Revealing excess protons in the infrared spectrum of liquid water

Using spectral-weight analysis, researchers experimentally identified short-lived hydronium and deuterated hydronium ions in liquid water, revealing that these fluctuation-born species constitute approximately 2% of the water content on the picosecond timescale and effectively render liquid water an ionic liquid in femtochemistry.

The Gist

Imagine liquid water not as a calm, static pool of identical molecules, but as a bustling, chaotic dance floor where particles are constantly swapping partners, spinning, and occasionally breaking apart into new forms for a split second.

For a long time, scientists thought of water mostly as a crowd of neutral dancers (H₂O molecules). They knew that occasionally, a dancer would lose a partner (becoming OH⁻) or grab an extra one (becoming H₃O⁺), but they assumed these "lonely" or "crowded" dancers were rare and long-lasting.

This paper reveals a shocking secret: The dance floor is actually teeming with these "extra" dancers, but they are so fast-moving that we've been blind to them.

Here is the story of how the authors found them, explained simply:

1. The Invisible Ghosts

In water, protons (hydrogen nuclei) are like hyperactive kids running between molecules. Sometimes, a molecule grabs an extra proton and becomes a positive ion (H₃O⁺), or loses one to become a negative ion (OH⁻).

• The Old View: We only counted the ions that stick around long enough to change the pH (like the ones in vinegar or soap). These are the "Long-Living" ions.
• The New Discovery: There is a massive population of "Short-Living" ions. They appear and disappear in the blink of an eye (femtoseconds to picoseconds). They are so fleeting that standard chemical tests (which are slow) miss them completely. The authors estimate that at any given tiny fraction of a second, about 2% of all water molecules are actually these short-lived ions. That's a huge crowd!

2. The Detective Work: The "Spectral Weight" Trick

How do you see something that vanishes before you can blink? You can't look at it directly. Instead, the authors used a clever trick called Spectral Weight Analysis.

Imagine you have three types of music players:

1. Player A plays a song by "Light Water" (H₂O).
2. Player B plays a song by "Heavy Water" (D₂O, where hydrogen is replaced by its heavier cousin, deuterium).
3. Player C plays a mix of both.

If you mix the songs perfectly, you should be able to predict exactly what the "Mixed" song sounds like by just adding the first two together.

The Mystery: When the scientists mixed the actual water and calculated what the "Mixed" song should sound like, it didn't match the real recording. There were "ghost notes" left over—tiny bumps and dips in the sound wave that shouldn't be there.

3. The "S-Shape" Clue

These ghost notes formed a distinct "S-shape" on their graphs.

• Think of it like this: If you try to draw a perfect circle using only straight lines, you'll get a jagged mess. The "S-shape" was the jagged mess left over because the scientists were trying to describe the water using only neutral molecules.
• The "S" was the fingerprint of the missing pieces: the Short-Living Ions.

By analyzing the shape and size of these "S" curves, the authors could mathematically deduce exactly how many of these fleeting ions were present. It was like looking at the shadow of a bird to figure out exactly what kind of bird was flying overhead, even if you couldn't see the bird itself.

4. Why Deuterium Was the Key

To make these ions visible, the scientists used Heavy Water (where hydrogen is swapped for deuterium).

• Analogy: Imagine a group of people running a race. If everyone wears the same shoes, it's hard to tell who is who. But if some wear heavy boots (deuterium) and others wear light sneakers (hydrogen), their footsteps sound different.
• By mixing light and heavy water, the "footsteps" (vibrations) of the ions shifted to different frequencies. This shift separated the ions' signals from the noise of the neutral water molecules, making the "S-shape" fingerprints stand out clearly.

5. The Big Picture: Water is an "Ionic Liquid"

The most exciting conclusion is that on the ultra-fast timescale of femtoseconds (quadrillionths of a second), liquid water behaves like an ionic liquid.

It's not just a sea of neutral molecules with a few stray ions. It's a dynamic soup where 2% of the time, the water is actually a bustling marketplace of positive and negative charges zipping around.

Why does this matter?

• Chemistry & Biology: Many reactions in our bodies and in nature happen incredibly fast. If we ignore these 2% of ions, our models of how water dissolves things, how proteins fold, or how electricity moves through water are incomplete.
• Simpler Models: The authors suggest that by acknowledging these "ghost ions," we can actually simplify the complex math used to describe water, making it easier to predict how water behaves in everything from batteries to biological cells.

Summary

The authors didn't just find a few extra ions; they found a hidden layer of reality in water. By using a mix of light and heavy water and listening to the "ghost notes" in the sound of light passing through it, they proved that water is much more electric and chaotic than we thought, acting as a highly active ionic liquid on the fastest timescales imaginable.

Technical Summary

1. Problem Statement

Liquid water contains, in addition to neutral $H_2O$ molecules, ionic species ($H_3O^+$ and $OH^-$) generated by autoionization. While the existence of "long-living" (LL) ions that determine pH is well-established, the dynamics of "short-living" (SL) ions formed by femtosecond-scale fluctuations remain elusive.

• The Challenge: SL ions have lifetimes of approximately 3 picoseconds and concentrations estimated around 1 M (approx. 2% of water molecules). Their spectral signatures are typically hidden within the broad, overlapping vibrational bands of neutral water molecules in standard infrared (IR) spectroscopy.
• The Gap: Previous studies relied on slow measurement techniques (NMR, potentiometry) that miss ultra-fast dynamics, or fast techniques (pump-probe, THz) that lack the resolution to distinguish low-concentration ions from the dominant neutral species. There has been no direct experimental assignment of specific spectral features in pure bulk water to these transient ionic species.

2. Methodology

The authors employed Fourier Transform Infrared (FTIR) spectroscopy in transmission mode (TIR) to analyze light water ($H_2O$), heavy water ($D_2O$), and their mixtures (semi-heavy water, $HDO$).

• Spectral Weight Analysis: Instead of analyzing absorbance directly, the authors converted spectra into dynamical conductivity ($\sigma(\nu)$). The integral of a mode in the $\sigma(\nu)$ curve is directly proportional to the number of charges involved, allowing for the quantification of ionic species concentrations.
• Isotopic Substitution Strategy:
  • They prepared mixtures with varying molar fractions ($f$) of deuterium ($D$).
  • They utilized a weighted sum model (Eq. 1) to calculate the theoretical spectrum of pure $HDO$ based on the spectra of pure $H_2O$ and $D_2O$.
  • The Logic: If water consisted only of neutral molecules ($H_2O, D_2O, HDO$), the experimental spectrum of a mixture should perfectly match the weighted sum of the pure components. Any deviation ("residuals") would indicate the presence of unaccounted species.
• Focus on Bending Modes: The analysis focused on the bending vibrational modes (< 2000 cm$^{-1}$) to avoid complications from Fermi resonances that affect stretching modes (> 2000 cm$^{-1}$).
• Modeling: The authors used a harmonic oscillator model to predict the vibrational frequencies of various protonated/deuterated ions ($H_3O^+, D_3O^+, DH_2O^+, HD_2O^+$) and fitted these to the experimental residuals using Lorentzian oscillators.

3. Key Results

A. Discovery of "S-Features"

When the authors subtracted the calculated theoretical $HDO$ spectrum (derived from pure $H_2O$ and $D_2O$) from the experimental mixture spectra, they observed distinct "S-shaped" mismatches (residuals) near the bending modes of $H-O-H$ (approx. 1650 cm$^{-1}$) and $D-O-D$ (approx. 1210 cm$^{-1}$).

• These features were reproducible and their amplitude scaled with the molar fraction $f$.
• The ratio of the positive to negative components of these S-features was consistently 3:1.

B. Assignment to Short-Living Ions

The authors attributed these S-features to the vibrational modes of short-living (SL) ionic species that are not accounted for in the neutral molecule model:

• Symmetric Ions: $H_3O^{+*}$ and $D_3O^{+*}$ (where * denotes short-living).
• Asymmetric Ions: $DH_2O^{+*}$ and $HD_2O^{+*}$.
• Mechanism: The 3:1 ratio of the residuals corresponds to the statistical probability of forming asymmetric ions (3 combinations) versus symmetric ions (1 combination) in the mixtures.
• Frequency Shifts: Using a three-mass, three-spring harmonic model, the authors calculated that the bending frequencies of these ions should be slightly shifted from neutral water (e.g., $H_3O^{+*}$ near 1695 cm$^{-1}$ and $D_3O^{+*}$ near 1195 cm$^{-1}$), which matched the experimental fit parameters.

C. Quantification of Concentrations

By integrating the spectral weight of the fitted ionic components, the authors calculated the concentration of these species:

• The total concentration of short-living ions was found to be approximately 2.5% of the total water molecules (approx. 1.4 M).
• Table II and Table IV in the paper detail the specific distribution of these ions across different isotopic mixtures, confirming that the concentration of ions is high enough to significantly influence the IR spectrum on the picosecond timescale.

4. Significance and Contributions

• Direct Experimental Evidence: This study provides the first direct experimental resolution of the "fingerprints" of short-living hydronium and hydroxide ions in the IR spectrum of pure bulk water, moving beyond theoretical simulations or studies of dilute solutions.
• Reframing Water's Nature: The findings suggest that on femtosecond-to-picosecond timescales, liquid water behaves as an effective ionic liquid with a high concentration of mobile charge carriers, rather than just a solvent with trace ions.
• Resolution of the "Missing" Species: The paper resolves the long-standing discrepancy in water spectroscopy where standard models failed to account for the full spectral weight, attributing the missing mass to these transient ionic fluctuations.
• Implications for Physical Chemistry: The results imply that models of water-related processes (solvation, proton transport, radiolysis, and electrochemical reactions) occurring on sub-picosecond scales must explicitly account for the high density of these transient ions, rather than relying solely on the equilibrium pH concept.
• Methodological Advancement: The use of spectral-weight analysis on isotopic mixtures to isolate hidden ionic contributions offers a robust framework for studying other complex fluid systems where transient species are difficult to detect.

In conclusion, Artemov et al. successfully demonstrated that the IR spectrum of liquid water contains distinct signatures of fluctuation-born, short-living ions, revealing a much richer ionic landscape in water than previously understood through conventional low-speed measurements.