Hydrated Excess Protons in Acetonitrile/Water Mixtures: Solvation Species and Ultrafast Proton Motions

Neural-network-based molecular dynamics simulations reveal that proton transport in water is doubly gated by sequential hydrogen-bond exchange

The transport of excess protons in water is central to acid-base chemistry, biochemistry and energy production. However, elucidating its mechanism has been challenging. Recent nonlinear vibrational spectroscopy experiments could not be explained by existing models. Here we use both vibrational spectroscopy calculations and neural-network-based molecular dynamics simulations that account for nuclear quantum effects for all atoms to determine the proton transport mechanism. Our simulations reveal an equilibrium between two stable proton-localized structures with distinct Eigen-like and Zundel-like hydrogen-bond motifs. Proton transport follows a three-step mechanism gated by two successive hydrogen-bond exchanges: the first reduces the proton-acceptor water coordination, leading to proton transfer, and the second, the rate-limiting step, prevents rapid back-transfer by increasing the proton-donor coordination. This sequential mechanism is consistent with experimental characterizations of proton diffusion, explaining the low activation energy and the prolonged intermediate lifetimes in vibrational spectroscopy. These results are crucial for understanding proton dynamics in biochemical and technological systems.

Atomically Precise Au24Pt(thiolate)12(dithiolate)3 Nanoclusters with Excellent Electrocatalytic Hydrogen Evolution Reactivity

[Au24Pt(C6)18]0 (C6 = 1-hexanethiolate) is twice as active as commercial Pt nanoparticles in promoting the electrocatalytic hydrogen evolution reaction (HER), thereby attracting attention as new HER catalysts with well-controlled geometric structures. In this study, we succeeded in synthesizing two new Au-Pt alloy nanoclusters, namely, [Au24Pt(TBBT)12(TDT)3]0 (TBBT = 4-tert-butylbenzenethiolate; TDT = thiodithiolate) and [Au24Pt(TBBT)12(PDT)3]0 (PDT = 1,3-propanedithiolate), by exchanging all the ligands of [Au24Pt(PET)18]0 (PET = 2-phenylethanethiolate) with mono- or dithiolates. Although [Au24Pt(TBBT)12(TDT)3]0 was synthesized serendipitously, a similar cluster, [Au24Pt(TBBT)12(PDT)3]0, was subsequently obtained by selecting the appropriate reaction conditions and optimal combination of thiolate and dithiolate ligands. Single crystal X-ray diffraction analyses revealed that the lengths and orientations of -Au(I)-SR-Au(I)- staples in [Au24Pt(TBBT)12(TDT)3]0 and [Au24Pt(TBBT)12(PDT)3]0 were different from those in [Au24Pt(C6)18]0, [Au24Pt(PET)18]0, and [Au24Pt(TBBT)18]0, and these subtle differences were reflected in the geometric and electronic structures as well as the HER activities of [Au24Pt(TBBT)12(TDT)3]0 and [Au24Pt(TBBT)12(PDT)3]0. Accordingly, the HER activities of products [Au24Pt(TBBT)12(TDT)3]0 and [Au24Pt(TBBT)12(PDT)3]0 were, respectively, 3.5 and 4.9 times higher than those of [Au24Pt(C6)18]0 and [Au24Pt(TBBT)18]0.

Thermal dependence of the hydrated proton and optimal proton transfer in the protonated water hexamer

Water is a key ingredient for life and plays a central role as solvent in many biochemical reactions. However, the intrinsically quantum nature of the hydrogen nucleus, revealing itself in a large variety of physical manifestations, including proton transfer, gives rise to unexpected phenomena whose description is still elusive. Here we study, by a combination of state-of-the-art quantum Monte Carlo methods and path-integral molecular dynamics, the structure and hydrogen-bond dynamics of the protonated water hexamer, the fundamental unit for the hydrated proton. We report a remarkably low thermal expansion of the hydrogen bond from zero temperature up to 300 K, owing to the presence of short-Zundel configurations, characterised by proton delocalisation and favoured by the synergy of nuclear quantum effects and thermal activation. The hydrogen bond strength progressively weakens above 300 K, when localised Eigen-like configurations become relevant. Our analysis, supported by the instanton statistics of shuttling protons, reveals that the near-room-temperature range from 250 K to 300 K is optimal for proton transfer in the protonated water hexamer.

The Reactivity-Enhancing Role of Water Clusters in Ammonia Aqueous Solutions

Among the many prototypical acid-base systems, ammonia aqueous solutions hold a privileged place, owing to their omnipresence in various planets and their universal solvent character. Although the theoretical optimal water-ammonia molar ratio to form NH4+ and OH- ion pairs is 50:50, our ab initio molecular dynamics simulations show that the tendency of forming these ionic species is inversely (directly) proportional to the amount of ammonia (water) in ammonia aqueous solutions, up to a water-ammonia molar ratio of ∼75:25. Here we prove that the reactivity of these liquid mixtures is rooted in peculiar microscopic patterns emerging at the H-bonding scale, where the highly orchestrated motion of 5 solvating molecules modulates proton transfer events through local electric fields. This study demonstrates that the reaction of water with NH3 is catalyzed by a small cluster of water molecules, in which an H atom possesses a high local electric field, much like the effect observed in catalysis by water droplets [ PNAS 2023, 120, e2301206120].

Electric-field induced entropic effects in liquid water

Externally applied electric fields in liquid water can induce a plethora of effects with wide implications in electrochemistry and hydrogen-based technologies. Although some effort has been made to elucidate the thermodynamics associated with the application of electric fields in aqueous systems, to the best of our knowledge, field-induced effects on the total and local entropy of bulk water have never been presented so far. Here, we report on classical TIP4P/2005 and ab initio molecular dynamics simulations measuring entropic contributions carried by diverse field intensities in liquid water at room temperature. We find that strong fields are capable of aligning large fractions of molecular dipoles. Nevertheless, the order-maker action of the field leads to quite modest entropy reductions in classical simulations. Albeit more significant variations are recorded during first-principles simulations, the associated entropy modifications are small compared to the entropy change involved in the freezing phenomenon, even at intense fields slightly beneath the molecular dissociation threshold. This finding further corroborates the idea that electrofreezing (i.e., the electric-field-induced crystallization) cannot take place in bulk water at room temperature. In addition, here, we propose a molecular-dynamics-based analysis (3D-2PT) that spatially resolves the local entropy and the number density of bulk water under an electric field, which enables us to map their field-induced changes in the environment of reference H2O molecules. By returning detailed spatial maps of the local order, the proposed approach is capable of establishing a link between entropic and structural modifications with atomistic resolution.

Amplification of mid-IR continuum for broadband 2D IR spectroscopy

We report the generation and characterization of microjoule level, broad bandwidth femtosecond pulses in the mid-infrared (MIR) using optical parametric amplification of continuum MIR seed pulses in GaSe. The signal (3 μm) and idler (6 μm) pulses have energies of 6 μJ and 3 μJ with bandwidths of ∼950 cm^-1 and 650 cm^-1 FWHM and pulse lengths of 34 fs and 80 fs. Broadband 2D IR spectra of O-H and N-H transitions are acquired with the signal beam demonstrating the capabilities of this source for cross peak and line shape measurements.

From Local Covalent Bonding to Extended Electric Field Interactions in Proton Hydration

Seemingly simple yet surprisingly difficult to probe, excess protons in water constitute complex quantum objects with strong interactions with the extended and dynamically changing hydrogen-bonding network of the liquid. Proton hydration plays pivotal roles in energy transport in hydrogen fuel cells and signal transduction in transmembrane proteins. While geometries and stoichiometry have been widely addressed in both experiment and theory, the electronic structure of these specific hydrated proton complexes has remained elusive. Here we show, layer by layer, how utilizing novel flatjet technology for accurate x-ray spectroscopic measurements and combining infrared spectral analysis and calculations, we find orbital-specific markers that distinguish two main electronic-structure effects: Local orbital interactions determine covalent bonding between the proton and neigbouring water molecules, while orbital-energy shifts measure the strength of the extended electric field of the proton.

Proton-transfer spectroscopy beyond the normal-mode scenario

A stochastic theory is developed to predict the spectral signature of proton-transfer processes and is applied to infrared spectra computed from ab initio molecular-dynamics simulations of a single [Formula: see text] cation. By constraining the oxygen atoms to a fixed distance, this system serves as a tunable model for general proton-transfer processes with variable barrier height. Three spectral contributions at distinct frequencies are identified and analytically predicted: the quasi-harmonic motion around the most probable configuration, amenable to normal-mode analysis, the contribution due to transfer paths when the proton moves over the barrier, and a shoulder for low frequencies stemming from the stochastic transfer-waiting-time distribution; the latter two contributions are not captured by normal-mode analysis but exclusively reported on the proton-transfer kinetics. In accordance with reaction rate theory, the transfer-waiting-contribution frequency depends inversely exponentially on the barrier height, whereas the transfer-path-contribution frequency is rather insensitive to the barrier height.

Electrofreezing of Liquid Ammonia

Here we prove that, in addition to temperature and pressure, another important thermodynamic variable permits the exploration of the phase diagram of ammonia: the electric field. By means of (path integral) ab initio molecular dynamics simulations, we predict that, upon applying intense electric fields on ammonia, the electrofreezing phenomenon occurs, leading the liquid toward a novel ferroelectric solid phase. This study proves that electric fields can generally be exploited as the access key to otherwise-unreachable regions in phase diagrams, unveiling the existence of new condensed-phase structures. Furthermore, the reported findings have manifold practical implications, from the safe storage and transportation of ammonia to the understanding of the solid structures this compound forms in planetary contexts.

The coupling of the hydrated proton to its first solvation shell

The Zundel ([Formula: see text]) and Eigen ([Formula: see text]) cations play an important role as intermediate structures for proton transfer processes in liquid water. In the gas phase they exhibit radically different infrared (IR) spectra. The question arises: is there a least common denominator structure that explains the IR spectra of both, the Zundel and Eigen cations, and hence of the solvated proton? Full dimensional quantum simulations of these protonated cations demonstrate that two dynamical water molecules and an excess proton constitute this fundamental subunit. Embedded in the static environment of the parent Eigen cation, this subunit reproduces the positions and broadenings of its main excess-proton bands. In isolation, its spectrum reverts to the well-known Zundel ion. Hence, the dynamics of this subunit polarized by an environment suffice to explain the spectral signatures and anharmonic couplings of the solvated proton in its first solvation shell.

Spectral signatures of excess-proton waiting and transfer-path dynamics in aqueous hydrochloric acid solutions

The theoretical basis for linking spectral signatures of hydrated excess protons with microscopic proton-transfer mechanisms has so far relied on normal-mode analysis. We introduce trajectory-decomposition techniques to analyze the excess-proton dynamics in ab initio molecular-dynamics simulations of aqueous hydrochloric-acid solutions beyond the normal-mode scenario. We show that the actual proton transfer between two water molecules involves for relatively large water-water separations crossing of a free-energy barrier and thus is not a normal mode, rather it is characterized by two non-vibrational time scales: Firstly, the broadly distributed waiting time for transfer to occur with a mean value of 200-300 fs, which leads to a broad and weak shoulder in the absorption spectrum around 100 cm-1, consistent with our experimental THz spectra. Secondly, the mean duration of a transfer event of about 14 fs, which produces a rather well-defined spectral contribution around 1200 cm-1 and agrees in location and width with previous experimental mid-infrared spectra.

Infrared fingerprints of water collective dynamics indicate proton transport in biological systems

Recent publications on spectroscopy of water layers in water bridge structures revealed a significant enhancement of the proton mobility and the dielectric contribution of translational vibrations of water molecules in the interfacial layers compared to bulk water. Herewith, the results of long-term studies of proton dynamics in solid-state acids have shown that proton mobility increases significantly with the predominance of hydronium, but not Zundel, cations in the aqueous phase. In the present work, in the light of these data, we reanalyzed our previously published results on broadband dielectric spectroscopy of bovine heart cytochrome c, bovine serum albumin, and the extracellular matrix and filaments of Shewanella oneidensis MR-1. We revealed that, just as in water bridges, an increase in electrical conductivity in these systems correlates with an increase in the dielectric contribution of water molecular translational vibrations. In addition, the appearance of spectral signatures of the hydronium cations was observed only in those cases when the system revealed noticeable electrical conductivity due to delocalized charge carriers.

Quantum mechanical effects in acid–base chemistry

Acid–base chemistry has immense importance for explaining and predicting the chemical products formed by an acid and a base when mixed together. However, the traditional chemistry theories used to describe acid–base reactions do not take into account the effect arising from the quantum mechanical nature of the acidic hydrogen shuttling potential and its dependence on the acid base distance. Here, infrared and NMR spectroscopies, in combination with first principles simulations, are performed to demonstrate that quantum mechanical effects, including electronic and nuclear quantum effects, play an essential role in defining the acid–base chemistry when 1-methylimidazole and acetic acid are mixed together. In particular, it is observed that the acid and the base interact to form a complex containing a strong hydrogen bond, in which the acidic hydrogen atom is neither close to the acid nor to the base, but delocalized between them. In addition, the delocalization of the acidic hydrogen atom in the complex leads to characteristic IR and NMR signatures. The presence of a hydrogen delocalized state in this simple system challenges the conventional knowledge of acid–base chemistry and opens up new avenues for designing materials in which specific properties produced by the hydrogen delocalized state can be harvested.

Acid-based theories do not consider the quantum mechanical nature of the acidic hydrogen shuttling potential. Here, it is demonstrated that this particularity is needed to explain the formation acid-base complex with a delocalized acidic hydrogen.

Molecular dissociation and proton transfer in aqueous methane solution under an electric field

Methane-water mixtures are ubiquitous in our solar system and they have been the subject of a wide variety of experimental, theoretical, and computational studies aimed at understanding their behaviour under disparate thermodynamic scenarios, up to extreme planetary ice conditions of pressures and temperatures [Lee and Scandolo, Nat. Commun., 2011, 2, 185]. Although it is well known that electric fields, by interacting with condensed matter, can produce a range of catalytic effects which can be similar to those observed when material systems are pressurised, to the best of our knowledge, no quantum-based computational investigations of methane-water mixtures under an electric field have been reported so far. Here we present a study relying upon state-of-the-art ab initio molecular dynamics simulations where a liquid aqueous methane solution is exposed to strong oriented static and homogeneous electric fields. It turns out that a series of field-induced effects on the dipoles, polarisation, and the electronic structure of both methane and water molecules are recorded. Moreover, upon increasing the field strength, increasing fractions of water molecules are not only re-oriented towards the field direction, but are also dissociated by the field, leading to the release of oxonium and hydroxyde ions in the mixture. However, in contrast to what is observed upon pressurisation (∼50 GPa), where the presence of the water counterions triggers methane ionisation and other reactions, methane molecules preserve their integrity up to the strongest field explored (i.e., 0.50 V Å^-1). Interestingly, neither the field-induced molecular dissociation of neat water (i.e., 0.30 V Å^-1) nor the proton conductivity typical of pure aqueous samples at these field regimes (i.e., 1.3 S cm^-1) are affected by the presence of hydrophobic interactions, at least in a methane-water mixture containing a molar fraction of 40% methane.

Resolving the Structural Debate for the Hydrated Excess Proton in Water

It has long been proposed that the hydrated excess proton in water (aka the solvated "hydronium" cation) likely has two limiting forms, that of the Eigen cation (H₉O₄⁺) and that of the Zundel cation (H₅O₂⁺). There has been debate over which of these two is the more dominant species and/or whether intermediate (or "distorted") structures between these two limits are the more realistic representation. Spectroscopy experiments have recently provided further results regarding the excess proton. These experiments show that the hydrated proton has an anisotropy reorientation time scale on the order of 1-2 ps. This time scale has been suggested to possibly contradict the picture of the more rapid "special pair dance" phenomenon for the hydrated excess proton, which is a signature of a distorted Eigen cation. The special pair dance was predicted from prior computational studies in which the hydrated central core hydronium structure continually switches (O-H···O)* special pair hydrogen-bond partners with the closest three water molecules, yielding on average a distorted Eigen cation with three equivalent and dynamically exchanging distortions. Through state-of-art simulations it is shown here that anisotropy reorientation time scales of the same magnitude are obtained that also include structural reorientations associated with the special pair dance, leading to a reinterpretation of the experimental results. These results and additional analyses point to a distorted and dynamic Eigen cation as the most prevalent hydrated proton species in aqueous acid solutions of dilute to moderate concentration, as opposed to a stabilized or a distorted (but not "dancing") Zundel cation.

Coupled Local-Mode Approach for the Calculation of Vibrational Spectra: Application to Protonated Water Clusters

Spectroscopic studies of protonated water clusters (PWCs) have yielded enormous insights into the fundamental nature of the hydrated proton. Here, we introduce a new coupled local-mode (CLM) approach to calculate PWC OH stretch vibrational spectra. The CLM method combines a sampling of representative configurations from density functional theory (DFT)-based ab initio molecular dynamics (AIMD) simulations with DFT calculations of local-mode vibrational frequencies and couplings. Calculations of inhomogeneous OH stretch vibrational spectra for H⁺(H₂O)₄ and H⁺(H₂O)₂₁ agree well with experiment and higher-level calculations, and decompositions of the calculated spectra in terms of the coupled modes aids in the interpretation of the spectra. This observation is consistent with the idea that capturing anharmonicity and coupling is as important to accuracy as the underlying level of electronic structure theory. The CLM calculations can easily discern the configuration that dominates the experimental measurement for H⁺(H₂O)₅, which can adopt several low-energy conformations.

Water at charged interfaces

The ubiquity of aqueous solutions in contact with charged surfaces and the realization that the molecular-level details of water-surface interactions often determine interfacial functions and properties relevant in many natural processes have led to intensive research. Even so, many open questions remain regarding the molecular picture of the interfacial organization and preferential alignment of water molecules, as well as the structure of water molecules and ion distributions at different charged interfaces. While water, solutes and charge are present in each of these systems, the substrate can range from living tissues to metals. This diversity in substrates has led to different communities considering each of these types of aqueous interface. In this Review, by considering water in contact with metals, oxides and biomembranes, we show the essential similarity of these disparate systems. While in each case the classical mean-field theories can explain many macroscopic and mesoscopic observations, it soon becomes apparent that such theories fail to explain phenomena for which molecular properties are relevant, such as interfacial chemical conversion. We highlight the current knowledge and limitations in our understanding and end with a view towards future opportunities in the field.

Infrared and NMR Spectroscopic Fingerprints of the Asymmetric H7+ O3 Complex in Solution

Infrared (IR) absorption in the 1000-3700 cm-1 range and 1 H NMR spectroscopy reveal the existence of an asymmetric protonated water trimer, H7+ O3, in acetonitrile. The core H7+ O3 motif persists in larger protonated water clusters in acetonitrile up to at least 8 water molecules. Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations reveal irreversible proton transport promoted by propagating the asymmetric H7+ O3 structure in solution. The QM/MM calculations allow for the successful simulation of the measured IR absorption spectra of H7+ O3 in the OH stretch region, which reaffirms the assignment of the H7+ O3 spectra to a hybrid-complex structure: a protonated water dimer strongly hydrogen-bonded to a third water molecule with the proton exchanging between the two possible shared-proton Zundel-like centers. The H7+ O3 structure lends itself to promoting irreversible proton transport in presence of even one additional water molecule. We demonstrate how continuously evolving H7+ O3 structures may support proton transport within larger water solvates.

Estimations of FH···X hydrogen bond energies from IR intensities: Iogansen's rule revisited

In this work the possibility of using the IR intensity of the stretching vibration ν_s of proton donor group for estimation of hydrogen bond strength was investigated. For a set of complexes with FH···X (X = F, N, O) hydrogen bonds in the wide range of energies (0.1-49.2 kcal/mol) vibrational frequencies ν_s and their intensities A were calculated (CCSD at complete basis set limit). The validity of the previously proposed linear proportionality between the intensification of the stretching vibration ν_s in IR spectra and hydrogen bond enthalpy -ΔH = 12.2 ∆ A (A. V. Iogansen, Spectrochimica Acta A 1999) was examined. It is shown that for a range of similar hydrogen bond types with complexation energies ∆E <15 kcal/mol the ∆E( ∆ A ) function remains similar to that proposed in the Iogansen's work, while upon strengthening this dependency becomes significantly nonlinear. We examined two other parameters ( ∆ A ν s and ∆ A ∙ m R ) related to IR intensity as descriptors of hydrogen bond strength which are proportional to transition dipole moment matrix element and mass-independent dipole moment derivative. It was found that the dependency ∆E( ∆ A ν s ) stays linear in the whole studied range of complexation energies and it can be used for evaluation of ∆E from infrared spectral data with the accuracy about 2 kcal/mol. The mass-independent product ∆ A ∙ m R is an appropriate descriptor for sets of complexes with various hydrogen bond types. Simple equations proposed in this work can be used for estimations of hydrogen bond strength in various systems, where experimental thermodynamic methods or direct calculations are difficult or even impossible.

Nuclear Quantum Effects Largely Influence Molecular Dissociation and Proton Transfer in Liquid Water under an Electric Field

Proton transfer in liquid water controls acid-base chemistry, crucial enzyme reactions, and the functioning of fuel cells. Externally applied static electric fields in water are capable of dissociating molecules and transferring protons across the H-bond network. However, the impact of nuclear quantum effects (NQEs) on these fundamental field-induced phenomena has not yet been reported. By comparing state-of-the-art ab initio molecular dynamics (AIMD) and path integral AIMD simulations of water under electric fields, I show that quantum delocalization of the proton lowers the molecular ionization threshold to approximately one-third. Moreover, also the water behavior as a protonic semiconductor is considerably modified by the inclusion of NQEs. In fact, when the quantum nature of the nuclei is taken into account, the proton conductivity is ∼50% larger. This work proves that NQEs sizably affect the protolysis phenomenon and proton transfer in room-temperature liquid water.

Nature of hydrated proton vibrations revealed by nonlinear spectroscopy of acid water nanodroplets

We use polarization-resolved femtosecond pump-probe spectroscopy to investigate the vibrations of hydrated protons in anionic (AOT) and cationic (CTAB/hexanol) reverse micelles in the frequency range 2000-3500 cm-1. For small AOT micelles the dominant proton hydration structure consists of H3O+ with two OH groups donating hydrogen bonds to water molecules, and one OH group donating a weaker hydrogen bond to sulfonate. For cationic reverse micelles, we find that the absorption at frequencies >2500 cm-1 is dominated by asymmetric proton-hydration structures in which one of the OH groups of H3O+ is more weakly hydrogen-bonded to water than the other two OH groups.

Decoding the 2D IR spectrum of the aqueous proton with high-level VSCF/VCI calculations

The aqueous proton is a common and long-studied species in chemistry, yet there is currently intense interest devoted to understanding its hydration structure and transport dynamics. Typically described in terms of two limiting structures observed in gas-phase clusters, the Zundel H₅O₂ ⁺ and Eigen H₉O₄ ⁺ ions, the aqueous structure is less clear due to the heterogeneity of hydrogen bonding environments and room-temperature structural fluctuations in water. The linear infrared (IR) spectrum, which reports on structural configurations, is challenging to interpret because it appears as a continuum of absorption, and the underlying vibrational modes are strongly anharmonically coupled to each other. Recent two-dimensional IR (2D IR) experiments presented strong evidence for asymmetric Zundel-like motifs in solution, but true structure-spectrum correlations are missing and complicated by the anharmonicity of the system. In this study, we employ high-level vibrational self-consistent field/virtual state configuration interaction calculations to demonstrate that the 2D IR spectrum reports on a broad distribution of geometric configurations of the aqueous proton. We find that the diagonal 2D IR spectrum around 1200 cm^-1 is dominated by the proton stretch vibrations of Zundel-like and intermediate geometries, broadened by the heterogeneity of aqueous configurations. There is a wide distribution of multidimensional potential shapes for the proton stretching vibration with varying degrees of potential asymmetry and confinement. Finally, we find specific cross peak patterns due to aqueous Zundel-like species. These studies provide clarity on highly debated spectral assignments and stringent spectroscopic benchmarks for future simulations.

Decelerated Liquid Dynamics Induced by Component-Dependent Supercooling in Hydrogen and Deuterium Quantum Mixtures

Isotopic mixtures of p-H₂ and o-D₂ molecules have been an attractive binary system because they include two kinds of purely isotopic molecules which possess the same electronic potential but the twice different mass inducing differently pronounced nuclear quantum effects (NQEs). Accessing details of structures and dynamics in such quantum mixtures combining complex molecular dynamics with NQEs of different strengths remains a challenging problem. Taking advantage of the nonempirical molecular dynamics method which describes p-H₂ and o-D₂ molecules, we found that the liquid dynamics slows down at a specific mixing ratio, which can be connected to the observed anomalous slowdown of crystallization in the quantum mixtures. We attributed the decelerated dynamics to the component-dependent supercooling of p-H₂ taking place in the mixtures, demonstrating that there is an optimal mixing ratio to hinder crystallization. The obtained physical insights will help in experimentally controlling and achieving unknown quantum mixtures including superfluid.

High-Level VSCF/VCI Calculations Decode the Vibrational Spectrum of the Aqueous Proton

The hydrated excess proton is a common species in aqueous chemistry, which complexes with water in a variety of structures. The infrared spectrum of the aqueous proton is particularly sensitive to this array of structures, which manifests as continuous IR absorption from 1000 to 3000 cm^-1 known as the "proton continuum". Because of the extreme breadth of the continuum and strong anharmonicity of the involved vibrational modes, this spectrum has eluded straightforward interpretation and simulation. Using protonated water hexamer clusters from reactive molecular dynamics trajectories, and focusing on their central H⁺(H₂O)₂ structures' spectral contribution, we reproduce the linear IR spectrum of the aqueous proton with a high-level local monomer quantum method and highly accurate many-body potential energy surface. The accuracy of this approach is first verified in the vibrational spectra of the two isomers of the protonated water hexamer in the gas phase. We then apply this approach to 800 H⁺(H₂O)₆ clusters, also written as [H⁺(H₂O)₂](H₂O)₄, drawn from multistate empirical valence bond simulations of the bulk liquid to calculate the infrared spectrum of the aqueous proton complex. Incorporation of anharmonic effects to the vibrational potential and quantum mechanical treatment of the proton produces a better agreement to the infrared spectrum compared to that of the double-harmonic approximation. We assess the correlation of the proton stretching mode with different atomistic coordinates, finding the best correlation with ⟨R_OH⟩, the expectation value of the proton-oxygen distance R_OH. We also decompose the IR spectrum based on normal mode vibrations and ⟨R_OH⟩ to provide insight on how different frequency regions in the continuum report on different configurations, vibrational modes, and mode couplings.