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“Everything in solids is held together by electrostatic forces,” says van Schilfgaarde. “You can think of this as a huge dance with an astronomically large number of particles that is essentially impossible to solve. The raw interactions among these particles are remarkably complex.
“Hedin replaced the raw interactions with ‘dressing’ the particle with a screened interaction,” van Schilfgaarde continues, “so the effective charge is much smaller. It becomes much more tractable but the equations become more complicated — you have an infinite number of an infinite number of terms. The hope is that the higher-order terms die out quickly.” “We’re pretty confident we got the approach right,” he says. He now would like another group to independently verify this way of framing the task.
The researchers use a molecular dynamics code, VASP, to model equations of state in high-energy-density matter. These equations of state depend on quantities like electrical conductivity. Calculating this requires detailed knowledge of the electronic structure — a perfect application for Faleev’s work. The researchers hope to describe optical spectra, calculate total energy, and account for more than 10 atoms in a unit cell at 100 times the current speed.
Accelerating the code would facilitate modeling in other research areas at Sandia, such as simulating titanium dioxide used in surface science, or aiding research into carbon nanotubes that might be used in electronic or optical devices.
“To calculate absorption or optical spectra is a huge problem,” Faleev says with anticipation. “To make it faster is a huge problem. To make it more accurate is a huge problem. To incorporate VASP is a huge problem.”
Van Schilfgaarde agrees. “It’s quite an accomplishment to do it at all. It takes someone who is very strong in math, and a clever programmer. We spent easily five to six man-years between us to make it work. If we can get the approach right, we can have a theory that’s universally accurate for anything we want — that’s really pretty neat, just requiring knowledge of where the atoms are.
Takao Kotani, of Arizona State University, is also an author on the Physical Review Letters paper.
Van Schilfgaarde believes the theory’s advantage would be to offer true insight into material behavior. “It’s kind of like adding night-vision goggles to soldiers working in the dark,” he says. “Probably in 10 years, everyone will use this.”
Technical contact: Sergey Faleev, (925) 294-3244, sfaleev@sandia.gov
Media contact: Mike Janes, (925) 294-2447, mejanes@sandia.gov