Direct Measurement of Competing Quantum Effects on the Kinetic Energy of Heavy Water upon Melting

Abstract

T he structure and dynamics of liquid water are directly influenced by quantum mechanics, not only in terms of the electronic structure and chemical bonding but also at the level of the nuclear motion. So-called nuclear quantum effects (NQEs) include zero-point energy, tunnelling, isotope effects in the thermodynamic properties, and, what is most relevant to the present work, large deviations from the classical, Maxwell− Boltzmann behavior of both the average nuclear kinetic energy ⟨E K ⟩ and the momentum distribution n(p).Even though NQEs are very large (the zero-point energy content of an O−H stretching vibration is in excess of 200 meV), it is often the case that their net effect on macroscopic properties is relatively small. For instance, the melting temperatures of light and heavy water differ by less than 4 K, and the boiling temperatures differ by just 1 K. Recent theoretical analyses 1,2 have suggested that this could stem from a partial cancellation between quantum effects in the intra-and intermolecular components of the hydrogen bond, so that the net effect is small even if the individual contributions are large. In particular, the competition between quantum effects can be seen very clearly when decomposing the changes in the quantum kinetic energy of protons and deuterons along different molecular axes. 3,4 The mechanism that underlies the competition between changes in the different components of the quantum kinetic energy can be understood by considering as an analogy a twolevel quantum system with an environment-dependent offdiagonal coupling β. A small change in the coupling Δβ, arising from a phase transition or some other change in the environment of the system, will shift its eigenvalues by the same amount proportional to Δβ, but in opposite directions. Even though this picture is clearly oversimplified, it is consistent with a diabatic state model of the hydrogen bond, 5 it demonstrates that the notion of competing quantum effects is nothing exotic, and explains why it returns in many circumstances in the study of water and other hydrogenbonded systems.Competing quantum effects have in fact been identified in a diverse variety of simulations, 1−4 and it seems entirely plausible

Temperature dependence of the zero point kinetic energy in ice and water above room temperature

“…Increased kinetic energy in the solid with respect to the liquid is also reported in Path Integral simulations of water using rigid models [54]. Such combined efforts should help to shed some light on the effects of isotopic substitution (H-D) or the behaviour of hE K ðTÞi in the region below room temperature or near the triple point, where the large discrepancies between experiments on water's protons and deuterons, and theories, are still unexplained [33,35]; we note, in passing, that indications of slight if not almost negligible differences in the deuteron kinetic energies were reported between room temperature liquid and solid heavy water close to the triple point [55], the solid showing in this case a slightly lower kinetic energy than the liquid. Values inferred from macroscopic thermodynamic free energy data on the proton kinetic energy in ice at 269 K and liquid water at 300 K predict a $ 0.5 meV increase from the solid to the liquid [56].…”

Probing the effects of 2D confinement on hydrogen dynamics in water and ice adsorbed in graphene oxide sponges

“…The latter was most recently employed for the understanding of the local environment of hydrogen in polycrystalline ice 47 and heavy water. 48 In M1, the momentum distribution is given by the GaussLaguerre expansion 34,43,49 …”

Effect of quantum nuclear motion on hydrogen bonding

“…This is the opposite trend to the X-H stretch. These opposite dependences lead to the notion of competing quantum effects [9,75,76].…”

“…Anisotropy in the ellipsoid reflects a directional dependence of bonding and the associated vibrational frequencies. Anisotropy in the associated kinetic energy of protons in liquid water and in ice was recently measured by inelastic neutron scattering [76].…”