# In silico investigation of the thermochemistry and photoactivity of pyruvic acid in an aqueous solution of NaCl

Rodolphe Pollet, Wutharath Chin

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Rodolphe Pollet, Wutharath Chin. In silico investigation of the thermochemistry and photoactivity of pyruvic acid in an aqueous solution of NaCl. Chemistry - A European Journal, 2023, 29 (55), pp.e202302225. 10.1002/chem.202302225. [hal-04284238](https://hal.science/hal-04284238v1)

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*In silico* investigation of the thermochemistry
and photoactivity of pyruvic acid in an aqueous
solution of NaCl

Rodolphe Pollet*,† and Wutharath Chin‡

† Université Paris-Saclay, CEA, CNRS, NIMBE, 91191, Gif-sur-Yvette, France.

‡ Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405, Orsay,
France

E-mail: rodolphe.pollet@cea.fr

Phone: +33 (1)690 83713
Abstract

The photochemistry of oxo-carboxylic acids contributes significantly to the com-
plex chemistry occurring in the atmosphere. In this regard, pyruvic acid undergoes
photoreactions that lead to many diverse products. The presence of sodium cation near
pyruvic acid in an aqueous solution, or its conjugate base in non-acidic conditions, in-
fluences the hydration equilibrium and the photosensitivity to UV-visible light of the
oxocarboxylic acid. We performed an ab initio metadynamics simulation which serves
two purposes: first, it unveils the mechanisms of the reversible hydration reaction be-
tween the keto and the diol forms, with a free-energy difference of only 2 kJ/mol at
300 K, which shows the influence of sodium on the keto/diol ratio; second, it provides
solvent-shared ion pairing (SSIP) and contact ion pairing (CIP) structures, including
Na⁺ coordinated to carbonyl, for the calculations of the electronic transition energies
to an antibonding π* orbital, which sheds light on the photoactivity of these two forms
in the actinic region.

Introduction

The chemical reactivity of volatile organic compounds is intrinsically of multiphasic nature
(gas, particle, liquid).¹ It is most complex for it involves phase-dependent reactions. Among
them, some organics play a significant role in the formation of secondary organic aerosols.²⁻⁴
Marine aerosols, fog, and cloud droplets are the sink of numerous and complex photochemical
reactions involving water. Many studies have been devoted to processes in neat water, while
fewer have focused on aqueous solutions with electrolytes. Fog and cloud droplets are char-
acterized by dilute electrolyte conditions⁵ but higher ionic strength can be found in aerosol
deliquescent particles⁶ or in marine aerosols.⁷ Ions can impact the properties of aqueously
solvated compounds in different ways, in particular by acting on their photoactivity. The ion
content may indeed greatly affect the optical absorption and hence the fate of atmospheric
compounds upon solar irradiation. It was reported that relatively high ion concentrations
as found in marine conditions⁷ could induce a bathochromic effect on the absorption of anionic chromophores.⁸,⁹ The spectral shift can be significant enough to photo-sensitize a photo-inactive compound, i.e., that initially does not absorb in the actinic region.

Pyruvic acid (PA), an oxidation product of isoprene, is the smallest and the most prevalent 2-oxo carboxylic acid in the atmosphere.¹⁰⁻¹³ Its photochemical behavior has been widely investigated in water.¹³⁻¹⁸ PA is assumed to contribute to the formation of secondary organic aerosols since its direct and indirect photolysis yield oxidized products and oligomers of higher mass.¹⁹⁻²⁵ Aqueous-phase pyruvic acid exists as four different species. The keto and the gem-diol forms are in equilibrium and both can be protonated or deprotonated according to the pH conditions ($pK_a = 1.7-2.2$).²⁶,²⁷ The keto species contribute to the photoactivity of PA in the atmospherically relevant region,¹³,¹⁵,¹⁶,²⁸⁻³⁰ while the diol absorbs out of the actinic window below 290 nm. The photochemistry of the acidic form has received a lot of attention but in water unless at low pH conditions,¹⁴,¹⁵,²⁶ PA is mainly present as the anionic pyruvate species¹⁵,¹⁶,³¹⁻³⁵ It was found that the optical properties were affected by the presence of salts by inducing for instance a bathochromic effect that varies upon the nature of the ion and the pH conditions.⁸,¹⁶,³⁶ Are these changes dictated by direct interactions between the ion and the anionic chromophore or is it due to the disruption of the hydrogen bonding network in water.⁹ A better comprehension of how electrolytes such as $Na^+$ influence the photoactivity of pyruvate can shed light on the perturbation induced by ions close to anionic chromophores. The ion content also significantly impacts the stabilization of the ketone and diol species and hence the keto-diol equilibrium.¹⁶

Theoretical investigations with an atomic scale resolution can reveal such organic molecules' structural and thermodynamical properties in salted water. As to PA, most of these studies have focused on geometries and energies of the ketone or diol form in the vacuum, continuum solvent, or surrounded by a few explicit water molecules.¹⁵,¹⁶,³³,³⁷⁻³⁹ However we have previously demonstrated that solvent effects need to be fully taken into account for an accurate prediction of these properties,³² and this should still hold true in the presence of
electrolytes. In explicit aqueous solution at finite temperature, chemical reactions such as
the diol formation can be accurately described by ab initio molecular dynamics simulations
(AIMD) coupled to accelerated sampling techniques. On an unbiased simulation timescale,
such a reactive event would be too rare preventing the reconstruction of the corresponding
free-energy landscape including free-energy minima and barriers.

In the present work, we combine the Car-Parrinello (CP) and the metadynamics (MTD)
methods to describe the reversible hydration of the conjugate base of PA in salted water
and to select the relevant configurations of ketone and diol hydrated complexes with Na⁺
for excited-state calculations. Our simulation of the aqueous solution of NaCl has been
designed with an ionic strength of approximately 0.5 M (see Computational Details), which
is close to typical seawater, therefore this work provides detailed reaction mechanisms for
the hydration and the dehydration of PA which should be relevant for nascent sea spray
aerosols.⁴⁰ In addition, the UV-visible spectroscopic data gauge the effect of Na⁺ on its
photoactivity.

Results and Discussion

Pyruvate-sodium pair in water from the unbiased simulation

The ab initio simulation without any bias potential provides a description of the compet-
ing interactions that involve pyruvate, Na+, and surrounding water molecules. Under these
conditions, there is one conformational family, where Na+ strongly interacts with one car-
boxylate oxygen (O₁ atom) only at an average distance of 2.29 (0.15) Å (Figure 1). It is
identified as a contact ion pair (CIP) in a monodentate mode. This configuration signifi-
cantly differs from the bidentate geometry between the carboxylate group of pyruvate and
Ca²+ reported by Luo *et al*.¹⁶ This difference may have several origins. In spite of its similar
size to Na+, the increased charge of Ca²+ results in higher polarizability, which may favor
a bidentate structure. In addition, in the study by Luo *et al.*, the optimization at 0 K and
the smaller size of the system, i.e., pyruvate surrounded by only six water molecules, may
not fully describe the entropic and solvent effects. During the last 20 ps, Na⁺ gets closer to
the O₃ carbonyl oxygen with an average distance of 4.44 (0.30) Å (Figure 2).

<figure><img src="image_2.png" /><figcaption>Figure 1: Representative configuration showing four water molecules and one carboxylate oxygen of keto pyruvate coordinated to Na⁺ (blue color), other solvent molecules (transparent), and Cl⁻ (green).</figcaption></figure>

We now examine each entity of the CIP, starting with the cation. The coordination
structure of Na⁺ is composed of the O₁ carboxylate oxygen and four water molecules in a
distorted trigonal bipyramidal geometry (Figure 1 and Figure S2 in Supplementary Infor-
mation). Two of these water molecules exhibit a few exchanges between the first and second
solvation shells. The geometry of the pyruvate anion is perpendicular with a O₃C₁CO₁ di-
hedral angle of -94 (±18) degrees. It is very close to the value of -92 degrees observed for
pyruvate in neat water³² and it matches very well the perpendicular structures reported in
the literature.³³,³⁸ The O₃ carbonyl oxygen mostly accepts two hydrogen bonds from the
<figure><img src="image_3.png" /><figcaption>Figure 2: Distances (in Å) between Na⁺ and (i) the carboxylate oxygen atoms in a CIP geometry (O₁ in purple and O₂ in green); (ii) the carbonyl oxygen atom O₃ (in blue) along the CP trajectory.</figcaption></figure>

surrounding water molecules, except for the last 17 ps, where only one hydrogen bond is present. This change in the hydrogen bonding is presumably linked to the approach of the cation closer to O₃ as shown by the shorter distance between Na⁺ and O₃ in Figure 2. This proximity introduces competition between water interacting with O₃ through hydrogen bonding or between water interacting with Na⁺. The latter appears more favorable. We showed previously that the hydration reaction of the keto form involved the carbonyl group.³² Therefore, one can expect that the keto-diol equilibrium is impeded compared to neat water conditions since the carbonyl is now less exposed to water. It will be discussed in the next section presenting the metadynamics results.

## Reversible hydration of pyruvate

The hydration of pyruvate has been reversibly observed along the accelerated metadynamics trajectory. Here we present the relative free-energy minima and barriers, and we discuss
the structures that represent each species. Figure 3 shows the reconstructed free-energy
landscape along the two collective variables (CV) which were designed to promote the hy-
dration reaction, namely the coordination number (CN) of O₃ to all water hydrogen atoms
(O₃...Hw) and the CN of C₁ to all water oxygen atoms (C₁...Ow) (see Computational
Details). Two main free-energy basins are identified: The keto and the gem-diol forms of
pyruvate. Their corresponding minima are located at coordinates (0.32, 0.16) and (1.16,
0.88), respectively. The former, with low coordination numbers, indeed corresponds to the
unhydrated species, whereas the latter, with large coordination numbers, corresponds to a
geminal diol with two hydroxyl groups. The transition state is located at intermediate values
at approximately (0.7, 0.6). In the presence of sodium, the diol is favored by approximately
2 kJ/mol with respect to the keto. It is much lower than the value found in neat water where
the diol was more stable by 16 kJ/mol,³² showing that the hydration is more exergonic in
water. Consequently, the free-energy barriers which we estimate at 71 kJ/mol for hydration
and at 73 kJ/mol for dehydration are comparable. The energetic difference between the
barriers calculated in our previous study in water was much higher at 68 and 84 kJ/mol, re-
spectively.³² It means that the dehydration process requires less energy in salted conditions,
thereby favoring the keto species at the expense of the diol species. It is in good agreement
with the lower diol/keto ratio measured in salted water (with Na⁺ and Ca²⁺ cations).¹⁶

We identified several pathways for hydration and dehydration reactions. From the keto
form to the diol, the first path proceeds in four steps (see Figure 4): (a) Na⁺ is coordinated
to the O₃ carbonyl (average distance of 2.18 Å), the geometry changes simultaneously from
perpendicular to planar; (b) there is a concerted attack of two water molecules onto O₃ and
C₁; (c) the first hydroxyl is formed on C₁; (d) the second hydroxyl is formed on O₃ yielding
the diol species. This mechanism is similar to what was observed in neat water, with the first
hydroxyl formed on the carbonyl carbon atom.³² A second path starts from a monodentate
CIP configuration, with Na⁺ bound to O₁ carboxylate (average distance of 2.31 Å) and closer
to C₁ carbonyl, (see Figure 5). The following steps lead to the diol: (a) a water molecule
<figure><img src="image_4.png" /><figcaption>Figure 3: Free-energy landscape (in kJ/mol). CV1 (O<sub>3</sub>···H<sub>W</sub> coordination number) as the x-axis and CV2 (C<sub>1</sub>···O<sub>W</sub> coordination number) as the y-axis.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 4: First hydration pathway (from keto to diol pyruvate) observed during the meta-dynamics: (a) coordination of Na<sup>+</sup> to the O<sub>3</sub> carbonyl; (b) concerted attack of two water molecules; (c) formation of the first hydroxyl on the C<sub>1</sub> site; (d) formation of the second hydroxyl on the O<sub>3</sub> site. See text for details. Most of the solvent molecules are not shown.</figcaption></figure>
shares one hydrogen with $O_3$ through hydrogen-bonding; (b) the first hydroxyl is formed on the $O_3$ site simultaneously with the formation of a chain of hydrogen-bonded water molecules; (c) the second hydroxyl is formed on the $C_1$ site after a cascade of proton transfers giving the diol. Although the first hydroxyl is formed here on $O_3$ carbonyl, the second hydroxyl appears after only a few MD steps, which is akin to a concerted reaction. Both hydration

<figure><img src="image_6.png" /><figcaption>Figure 5: Second hydration pathway (from keto to diol pyruvate) observed during metadynamics: (a) hydrogen shared between water and $O_3$; (b) formation of the first hydroxyl on $O_3$; (c) formation of the second hydroxyl on $C_1$. See text for details. Most of the solvent molecules are not shown.</figcaption></figure>

paths involve direct interactions with the carbonyl group but the precise mechanisms are distinct. In the first hydration path, $O_3$ is less available for water attack because of the close contact with $Na^+$ (2.04 Å in Figure 4a). This interaction polarizes the carbonyl bond rendering the $C_1$ carbon atom more electrophilic and hence more prone to water attack, explaining the formation of the first hydroxyl on this site. After this step, $Na^+$ moves away from pyruvate (2.10 Å then 2.51 Å), leaving room for the hydration on the $O_3$ site by water. In the second path, $Na^+$ is close to the carboxylate oxygen (2.31 Å in Figure 5a). Therefore the approach of water towards $O_3$ carbonyl is not hindered so that the first hydroxyl is formed on the $O_3$ site. The formation of a chain of hydrogen-bonded water molecules is enabled by the electrostatic interaction between $Na^+$ and $COO^-$.

This interaction is absent in neat water, preventing the appearance of such bridged water molecules.³²
coordinated to O₃, which weakens the O₃-H hydroxyl bond; (b) a five-membered ring with a hydrogen atom bridging O₃ to the carboxylate oxygen is formed; (c) it is followed by the hydrogen-transfer to the carboxylate oxygen; (d) the carboxylic group then rotates towards a perpendicular geometry; (e) allowing for the formation of a hydrogen bridge between the remaining hydroxyl oxygen and the carboxylic hydrogen; (f) proton transfer to the hydroxyl group takes place giving a free water molecule and the keto species. An alternative

<figure><img src="image_7.png" /><figcaption>Figure 6: First dehydration pathway (from diol to keto pyruvate) observed during the metadynamics: (a) coordination of Na⁺ to O₃; (b) formation of a five-membered ring; (c) proton transfer; (d) rotation of the carboxylic group; (e) formation of a hydrogen bridge; (f) proton transfer giving a free water molecule and the keto species. See text for details. Most of the solvent molecules are not shown.</figcaption></figure>

dehydration path is also observed at the end of the metadynamics simulation (see Figure 7). The reaction also implies a five-membered ring but on the opposite side of Na⁺: (a) Na⁺ is coordinated to the carboxylate and one hydroxyl (at 2.34 and 2.42 Å, respectively) in a CIP bidentate geometry; (b) a five-membered ring is formed between the "free carboxylate" and the hydroxyl group at the opposite of Na⁺; (c) the O-H detaches from the pyruvate giving a free water molecule; (d) the hydrogen from the other hydroxyl group dissociates to form the keto. The coordination of Na⁺ therefore opens a novel "H-bridge" pathway. By weakening the hydroxyl bond, Na⁺ triggers the dehydration reaction by allowing the formation of an intramolecular hydrogen bond, which favors a hydrogen transfer. It is a likely explanation for the lower free-energy barrier for the dehydration process (73 kJ/mol instead of 84 kJ/mol
<figure><img src="image_8.png" /><figcaption>Figure 7: Second dehydration pathway observed at the end of the metadynamics: (a) bidentate coordination of Na⁺ to OH and carboxylate; (b) formation of a five-membered ring on the opposite side; (c) detachment of O₃H to form a free water molecule; (d) dissociation of the other hydroxyl group (keto species). See text for details. Most of the solvent molecules are not shown.</figcaption></figure>

in water) and hence for the reduced diol/keto ratio compared to neat water.

We present the separate structural analyses for the keto and diol forms and for the transition state region. To this aim, three families of configurations were extracted from the MTD trajectory based on the values of the two collective variables, according to some well-chosen boundaries. They respectively include 9893, 13925, and 1292 configurations. We observe that the transition state exhibits a protonated carboxylic group, whereas only the pyruvate anion is present in the keto and diol basins (see Figure S3 in Supplementary Information). In the case of the diol, the formation of the anionic species solely is certainly caused by the presence of the Na⁺ cation, since a mixture of protonated and deprotonated diol forms was observed in neat water.³² We now examine the interaction between the sodium cation and the pyruvate anion more closely. By discussing the Na⁺···O₃ distance, d<sub>NaO₃</sub>. Nearly 50% of the configurations at the bottom of the keto basin have the d<sub>NaO₃</sub> distance fluctuating around 2.4 (0.3) Å, indicating that Na⁺ is strongly coordinated to the carbonyl but has no contact with the carboxylate group. Such an interaction has been evidenced in several works although it is chemically not intuitive and seems non-standard. The X-ray crystal structure of sodium pyruvate reported a structure with a pseudo-five-membered ring where Na⁺ connects with the carbonyl oxygen and one carboxylate oxygen.⁴¹ More than 40% of the configurations show Na⁺ lying further from O₃ carbonyl and coordinated to one carboxylate
oxygen in a monodentate CIP configuration (respective average distance of 4.5 (0.4) Å and 2.3 (0.1) Å). We do not observe any symmetrical bidentate CIP configuration between Na⁺ and COO⁻. It underlines that a simple intuition based on electrostatics only is not valid in salted water conditions. Less than 10 % of the configurations exhibit a solvent-shared ion pairing (SSIP) structure, with Na⁺ in a fully solvated environment by water molecules (at more than 4 Å from pyruvate). On the pyruvate side, the interaction between Na⁺ and O₃ directly impacts the structure of the anion. We indeed observe a strong correlation (i.e., Pearson coefficient of -0.7) between d<sub>NaO₃</sub> and the torsion of pyruvate, with average OCCO dihedral angles of -56° (22°) and -105° (26°) for short and long d<sub>NaO₃</sub> distances, respectively. In other words, the pyruvate keto tends to deviate from the perpendicular geometry<sup>32,33,38</sup> whenever Na⁺ is coordinated to the O₃ carbonyl oxygen. This structural change is observed in the beginning of the first hydration path described above. Near the bottom of the diol basin, in contrast with keto, the SSIP structure is predominant (65% of the configurations) with Na⁺ fully solvated by water and showing no coordination to pyruvate. It shows that overall the interaction between sodium and the anion is weaker for the diol. Other common configurations display a direct interaction between Na⁺ and pyruvate. Almost 20% show a bidentate CIP structure where Na⁺ is coordinated to the carboxylate and to one hydroxyl group. They present a five-membered ring structure formed by Na, O₁, C₂, C₁, and OH. Less than 15% are in a Na⁺-hydroxyl monodentate mode. As to the transition state region, one common feature of all configurations is the presence of an oxygen atom (from a water molecule or a hydroxide ion) at 1.82 (± 0.06) Å from C₁, as already observed for glyoxylic and pyruvic acids in neat water although this distance was slightly larger.<sup>32</sup> For dehydration, Figure 6-b is representative of the transition state, with a five-membered ring structure formed by a hydrogen bridge and therefore a planar geometry.

To summarize, the metadynamics provides a more detailed picture of the structural arrangements than the unbiased CP simulation. It reveals crucial details on the different coordination modes of Na⁺ to keto pyruvate, either involving the carboxylate or the carbonyl
groups. It also points out that solvent shared structures are favored for the cation-diol pair. Sodium is coordinated to pyruvate in all the identified hydration and dehydration processes. Importantly, Na⁺ could act as a catalyst for the dehydration reaction since its coordination to pyruvate can trigger the formation of "H-bridge" structures leading to the keto form. Its impact on the photoactivity of pyruvate is examined in the next section.

## Excitation of the keto and diol forms of pyruvate

The calculations of the vertical excited states for the keto and the diol species are presented in this section. All results are summarized in Table 1.

<table><caption>Table 1: Vertical excited state energies and oscillator strengths calculated with the ADC(2)/def2-TZVPP method for six configurations extracted from the the keto ($K_{i=1,3}$) and diol ($D_{i=1,3}$) free-energy basins. Na⁺ is coordinated to carboxylate in K1 (CIP structure), to the $O_3$ carbonyl in K2 and in a SSIP geometry in K3. Na⁺ is coordinated to a hydroxyl oxygen in D1, far from the pyruvate molecule in D2, or part of a five-membered ring structure in D3.</caption><thead><tr><th rowspan="2"></th><th colspan="3"><i>S</i><sub>1</sub></th><th colspan="3"><i>S</i><sub>2</sub></th></tr><tr><th>E (eV)</th><th>E(nm)</th><th>f × 10<sup>-3</sup></th><th>E (eV)</th><th>E(nm)</th><th>f × 10<sup>-3</sup></th></tr></thead><tbody><tr><td>K1</td><td>3.93</td><td>316</td><td>0.2</td><td>4.94</td><td>251</td><td>26.9</td></tr><tr><td>K2</td><td>3.45</td><td>359</td><td>1.4</td><td>4.07</td><td>304</td><td>24.4</td></tr><tr><td>K3</td><td>3.69</td><td>336</td><td>0.8</td><td>5.20</td><td>238</td><td>1.4</td></tr><tr><td>D1</td><td>3.74</td><td>331</td><td>0.7</td><td>4.35</td><td>285</td><td>3.2</td></tr><tr><td>D2</td><td>4.17</td><td>297</td><td>0.7</td><td>4.77</td><td>260</td><td>0.6</td></tr><tr><td>D3</td><td>4.87</td><td>255</td><td>0.2</td><td>5.17</td><td>240</td><td>1.3</td></tr></tbody></table>

The configurations in the keto basin have been described in the previous section. Briefly, K1 is representative of the monodentate Na⁺-carboxylate (CIP) structures, K2 of the Na⁺-carbonyl structures, and K3 of the SSIP configurations where Na⁺ is screened by the solvent and is not coordinated to pyruvate. The geometries are displayed in Figure 8. For the excited states calculations, we keep only the closest water molecules (ten, nine, and nine, respectively). The $S_1$ states of K1, K2, and K3 configurations lie in the actinic region at 316, 359, and 336 nm, respectively. They show a very weak oscillator strength. For K1 and K3, only the $S_0 \rightarrow S_1$ transition is relevant to atmospheric purposes so excitations to
<figure><img src="image_9.png" /><figcaption>Figure 8: Representative configurations in the keto anion basin. Na⁺ is coordinated to carboxylate in K1 (CIP structure), to the O₃ carbonyl in K2 and in a SSIP geometry in K3.</figcaption></figure>

higher lying-states are not discussed further. The virtual natural transition orbitals (NTOs) of the *S*₁ states have a strong π* character, and their associated occupied NTOs include the p-type lone pair (*n*) of the carbonyl oxygen (see Figures S4 to S6 in Supplementary Information). The *S*₁ state of K1 at 316 nm compares well with results reported in the literature. The absorption spectrum of bare pyruvate averaged over 500 structures, calculated at the SCS-ADC(2)/cc-pVTZ level by Clarke et al³³ is found to peak at 318 nm. The work of Cao et al. reports calculated absorption in the same domain for pyruvate and its micro-solvated complexes with up to five water molecules.³⁸ Our value also matches well the experimental absorption spectrum (maximum near 318 nm, see Figure S7 in Supplementary Information).¹⁶ We note however differences with the calculations of Shemesh et al.¹⁵ that predict a red-shifted absorption at 331-349 nm region. It is probably due to unconverged calculations yielding more planar geometries for pyruvate instead of perpendicular. In fact we also observe non perpendicular geometries in our simulation, represented by the K2 configuration where Na⁺ is coordinated to the carbonyl group (average *d*<sub>NaO₃</sub> = 2.38 Å and OCCO dihedral angle of -56°). We postulate that the close contact of the cation with the carbonyl chromophore dictates the more planar geometries of the K2-like configurations. The direct interaction of Na⁺ with the main UV chromophore has a very strong impact (see
the NTO analysis in Supplementary Information). First, it induces a large 43 nm red-shift of the *S*₁ state compared with K1 (53 nm for *S*₂). Second, the oscillator strength of the *S*₀ → *S*₁ transition of K2 is larger by one order of magnitude than its counterpart for K1 and K3. Moreover, the *S*₀ → *S*₂ transition lies also in the actinic region at 304 nm and bears a very high oscillator strength. Hence not only K1-like configurations are relevant for the photochemistry of pyruvate but K2-like structures should also be taken into account since they may represent a large fraction of pyruvate in salted water. Experimentally, the red shift measured at elevated salt concentrations⁸ (maximum absorption near 330 nm) could be rationalized by a larger contribution due to K2, where the cation directly interacts with the carbonyl chromophore.

<figure><img src="image_10.png" /><figcaption>Figure 9: Representative configurations in the diol anion basin: a) D1, b) D2 (SSIP), c) D3 (CIP).</figcaption></figure>

For comparison, we also calculated the vertical excitation energies of three representative configurations in the diol basin labeled D1, D2, and D3, mentioned previously in the Reversible hydration of pyruvate section. They respectively include 12, 9, and 8 water molecules (Figure 9). In the D1 configuration, Na⁺ is in contact with one hydroxyl oxygen at a distance of 2.43 Å and is surrounded by three water molecules within a 2.60 Å distance. D1 shows no interaction between Na⁺ and the carboxylate. In the D2 (SSIP) configuration, the Na⁺ cation is far from the hydroxyl groups (at 4.64 Å from the closest one) and is fully solvated
by four water molecules. D3 configuration is a bidentate CIP geometry with Na⁺ interacting
with the carboxylate and one hydroxyl group (respectively at 2.27 and 2.68 Å). Similarly
to keto, we have considered excitations to the S₁, S₂ states of the diols. The energies are
given in Table 1. Interestingly, our whole set of computed energies is significantly lower than
the values reported in the literature. To our knowledge, only two theoretical studies in the
gas phase mention the electronic properties of the diol and its monohydrated complex with
transitions lying above 5.6 eV.¹⁵,³⁹ The addition of water seems to induce a small down-shift
in the transition of the neutral diol, and a slight up-shift in the case of the anion diol. It is
unlikely that the difference between our values and literature only stems from the higher level
of theory used in our approach or from the larger number of water molecules in our system.
The discrepancy with the neutral diol can be understood in terms of the protonated state
of the diol, i.e. deprotonated in the present work and neutral in Ref. 15,39. As to the anion
diol, the higher excitation energy may result from the symmetrical structure considered in
the work of Shemesh et al.¹⁵ Our simulations in explicit water conditions - with or without
electrolytes - exhibit no such symmetrical geometries which we think are not realistic in
water. In aqueous solutions with electrolytes, PA exhibits experimental red-shifts of 2-13
nm depending on the nature and the concentration of the electrolytes.⁸,¹⁶ It is much weaker
than those found by our calculations on the diol, confirming that the diol is a minor species.
However, the diol form may become a photosensitizer when it is predominant as in the case
of acetic acid, glyoxylic acid,⁴² glyoxal,⁴³ methylglyoxal,⁴⁴ etc.

Summary and conclusion

The ab initio metadynamics simulation in salted aqueous solution combined with excited
states calculations has revealed that the sodium cation can interact with different parts
of the pyruvate molecule, including the carbonyl group, thus impacting both its hydration
equilibrium and its electronic absorption spectrum. A stringent consequence is that the
diol-to-keto ratio is reduced in comparison with neat water. Some dehydration pathways directly involving sodium have been observed and are a likely explanation for the decreased stabilization of the diol form in salted water conditions. New photochemical pathways with a direct interaction between sodium and the carbonyl chromophore could be explored for the keto species. Although it is clear that the monodentate contact ion pairs between Na⁺ and the carboxylate are the favored geometries and are mainly responsible for the absorption spectrum of pyruvate, the stabilization of 'new' complexes such as sodium-carbonyl or sodium-diol can induce a significant bathochromic effect and therefore make them act as new photosensitizers. We assume that the entropic effects of water and the solvation of Na⁺ probably prevent the stabilization of the bidentate configurations. Further investigations including the Ca²⁺ cation, which is generally assumed to bind to the carboxylate group in a bidentate mode, could reveal if similar influences on thermochemistry and photoactivity take place due to the cation mobility around the acid. More generally, the ionic strength has a crucial influence on the physical chemistry properties of oxo-carboxylic acids, and organic acids, and should be taken into account since compounds that do not present photochemistry in the actinic region may become photoactive in the presence of ions. This may have a strong effect on the formation of secondary organic aerosols.

Given the direct interaction of Na⁺ with pyruvate, the present work also suggests that an improved free-energy landscape would be obtained by an extended metadynamics simulation incorporating additional collective variables as functions of the sodium cartesian coordinates. This would help disentangle the most stable configurations in each free-energy basin and estimate the free-energy barriers more accurately. Such time-consuming simulations could rely on methods such as the bias-exchange variant.⁴⁵
# Computational details

## Ab initio molecular dynamics

The Car-Parrinello (CP) method$^{46,47}$ coupled to the metadynamics technique$^{45,48–52}$ was used within the CPMD code$^{53}$ to reconstruct the free-energy landscape of the hydration-dehydration reaction of pyruvate in an aqueous solution with NaCl. The computational details were given in our previous work$^{32}$ and we only briefly describe the present simulation (see also the monitoring of the fictitious kinetic energy in Figure S1). The system consists of a cubic supercell of 15 Å including PA, 108 water molecules, and one NaCl with a molarity and ionic strength of 0.49 M (as estimated from the volume of the box). Compared to Ref. 32, there is an additional NaCl electrolyte, and the size of the system is larger, which provides a better description of the aqueous solution. For $Na^+$, we use an ultrasoft pseudopotential$^{54}$ whose correctness has been proven on a system containing sodium oxide, where the $2s2p$ semicore electrons are excluded from the valence space.$^{55}$ In the initial configuration, this cation is coordinated to the two oxygen atoms of the carboxylate group $O_1$ and $O_2$. However, during the equilibration process, the configuration evolves towards a structure where $Na^+$ is solvated by more water molecules and is bound to $O_1$ carboxylate in a monodentate mode (Figure 1).

The whole simulation included a preliminary, unbiased, CP simulation of 91 ps, including an equilibration period of 13 ps, at a controlled temperature of 300 K, followed by an *ab initio* MTD simulation (in its extended Lagrangian version). Both forward and backward transitions of the reversible hydration reaction were explored in the same run with a unique set of collective variables (CVs), which requires several barrier recrossings. This strategy has been chosen instead of running separate runs for the forward and backward transitions with possibly distinct sets of CVs because it is more accurate although more time-consuming. We took the same two CVs and their associated parameters as those used in our previous study for the MTD calculations.$^{32}$ They were specifically designed to accelerate the formation of
the hydroxyl groups of the geminal diol form. CV1 represents the coordination number (CN) of the carbonyl oxygen O3 to all water protons and CV2 the CN of the carbonyl carbon C1 to all water oxygens with:⁵⁶,⁵⁷

$$CN = \sum_{i} \frac{1 - (d_{i}/d_{0})^{p}}{1 - (d_{i}/d_{0})^{p+q}} \qquad (1)$$

where $d_i$ is the distance between the O3 and the i-th solvent hydrogen ($d_0 = 1.4$ Å) or between C1 and the i-th solvent oxygen ($d_0 = 1.8$ Å), $p = 6$ and $q = 6$. Thus a CN value close to one corresponds to a coordinated atom while a CN value approaching zero means that the atom is free. We have checked a posteriori that this choice of CVs led to clearly separated basins for the reactant, product, and transition state. It is a minimum criterion to be fulfilled for an MTD simulation. In total, more than nine thousand hills were accumulated along the MTD trajectory, during which the forward transition from the keto form to the gem-diol was sampled twice and the reverse transition twice. The MTD simulation was stopped when the oxygen atom of the carbonyl group O3 was detached from the carbon atom C1, a few MD steps before the formation of the keto form, since the first CV could not be relevant anymore.

## Excited states

The vertical excited states transition energies were computed using the TURBOMOLE package⁵⁸ with the algebraic diagrammatic construction through second-order, ADC(2),⁵⁹,⁶⁰ with the RI scheme,⁶¹ and the frozen core approximation. The def2-TZVPP extended atomic basis set was used. Based on a benchmark on 80 molecules, the ADC(2) had been recommended instead of TD-DFT, especially for keto dyes (with at least one carbonyl group), yielding results that are similar to the CC2 method for an acceptable computational effort.⁶² Since a recent issue has been raised regarding the application of this method to molecules bearing a carbonyl group,⁶³ we carefully checked that the error on the vertical excited state energies of
K1, K2, and K3 configurations was less than 0.25 eV with respect to CC2 calculations (see Table S1 in Supplementary Information). To visualize the excitations, occupied and virtual natural transition orbitals (NTOs) were obtained from a singular value decomposition of the excitation amplitudes.⁶⁴
Acknowledgements

This work was supported by the ANR DYNAAMIX project (ANR-17-CE29-0001-01) of the French Agence Nationale de la Recherche. This work was granted access to the HPC resources of CINES under the allocation 2020-A0100810750 made by GENCI (Grand Equipement National de Calcul Intensif).

Conflict of Interest

There are no conflicts to declare.

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