In a typical solid
material, atoms don't just stand still. They tend to vibrate near an
equilibrium configuration. Heat the solid and its atoms vibrate even
faster. The atoms will move various distances and directions from each
other. How fast atoms vibrate (vibrational frequency) and how far and
which way they move relative to their neighbors (vibrational mode) are
of interest to scientists seeking insights into the structure and behavior
of various materials.
Since the 1950s,
scientists have used computational methods for normal coordinate analysis
(NCA) of systems of atoms. With these methods they have sought to calculate
vibrational frequencies and vibrational modes from the known forces
between the atoms that determine the strength of the chemical bonds
that bind atoms together in a material. But in recent years NCA has
hit a brick wall.
Scientists have
been unable to model more than a few thousand atoms at a time. For larger
systems, the computation becomes enormously expensive. Moreover, some
of the computed frequencies often turn out to be negative, suggesting
that a system known to be stable is, in fact, unstable. According to
an article that appeared in Annual Review of Physical Chemistry
in 1995, "normal coordinate analysis in Cartesian coordinate space is,
with even the most powerful supercomputers, still impossible for proteins
larger than roughly 150 residues."
In 1998 Don Noid
and Bobby Sumpter, both of ORNL's Chemical and Analytical Sciences Division
(CASD), developed an algorithm that allowed them to model 6000 carbon
and hydrogen atoms in polyethylene, the simplest polymer in terms of
chemical structure. Thanks to their innovative computational procedure,
the researchers were able to calculate the forces between each pair
of polyethylene atoms about 1000 times faster than had been done before
using the traditional NCA algorithm.
But a more computationally
challenging task is to extract a set of low-frequency vibrational modes
from the force calculation. For the 6000-atom polyethylene model, the
traditional method would require more than 2 gigabytes of memory and
trillions of calculations per second.
Fortunately, Chao
Yang came to ORNL just in time to make the ORNL algorithm even better.
Yang was hired as the 1999 Alston Householder Fellow in ORNL's Computer
Science and Mathematics Division (CSMD). Householder directed the mathematical
activities of ORNL from 1946 until 1969.
While earning
his Ph.D. degree in computation and applied mathematics from Rice University,
Yang helped develop ARPACK, a popular numerical tool for solving large-scale
eigenvalue problems. When he came to ORNL, he adapted the ARPACK program
to perform large-scale NCA on parallel processors, such as the new IBM
RS/6000 SP supercomputer at the Laboratory, which can now make a trillion
calculations per second. Yang also included sparse matrix techniques
to improve the efficiency of the calculation. This effort has led to
a new "large-scale, time-averaged NCA" algorithm.
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Refrigerator-sized
cabinets house the IBM RS/6000 SP supercomputer on which Chao
Yang runs his algorithm.
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"With the traditional
algorithm," says Chuck Romine of CSMD, "it takes days to calculate vibrational
modes in a 6000-atom system with 18,000 degrees of freedom, which relate
to the directions in which an atom can move. With the new ORNL technique,
it takes less than an hour to calculate vibrational modes in a 6000-atom
system."
To obtain vibrational
frequencies and modes between atoms in a large system, researchers calculate
an array of numbers and zeroes in rows and columns called a matrix.
A zero could represent the force between too widely separated atoms,
and a nonzero number represents the magnitude of force between a pair
of atoms. Yang's technique does not require the storage of thousands
of zeroes in the matrix as does the traditional algorithm, saving time
and data storage space.
In 1999, the new
algorithm allowed the IBM supercomputer to calculate the forces among
24,000 atoms of polyethylene, a world's record. Currently, 100,000 atoms
of the same material are being modeled using the new algorithm.
"Our goal," Yang
says, "is to develop a software tool to allow scientists to study more
general large-scale molecular systems. The user can input known or conjectured
values for the forces and conduct computational experiments. Then, by
comparing predicted results with actual experimental measurements, the
model can be fine tuned to make it better represent the actual material."
In the past year,
Yang and his colleagues have published five papers in technical journals
concerning the use of the new algorithm. Because of their paper in Chemical
Physics Letters, a group at the California Institute of Technology
led by Rudolph Marcus, who won the Nobel Prize for chemistry in 1992,
is collaborating with Yang, Romine, Noid and Sumpter on studying a vital
plant protein that uses light to produce atmospheric oxygen.
Yang will soon
apply the new algorithm to calculate vibrational modes of a rhinovirus,
which causes the common cold. This information could provide insights
into virus structure that could be valuable for development of a cure.
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