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Computational Shortcut Speeds Quantum Chemical Calculations

September 11, 1997
Duke University
A Duke University theoretical chemist has described the development and application of a "divide and conquer" method requiring far fewer calculations to model the electronic structure of large molecules.

LAS VEGAS -- A Duke University theoretical chemist has described the development and application of a "divide and conquer" method requiring far fewer calculations to model the electronic structure of large molecules.

Weitao Yang described the technique in two invited talks prepared for this week's annual national meeting of the American Chemical Society. His research is supported by the National Institutes of Health and the National Science Foundation.

Until Yang developed his computational method, theoretical chemists trying to precisely describe the electronic structures of large molecules were stymied by the daunting size of their calculations.

To show how the hordes of electrons in a large molecule interact scientists must use the complex equations of quantum mechanics, said Yang, an associate professor of chemistry. Such interaction determines the molecule's shape and possible functions.

Quantum mechanics describe the behavior of electrons and other subatomic particles so tiny that they no longer behave as everyday objects. They may act as both waves and pinpoint particles, for example, and their locations at any given instant can usually be defined only as probabilities.

"Electrons do not fit in our picture of the classical world," Yang said in an interview. "We need quantum mechanics to describe electrons. And when we do that, we are able to describe

chemical reactions, the breaking and formation of chemical bonds, and many other interesting processes in chemistry and biology."

But, traditionally, chemists doing such quantum mechanical calculations had to look at the big picture. "If they wanted to calculate one part of the molecule they had to calculate the entire molecule at the same time," Yang said.

Such calculations were impossible for molecules bigger than a few hundred atoms, he noted, because the required computations rose by a cube of the number of those atoms. "You soon run out of computer capability," he added.

Yang and his associates changed all that by introducing a method that allows such big quantum mechanical calculations to be vastly speeded up by breaking up the problem.

"We call it the `divide and conquer' method," he said. "In essence, the method enables us to calculate a molecule one piece at a time in a very sophisticated way. Such division is possible because we chemists know that the properties of a molecule are very localized. And these properties depend on the local structure."

Calculations done by Yang's method rise linearly with molecule size, rather than rising by the cube of the molecule's size. "If it takes an hour to do the calculation for 100 atoms, it would take two hours to do the calculations for 200," he explained. "So it's much quicker. We are able to do calculations on our workstations that were impossible before."

Yang first reported on his concept in a paper entitled "Direct Calculation of Electron Density in Density Functional Theory" in the March 18, 1991, issue of the journal Physical Review Letters. His Duke research team subsequently reported on refinements and applications of the method in articles in other journals.

Yang's co-investigators include Taisung Lee, now a post doctoral fellow at Duke, and Darrin York, now a National Institutes of Health postdoctoral fellow at Harvard.

Because Yang's method predicts electron properties so precisely, it can provide researchers a more refined picture of the behavior of big molecules, such as proteins. "We think of proteins as being made up of atoms," he said. "But those atoms have electrons, and electrons are the mediating forces between the atoms."

In joint research with the University of North Carolina at Chapel Hill, Yang's method was recently used to reveal the locations of some of the hydrogen atoms in an enzyme called cytidine deaminase. He said knowledge of the locations of two particular hydrogen atoms is very important for illuminating details of the enzyme's mechanism.

Knowledge of how the enzyme promotes chemical reactions may have important therapeutic uses in anti-tumor drugs, he said.

Hydrogen atoms, made up of a single electron and proton, are too light to be revealed by the standard analytical protein mapping process called X-ray crystallography. That test reveals only the heavier atoms in the protein.

"So it is not possible to really tell where all the hydrogens were from experiments," Yang said. "One can only guess. But our calculations have nailed down hydrogen."

In that work, he is collaborating with UNC-CH theoretical biophysicist Yan Hermans and experimental biochemist Charles Carter, as well as a jointly shared postdoctoral researcher, James Lewis.

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