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Four Atoms and a Supercomputer

Aron Kuppermann

Ken Museth
Desheng Wang
Mark Wu

T hose ball-and-stick molecule models in high school chemistry class were useful simplifications that hid the complicated reality of chemical reactions at the atomic level. To truly understand the dynamics and energetics of chemical reactions, it is necessary to perform astonishingly complex numerical calculations involving quantum mechanics. Caltech's Aron Kuppermann has been a pioneer in the quantum mechanical theory of chemical reactions and in the use of supercomputers to model and predict their cross sections and rates from first principles. With his research staff and assistance from the Caltech Center for Advanced Computing Research (CACR), an NPACI Resource Partner, Kuppermann is advancing his quantum reaction scattering codes and evolving them to accommodate more complex chemical reactions. His current efforts will run on NPACI's newest machines--initially the Hewlett-Packard V2500 at CACR, then Blue Horizon, the teraflops IBM RS/6000 SP at SDSC.



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NPACI's HP V2500 at Caltech

For nearly two decades, Kuppermann has been a leader in the field of ab initio computational chemistry and theoretical chemical dynamics. Six years ago he and his research associate Mark Wu discovered a fundamental quantum phenomenon in a three-atom reaction, in which a two-atom hydrogen molecule collides with a lone hydrogen atom resulting in an exchange between that atom and one of the molecule's atoms.
This phenomenon, called the geometric phase effect, results from the evolution of the three-body system along alternative paths from one configuration to another during the reaction; its discovery closed a gap between experimental results and dynamical theory. To demonstrate the potential of distributed computing, some of these calculations used the supercomputing resources of both Caltech and SDSC, linked into a distributed processing system by one of the fastest networks in existence at that time.


"At the time, we could only dream of the day when we would be able to tackle a four-atom calculation," Kuppermann said. "We knew we would need a computer in the teraflops range to handle the problem efficiently. Such machines didn't exist."

They do now. Kuppermann's current project as an allocated user of NPACI resources, is an effort to perform calculations for reactive collisions in the reaction OH + H2 * H + H2O--the first accurate state-to-state reaction dynamic calculation for a four-atom chemical reaction.

The project will establish state-to-state cross sections for the reaction, a "benchmark-quality" database for the computational chemistry community. The four-atom benchmark calculations, being developed jointly with postdoctoral researchers Desheng Wand and Ken Museth, can serve as important testing grounds for approximate methods, as they have for triatomic calculations in the past.

"The quantum dynamics of four-atom systems are important in chemistry," Kuppermann said, "because they play a central role in many chemical processes, including combustion, atmospheric chemistry, and plasma chemistry. There is the intriguing possibility of learning enough about these processes to be able to influence the course of a reaction by, for example, selecting the vibrational energy of the reagents."

The quantum dynamical evaluation of chemical reaction cross sections involves two major steps. One is the generation of a set of surface functions for the expansion of the time-independent Schrödinger equation. The other involves solving a set of coupled second-order ordinary differential equations; this step requires matrix inversions and runs efficiently on massively parallel machines.

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"Each additional atom adds three more vibrational degrees of freedom to the system," said Kuppermann, "and the number of coupled equations to be solved increases significantly." For four-atom reactions, the number of such equations can range from 4,000 to 10,000 or more, and highly parallel computers that can sustain rates in the teraflops range are needed to solve them.

With the assistance of Wu and the CACR staff, the project is porting the algorithm to Caltech's new 128-processor Hewlett-Packard V2500 supercomputer at CACR, which entered full production this past May. The V2500--actually a linked pair of 64-processor systems--features 128 gigabytes of memory, more than a terabyte of on-line disk storage, and peak system performance rated at 225 gigaflops.

"The V2500 performs at about a quarter of a teraflops," Kuppermann said. "Our initial efforts focus on this machine. When the project is completed, we anticipate making the code and the results available to the reaction dynamics community at large."

Later efforts will port the quantum reaction dynamics code package to NPACI's teraflops-scale Blue Horizon, the 1,152-processor IBM SP system at SDSC. "We are eager to try out our code on this machine," Kuppermann said.

Kuppermann's work may prove to have applications in computational chemistry beyond the reaction dynamics of simple molecular systems. The reactions of large biological molecules often involve only three or four centers, and some of the quantum mechanical evaluation techniques he is pioneering may prove useful for understanding these larger systems. --MG *

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