Gold is shiny, diamonds are transparent, and iron is magnetic. Have you ever wondered why that is?
Electronic structure determines many material properties, including electrical, optical, and magnetic. Sandia relies extensively on using and controlling such properties, for everything from assuring weapons reliability to creating devices from nanomaterials.
Predicting a material’s properties by first calculating its electronic structure would cut down experimental time and might lead researchers to uncover new materials with unexpected benefits.
However, commonly used simulations are inaccurate, especially for materials like silicon, whose strongly correlated electrons influence each other over a distance and make simple calculations difficult.
Now a Sandia team may have a solution that offers huge potential. Sergey Faleev (8756) and colleagues applied theoretical innovations and novel algorithms to make a hard-to-use theoretical approach from 1965 amenable to computation. The team’s approach may open the door to discovering new phases of matter, creating new materials, or optimizing performance of compounds and devices such as alloys and solar cells.
Their paper, “Quasiparticle Self-Consistent GW Theory,” appeared in the June 9, 2006, issue of Physical Review Letters. GW refers to Lars Hedin’s 1965 theory that elegantly predicts electronic energy for ground and excited states of materials. “G” stands for the Greens function — used to derive potential and kinetic energy — and “W” is the screened Coulomb interaction, which represents electrostatic force acting on the electrons. “Quasiparticles” are a concept used to describe particle-like behavior in a complex system of interacting particles. Self-consistent means the particle’s motion and effective field, which determine each other, are iteratively solved, coming closer and closer to a solution until the result stops changing.
“Our code has no approximation except GW itself,” Sergey says. “It’s considered to be the most accurate of all GW implementations to date.”
“It works well for everything in the periodic table,” adds coauthor Mark van Schilfgaarde, a former Sandian now at Arizona State University. The paper reports results for diverse materials whose properties cannot be consistently predicted by any other theory. The 32 examples include alkali metals, semiconductors, wide band-gap insulators, transition metals, transition metal oxides, magnetic insulators, and rare earth compounds.
“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, 1023, that is essentially impossible to solve. The raw interactions among the 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.”
The researchers’ use of GW makes the expansion much more rapidly convergent.
“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.
Promise and challenges ahead
In 2006, Sergey was invited to present this work to pulsed power and materials researchers at Sandia/New Mexico. They use a molecular dynamics code, VASP (Vienna Ab-initio Simulation Package) to model, for example, 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 Sergey’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. These are goals Sergey and collaborators are pursuing through Laboratory Directed Research and Development funding.
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,” Sergey 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.”
The quest for precision
The 1998 Nobel Prize in chemistry was awarded for the widely popular density functional theory (DFT). A simplification often used at its core called the local density approximation (LDA) approximates small fluctuations in electron density by using an effective potential in place of many-body interactions. LDA is very good at predicting certain properties of materials, but has serious limitations. For example, in insulators and semiconductors it is well-known to underestimate band gaps (which an electron cannot cross) by
1 eV or more. Despite its limitations, this approach has garnered 30,000 physics citations in the last five years. (For Sandia connections to DFT Nobel laureate Walter Kohn, who trained some Labs researchers, see Lab News articles from the Oct. 23, 1998, and Aug. 23, 2002, issues.)
The work done at Sandia goes beyond this approach, taking advantage of the expertise of the three researchers. Van Schilfgaarde had previously written a large DFT code. Sergey studied electron interactions in graduate school. Takao Kotani of Osaka University asked about making a GW code from van Schilfgaarde’s large DFT code. He was invited to visit Sandia in the 2000-2001 academic year, the same year Sergey was hired. Sergey eliminated the dependence of GW on LDA, making it 10 times as accurate as DFT. (Small band-gap discrepancies remain, on the order of 0.1 eV, and can be attributed to neglecting higher-order terms.)