Review articleAtomic-scale investigation of nuclear quantum effects of surface water: Experiments and theory
Introduction
Water is vital to human’s daily life and has been extensively investigated throughout the history of science. However, the molecular-level understanding of the structure and many unusual properties of water still remains a great challenge in spite of the persistent development of new scientific instruments and theoretical methods. The mystery of water mainly arises from the intermolecular hydrogen-bonding (H-bonding) interaction. It is well known that H bonds have a strong classic component coming from electrostatics. However, its quantum component can be exceptionally prominent due to the quantum motion of light H nuclei (proton), which play important roles in the structure, dynamics, and macroscopic properties of H-bonded materials [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. Therefore, the accurate assessment of NQEs has been a key issue for the understanding of many extraordinary physical and chemical properties of water.
The NQEs of water mainly arise from quantum tunneling and zero-point motion (ZPM) of protons. In water, the H atom links two oxygen atoms via a covalent bond at one side and a H bond at the other side. Classically, the covalent bond and H bond could be switched through over-barrier proton hopping, as shown in Fig. 1a. Nevertheless, such a switching can be also realized by proton tunneling (Fig. 1a) when the height and width of the potential barrier is sufficiently small, which has been observed in many H-bonded systems [1], [11], [12], [13], [14], [15], [16], [17]. Another quantum nature of proton is ZPM or quantum fluctuation. Unlike classical particles, which are localized in the local minimum of potential well, protons constantly fluctuate at zero-point energy (ZPE) state due to the Heisenberg uncertainty principle. In a harmonic potential well, the ZPM is symmetric, making the averaged position of the proton coincides with the local minimum of potential well (Fig. 1b). However, the real potential profile of OH⋯O has an anharmonic character. The anharmonic ZPM of H nuclei causes the OH covalent bond to expand with respect to the case under harmonic potential, thus the H-bonding strength is enhanced (Fig. 1b). Once the reaction barrier of the proton transfer is significantly reduced, the ZPE plays a decisive role. In this situation, the proton will be totally delocalized and equally shared by the oxygen atoms, leading to a symmetric H bond (Fig. 1c).
The NQEs usually show up in isotopic substitution experiments. When replacing hydrogen (H) atoms with heavier deuterium (D) atoms, macroscopic properties of water exhibit significant isotope effects, which have been explicitly summarized in a recent review [7]. For example, the melting temperature is increased by 3.82 K upon substituting D with H [18], [19] and the temperature of the maximum density is 7.21 K higher in D2O compared with H2O [20], [21]. Upon deuteration, the viscosity increases 23% accompanied by a 23% decrease in water diffusion [19], [20], [22], [23]. Spectroscopic studies of liquid water at ambient temperature provide evidence that D2O is more structured than H2O [2], [24], [25], [26], [27]. These observations suggest that the H-bonding strength is enhanced when exchanging H with D, namely, the NQEs incline to weaken the H-bonding strength in liquid water at room temperature. However, the opposite trend appears at higher temperature [18], [28] and conflicting theoretical simulations also exist [29]. So far, a consensus is not reached and it remains an open question how large the quantum component of H bond is.
The NQEs in water/ice become more prominent at low temperature or when the OO distance of water molecules is small [1], [30], [31], for example, under high pressure, confined in the nano-cavity or at interfaces. The proton dynamics in ice Ih (hexagonal ice) and ice Ic (cubic ice) does not freeze out even down to 5 K, suggesting the existence of the concerted proton tunneling [17]. However, the direct evidence of the concerted proton tunneling is still lacking and under debate [11], [17], [32], [33], [34]. In particular, high-pressure ice has received considerable attention since the intermolecular distance can be continuously tuned by applying high pressure. As the pressure is increased, the ice undergoes phase transition from ice VIII to ice VII, which is believed to be driven by proton tunneling [1]. Symmetric ice X appears at even higher pressure as a result of zero-point fluctuations, in which the proton sits exactly halfway between the two oxygen atoms [1], [35], [36], [37].
The adsorption of water on various solid surfaces gained extensive attention as well, as it is ubiquitous in nature and plays a crucial role in a great many environmental, biophysical, catalysis and even technological processes [3], [38], [39], [40], [41], [42], [43], [44]. The distance between adjacent water molecules is subjected to the atomic arrangement of the surfaces because of the water-substrate interaction. Li et al. reported the substrate dependent NQEs of the H bond by quantum calculations, where the magnitude of proton delocalization between two oxygen atoms was determined by the substrate lattice constant, resulting in partially (on Pt(111) and Ru(0001)) or totally (on Ni(111)) symmetric H bonds [45]. Meanwhile, Kumagai et al. discovered the symmetric H bond in a water-hydroxyl complex on Cu(110) from real-space experiments [46]. In addition, the high diffusion rate of water dimers on Pd(111) at low temperature [47] was supposed to arise from the H-bonding tunneling dynamics of the dimer [48]. Then proton tunneling processes were visualized in a water dimer adsorbed on a Cu(110) surface [49].
Interestingly, water under nano-confinement shows many anomalous behaviors [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61]. For example, extremely fast proton transport through nanochannels and exceedingly wide-range phase transition temperature of water confined in carbon nanotubes were reported [50], [51], [53], [61]. Water confined in a carbon nanotube shows the signature of proton delocalization at low temperature [56]. More strikingly, it was recently found that a single water molecule confined inside a hexagonal shaped channel of the gemstone beryl exhibited a new quantum state, in which the proton is delocalized and tunnels between the six symmetrically equivalent positions [60].
Besides water, NQEs exist in other H-bonded materials as well. In the recently discovered superconducting hydrogen sulfide (H3S) system, which shows the highest superconducting transition temperature Tc of 203 K under high pressure, there is a pronounced isotope effect on Tc [62]. In addition, it was revealed that the superconducting phase only emerged upon H-bond symmetrization, in which the H atoms reside exactly midway between two sulfur atoms [5]. When the protons are treated as quantum particles, the symmetrization pressure will be greatly lowered due to the ZPM of the protons. Therefore, NQEs influence the superconducting phase diagram of hydrogen sulfide dramatically [5]. NQEs could also influence H-bonding interactions and consequently the structure of other H-bonded materials, for instance, hydrogen fluoride (HF) systems [63], [64], cyclohexane (C6H12) molecules and superstructures on metal surfaces [65], protonated and hydroxylated water [30], [31].
NQEs also play key roles in many biological processes such as DNA tautomerization [66], [67], [68] and enzyme catalysis reactions [69], [70], [71], [72], [73], [74]. It was shown that the enzyme-catalyzed reaction was dominated by proton tunneling [75] and exhibited a large kinetic isotope effect greater than 100 [76], [77]. The enzyme ketosteroid isomerase contains a H-bonded network at its active site, which facilitates the quantum delocalization of protons, leading to a pronounced isotope effect on its acidity [73]. Another interesting finding is that protein is more stable in D2O compared with H2O [78], [79] and the bacteria can survive in pure D2O environment [80].
Now we can clearly see that NQEs could not just be treated as corrections to the classical H bond interactions. Instead, NQEs could have a decisive impact in the structure, dynamics, and macroscopic properties of H-bonded materials and biological systems. Although the studies of NQEs in water and aqueous systems have been summarized in several excellent reviews [4], [7], [8], [9], the accurate and quantitative description of NQEs is very scarce mainly due to the great challenge in pursuing a proper treatment of the nuclear motion at a quantum mechanical level in theory and the lack of atomic-scale experimental techniques for condensed phases. In this review, we focused on the atomic-scale investigation of NQEs of surface water with the recently advanced STM technique and PIMD calculation method.
Theoretically, one needs to go beyond the traditional “ball-and-stick” model for the description of the chemical bonding interactions [81]. The most rigorous treatment resides on generating a high-dimensional potential energy surface (PES) for all nuclear degrees of freedom in the configuration space and solving the corresponding Schrödinger equation for the many-body entity of the nuclei. Because of the scaling problem, the targeting systems are normally restricted to very small ones related to gas phase reactions [82], [83], [84]. Starting from the 1980s, an alternative treatment based on the Feynman’s path-integral representation of the quantum mechanics has earned popularity in simulations of large molecular and condensed matter systems [30], [31], [45], [85], [86], [87], [88], [89], [90], [91], [92], [93], [94], [95], [96], [97], [98], [99], [100], [101], [102]. Simulations on the influence of NQEs on H bonds, on surface geometries and reactions, and surface water emerged and started to shed light on the atomic level details of these problems [7], [29], [32], [63], [64], [103], [104], [105], [106], [107], [108], [109], [110], [111]. Despite enormous theoretical efforts toward pursuing proper treatment of the nuclear motion at a quantum mechanical level, accurate and quantitative description of NQEs on the H-bonding interaction has proven to be experimentally challenging.
Conventional experimental methods of studying NQEs are summarized in Table 1, such as sum-frequency generation (SFG) [126], X-ray diffraction (XRD) [2], [35], nuclear magnetic resonance (NMR) [11], neutron scattering [60], [112], [113], [114], [120], [134], [135], and so on. Spectroscopic studies offer valuable insights into the nuclear quantum behaviors of H-bonded materials. However, those techniques have poor spatial resolution and only measure the average properties of many H bonds, which are susceptible to structural inhomogeneity and local environments [15], [136]. Subsequently, the spatial variation and interbond coupling of H bonds lead to spectral broadening, which on the one hand results in the difficulty of spectral assignment, on the other hand may easily smear out the subtle details of NQEs.
Scanning tunneling microscopy (STM) is a promising tool to probe the NQEs of surface water at the atomic-level, with sub-Ångström spatial resolution [137], [138], [139], single-bond vibrational sensitivity [140], [141], [142] and atom/molecule manipulation capability [143], [144]. In the past decade, STM has been extensively used to investigate the structure and dynamics of water on solid surfaces [3], [15], [40], [145], [146], [147], [148], [149], [150]. However, it is not easy to apply STM to study the NQEs of surface water. The main reason lies in that STM is based on the principle of electron quantum tunneling and the tunneling current is only sensitive to the density of states (DOS) of electrons around the Fermi level (EF) rather than the nuclei. One viable way to probe the NQEs is via electron-nuclei coupling, but this requires exceptionally high sensitivity of STM to the frontier orbitals. Unfortunately, water is a close-shell molecule, so the frontier orbitals of adsorbed water are located far away from the EF, resulting in very poor signal-to-noise ratio for imaging and spectroscopy of STM.
In order to overcome the intrinsic limitation, we have developed a series of experimental techniques based on STM, which allow us to access the degree of freedom of protons both in real and energy space. As shown in Section 2, we achieved submolecular-resolution orbital imaging of water by tuning the tip-water coupling, from which we can discern the OH directionality of water monomer and discriminate the H-bonding chirality of water clusters. By developing tip-enhanced inelastic electron tunneling spectroscopy (IETS) [140], [151], [152], we obtained the vibrational spectroscopy of water with enhanced signal-to-noise ratio at single molecule level, which can be employed as an ideal probe for sensing the quantum motion of protons. Theoretically, we have implemented highly efficient path-integral molecular dynamics (PIMD) simulations, in which both electrons and nucleus are treated as quantum particles (Section 3). Based on those novel techniques and methods, we highlight the possibility of atomic-scale investigation of NQEs of surface water in the subsequent sections. In Section 4, we directly visualized the concerted quantum tunneling of protons within the water tetramer by monitoring the reversible interchange of H-bonding chirality in a controlled fashion with a Cl-terminated tip. The influence of the atomic-scale local environment on the concerted proton tunneling is also discussed. In Section 5, we quantitatively assessed the quantum component of a single H bond at a water-solid interface, revealing that the anharmonic quantum fluctuations of H nuclei weaken the weak H bonds and strengthen the relatively strong ones. However, this trend could be reversed when the H bond is strongly coupled to the atomic-scale polar environment. Finally, we summarize the review in Section 6 and provide an outlook for the future investigation of NQEs in water as well as the new possibilities provided by recently developed scanning probe techniques.
Section snippets
Background
One basic requirement for studying the NQEs of water by scanning probe methods is to locate in real space the position of protons within the H-bonded network, such that the motion of the protons can be tracked. This requires the ability to access the internal degree of freedom of water molecule, namely, to achieve submolecular-resolution imaging. To date, STM has been extensively applied to image the H-bonding configurations of water at surfaces since the beginning of this century. So far, the
Recent developments of ab initio PIMD and applications to surface water
In the above sections, we have summarized the recent advances of STM/S measurements on surface water, especially the ability of accessing the degree of freedom of protons. Now we turn to the theoretical part of this review. Developments of the first-principle methods mean that nowadays many of the experimental measurements can be understood in detail. These methods include STM imaging [207], surface and adsorption energy calculations [208], finite-temperature MD [209], and transition state
Background
Proton tunneling is fundamental to many physical, chemical and biological processes [1], [8], [9], [75], [224], [225], [226], [227], [228]. In comparison with the well-studied single proton tunneling, many-body tunneling is more complicated but participates in much broader proton dynamic processes, for instance, the phase transition of ice [11], [17], [32], molecular tautomerization and enzyme catalysis reactions [66], [67], [70], [71], [133]. However, our understanding of multiple proton
Background
NQEs, in terms of zero-point fluctuation, could influence the H-bonding interactions and consequently the structure of H-bonded networks due to the anharmonic nature of the potential well (see Section 1.1). For instance, high-pressure ice exhibits a prominent proton delocalization effect between the oxygen atoms due to the relatively small OO separation, leading to the blurring between covalent bond and H bond [1], [35], [107], [243]. The magnitude of proton delocalization is quite sensitive to
Summary and outlook
In this review, we have presented the atomic-scale investigation of NQEs of water adsorbed on the NaCl(001) surface. This was achieved by developing a series of imaging and spectroscopic techniques based on STM, which allow tracking the quantum motion of H nuclei both in real space and energy space. Thanks to those novel techniques, it is possible to directly visualize the concerted quantum tunneling of protons within the H-bonded network and quantify the quantum component of a single H bond at
Acknowledgements
We thank many people who have supported us to fulfill the works in this manuscript: Jing-Tao Lü, Yexin-Feng, Ji Chen, Andrew Hodgson, Angelos Michaelides, Limei Xu, Junren Shi, Xiangzhi Meng, Jinbo Peng, Zeren Lin, Zhichang Wang. X.Z.L. also acknowledge helpful discussion with Zhigang Sun on quantum dynamics. This work is funded by the National Key R&D Program under Grant No. 2016YFA0300901, 2017YFA0205003, and 2016YFA0300903, the National Natural Science Foundation of China under Grant No.
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2023, Physics ReportsCitation Excerpt :According to an article appeared in the Rev Mod Phys in 2016 [11], the more input of resources, the more difficulty of the questions; the more advancement of the instrument, the more problems arise. Since the earlier 1930’s when Bernal–Fowler–Pauling [10,11] proposed that protons frustrate randomly in the THz frequency between adjacent oxygen atoms, there have been numerous approaches attacking the mysteries of water and ice in terms of continuum thermodynamics [12–15], molecular dynamics [16–20], and nuclear quantum effect [21–23]. Debating is still going on regarding issues such as the exact number of coordinating neighbors (CN or z) of a molecule in bulk water [24–26], the manner and mobility of proton and molecular motion [12,13,27], the volume fraction of the domain-resolved lower-density and higher-density fragments [28], and the physical origin of premelting, supercooling, and superheating [29], as well as ice slipperiness [30–33], for instances.
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2022, Advances in Colloid and Interface ScienceCitation Excerpt :According to a Colloquium in the Rev Mod Phys in 2016 [7], the more input of resources, the more difficulty of the questions; the more advancement of the instrument, the more problems arise [8]. Since the 1930's when Bernal-Fowler-Pauling [9,10] proposed that protons frustrate randomly in the THz frequency between adjacent oxygen atoms, there have been numerous models addressing the performance of water and ice such as continuum thermodynamics [11–14], molecular dynamics (MD) [15–19], and nuclear quantum effect [20–22]. Debating is still going on regarding issues such as the coordination number (CN or z) of a water molecule [23–25], the manner and mobility of proton and molecular motion [9,10,26,27], the volume fraction of the domain-resolved lower-density and higher-density fragments [7], and the physical origin of premelting, supercooling, and superheating [28], for instance.
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2022, Current Opinion in ElectrochemistryCitation Excerpt :This has been associated with unusually large kinetic isotope effects (KIEs) [12], that is, the ratio between rate constants for the process with hydrogen and deuterium (KH/D = kH/kD). Recent development in both experimental and theoretical work has provided further insight into the NQEs at electrochemical interfaces [2,4–7,13–17]. Experimentally, the quantum proton tunneling at electrochemical interfaces has been investigated by quantifying the KIE, finding that it can be rather important for oxygen reduction, but it is negligible or weak for hydrogen evolution reaction on Pt under alkaline conditions [4,5,7].
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2021, Surfaces and InterfacesCitation Excerpt :The coincidence of these findings suggests that water diffusing into the more hydrophobic matrix preferentially coordinates with matrix silanol groups, which then partially deprotonate as the consequence. Proton conductivity along fine nanochannels of silanol-coordinated water [77,78] could explain the sudden occurrence of the dip by a percolation phenomenon that sets in after about 6 hours. This is also consistent with the relative change of the integral silanol signal displayed in Fig. 2d. Although the loss of silanol signal occurs nanometers below the surface, this very process seems to have a reordering effect on the molecular orientation of interfacial water as discussed above (Fig. 2a), likely occurring around the defect spots at the surface that can be understood as an entrance for the nanochannels.
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2021, Surface Science ReportsCitation Excerpt :STM has also been applied to imaging at high pressure [35], which can trace on-going reactions and adsorption of NO at surfaces [36–43]. In addition to surface topographies, the chemical and physical properties of individual molecules which derive from the local electronic structure can be elucidated by STM: the chemistry of adsorbates studied by using spectroscopy and manipulation with STM (known as “single-molecule chemistry”) has been demonstrated for a variety of small molecules such as CO, O2, H2, H2O, hydrocarbons and metal adatoms [44–56]. Most importantly, STS [57] can reveal the valence states of adsorbed molecules, which is useful for the study of the hybridization of 2π∗ orbital of NO and its magnetic property on the surface.