Collective proton transfer in ordinary ice: local environments, temperature dependence and deuteration effects

Abstract

The transfer of multiple protons in hydrogen-bonded networks usually occurs one proton at a time. At sufficiently high temperatures, each proton transfers via thermally activated hopping along its hydrogen bond, thereby moving a charge defect through the network. At low temperatures, quantum-mechanical tunnelling might set in instead, thus avoiding hopping over the energy barriers. In the case of several transferring protons, independent thermal hopping or quantum tunnelling of the individual protons becomes less favourable because of a significant creation of charge defects. In individual molecules or hydrogen-bonded molecular complexes, for instance, double proton transfer is often found to be concerted. Multiple proton transfer that avoids charge defects can occur in cyclic topologies built from several hydrogen bonds that allow for directional chains of proton transfer. This requires perfect proton order within these rings, which imposes handedness and thus chirality, and changes parity upon transfer of all protons. Ordinary ice, which is hexagonal ice I, is the most stable form of crystalline ice obtained upon freezing liquid water at ambient pressure and consists of interconnected six rings of oxygen atoms that host six protons each. These hexagonal rings remain proton disordered even down to low temperatures, as heralded by the residual entropy of ice I. However, owing to combinatorics, a certain number of these six rings is proton ordered in macroscopic crystals. These chiral hexameric rings might support coherent tunnelling of the hosted protons. Indeed, there is some evidence in the recent literature, both experimental and simulational, that correlated tunnelling of all six protons might be possible in proton-ordered six rings in ice I if temperatures are low enough. In this Perspective, the key ideas and previous findings will be reviewed in the light of relevant experiments with a focus on available ab initio path integral simulation work supplemented with additional data provided herein.

The Case of Formic Acid on Anatase TiO2(101): Where is the Acid Proton?

“…Secondly, earlier studies suggest that while quantum fluctuations dominate at low temperatures, the thermally activated classical behavior should prevail at room temperature . To explore this hypothesis, we simulated the adsorption of DCOOD at 300 K, which is less sensitive to quantum effects than HCOOH . This simulation reveals that even the acid deuteron shuttles between TiO 2 and formate (Figure S5).…”

The Case of Formic Acid on Anatase TiO2(101): Where is the Acid Proton?

“…Fort he two PBE minima, we calculated the harmonic frequencies (Table 1): in line with the 300 Ks pectrum, there are no OH signals at wavenumbers > 3000 cm À1 ,a nd the n(CH) modes are at much higher energies.T he low n(OH) values are due to very strong molecule-surface H-bonding,as [a] Experimental data [9] included for comparison refer to monodentate species on non-defective anatase(101). So far, we discussed the thermal behavior of HCOOH on anatase TiO 2 (101) in ac lassical-mechanics frame.A ctually, proton-transfer events can be influenced by quantum effects, [19][20][21][22][23] in particular by zero-point energies (ZPE). [22] Although tunnelling may be relevant for intramolecular proton transfers, [24] an overwhelming dominance of ZPE effects was demonstrated for intermolecular and/or surfacemediated proton transfers.…”

“…So far, we discussed the thermal behavior of HCOOH on anatase TiO 2 (101) in ac lassical-mechanics frame.A ctually, proton-transfer events can be influenced by quantum effects, [19][20][21][22][23] in particular by zero-point energies (ZPE). [22] Although tunnelling may be relevant for intramolecular proton transfers, [24] an overwhelming dominance of ZPE effects was demonstrated for intermolecular and/or surfacemediated proton transfers. [20,25] Thus,w eo ptimized the structure of the activated complex III using the PBE functional.…”

“…[9,8c] Secondly,e arlier studies suggest that while quantum fluctuations dominate at low temperatures,t he thermally activated classical behavior should prevail at room temperature. [22,27] To explore this hypothesis,w es imulated the adsorption of DCOOD at 300 K, which is less sensitive to quantum effects than HCOOH. [22,27] This simulation reveals that even the acid deuteron shuttles between TiO 2 and formate ( Figure S5).…”

“…[22,27] To explore this hypothesis,w es imulated the adsorption of DCOOD at 300 K, which is less sensitive to quantum effects than HCOOH. [22,27] This simulation reveals that even the acid deuteron shuttles between TiO 2 and formate ( Figure S5). Hence,aclassical double-well model may be eligible to describe room-temperature HCOOH adsorption on defect-free anatase TiO 2 (101), and might be likely transferable to stoichiometric anatase nanoparticles mainly terminated by {101} facets,w ith defects mostly localized at edges and corners.…”