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The hydroxide anion plays an essential role in many chemical and biochemical reactions. But a molecular-scale description of its hydration state, and hence also its transport, in water is currently controversial. A preeminent challenge in liquid-state physics is the understanding of aqueous phase chemical transformations on a molecular scale. Water undergoes limited autoprotolysis, which is enhanced in the presence of highly charged metal ions such as Be 2ϩ (1, 2). Understanding the hydration and transport of the autoprotolysis products, H ϩ and HO Ϫ , presents unique and interesting challenges for molecular-scale theories of solutions and for simulations. In this paper we focus on HO Ϫ (aq).Because H ϩ and HO Ϫ constitute the underlying aqueous matrix, it is not unreasonable to expect that their transport in water is different from the transport of other aqueous ions. This anomalous diffusion of the H ϩ (aq) and HO Ϫ (aq) has received extensive scrutiny over the years (for example, refs. 3-5), but recently ab initio molecular dynamics (AIMD) capabilities have evolved to provide new information on the solution condition and transport of these species. Over a similar period, the statistical mechanical theory of liquids (especially water) has also become more sophisticated (for example, ref. 6). These two approaches can be complementary, but in typical practice they remain imperfectly connected (but see refs. 2 and 7-11).In an initial AIMD study (12) Ϫ species was 2-3 ps, but statistical characterization was sketchy.Discussions of a transport mechanism for HO Ϫ (aq) typically focus on Agmon's (14, 15) extraction of an activation energy for hydroxide transport from the temperature dependence of the experimental mobilities. Near room temperature that empirical parameter is about 3 kcal͞mol, but it increases by roughly a factor of 2 for slightly lower temperatures. As a mechanical barrier this value, about 5-6 k B T, may be low enough to require some subtlety of interpretation (16); the observed temperature sensitivity of the activation energy, and particularly its increase with decreasing temperature, supports that possibility. We note that a standard inclusion of a tunneling correction would be expected to lead to a decrease of activation energy with decreasing temperature.Ref. 13 framed the consideration of HO Ϫ transport in terms of classical transition state theory and extracted an activation energy from the gas-phase study of Novoa et al. (17). Ref. 13 also considered the importance of tunneling in lowering the barrier for proton transfer by performing path integral calculations. Their combined value of 3

Stochastic dynamics simulations of vibrational relaxation rates are reported for a carbon monoxide molecule adsorbed on the (100) face of copper. A recently developed ‘‘molecular dynamics with electronic friction’’ scheme that self-consistently incorporates both phonon and nonadiabatic electron–hole (e-h) pair mechanisms of energy dissipation is employed. Lifetimes of the C–O stretch, the CO-surface stretch, the frustrated rotation, and the frustrated in-plane translation are examined as a function of temperature between 0 and 450 K. e-h pair dissipation plays a significant role for all modes above 150 K. For the C–O internal stretching mode, the e-h pair mechanism dominates and the lifetime depends weakly on temperature. The frustrated rotational (bending) mode is calculated to have the shortest lifetime at all temperatures, and the temperature dependence is weak. The e-h pair contribution is again largest although the phonon contribution is significant. The CO-surface stretch and the frustrated in-plane translation are the longest lived modes, but exhibit a dramatic decrease in lifetime with increasing temperature. The results suggest that e-h pair dissipation plays a significant role in adsorbate dynamics at metal surfaces when there are chemisorption interactions.