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At non-zero temperature and when a system has low-lying excited electronicstates, the ground-state Born--Oppenheimer approximation breaks down and thelow-lying electronic states are involved in any chemical process. In this work,we use a temperature-dependent effective potential for the nuclei which canaccomodate the influence of an arbitrary number of electronic states in asimple way, while at the same time producing the correct Boltzmann equibriumdistribution for the electronic part. With the help of this effectivepotential, we show that thermally-activated low-lying electronic states canhave a significant effect in molecular properties for which electronicexcitations are oftentimes ignored. We study the thermal expansion of theManganese dimer, Mn$_2$, where we find that the average bond length experiencesa change larger than the present experimental accuracy upon the inclusion ofthe excited states into the picture. We also show that, when these states aretaken into account, reaction rate constants are modified. In particular, westudy the opening of the ozone molecule, O$_3$, and show that in this case therate is modified as much as a 20% with respect to the ground-stateBorn--Oppenheimer prediction.

Non-adiabatic effects within a single thermally-averaged potential energy surface: Thermal expansion and reaction rates of small molecules