electronic properties of materials.

Jim Chelikowsky leads the Center for Computational Materials, which set a new standard for the number of atoms that can be modeled. They didn’t just raise the bar though. They smashed it – multiplying the previously held record number by a factor of 10.

Chelikowsky along with Oden Institute PhD graduate, Kai-Hsin Liou and postdoctoral fellow, Mehmet Dogan, led the team behind this significant technical advancement in atomic modeling. Working with silicon atoms, they increased the number that could be modeled simultaneously from around 10,000 to over 100,000.

One mathematical way to approach such complex systems is by describing solutions in sines and cosines. This is useful for crystalline matter because it is periodic and we know that the properties of a little piece of a crystal will inform the whole crystal.

The sine and cosine approach does not play well with high performance computing machines though. “Too much time is spent in communicating data between processors as opposed to computational operations. So, this approach fails for large systems,” Chelikowsky explained.

Secondly, if we want to examine systems that are not crystalline, such as clusters, surfaces or amorphous solids, the sine-cosine approach can only be used by artificially replicating the system of interest. This replication operation is cumbersome and has additional technical limitations.

The researchers used what’s known as real space methods – laying down a grid of points, and then solving equations based on the data from those points.

Modeling materials in this way isn’t easy. Most solids (or condensed matter), have around 10^23 atoms per cubic centimeter. Things get even more complex at the quantum scale. In a quantum description, each electron is characterized by a state consisting of 31,000,000 grid points for the case at hand. The number of states is around 250,000 for a 100,000-atom system of silicon. We need to compute roughly 10^13 pieces of information to a high degree of accuracy. If this were not a quantum system, we would need only 3 numbers per atom (not 31 million grid points). In other words, the quantum calculation is roughly ten million times more complicated by that measure.

The equations of interest combine three physical concepts methods to help simplify a solution for the quantum mechanical properties of materials.

“First we look at how the electrons are distributed by assuming whatever happens for an atom will be the same for a solid,” said Chelikowsky. “This is a well-established way to achieve a good starting point, albeit somewhat approximate. Second, we use density functional theory, another extremely popular method. There are literally hundreds, if not thousands, of papers published each year using this technique, which was recognized by a Nobel Prize in Chemisty in 1998.”

Finally, the scientists implement a “pseudopotential model” of the material in question. The pseudopotential model of an atom refers to a method for providing simplified descriptions of complex systems. In this case, the pseudopotential of the silicon atoms’ is found by looking at its chemically important electrons only.

With so much complex mathematics involved in research of this kind, the team relied heavily on resources at Texas Advanced Computing Center (TACC). “We are very fortunate to have such an incredible resource on campus,” said Chelikowsky.