A Quantum Mechanical Tweak | February 4, 2008 Issue - Vol. 86 Issue 5 | Chemical & Engineering News
Volume 86 Issue 5 | p. 29
Issue Date: February 4, 2008

A Quantum Mechanical Tweak

Study combining experiment and theory demonstrates that electron-nucleus coupling has minor effect on reactions
Department: Science & Technology
Energy Probe
A laser photodetaches an electron from ClH2- to elucidate the reactivity of Cl + H2.
Credit: Etienne Garand
Energy Probe
A laser photodetaches an electron from ClH2- to elucidate the reactivity of Cl + H2.
Credit: Etienne Garand

THE BORN-OPPENHEIMER (BO) approximation says that because electrons move so much faster than atomic nuclei, the motions of the two can be treated separately to simplify quantum mechanical calculations. In recent years, experimental and theoretical studies of the reactions of the halogens Cl or F with H2 or D2 have led to a controversy over whether the approximation is valid or whether electronic and nuclear coupling interactions must be included in reaction-modeling calculations.

Such three-atom reactions are simple enough "that we should, in principle, be able to measure and calculate everything and get perfect agreement," says Daniel M. Neumark, a chemistry professor at the University of California, Berkeley. "But it turns out that we can't."

Now, a team led by Neumark; Millard H. Alexander, a chemistry professor at the University of Maryland; and David E. Manolopoulos, a chemistry professor at the University of Oxford, has furthered the understanding of such systems (Science 2008, 319, 72). They demonstrate that although including coupling can improve agreement between theory and experiment, the effects are minor and theoretical chemists can continue to use the BO approximation.

The controversy stems from work by research fellow Kopin Liu of Academia Sinica, in Taiwan, and coworkers, who used crossed-molecular beam experiments to study the Cl + H2 system. For halogen-H2 or -D2 systems, the BO approximation dictates that Cl or F should be reactive in its ground spin-orbit state, a state in which an electron's spin and orbit are coupled, but not in its excited state (Cl* or F*). Liu's group demonstrated, however, that at high collision energies the BO-forbidden Cl* + H2 reaction occurs two times more often than the ground state Cl + H2 reaction (J. Chem. Phys. 2001, 115, 1197). The result indicates that the BO approximation doesn't work.

IN CONTRAST, experimental and theoretical work on the F + D2 system showed that the F* + D2 reaction becomes significant only at very low collision energies (Science 2007, 317, 1061), confirming that the BO approximation does work. That research was led by Maryland's Alexander along with Xueming Yang, a chemistry professor at Dalian Institute of Chemical Physics of the Chinese Academy of Sciences, and Hans-Joachim Werner, a chemistry professor at the University of Stuttgart, in Germany. The work also agreed with earlier theoretical calculations on F + H2 (J. Chem. Phys. 2000, 113, 11084) and Cl + H2 (Science 2002, 296, 715), research that also involved Alexander and Werner.

Therefore, although Liu's experiments on Cl + H2 seemed to invalidate the BO approximation, experiments on F + H2 and theoretical work on both systems supported it. To address the discrepancy, the new study from Neumark and colleagues used a variant of photoelectron spectroscopy called slow electron velocity-map imaging (SEVI) to photodetach an electron from the ClH2- anion and measure its kinetic energy. This method allowed the group to probe the prereactive region of the Cl + H2 potential energy surface, where BO-forbidden effects are expected to be strongest. This approach should be complementary to Liu's crossed-molecular beam experiments, which detect reaction products.

Comparing the SEVI experimental data with predictions from quantum mechanical calculations, the researchers found that incorporating electronic and nuclear coupling interactions did indeed improve the agreement of theory and experiment, but only by a small amount. When the energy of photodetached electrons is plotted as a function of electron signal, peaks in the spectrum corresponding to the vibrational energy states of ClH2 and Cl*H2 shift by merely 10 cm-1-nowhere near enough to account for the twofold increase in reactivity of Cl* over Cl observed by Liu.

Joel M. Bowman, a chemistry professor at Emory University, notes that the results demonstrate "spectacularly good agreement between theory and experiment." The fact that the researchers saw the same results for ClD2- as ClH2- virtually rules out the possibility that the agreement could have been accidental, he adds.

The results tip the balance in favor of minor non-BO couplings and away from the large effects seen by Liu and coworkers, Bowman says. He cautions, however, that the energy of the Cl* + H2 reaction is higher than the range probed by the SEVI experiments, and he notes that theory and experiment may agree within one range but not another. He would like to see further molecular beam experiments to finally put the disagreement to rest.

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