Subject: physorg: representation/simplification of many-electron calculations through two electrons

From: Eugen Leitl <eugen(at)leitl.org>
Date: Wed, 17 Nov 2004 13:38:25 +0100

http://www.physorg.com/news2000.html

Breaking old barrier to better electron representation in molecular
computations

November 17, 2004
Results apply to fields ranging from medicine to superconductivity 

University of Chicago quantum chemist David Mazziotti has proposed a new
research tool that could help scientists more rapidly solve problems in
atmospheric chemistry, combustion, medicine and other areas of research
where the behavior of electrons plays a key role.

"We're in the pioneering stage so we're not going to go and treat all of
these problems right away," said Mazziotti, an Assistant Professor in
Chemistry. But with his new method, "we can do chemistry that cannot be
done otherwise," he said. 

Mazziotti explains his method in the Nov. 19 issue of Physical Review
Letters. Further details will follow in early December in the Journal of
Chemical Physics. 

The key to understanding whether or not a particular chemical reaction
will occur depends on a detailed statistical description of the
electrons' positions in the molecules involved. Until now, scientists
have found it necessary to attempt to represent the motion of all the
electrons in the molecule of interest-a daunting task requiring vast
quantities of computer power. "Just a single water molecule has 10
electrons," Mazziotti said. 

But in the 1950s, researchers theorized that it should be possible to
accurately and more efficiently calculate the electronic properties of a
molecule using only a pair of electrons representing many-even
hundreds-of electrons in a molecular system. Mazziotti compares the feat
to assembling a set of architectural blueprints, which represent in two
dimensions a structure that can be built in three dimensions. 

An architect follows certain rules to ensure that a builder can
translate a two-dimensional sketch into a three-dimensional structure.
"In the same way atoms and molecules consist of many electrons, but
there is a way to represent all of the electrons rigorously with only
two electrons. Certain rules have to be followed to ensure the
two-electron 'sketch' of the molecule accurately represents all the
electrons in the atom or molecule," Mazziotti explained. 

Mazziotti's Physical Review Letters paper realizes a dream that
scientists have pursued for 50 years by introducing a set of
instructions for accurately and efficiently computing with a pair of
electrons that represent the many electrons of the molecule. These
instructions dramatically reduce the amount of computer time and memory
required to compute the electronic properties of a molecule. Now
Mazziotti can do some of the same calculations on his desktop computer
that previously required Japan's Earth Simulator, the world's largest
supercomputer. 

"David has really made a huge contribution in turning the dreams of 50
years ago into useful tools," said Bob Erdahl, a professor of
mathematics at Queens University in Kingston, Ontario. Erdahl said
Mazziotti's Physical Review Letters paper has applications to his own
research in computing how behavior at the subatomic level brings about
macroscopic changes in materials, such as the transition to the
superconducting state. 

"I'm certainly going to look very closely and try to incorporate David's
latest innovation into my work. I think we will very quickly be able to
beat other approaches in this area of solids and compute things that
were out of reach before," Erdahl said. 

Erdahl is especially interested in determining why superconductivity
manifests itself only in two-dimensional layers rather than in
three-dimensional solids. "The computations are of course very difficult
to do. These methods that David is developing and that we're developing
are very helpful in attacking that problem." 

While Erdahl works in mathematical physics, understanding the electronic
energies that atoms and molecules possess also affects almost every area
of chemistry. One such area, Mazziotti said, has broad applications
includes the chemistry of free radicals-highly reactive unpaired
electrons. 

In atmospheric chemistry, free radicals are instrumental in reactions
leading to ozone depletion and the creation of greenhouse gases. Another
area is the combustion of hydrocarbon fuels, which creates a variety of
carbon-based radicals. 

"A lot of people want to know which radicals are present in a given
combustion process and what reactions those were undergoing because
that's going to affect fuel efficiency," Mazziotti said. 

A third area is medicine, because radical-type reactions are common in
the human body. Mazziotti noted that hydroxy urea therapy combats
sickle-cell anemia by forming a radical that triggers a cascade of
additional reactions. "There is a 40 percent reduction in mortality for
patients who receive hydroxy urea treatment for sickle cell," he said. 

Despite the advances that Mazziotti and others have contributed to the
representation of electrons in atoms and molecules, further advances
could be in the offing. He said the field is experiencing a new wave of
research. "We're not done by any means." 

Source: University of Chicago

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Eugen* Leitl http://leitl.org
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