The Geometric Phase Shows up in Chemical Reactions

One of the simplest chemical exchange reactions involves a system of three hydrogen atoms: $\mathrm{H}+{\mathrm{H}}_2\to {\mathrm{H}}_2+\mathrm{H}.$ Surely, chemists have felt, one should be able to calculate the cross sections for this reaction from first principles. But the computations have not been easy. Only in the last six years or so have theorists, aided by efficient methodologies and access to supercomputers, been able to predict the cross sections in sufficient detail for comparison with experiments, which themselves have evolved in precision. The agreement has been good—well, almost. Small discrepancies, especially at higher total energies, stubbornly refused to yield to adjustments in either the calculations or the experiments. Now Yi‐Shuen Mark Wu and Aron Kuppermann of Caltech have erased these pesky discrepancies by including a topological effect known as the geometric phase. Michael Berry (University of Bristol) has called attention to the presence of this phase, which now bears his name, in a wide variety of physical systems. (See Berry’s article in PHYSICS TODAY, December 1990, page 34.)