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Science  05 May 2006:
Vol. 312, Issue 5774, pp. 659
DOI: 10.1126/science.312.5774.659b

Nearly 80 years ago, Born and Oppenheimer showed that during a typical molecular transformation, electronic and nuclear motions can be treated independently of each other. The validity of this Born-Oppenheimer (BO) approximation arises from the nearly 2000-fold mass difference between electrons and protons, which results in the electrons completing their rearrangement before the slower, heavier nuclei begin to move. The approximation provides a mathematically tractable framework for accurate modeling of many chemical reactions (for example, see Nieto et al., Reports, 7 April 2006, p. 86). Although there are a number of well-established cases in which the approximation breaks down, these systems generally involve coupling between electronic and vibrational coordinates, rather than mass variations.

Takahashi and Takatsuka explore the breakdown of the BO approximation in unusual molecules, of interest in fusion research, which host more massive negatively charged particles in place of electrons. Specifically, they model H2+ analogs in which two protons bind either an antiproton or a muon (a product of nuclear decay ∼200 times heavier than an electron). Using semiclassical trajectory calculations, they find that the error in the approximation scales with the 3/2 power of the light-to-heavy particle mass ratio. This result implies that the BO approximation is valid over a wider mass range than is commonly assumed from a 1/4 power mass dependence that appears in the theory's derivation. The authors further confirm this error-scaling relation by carrying out an analysis of the system's energy based on the same perturbational approach used by Born and Oppenheimer. — JSY

J. Chem. Phys. 124, 144101 (2006).

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