Dissociation Constants of Weak Acids from ab Initio Molecular Dynamics Using Metadynamics: Influence of the Inductive Effect and Hydrogen Bonding on pKa Values

FTIR spectroscopy and molecular level insight of diluted aqueous solutions of acetic acid

Aqueous solutions of acetic acid (AA) have been intensively explored for decades with a particular attention addressed to the hydrogen bond network generated by COOH group at different concentrations. In majority of studies conducted so far the envelope originated from νCO is decomposed into two bands assigned to differently hydrated monomers: the one presumably to AA···H2O, and another one to AA···(H2O)2. In order to examine if species other than the mentioned monomers produce this spectral signature, we performed computational and FTIR spectroscopic study of AA in aqueous solutions. Dilute solutions of deuterated acetic acid (CD3COOD) in D2O and in C2Cl4 as a reference were prepared (c0 = 0.001, 0.01 and 0.1 mol dm-3) as well as of deuterated sodium acetate (CD3COONa) in D2O. CD3COOD in 0.1 mol dm-3 solution in D2O displays a feature that separated in two signals with maxima at 1706 cm-1 and 1687 cm-1. A combined DFT and molecular dynamics study performed in this work showed the assignation of those spectral bands to be a more complex problem than previously thought, with syn-anti isomerism and hydration contributing to the experimentally observed broad νCO envelope.

Advantages of Multidimensional Biasing in Accelerated Dynamics: Application to the Calculation of the Acid pKa for Acetic Acid

The use of accelerated sampling methods such as metadynamics has shown a significant advantage in calculations that involve infrequent events, which would otherwise require sampling a prohibitive number of configurations to determine the difference in free energies between two or more chemically distinct states such as in the calculation of acid dissociation constants Ka. In this case, the most common method is to bias the system via a single collective variable (CV) representing the coordination number of the proton donor group, which yields results in reasonable agreement with experiments. Here we study the deprotonation of acetic acid using the reactive force field ReaxFF and observe a significant dependence of Ka on the simulation box size when biasing only the coordination number CV, which is due to incomplete sampling of the deprotonated state for small simulation systems and inefficient sampling for larger ones. Incorporating a second CV representing the distance between the H3O+ cation and the acetate anion results in substantially more efficient sampling, both accelerating the dynamics and virtually eliminating the computational box size dependence.

Selective Separation of Lithium, Magnesium and Calcium using 4-Phosphoryl Pyrazolones as pH-Regulated Receptors

Ensuring continuous and sustainable lithium supply requires the development of highly efficient separation processes such as LLE (liquid-liquid extraction) for both primary sources and certain waste streams. In this work, 4-phosphoryl pyrazolones are used in an efficient pH-controlled stepwise separation of Li⁺ from Ca²⁺ , Mg²⁺ , Na⁺ and K⁺ . The factors affecting LLE process, such as the substitution pattern of the extractant, diluent/water distribution, co-ligand, pH, and speciation of the metal complexes involved, were systematically investigated. The maximum extraction efficiency of Li⁺ at pH 6.0 was 94 % when Mg²⁺ and Ca²⁺ were previously separated at pH<5.0, proving that the separation of these ions is possible by simply modulating the pH of the aqueous phase. Our study points a way to separation of lithium from acid brine or from spent lithium ion battery leaching solutions, which supports the future supply of lithium in a more environmentally friendly and sustainable manner.

Highly Tunable 4-Phosphoryl Pyrazolone Receptors for Selective Rare-Earth Separation

Highly selective rare-earth separation has become increasingly important due to the indispensable role of these elements in various cutting-edge technologies including clean energy. However, the similar physicochemical properties of rare-earth elements (REEs) render their separation very challenging, and the development of new selective receptors for these elements is potentially of very considerable economic and environmental importance. Herein, we report the development of a series of 4-phosphoryl pyrazolone receptors for the selective separation of trivalent lanthanum, europium, and ytterbium as the representatives of light, middle, and heavy REEs, respectively. X-ray crystallography studies were employed to obtain solid-state structures across 11 of the resulting complexes, allowing comparative structure-function relationships to be probed, including the effect of lanthanide contraction that occurs along the series from lanthanum to europium to ytterbium and which potentially provides a basis for REE ion separation. In addition, the influence of ligand structure and lipophilicity on lanthanide binding and selectivity was systematically investigated via n-octanol/water distribution and liquid-liquid extraction (LLE) studies. Corresponding stoichiometry relationships between solid and solution states were well established using slope analyses. The results provide new insights into some fundamental lanthanide coordination chemistry from a separation perspective and establish 4-phosphoryl pyrazolone derivatives as potential practical extraction reagents for the selective separation of REEs in the future.

Modeling the Solvation and Acidity of Carboxylic Acids Using an Ab Initio Deep Neural Network Potential

Formic and acetic acid constitute the simplest of carboxylic acids, yet they exhibit fascinating chemistry in the condensed phase such as proton transfer and dimerization. The go-to method of choice for modeling these rare events have been accurate but expensive ab initio molecular dynamics simulations. In this study, we present a deep neural network potential trained using accurate ab initio data that can be used in tandem with enhanced-sampling methods to perform an efficient exploration of the free-energy surface of aqueous solutions of weak carboxylic acids. In particular, we show that our model captures proton dissociation and provides a good estimate of the pK_a, as well as the dimerization of formic and acetic acid. This provides a suitable starting point for applications in different research areas where computational efficiency coupled with the accuracy of ab initio methods is required.

Advanced Theory and Simulation to Guide the Development of CO2 Capture Solvents

Increasing atmospheric concentrations of greenhouse gases due to industrial activity have led to concerning levels of global warming. Reducing carbon dioxide (CO₂) emissions, one of the main contributors to the greenhouse effect, is key to mitigating further warming and its negative effects on the planet. CO₂ capture solvent systems are currently the only available technology deployable at scales commensurate with industrial processes. Nonetheless, designing these solvents for a given application is a daunting task requiring the optimization of both thermodynamic and transport properties. Here, we discuss the use of atomic scale modeling for computing reaction energetics and transport properties of these chemically complex solvents. Theoretical studies have shown that in many cases, one is dealing with a rich ensemble of chemical species in a coupled equilibrium that is often difficult to characterize and quantify by experiment alone. As a result, solvent design is a balancing act between multiple parameters which have optimal zones of effectiveness depending on the operating conditions of the application. Simulation of reaction mechanisms has shown that CO₂ binding and proton transfer reactions create chemical equilibrium between multiple species and that the agglomeration of resulting ions and zwitterions can have profound effects on bulk solvent properties such as viscosity. This is balanced against the solvent systems needing to perform different functions (e.g., CO₂ uptake and release) depending on the thermodynamic conditions (e.g., temperature and pressure swings). The latter constraint imposes a "Goldilocks" range of effective parameters, such as binding enthalpy and pK _a, which need to be tuned at the molecular level. The resulting picture is that solvent development requires an integrated approach where theory and simulation can provide the necessary ingredients to balance competing factors.

Connecting Gas-Phase Computational Chemistry to Condensed Phase Kinetic Modeling: The State-of-the-Art

In recent decades, quantum chemical calculations (QCC) have increased in accuracy, not only providing the ranking of chemical reactivities and energy barriers (e.g., for optimal selectivities) but also delivering more reliable equilibrium and (intrinsic/chemical) rate coefficients. This increased reliability of kinetic parameters is relevant to support the predictive character of kinetic modeling studies that are addressing actual concentration changes during chemical processes, taking into account competitive reactions and mixing heterogeneities. In the present contribution, guidelines are formulated on how to bridge the fields of computational chemistry and chemical kinetics. It is explained how condensed phase systems can be described based on conventional gas phase computational chemistry calculations. Case studies are included on polymerization kinetics, considering free and controlled radical polymerization, ionic polymerization, and polymer degradation. It is also illustrated how QCC can be directly linked to material properties.

Computational Prediction of All Lanthanide Aqua Ion Acidity Constants

The protonation state of lanthanide-ligand complexes, or lanthanide-containing porous materials, with many Brønsted acid sites can change due to proton loss/gain reactions with water or other heteroatom-containing compounds. Consequently, variations in the protonation state of lanthanide-containing species affect their molecular structure and desired properties. Lanthanide(III) aqua ions undergo hydrolysis and form hydroxides; they are the best characterized lanthanide-containing species with multiple Brønsted acid sites. We employed constrained ab initio molecular dynamics simulations and electronic structure calculations to determine all acidity constants of the lanthanide(III) aqua ions solely from computation. The first, second, and third acidity constants of lanthanide(III) aqua ions were predicted, on average, within 1.2, 2.5, and 4.7 absolute pK_a units from experiment, respectively. A table includes our predicted pK_a values alongside most experimentally measured pK_a values known to date. The approach presented is particularly suitable to determine the Brønsted acidity of lanthanide-containing systems with multiple acidic sites, including those whose measured acidity constants cannot be linked to specific acid sites.

Nuclear quantum effects on autoionization of water isotopologs studied by ab initio path integral molecular dynamics

In this study, we investigate the nuclear quantum effects (NQEs) on the acidity constant (pK_A) of liquid water isotopologs under the ambient condition by path integral molecular dynamics (PIMD) simulations. We compared simulations using a fully explicit solvent model with a classical polarizable force field, density functional tight binding, and ab initio density functional theory, which correspond to empirical, semiempirical, and ab initio PIMD simulations, respectively. The centroid variable with respect to the proton coordination number of a water molecule was restrained to compute the gradient of the free energy, which measures the reversible work of the proton abstraction for the quantum mechanical system. The free energy curve obtained by thermodynamic integration was used to compute the pK_A value based on probabilistic determination. This technique not only reproduces the pK_A value of liquid D₂O experimentally measured (14.86) but also allows for a theoretical prediction of the pK_A values of liquid T₂O and aqueous HDO and HTO, which are unknown due to their scarcity. It is also shown that the NQEs on the free energy curve can result in a downshift of 4.5 ± 0.9 pK_A units in the case of liquid water, which indicates that the NQEs plays an indispensable role in the absolute determination of pK_A. The results of this study can help inform further extensions into the calculation of the acidity constants of isotope substituted species with high accuracy.

Exploring Free Energy Profiles of Enantioselective Organocatalytic Aldol Reactions under Full Solvent Influence

We present a computational study on the enantioselectivity of organocatalytic proline-catalyzed aldol reactions between aldehydes in dimethylformamide (DMF). To explore the free energy surface of the reaction, we apply two-dimensional metadynamics on top of ab initio molecular dynamics (AIMD) simulations with explicit solvent description on the DFT level of theory. We avoid unwanted side reactions by utilizing our newly developed hybrid AIMD (HyAIMD) simulation scheme, which adds a simple force field to the AIMD simulation to prevent unwanted bond breaking and formation. Our condensed phase simulation results are able to nicely reproduce the experimental findings, including the main stereoisomer that is formed, and give a correct qualitative prediction of the change in syn:anti product ratio with different substituents. Furthermore, we give a microscopic explanation for the selectivity. We show that both the explicit description of the solvent and the inclusion of entropic effects are vital to a good outcome-metadynamics simulations in vacuum and static nudged elastic band (NEB) calculations yield significantly worse predictions when compared to the experiment. The approach described here can be applied to a plethora of other enantioselective or organocatalytic reactions, enabling us to tune the catalyst or determine the solvent with the highest stereoselectivity.

Simulating Solvation and Acidity in Complex Mixtures with First-Principles Accuracy: The Case of CH3SO3H and H2O2 in Phenol

We present a generally applicable computational framework for the efficient and accurate characterization of molecular structural patterns and acid properties in an explicit solvent using H₂O₂ and CH₃SO₃H in phenol as an example. To address the challenges posed by the complexity of the problem, we resort to a set of data-driven methods and enhanced sampling algorithms. The synergistic application of these techniques makes the first-principle estimation of the chemical properties feasible without renouncing to the use of explicit solvation, involving extensive statistical sampling. Ensembles of neural network (NN) potentials are trained on a set of configurations carefully selected out of preliminary simulations performed at a low-cost density functional tight-binding (DFTB) level. The energy and forces of these configurations are then recomputed at the hybrid density functional theory (DFT) level and used to train the neural networks. The stability of the NN model is enhanced by using DFTB energetics as a baseline, but the efficiency of the direct NN (i.e., baseline-free) is exploited via a multiple-time-step integrator. The neural network potentials are combined with enhanced sampling techniques, such as replica exchange and metadynamics, and used to characterize the relevant protonated species and dominant noncovalent interactions in the mixture, also considering nuclear quantum effects.

How accurate are approximate quantum chemical methods at modelling solute-solvent interactions in solvated clusters?

In this paper, the performance of a wide range of DFT methods is assessed for the calculation of interaction energies of thermal clusters of a solute in water. Three different charge states (neutral, proton transfer transition state and zwitterion) of glycine were solvated by 1 to 40 water molecules as sampled from molecular dynamics simulations. While some ab initio composite methods that employ insufficiently large basis sets incurred significant errors even for a cluster containing only 5 water molecules relative to the W1X-2 benchmark, the DLPNO-CCSD(T)/CBS and DSD-PBEP86 (triple zeta basis set) levels of theory predicted very accurate interaction energies. These levels of theory were used to benchmark the performance of 16 density functionals from different rungs of Jacob's Ladder. Of the Rung 4 functionals examined, the ωB97M-V and ωB97X-V functionals stood out for predicting absolute interaction energies in 40-water clusters with mean absolute deviations (MAD) ∼4 kJ mol-1. The B3LYP-D3(BJ) functional performed exceptionally well with a MAD ∼1.7 kJ mol-1 and is the overall best performing method. Calculations of relative interaction energies allow for cancellation of systematic errors, including basis set truncation and superposition errors, and the ωB97M-V and B3LYP-D3(BJ) double zeta basis set calculations yielded relative interaction energies that are within ∼3 kJ mol-1 of the benchmark. The ONIOM approximation provides another strategy for accelerating the calculation of accurate absolute interaction energies provided that the calculations have converged with respect to the size of the "high-level-layer".

Ab Initio Molecular Dynamics Simulations of the Influence of Lithium Bromide Salt on the Deprotonation of Formic Acid in Aqueous Solution

The deprotonation of formic acid is investigated using metadynamics in tandem with Born-Oppenheimer molecular dynamics simulations. We compare our findings for formic acid in pure water with previous studies before examining formic acid in aqueous solutions of lithium bromide. We carefully consider different definitions for the collective variable(s) used to drive the metadynamics, emphasizing that the variables used must include all of the possible reactive atoms in the system, in this case carboxylate oxygens and water hydrogens. This ensures that all the various possible proton exchange events can be accommodated and the collective variable(s) can distinguish the protonated and deprotonated states, even over rather long ab initio simulation runs (ca. 200-300 ps). Our findings show that the formic acid deprotonation barrier and the free energy of the deprotonated state are higher in concentrated lithium bromide, in agreement with the available experimental data for acids in salt solution. We show that the presence of Br^- in proximity to the formic acid hydroxyl group effectively inhibits deprotonation. Our study extends previous work on acid deprotonation in pure water and at air-water interfaces to more complex multicomponent systems of importance in atmospheric and marine chemistry.

The multiple dissociation constants of glutathione disulfide: interpreting experimental pH-titration curves with ab initio MD simulations

The hexapeptide glutathione disulfide (GSSG) has six ionizable groups with six associated dissociation constants. The experimentally measured pH-titration curve, however, does not exhibit the six corresponding equivalence points and bears little resemblance to standard textbook examples of acid-base pH-titration curves. The curve highlights the difficulties in determining multiple pKa values of polyprotic acids - typically proteins and peptides - from experiment. The six pKa values of GSSG can, however, be estimated using Car-Parrinello molecular dynamics (CPMD) simulations in conjunction with metadynamics sampling of the underlying free energy landscape of the dissociation reactions. Ab initio MD simulations were performed on a GSSG molecule solvated by 200 water molecules. Using the estimated pKa values the theoretical titration curve was calculated and found to be in good agreement with experiment. The results clearly highlight how dissociation constants estimated from ab initio MD simulations can facilitate the interpretation of the pH-titration curves of complex chemical and biological systems.

Predicting Mole-Fraction-Dependent Dissociation for Weak Acids

We demonstrate for formic and acetic acid dissolved in water as examples that the binary quantum cluster equilibrium (bQCE) approach can predict acid strengths over the whole range of acid concentrations. The acid strength increases in a complex rather than a simple way with increasing mole fraction of the acid from 0 to 0.7, reflecting the complex interplay between the dissociated ions or conjugate bases available as compared to the acid and water molecules. Furthermore, our calculated ion concentrations meet the experimental maximum of the conductivity with excellent agreement for acetic acid and satisfactorily for the formic acid/water mixture. As only a limited number of simple quantum-chemical calculations are required for the prediction, bQCE is clearly a valuable approach to access these quantities also in non-aqueous solutions. It is a highly valuable asset for predicting ionization processes in highly concentrated solutions, which are relevant for biological and chemical systems, as well as technological processes.

Microscopic description of acid-base equilibrium

Acid-base reactions are ubiquitous in nature. Understanding their mechanisms is crucial in many fields, from biochemistry to industrial catalysis. Unfortunately, experiments give only limited information without much insight into the molecular behavior. Atomistic simulations could complement experiments and shed precious light on microscopic mechanisms. The large free-energy barriers connected to proton dissociation, however, make the use of enhanced sampling methods mandatory. Here we perform an ab initio molecular dynamics (MD) simulation and enhance sampling with the help of metadynamics. This has been made possible by the introduction of descriptors or collective variables (CVs) that are based on a conceptually different outlook on acid-base equilibria. We test successfully our approach on three different aqueous solutions of acetic acid, ammonia, and bicarbonate. These are representative of acid, basic, and amphoteric behavior.

A computational scheme of pKa values based on the three-dimensional reference interaction site model self-consistent field theory coupled with the linear fitting correction scheme

A scheme for quantitatively computing the acid dissociation constant, pKa, of hydrated molecules is proposed. It is based on the three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) theory coupled with the linear fitting correction (LFC) scheme. In LFC/3D-RISM-SCF, pKa values of target molecules are evaluated using the Gibbs energy difference between the protonated and unprotonated states calculated by 3D-RISM-SCF and the parameters fitted by the LFC scheme to the experimental values of training set systems. The pKa values computed by LFC/3D-RISM-SCF show quantitative agreement with the experimental data.

ReaxFF molecular dynamics simulation of intermolecular structure formation in acetic acid-water mixtures at elevated temperatures and pressures

The intermolecular structure formation in liquid and supercritical acetic acid-water mixtures was investigated using ReaxFF-based molecular dynamics simulations. The microscopic structures of acetic acid-water mixtures with different acetic acid mole fractions (1.0 ≥ x_HAc ≥ 0.2) at ambient and critical conditions were examined. The potential energy surface associated with the dissociation of acetic acid molecules was calculated using a metadynamics procedure to optimize the dissociation energy of ReaxFF potential. At ambient conditions, depending on the acetic acid concentration, either acetic acid clusters or water clusters are dominant in the liquid mixture. When acetic acid is dominant (0.4 ≤ x_HAc), cyclic dimers and chain structures between acetic acid molecules are present in the mixture. Both structures disappear at increased water content of the mixture. It was found by simulations that the acetic acid molecules released from these dimer and chain structures tend to stay in a dipole-dipole interaction. These structural changes are in agreement with the experimental results. When switched to critical conditions, the long-range interactions (e.g., second or fourth neighbor) disappear and the water-water and acetic acid-acetic acid structural formations become disordered. The simulated radial distribution function for water-water interactions is in agreement with experimental and computational studies. The first neighbor interactions between acetic acid and water molecules are preserved at relatively lower temperatures of the critical region. As higher temperatures are reached in the critical region, these interactions were observed to weaken. These simulations indicate that ReaxFF molecular dynamics simulations are an appropriate tool for studying supercritical water/organic acid mixtures.

Antioxidant activity and calcium binding of isomeric hydroxybenzoates

The association constant for calcium binding to hydroxybenzoates in aqueous 0.16 M NaCl at 25 °C was found electrochemically to have the value K_ass = 280 mol L⁻¹ with ΔH^o = −51 kJ mol⁻¹, ΔS^o = −122 J mol⁻¹ K⁻¹ for the 2-isomer (salicylate), K_ass = 7 mol L⁻¹ with ΔH^o = −39 kJ mol⁻¹, ΔS^o = −116 J mol⁻¹ K⁻¹ for the 3-isomer, and K_ass = 8 mol L⁻¹ with ΔH^o = −51 kJ mol⁻¹, ΔS^o = −155 J mol⁻¹ K⁻¹ for the 4-isomer. The 3- and 4-isomers were found more efficient as antioxidants than the 2-isomer in decreasing oxygen consumption rate in a peroxidating methyl linoleate emulsion and less sensitive to presence of calcium. All isomers were found prooxidative for iron-catalyzed initiation of oxidation due to enhanced radical formation as shown by electron spin resonance spectroscopy. Calcium salicylate was found to have low solubility with a solubility product K_sp = 4.49·10⁻⁶ based on activity with ΔH^o = 67 kJ mol⁻¹, ΔS^o = 123 J mol⁻¹ K⁻¹ for dissolution in water, when corrected for the strong complex formation. Calcium in food and beverages may thus lower antioxidant activity of plant phenols through complexation or by precipitation.

Development of a ReaxFF reactive force field for lithium ion conducting solid electrolyte Li1+xAlxTi2−x(PO4)3 (LATP)

Using a ReaxFF reactive force field, we investigated the composition-dependent ionic conductivity and the Li migration behaviors in Li_1+xAl_xTi_2−x(PO₄)₃ solid electrolyte.

Ab Initio MD Simulations of the Brønsted Acidity of Glutathione in Aqueous Solutions: Predicting pKa Shifts of the Cysteine Residue

The tripeptide glutathione (GSH) is one of the most abundant peptides and the major repository for nonprotein sulfur in both animal and plant cells. It plays a critical role in intracellular oxidative stress management by the reversible formation of glutathione disulfide with the thiol-disulfide pair acting as a redox buffer. The state of charge of the ionizable groups of GSH can influence the redox couple, and hence the pKa value of the cysteine residue of GSH is critical to its functioning. Here we report ab initio Car-Parrinello molecular dynamics simulations of glutathione solvated by 200 water molecules, all of which are considered in the simulation. We show that the free-energy landscape for the protonation-deprotonation reaction of the cysteine residue of GSH computed using metadynamics sampling provides accurate estimates of the pKa and correctly predicts the shift in the dissociation constant values as compared with the isolated cysteine amino acid.

Ab Initio Molecular Dynamics Simulations of Amino Acids in Aqueous Solutions: Estimating pKa Values from Metadynamics Sampling

Changes in the protonation and deprotonation of amino acid residues in proteins play a key role in many biological processes and pathways. Here, we report calculations of the free-energy profile for the protonation-deprotonation reaction of the 20 canonical α amino acids in aqueous solutions using ab initio Car-Parrinello molecular dynamics simulations coupled with metadynamics sampling. We show here that the calculated change in free energy of the dissociation reaction provides estimates of the multiple pKa values of the amino acids that are in good agreement with experiment. We use the bond-length-dependent number of the protons coordinated to the hydroxyl oxygen of the carboxylic and the amine groups as the collective variables to explore the free-energy profiles of the Bronsted acid-base chemistry of amino acids in aqueous solutions. We ensure that the amino acid undergoing dissociation is solvated by at least three hydrations shells with all water molecules included in the simulations. The method works equally well for amino acids with neutral, acidic and basic side chains and provides estimates of the multiple pKa values with a mean relative error, with respect to experimental results, of 0.2 pKa units.

Estimating successive pKa values of polyprotic acids from ab initio molecular dynamics using metadynamics: the dissociation of phthalic acid and its isomers

pKa values of polyprotic acids estimated from ab initio molecular dynamics computation of the change in free energy upon dissociation.