October 1999

Novel nanoscale normal modes

## Nanoscale science is by definition about things very small, and because nanosystems are on such a tiny scale, much of the progress in research depends on successful computational modeling of the nanosystem’s properties.

CASD, CSMD researchers explore new and bigger ways to model small systemsThose research techniques have met their limits as scientists tackle systems larger than a relatively few atoms or molecules. An ORNL team that includes a newly arrived Householder fellow has devised a new computational approach that could lead researchers toward developing larger and larger nanoscale systems.

“We think this could open a pathway to larger systems,” says Don Noid of the Chemical and Analytical Sciences Division. “This is precisely the size scale that is ideal for molecular simulations.”

Noid and CASD’s Bobby Sumpter, both of whom took an early interest in nanoscience, are working with the Computer Science and Mathematics Division’s Chao Yang to study the vibrational properties of large systems of polymer particles. One of the main computational tools they’ve used is the ARPACK software that Yang helped develop as a graduate student at Rice University.

Currently, Yang is at ORNL through his Householder fellowship, a two-year DOE program for exceptional researchers in computational mathematics.

Sumpter explains that as nanosystem science advances, the systems get larger, atomically speaking. This expansion challenges the usual methods of determining eigenvalues, algebraic variables that provide information on the nanosystems’ properties, such as thermodynamics and mechanical properties.

“Normal-mode analysis is a pillar of computational chemistry, but it’s the least developed method for large systems,” says Noid. He explains that expanding the number of atoms in a model expands the task exponentially.

“Before Yang’s work, it was hard to get models beyond 1000 atoms. In three dimensions that’s a matrix of 3000 times 3000. Storing that is 72 megabytes. That used to be a big problem, although not any more. But double it, and it takes up four times the memory. You’re still limited by the size of the system.”

An ORNL VizLab image of the atomic motion of a 6000-atom polymer particle.The “matrix elements” are values expressed as numbers, including zero. Typically, most—about 98 percent—of the matrix elements are zero or so small that they can be treated as zeros. Factoring out the zeros and storing and operating on the nonzero elements can amount to significant savings of work.

“ARPACK allows the users to take advantage of the sparsity of the matrix, thereby minimizing the storage requirement and improving the computational efficiency,” says Yang.

Noid, Sumpter and Yang have used ARPACK to model a large polymer system of up to 300,000 atoms with good success. Using various techniques, they were able to obtain a large number of vibrational modes within a few hours.

“We wanted to study the vibrational frequency of an exponentially large system,” Sumpter says. “If you apply textbook normal-mode analysis, you get wrong answers. The analysis told us there were instabilities when we knew they were completely stable. We modeled a 6000-atom polymer drop with the standard method and essentially got back garbage.”

Noid and Sumpter, together with former postdoc Bob Tuzan, who is now at the State University of New York, discovered that the unstable modes can be completely eliminated by correctly averaging the atomic interactions. “Over the past few years, we have developed an efficient way to do that, and this makes time-averaging entirely feasible,” says Noid.

Noid and Sumpter plan to model a 24,000-atom polymer, which amounts to 72,000 frequencies in three dimensions. “We need all 72,000 frequencies,” Noid says. “Yang has developed an efficient sliding-window technique to obtain the entire spectrum. No one has calculated a complete spectrum for a system this big.”

Yang says that the calculations, while currently being performed on serial computers, can be adapted to parallel computers as the systems grow larger. Researchers including CASD’s Mike Barnes have been developing more advanced models for nano and microscale particles and have an increasing need for information on thermodynamic and mechanical properties.

“The payoff for this field of science is better materials—from better coatings to advanced industrial materials,” Noid says.

“Chao has been here for only a few months and has already had quite an impact on computational chemistry at ORNL.”—

B.C.