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January 1993


Aron Kuppermann, Mark Wu, California Institute of Technology

Aron Kuppermann and Mark Wu have achieved a milestone in fundamental chemistry by discovering that even the simplest of all chemical reactions requires the inclusion of a property of the geometry of the electronic states of the reacting system, called the geometric phase. This property, although known, had been disregarded by other scientists because it was assumed that it made an indiscernible difference to simple gas-phase reactions at the low atom-molecule collision energies studied.

Though these reactions look simple, "The detailed dynamics are tough to calculate but even harder to measure in the lab" Kupperman pointed out. "Yet these simplest three- and four-body reactions are at the heart of chemistry, because, in a sense, complex reactions are really just a series of the simple ones."

Using a distributed setup of the Intel Delta machine at Caltech and the Cray C90 at the San Diego Supercomputer Center, Kuppermann and Wu effectively calculated the effect of the geometry phase of the reacting system on the dynamics of a simple gas-phase reaction. The test run was a calculation of the hydrogen-deuterium exchange reaction at a total energy of 1.5 eV. With distributed supercomputing, they had the computational power to include the effects of geometric phase and achieve accurate calculations of these reactions. Wu notes, "The calculations were as accurate as the potential energy surfaces used for input. The spectrum of directions taken by reaction products and their energies, can be exactly calculated at a given input energy."

Equally impressive with their results was the speedup they achieved using a distributed computing setup. In their test calculation, Kuppermann and Wu were able to reduce to five hours on the Delta and C90 work that had taken 30 hours on a CRAY Y-MP a year ago.

The speedup was achieved because each part of the problem was tackled by the architecture best adapted to solving it. For the computations to run efficiently, the computer program had two phases that each required the unique capabilities of one of these machines. The generation of a set of surface functions for the expansion of the time-independent Schršedinger equation was performed on the C90 because the machine was well suited to handle the required sequential operations.

The second part of the code used log- derivative propagation methods to solve a coupled ordinary differential equation. This involved a matrix inversion, which ran most efficiently on a massively parallel machine like the Delta. The two parts kept iterating until the calculation was well converged.

The experiment was part of the CASA Gigabit Testbed, one of five "supernetworking" experiments being carried out through the Corporation for National Research Initiatives with funding from NSF and ARPA. The Delta at Caltech was acquired through the formation of the Caltech Concurrent Supercomputing Consortium, an organization of which CRPC is a member.

At present Kupperman and Wu are planning to do a new series of distributed runs using all eight processors of the C90 and its large solid-state-disk memory, as well as the entire 512 nodes of the Delta machine. These runs should further increase the speed of the calculations.

Source: HPCwire, February 4, 1994 Merry Maisel, San Diego Supercomputer Center

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