Theory Aims to Describe Fundamental Properties of
Gold is shiny, diamonds are
transparent, and iron is magnetic. Why is that?
The answer lies with a material's electronic structure, which determines its
electrical, optical, and magnetic properties. 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.
But 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.
a team of researchers at Sandia National Laboratories may have a solution that
offers huge potential. Through both internal and Department of Energy Office of
Science funding, Sergey Faleev and his 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," said Faleev. "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
"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
The researchers 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
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
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
"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."
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," adds Sergey,
"everyone will use this."
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed
Martin company, for the U.S. Department of Energy's National Nuclear Security
Administration. Sandia has major R&D responsibilities in national security,
energy and environmental technologies, and economic competitiveness.
Sandia National Laboratories
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