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The nature of the aqueous proton has been traditionally interpreted through two limiting structural motifs: the Zundel and Eigen cations. However, experimental infrared (IR) spectra of the solvated proton reveal a far more dynamic character, as evidenced by distinct intensity modulations within the characteristic continuum absorption band. In fact, recent ultrafast two-dimensional IR spectroscopy suggests that solvation-induced structural distortions around H 2 O⋯H + ⋯OH 2 motifs critically shape the IR response. Here we investigate the role of such asymmetry through full-dimensional quantum dynamics simulations of the extended Zundel complex H + (H 2 O) 6 , which structurally encompasses both Zundel and Eigen motifs. Systematic removal of one water molecule from the second solvation shell gradually introduces deviations from the perfectly symmetric Zundel-like complex towards Eigen-like spectral features. These results provide a direct map between the asymmetric solvation environment and the structural response of the first and second solvation shells of the aqueous proton, offering a structural and dynamical basis for understanding how this asymmetry governs proton mobility in aqueous environments.

Understanding the nature of the aqueous proton is of essential importance for both fundamental science 1 and technological applications 2 , 3 , such as the concept of pH in acid, base chemistry 4 , proton transfer across membranes in metabolic processes 5 , 6 , and proton exchange in batteries for energy storage 7 . However, even though pioneering attempts to understand the hydrated proton and its transport mechanism date back more than 200 years 8 , 9 , consensus is still lacking on the microscopic structure and dynamics of excess protons in liquid water 10 , 11 , 12 , 13 .

Two important archetypes emerged early on from attempts to characterize the very nature of a proton embedded in water 14 : the so-called Zundel (Z: H 5 O 2 + ) and Eigen (E: H 9 O 4 + ) cations 15 , 16 . In the case of the Zundel cation, the solvated proton is clamped in a symmetrical complex where there is a strong hydrogen bond between two water molecules (H 2 O⋯H + ⋯OH 2 ), whereas in the case of the the Eigen cation, a central hydronium core is hydrogen-bonded to three surrounding water molecules (H 3 O + (H 2 O) 3 ). More recent computational 4 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 and experimental 4 , 10 , 13 , 33 , 34 , 36 , 37 , 41 , 42 , 43 , 44 , 45 , 46 , 47 work suggests that these structures are not mutually exclusive; rather, they represent two limiting cases 9 , 48 , 49 with significant impact on the IR response within more complex and dynamically fluctuating local solvation environments. This has led to considerable interest in the study of the larger extended Zundel (eZ) complex 36 , 39 , 42 , 50 , 51 , 52 , H + (H 2 O) 6 (compare ref. 53 ), which structurally encompasses both the Zundel (Z) and Eigen (E) motifs as schematically visualized in Fig. 1b .

a , Schematic representation of representative structures associated with the aqueous proton within eZ as solvation asymmetry increases from left to right, together with the stroboscopic sequence of IR responses of the central hydrogen bond. The calculated rigorous quantum IR response of the central proton (see text and caption of Fig. 4 ), covering a width of more than 1,500 cm −1 as a function of asymmetry, explains the extremely broad IR response of the aqueous proton when considered in actual fluctuating environments. b , Molecular structures of the limiting motifs: (left to right) the Zundel (Z), extended Zundel (eZ) and Eigen (E) complexes. In the eZ complex, we denote the two water molecules of its Zundel core (H 5 O 2 + : orange rectangle) as the ‘inner’ water molecules and the remaining four monomers as the ‘outer’ water molecules. The eZ complex can also be viewed as an E core (H 9 O 4 + : green triangle) solvated by two water molecules that break the three-fold symmetry of the bare E cation; this asymmetric E-like configuration arises upon full transfer of the excess proton along the central hydrogen bond in eZ, which has also been referred to as the ‘most active proton’ 24 , thus forming the nascent hydronium core, H 3 O + .

What is the reason for such ambiguity in establishing the microscopic structure of the hydrated proton? Part of the challenge lies in the inherent complexity of its infrared (IR) absorption spectrum 34 , 44 , 46 , 47 , which cannot be readily explained by a simple superposition of the gas-phase spectra of the limiting Z, E and eZ motifs shown in Fig. 2 . Instead, it consists of a modulated continuum absorption, the broad characteristics of which extend from ~1,000 to 3,500 cm −1 , as seen in the experimental difference IR spectra shown in Fig. 2d for various measurements and subtraction schemes 34 , 44 , 46 , 47 . Accordingly, the need to go beyond the normal mode picture has been explicitly demonstrated to be necessary to consistently capture the IR spectroscopic impact of interconversions between Zundel-like and Eigen-like excess proton states 4 . Furthermore, recent developments in two-dimensional (2D) IR spectroscopy 44 , 46 , 47 have provided unprecedented access to lifetimes and vibrational couplings of the hydrated proton in solution. These reveal a complex interplay between the excess proton and its surrounding water molecules, while suggesting a prominent role of ‘asymmetric Zundel-like H 5 O 2 + motifs’.

a, c , Experimental IR spectra of the bare Zundel cation (Z: H 5 O 2 + or H + (H 2 O) 2 ) from ref. 58 ( a ), the bare Eigen cation (E: H 9 O 4 + or H + (H 2 O) 4 ) from refs. 59 , 60 ( b ) and the extended Zundel complex (eZ: H 13 O 6 + or H + (H 2 O) 6 ) from ref. 51 ( c ). d , Experimental difference IR spectra corresponding to the aqueous proton H + (aq) contribution in acidic solutions at various concentrations obtained by applying different subtraction schemes 34 , 44 , 46 , 47 (see legend); the coloured frequency windows serve as visual guides to align and compare this panel with panels b and c in Fig. 4 .

Clearly, the fundamental nature of the aqueous proton remains an open debate. Consequently, a wealth of mechanistic models have been proposed to explain the proton continuum band in the computational literature, often directly complementing experimental studies 29 , 31 , 33 , 34 , 35 , 36 , 37 , 38 , 44 , 47 (see Supplementary Section 1 for an extended discussion). In this regard, a new twist to the story was recently added with the proposal of a novel three-step proton transport mechanism to explain Grotthuss diffusion and, consequently, the continuum IR absorption of the aqueous proton 39 . This idea is based on a thermal equilibrium involving two stable proton-localized structures with distinct Eigen-like and Zundel-like hydrogen-bond motifs. Notably in the stable Zundel-like hydrogen-bond motif, the excess proton is localized closer to one of the two inner water molecules, but within a larger symmetric hydrogen-bonding environment 39 . In other words, once again we find the recurrent key role of an asymmetric Zundel-like H 5 O 2 + motif. In this case, the transferring proton within the most active hydrogen bond 24, also dubbed a special bond 18 or special pair 27, forms a hydronium core H 3 O + , while the ideal Zundel structure with a centred hydrogen bond is found to be slightly unstable 39 . Nonetheless, it remains unclear how these species contribute to the observed spectral features in the aqueous proton, in particular how the local environment and asymmetry affect the IR response in the solvated H 2 O⋯H + ⋯OH 2 motif.

To address this, we introduce a ‘stroboscopic movie’ approach (Fig. 1a ) that differs from both the ingenious IR experiments with cryogenic clusters and their associated computational modelling based on normal modes around equilibrium ‘stable’ structures, as well as from molecular dynamics-based approaches, which sample snapshot configurations from statistical ensembles that have been obtained by relying on density functional theory. Instead, we systematically desolvate the Zundel core within eZ in quasi-continuous steps ( Methods ). This is particularly relevant to the problem at hand, as it directly provides information on the exact nature of the motions underlying IR resonances of excess protons in aqueous environments, resolved as a quasi-continuum of stroboscopic frames, as they evolve through a whole range of configurations (see the filmstrip inset in Fig. 1a ).

To achieve this, we use state-of-the-art full-dimensional quantum dynamics simulations (51 fully coupled anharmonic degrees of freedom) in combination with highly accurate potential energy and dipole moment surfaces of the eZ cation. The excellent agreement between the calculated and experimental spectra of unperturbed eZ in the full spectral range validates the model’s predictive power. Further analysis of the resulting molecular quantum dynamics, for both the equilibrium and distorted cases, allows us to assign the observed IR peaks and reveal the corresponding coupled motions within the local solvation environment. Notably, we find that when gradually introducing asymmetry into the second solvation shell around the Zundel core, one observes a seamless transition from the IR responses of the perfectly symmetric Zundel complex to the signatures of asymmetrically hydrogen-bonded Zundel motifs, and up to Eigen-like patterns of the hydrated proton (Fig. 1a ). Importantly, tracking these gradual changes enables us to link the IR spectrum of the asymmetric eZ complex to the experimental spectra of the aqueous proton, thereby providing an accurate spectroscopic model that connects the observed continuum absorption band with the micro-solvation structure of the Zundel core (Fig. 1b ).

The calculated IR spectrum of the eZ complex is shown in Fig. 3a , together with the experimental spectrum reported in ref. 51 that was achieved via isomer-selective double-resonance population labelling spectroscopy in messenger-tagged H + (H 2 O) 6 ·H 2 complexes, implying that experimental intensities might differ from those of the linear absorption spectrum. Meanwhile, the total spectrum is decomposed according to localized excitations of specific coordinates in Fig. 3b . Every excitation produces a spectral fingerprint (depicted in a different colour and type of line), which is then superimposed on the dipole spectrum. Broadly, we divide the spectrum into five distinct spectral regions, I to V.

a , Calculated linear IR absorption spectrum (black) and experimental vibrational spectrum from IR 2 MS 2 spectroscopy 51 (blue) of the protonated water hexamer H + (H 2 O) 6 ; the grey line shades out an ill-resolved frequency window given the flat 2,000, 3,000 cm −1 baseline reported in fig. 5e of ref. 61 based on Ar tagging spectroscopy. The labelling of the simulated spectrum indicates the main groups of bands by roman numbers (I, II, …) and corresponding subbands by letters (a 1 , a 2 , …). b , Decomposition of the full spectrum (grey) from a using localized vibrational excitations as well as the assignment of the most relevant peaks in terms of vibrational motion (colours, inset) as detailed in the text.

Region I, below 800 cm −1 , is dominated by slow and highly anharmonic modes of the outer water molecules, namely the angular displacements (wagging, rocking) of the outer water molecules and the stretch vibration of the outer oxygen, oxygen atoms. In particular, band a 19 , centred at ~220 cm −1 , corresponds