A theoretical model linking solute-induced hydrogen-bond rearrangement in water to the solvatochromic solvent features of aqueous solutions

Dissolved solutes rearrange the hydrogen-bond network of water, and the relative intensities of four Gaussian components of the ATR-FTIR OH-stretch band — interpreted as four water subpopulations with different hydrogen-bond arrangements — are known to correlate linearly with the Kamlet–Taft solvatochromic solvent features (dipolarity/polarizability $\pi^*$, hydrogen-bond donor acidity $\alpha$, hydrogen-bond acceptor basicity $\beta$) in aqueous solutions of salts, osmolytes, and polymers. These linear relationships are, however, purely empirical: no theoretical model derives them, and it is not known which structural properties of the solute (such as shape, anisotropy, charge delocalization, polarizability) set the per-solute coefficients or why some solvent features respond more strongly than others. The problem is to construct such a molecular-level theory — identifying the solute descriptors that control the redistribution of water subpopulations and deriving the observed linear relations with quantitative, ideally predictive, coefficients. The source paper (da Silva et al., 2021) established the empirical relations without offering any theoretical account, and the group's subsequent open-access publications leave the structural basis of the subpopulations — and hence which solute features control their redistribution — explicitly unknown.

Background

Liquid water's distinctive properties stem from its hydrogen-bond network, in which each molecule can donate and accept hydrogen bonds whose strength varies with the local geometry. When a solute dissolves, it perturbs this network. Attenuated total reflection Fourier-transform infrared (ATR-FTIR) spectroscopy probes this perturbation through the OH-stretching band (roughly 2700–4000 cm⁻¹), which is conventionally decomposed into a set of Gaussian sub-bands: components at lower optical frequency are assigned to water molecules in strong, ice-like tetrahedral hydrogen-bond environments, and components at higher frequency to water in weaker or distorted hydrogen-bond environments. For aqueous solutions of nine solutes (the salts $\mathrm{Na_2SO_4}$, NaCl, $\mathrm{NaClO_4}$, NaSCN; urea; trimethylamine N-oxide; and three nonionic polymers), da Silva et al. (2021) showed that a decomposition into exactly four Gaussians peaking at about 3080, 3230, 3400, and 3550 cm⁻¹ fits every measured spectrum with flat residuals, and that these four components represent four subpopulations of water with different hydrogen-bond arrangements: (I) four tetrahedral bonds; (II) four distorted bonds; (III) loosely arranged four- and three-bond molecules; (IV) three, two, and single bonds. A later covariance analysis by the same group found this four-component set necessary and sufficient (superior to three or five components). Independently, solvent quality of an aqueous medium is quantified by the Kamlet–Taft solvatochromic parameters, obtained from the solvatochromic shifts (spectral shifts of probe dyes that report their solvation environment) of water-soluble dyes: $\pi^*$ for solvent dipolarity/polarizability (measured with 4-nitroanisole), $\alpha$ for hydrogen-bond donor acidity (Reichardt's carboxylated betaine dye), and $\beta$ for hydrogen-bond acceptor basicity (4-nitrophenol). The Zaslavsky-group program established that these solvent features of water vary with the nature and concentration of the solute, that $\pi^*$ and $\alpha$ in particular linearly describe numerous physicochemical properties of aqueous solutions (water activity, osmotic coefficients, surface tension, viscosity, relative permittivity, solubilities, salting-out constants, and solute partitioning in aqueous two-phase systems), and — the key empirical finding of the 2021 source paper — that the solvent features are strongly correlated with the FTIR-derived relative fractions of the water subpopulations. For every solute $j$ and concentration $i$ examined, each solvent feature $\mathrm{SF}_{ji}$ (each of $\pi^*$, $\alpha$, $\beta$) is described by a linear relation in one or two of the subpopulation fractions, $\mathrm{SF}_{ji} = k_{0j} + k_{mj} A_{ji}^{m} + k_{nj} A_{ji}^{n}$, where $A_{ji}^{m}$, $A_{ji}^{n}$ are the fractions of two solute-specific subpopulations. For example, in NaSCN solutions, $\pi^*$ depends only on subpopulation II (3230 cm⁻¹), $\beta$ only on subpopulation IV (3550 cm⁻¹), and $\alpha$ on both. Because the solvatochromic probes are far too large to fit inside a solute's hydration shell, these correlations imply that solutes change the relative amounts of hydrogen-bond subpopulations in bulk water. Yet the Gaussian sub-band assignments themselves rest, in the authors' own words, on rather uncertain models of water structure, and the linear relations, the choice of which subpopulations enter for a given solute, and the differing sensitivities of $\pi^*$, $\alpha$, and $\beta$ remain unexplained empirical facts: no theoretical model connects solute structure to the redistribution of water subpopulations and from there to the measured solvent features.

Problem Statement

Construct a theoretical model that explains, at the molecular level, how dissolved solutes rearrange the hydrogen-bond network of water and thereby determine the solvatochromic solvent features of aqueous solutions, reproducing the experimentally established linear relationships of da Silva et al. (2021). Specifically: (1) derive the observed linear form $\mathrm{SF}_{ji} = k_{0j} + k_{mj} A_{ji}^{m} + k_{nj} A_{ji}^{n}$, where $\mathrm{SF}_{ji}$ is each of the Kamlet–Taft solvent features ($\pi^*$, $\alpha$, $\beta$) and $A_{ji}^{m}$, $A_{ji}^{n}$ are the relative fractions of the FTIR-derived water subpopulations (Gaussian components of the OH-stretch band near 3080, 3230, 3400, and 3550 cm⁻¹) for solute $j$ at concentration $i$ — including which subpopulations enter for a given solute and why (e.g., for NaSCN, $\pi^*$ couples only to subpopulation II, $\beta$ only to subpopulation IV, $\alpha$ to both); (2) identify which structural features of the solute (such as shape, anisotropy, charge delocalization, or polarizability) control the coefficients $k_{0j}$, $k_{mj}$, $k_{nj}$, and hence why some solutes influence certain solvent features more strongly than others; and (3) make the model quantitatively account for the published spectra and solvent-feature data across the examined solute classes (inorganic salts, small organic osmolytes, nonionic polymers), with predictive coefficients desirable but not required. Parts (1)–(3) are aspects of one objective: a molecular-level theory of solute-induced hydrogen-bond rearrangement in water.

References

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