Quantifying Uncertainties in Solvation Procedures for Modeling Aqueous Phase Reaction Mechanisms

On the stability constants of metal-nitrate complexes in aqueous solutions

Stability constants of simple reactions involving addition of the NO3- ion to hydrated metal complexes, [M(H2O)x]n+ are calculated with a computational workflow developed using cloud computing resources. The computational workflow performs conformational searches for metal complexes at both low and high levels of theories in conjunction with a continuum solvation model (CSM). The low-level theory is mainly used for the initial conformational searches, which are complemented with high-level density functional theory conformational searches in the CSM framework to determine the coordination chemistry relevant for stability constant calculations. In this regard, the lowest energy conformations are found to obtain the reaction free energies for the addition of one NO3- to [M(H2O)x]n+ complexes, where M represents Fe(II), Fe(III), Sr(II), Ce(III), Ce(IV), and U(VI), respectively. Structural analysis of hundreds of optimized geometries at high-level theory reveals that NO3- coordinates with Fe(II) and Fe(III) in either a monodentate or bidentate manner. Interestingly, the lowest-energy conformations of Fe(II) metal-nitrate complexes exhibit monodentate or bidentate coordination with a coordination number of 6 while the bidentate seven-coordinated Fe(II) metal-nitrate complexes are approximately 2 kcal mol-1 higher in energy. Notably, for Fe(III) metal-nitrate complexes, the bidentate seven-coordinated configuration is more stable than the six-coordinated Fe(II) complexes (monodentate or bidentate) by a few thermal energy units. In contrast, Sr(II), Ce(III), Ce(IV), and U(VI) metal ions predominantly coordinate with NO3- in a bidentate manner, exhibiting typical coordination numbers of 7, 9, 9, and 5, respectively. Stability constants are accordingly calculated using linear free energy approaches to account for the systematic errors and good agreements are obtained between the calculated stability constants and the available experimental data.

A focus on delocalization error poisoning the density-functional many-body expansion

Broderick and Herbert's article (D. R. Broderick and J. M. Herbert, Chem. Sci., 2024, 15, 19893-19906, https://doi.org/10.1039/D4SC05955G) explores an open concern about using energies from density-functional approximations when developing force fields and machine learning potentials for large-scale simulations. The authors explicitly decomposed self-interaction errors (SIEs) from density-functional approximations (DFAs) and found how they behave in many-body expansions (MBEs) that are leveraged in large-scale simulations. For DFAs to be deemed reliable for developing many-body potentials, they would ideally provide stable energetics within the MBE terms that are most often used by force fields and machine learning potentials (MLPs), i.e., within their three- and four-body terms. It was instead found that many widely used DFAs produce wild oscillations in these MBE terms, whereby three-body terms can become problematically enormous. This raises concerns that any force field and/or MLP that appears well-fitted to DFA data on small systems might be poorly conditioned for large-scale simulations due to intrinsic SIEs. This commentary provides more context of Broderick and Herbert's work and its consequences for members of the multiscale modeling community.

Understanding the Selective Removal of Perfluoroalkyl and Polyfluoroalkyl Substances via Fluorine-Fluorine Interactions: A Critical Review

As regulatory standards for per- and polyfluoroalkyl substances (PFAS) become increasingly stringent, innovative water treatment technologies are urgently demanded for effective PFAS removal. Reported sorbents often exhibit limited affinity for PFAS and are frequently hindered by competitive background substances. Recently, fluorinated sorbents (abbreviated as fluorosorbents) have emerged as a potent solution by leveraging fluorine-fluorine (F···F) interactions to enhance selectivity and efficiency in PFAS removal. This review delves into the designs and applications of fluorosorbents, emphasizing how F···F interactions improve PFAS binding affinity. Specifically, the existence of F···F interactions results in removal efficiencies orders of magnitude higher than other counterpart sorbents, particularly under competitive conditions. Furthermore, we provide a detailed analysis of the fundamental principles underlying F···F interactions and elucidate their synergistic effects with other sorption forces, which contribute to the enhanced efficacy and selectivity. Subsequently, we examine various fluorosorbents and their synthesis and fluorination techniques, underscore the importance of accurately characterizing F···F interactions through advanced analytical methods, and emphasize the significance of this interaction in developing selective sorbents. Finally, we discuss challenges and opportunities associated with employing advanced techniques to guide the design of selective sorbents and advocate for further research in the development of sustainable and cost-effective treatment technologies leveraging F···F interactions.

Hybrid Cluster-Continuum Method for Single-Ion Solvation Free Energy in Acetonitrile Solvent

A new hybrid discrete-continuum approach named the cluster-continuum static approximation (CCSA) has been proposed for acetonitrile solvent. The continuum part uses the conductor-like polarizable continuum model for electrostatic and a surface area-dependent term for nonelectrostatic solvation. The CCSA includes only one explicit acetonitrile solvent molecule and a damping function, which makes the CCSA method reduce to pure continuum solvation in the case of weaker potential of mean force for solute-solvent interaction. The performance of the model was tested for 22 anions and 22 cations, including challenge species that cannot be adequately described by pure continuum solvation. A comparison was done with the widely used solvent model density (SMD) model. For anions, the CCSA reduces to pure continuum solvation and the method has the same performance as the SMD model, with a standard deviation of the mean signed error (SD-MSE) of 2.7 kcal mol-1 for both models. However, the CCSA method for cations considerably outperforms the SMD model, with an SD-MSE of 3.3 kcal mol-1 for the former and 8.4 kcal mol-1 for the latter. The method can be automated, and the present study suggests that continuum solvation models could be parameterized taking into account the explicit solvation as proposed in this work.

Metal-water interface formation: Thermodynamics from ab initio molecular dynamics simulations

Metal-water interfaces are central to many electrochemical, (electro)catalytic, and materials science processes and systems. However, our current understanding of their thermodynamic properties is limited by the scarcity of accurate experimental and computational data and procedures. In this work, thermodynamic quantities for metal-water interface formation are computed for a range of FCC(111) surfaces (Pd, Pt, Au, Ag, Rh, and PdAu) through extensive density functional theory based molecular dynamics and the two-phase entropy model. We show that metal-water interface formation is thermodynamically favorable and that most metal surfaces studied in this work are completely wettable, i.e., have contact angles of zero. Interfacial water has higher entropy than bulk water due to the increased population of low-frequency translational modes. The entropic contributions also correlate with the orientational water density, and the highest solvation entropies are observed for interfaces with a moderately ordered first water layer; the entropic contributions account for up to ∼25% of the formation free energy. Water adsorption energy correlates with the water orientation and structure and is found to be a good descriptor of the internal energy part of the interface formation free energy, but it alone cannot satisfactorily explain the interfacial thermodynamics; the interface formation is driven by the competition between energetic and entropic contributions. The obtained results and insight can be used to develop, parameterize, and benchmark theoretical and computational methods for studying metal-water interfaces. Overall, our study yields benchmark-quality data and fundamental insight into the thermodynamic forces driving metal-water interface formation.

Machine learning from quantum chemistry to predict experimental solvent effects on reaction rates

Fast and accurate prediction of solvent effects on reaction rates are crucial for kinetic modeling, chemical process design, and high-throughput solvent screening. Despite the recent advance in machine learning, a scarcity of reliable data has hindered the development of predictive models that are generalizable for diverse reactions and solvents. In this work, we generate a large set of data with the COSMO-RS method for over 28 000 neutral reactions and 295 solvents and train a machine learning model to predict the solvation free energy and solvation enthalpy of activation (ΔΔG‡solv, ΔΔH‡solv) for a solution phase reaction. On unseen reactions, the model achieves mean absolute errors of 0.71 and 1.03 kcal mol-1 for ΔΔG‡solv and ΔΔH‡solv, respectively, relative to the COSMO-RS calculations. The model also provides reliable predictions of relative rate constants within a factor of 4 when tested on experimental data. The presented model can provide nearly instantaneous predictions of kinetic solvent effects or relative rate constants for a broad range of neutral closed-shell or free radical reactions and solvents only based on atom-mapped reaction SMILES and solvent SMILES strings.

Electrocatalytic Mechanisms for an Oxygen Evolution Reaction at a Rhombohedral Boron Monosulfide Electrode/Alkaline Medium Interface

Rhombohedral boron monosulfide (r-BS) with a layer stacking structure is a promising electrocatalyst for an oxygen evolution reaction (OER) within an alkaline solution. We investigated the catalytic mechanisms at the r-BS electrode/alkaline medium interface for an OER using hybrid solvation theory based on the first-principles method combined with classical solution theory. In this study, we elucidate the activities of the OER at the outermost r-BS sheet with and without various surface defects. The Gibbs free energies along the OER path indicate that the boron vacancies at the first and second layers of the r-BS surface (VB1 and VB2) can promote the OER. However, we found that the VB1 is easily occupied by the oxygen atom during the OER, degrading its electrocatalytic performance. In contrast, VB2 is suitable for the active site of the OER due to its structure stability. Next, we applied a bias voltage with the OER potential to the r-BS electrode. The bias voltage incorporates the positive excess surface charge into pristine r-BS and VB2, which can be understood by the relationship between the OER potential and potentials of zero charge at the r-BS electrode. Because the OH- ions are the starting point of the OER, the positively charged surface is kinetically favorable for the electrocatalyst owing to the attractive interaction with the OH- ions. Finally, we qualitatively discuss the flat-band potential at a semiconductor/alkaline solution interface. It suggests that p-type carrier doping could promote the catalytic performance of r-BS. These results explain the previous measurement of the OER performance with the r-BS-based electrode and provide valuable insights into developing a semiconductor electrode/water interface.

A Combined Reaction Path Search and Hybrid Solvation Method for the Systematic Exploration of Elementary Reactions at the Solid-Liquid Interface

We present a combined simulation method of single-component artificial force induced reaction (SC-AFIR) and effective screening medium combined with the reference interaction site model (ESM-RISM), termed SC-AFIR+ESM-RISM. SC-AFIR automatically and systematically explores the chemical reaction pathway, and ESM-RISM directly simulates the precise electronic structure at the solid-liquid interface. Hence, SC-AFIR+ESM-RISM enables us to explore reliable reaction pathways at the solid-liquid interface. We applied it to explore the dissociation pathway of an H2O molecule at the Cu(111)/water interface. The reaction path networks of the whole reaction and the minimum energy paths from H2O to H2 + O depend on the interfacial environment. The qualitative difference in the energy diagrams and the resulting change in the kinematically favored dissociation pathway upon changing the solvation environments are discussed. We believe that SC-AFIR+ESM-RISM will be a powerful tool to reveal the details of chemical reactions in surface catalysis and electrochemistry.

Concerted Proton-Coupled Electron Transfer to a Graphite Adsorbed Metalloporphyrin Occurs by Band to Bond Electron Redistribution

Surface immobilized catalysts are highly promising candidates for a range of energy conversion reactions, and atomistic mechanistic understanding is essential for their rational design. Cobalt tetraphenylporphyrin (CoTPP) nonspecifically adsorbed on a graphitic surface has been shown to undergo concerted proton-coupled electron transfer (PCET) in aqueous solution. Herein, density functional theory calculations on both cluster and periodic models representing π-stacked interactions or axial ligation to a surface oxygenate are performed. As the electrode surface is charged due to applied potential, the adsorbed molecule experiences the electrical polarization of the interface and nearly the same electrostatic potential as the electrode, regardless of the adsorption mode. PCET occurs by electron abstraction from the surface to the CoTPP concerted with protonation to form a cobalt hydride, thereby circumventing Co(II/I) redox. Specifically, the Co(II) d-state localized orbital interacts with a proton from solution and an electron from the delocalized graphitic band states to produce a Co(III)-H bonding orbital below the Fermi level, corresponding to redistribution of electrons from the band states to the bonding states. These insights have broad implications for electrocatalysis by chemically modified electrodes and surface immobilized catalysts.

Molecular Understanding and Practical In Silico Catalyst Design in Computational Organocatalysis and Phase Transfer Catalysis-Challenges and Opportunities

Through the lens of organocatalysis and phase transfer catalysis, we will examine the key components to calculate or predict catalysis-performance metrics, such as turnover frequency and measurement of stereoselectivity, via computational chemistry. The state-of-the-art tools available to calculate potential energy and, consequently, free energy, together with their caveats, will be discussed via examples from the literature. Through various examples from organocatalysis and phase transfer catalysis, we will highlight the challenges related to the mechanism, transition state theory, and solvation involved in translating calculated barriers to the turnover frequency or a metric of stereoselectivity. Examples in the literature that validated their theoretical models will be showcased. Lastly, the relevance and opportunity afforded by machine learning will be discussed.

Understanding the Role of Intramolecular Ion-Pair Interactions in Conformational Stability Using an Ab Initio Thermodynamic Cycle

Intramolecular ion-pair interactions yield shape and functionality to many molecules. With proper orientation, these interactions overcome steric factors and are responsible for the compact structures of several peptides. In this study, we present a thermodynamic cycle based on isoelectronic and alchemical mutation to estimate the intramolecular ion-pair interaction energy. We determine these energies for 26 benchmark molecules with common ion-pair combinations and compare them with results obtained using intramolecular symmetry-adapted perturbation theory. For systems with long linkers, the ion-pair energies evaluated using both approaches deviate by less than 2.5% in the vacuum phase. The thermodynamic cycle based on density functional theory facilitates calculations of salt-bridge interactions in model tripeptides with continuum/microsolvation modeling and four large peptides: 1EJG (crambin), 1BDK (bradykinin), 1L2Y (a mini-protein with a tryptophan cage), and 1SCO (a toxin from the scorpion venom).

Predicting Solvent Effects on SN2 Reaction Rates: Comparison of QM/MM, Implicit, and MM Explicit Solvent Models

Solvents are one of the key variables in the optimization of a synthesis yield or properties of a synthesis product. In this paper, contemporary solvent models are applied to predict the rates of S_N2 reactions in a range of aqueous and non-aqueous solvents. High-level CCSD(T)/CBS//M06-2X/6-31+G(d) gas phase energies were combined with solvation free energies from SMD, SM12, and ADF-COSMO-RS continuum solvent models, as well as molecular mechanics (MM) explicit solvent models with different atomic charge schemes to predict the rate constants of three S_N2 reactions in eight protic and aprotic solvents. It is revealed that the prediction of rate constants in organic solvents is not necessarily less challenging than in water and popular solvent models struggle to predict their rate constants to within 3 log units of experimental values. Among the continuum solvent models, the ADF-COSMO-RS model performed the best in predicting absolute rate contants while the SM12 model was best at predicting relative rate constants with an average accuracy of about 1.5 and 0.8 log units, respectively. The use of computationally more demanding MM explicit solvent models did not translate to improvements in absolute rate constants but was quite effective at predicting relative rate constants due to systematic error cancellation. Free energy barriers obtained from umbrella sampling with explicit solvent QM/MM simulations led to excellent agreement with experimental values, provided that a validated level of theory is used to treat the QM region.

Multilevel Computational Studies Reveal the Importance of Axial Ligand for Oxygen Reduction Reaction on Fe-N-C Materials

The systematic improvement of Fe-N-C materials for fuel cell applications has proven challenging, due in part to an incomplete atomistic understanding of the oxygen reduction reaction (ORR) under electrochemical conditions. Herein, a multilevel computational approach, which combines ab initio molecular dynamics simulations and constant potential density functional theory calculations, is used to assess proton-coupled electron transfer (PCET) processes and adsorption thermodynamics of key ORR intermediates. These calculations indicate that the potential-limiting step for ORR on Fe-N-C materials is the formation of the Fe^III-OOH intermediate. They also show that an active site model with a water molecule axially ligated to the iron center throughout the catalytic cycle produces results that are consistent with the experimental measurements. In particular, reliable prediction of the ORR onset potential and the Fe(III/II) redox potential associated with the conversion of Fe^III-OH to Fe^II and desorbed H₂O requires an axial H₂O co-adsorbed to the iron center. The observation of a five-coordinate rather than four-coordinate active site has significant implications for the thermodynamics and mechanism of ORR. These findings highlight the importance of solvent-substrate interactions and surface charge effects for understanding the PCET reaction mechanisms and transition-metal redox couples under realistic electrochemical conditions.

Challenges in predicting ΔrxnG in solution: The chelate effect

Gibbs energies for reactions involving aqueous ions are challenging to predict due to the large solvation energies of such ions. A stringent test would be the ab initio reproduction of the aqueous-phase chelate effect, an entropic effect in reactions of very small enthalpy changes. This paper examines what is required to achieve such a reproduction for the paradigmatic reaction M(NH3)42+ + 2 en → M( en)22+ + 4 NH3 ( en = 1,2-ethylenediamine), for which ΔrxnG* and ΔrxnH* are −2.3 and +1.6 kcal mol−1, respectively, if M = Zn. Explicit solvation via simulation was avoided in order to allow sufficiently accurate electronic structure models; this required the use of continuum solvation models (CSMs), and a great deal of effort was made in attempting to lower the relative errors of ΔsolvG*[M(NH3)42+] vs ΔsolvG*[M( en)22+] from the CSMs available in Gaussian software. CSMs in ADF and JDFTx software were also tested. A uniform 2.2 kcal mol−1 accuracy in ΔrxnG* for all three metal-atom choices M = {Zn, Cd, Hg} was eventually achieved, but not from any of the known CSMs tested, nor from cavity size reoptimization, nor from semicontinuum modeling: post facto solvation energy corrections [one per solute type, NH3, en, M(NH3)42+, M( en)22+] were needed. It is hoped that this study will aid (and encourage) further CSM development for coordination-complex ions.

New insight to superoxide radical-mediated degradation of pentachlorophenate: Kinetic determination and theoretical calculations

This study reported the reactivity and mechanisms of superoxide radical (O₂˙^-)-mediated transformation of pentachlorophenate. Our results indicated that O₂˙^- alone exhibits limited effects on its degradation, and bimolecular nucleophilic substitution is the dominant reaction pathway.

Single-ion solvation free energy: A new cluster-continuum approach based on the cluster expansion method

Accurate calculation of the solvation free energy of single ions remains an important goal, involving development in the dielectric continuum solvation models, and statistical mechanics with explicit solvent and hybrid discrete-continuum methods. In the last case, many of the research studies involve a quasi-chemical approach using the monomer cycle or the cluster cycle to calculate the solvation free energy of single ions. In this work, a different cluster-continuum approach based on the cluster expansion method was tested for solvation of 16 cations and 32 anions in aqueous solution. The SMD model was used for the dielectric continuum part and three explicit water molecules were introduced in the region of the solute with the highest interaction energy. Harmonic frequency calculations and molecular dynamics sampling of configurations are not required. An empirical γ_N parameter for cations and another for anions is introduced. The method produces a substantial improvement of the SMD model with a mean absolute deviation of 2.3 kcal mol^-1 for cations and 2.9 kcal mol^-1 for anions. The analysis of the correlation between theoretical and experimental data produces a linear regression line with a slope of 1.09 for cations and 1.01 for anions. The good results of this approximated cluster expansion approach suggest that the method could be further improved by including more solvent molecules and sampling the configurations.

Beyond Continuum Solvent Models in Computational Homogeneous Catalysis

In homogeneous catalysis solvent is an inherent part of the catalytic system. As such, it must be considered in the computational modeling. The most common approach to include solvent effects in quantum mechanical calculations is by means of continuum solvent models. When they are properly used, average solvent effects are efficiently captured, mainly those related with solvent polarity. However, neglecting atomistic description of solvent molecules has its limitations, and continuum solvent models all alone cannot be applied to whatever situation. In many cases, inclusion of explicit solvent molecules in the quantum mechanical description of the system is mandatory. The purpose of this article is to highlight through selected examples what are the reasons that urge to go beyond the continuum models to the employment of micro-solvated (cluster-continuum) of fully explicit solvent models, in this way setting the limits of continuum solvent models in computational homogeneous catalysis. These examples showcase that inclusion of solvent molecules in the calculation not only can improve the description of already known mechanisms but can yield new mechanistic views of a reaction. With the aim of systematizing the use of explicit solvent models, after discussing the success and limitations of continuum solvent models, issues related with solvent coordination and solvent dynamics, solvent effects in reactions involving small, charged species, as well as reactions in protic solvents and the role of solvent as reagent itself are successively considered.

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

Properties of the Pt(111)/electrolyte electrochemical interface studied with a hybrid DFT-solvation approach

Self-consistent modeling of the interface between solid metal electrode and liquid electrolyte is a crucial challenge in computational electrochemistry. In this contribution, we adopt the effective screening medium reference interaction site method (ESM-RISM) to study the charged interface between a Pt(111) surface that is partially covered with chemisorbed oxygen and an aqueous acidic electrolyte. This method proves to be well suited to describe the chemisorption and charging state of the interface at controlled electrode potential. We present an in-depth assessment of the ESM-RISM parameterization and of the importance of computing near-surface water molecules explicitly at the quantum mechanical level. We found that ESM-RISM is able to reproduce some key interface properties, including the peculiar, non-monotonic charging relation of the Pt(111)/electrolyte interface. The comparison with independent theoretical models and explicit simulations of the interface reveals strengths and limitations of ESM-RISM for modeling electrochemical interfaces.

Mechanisms of a Cyclobutane-Fused Lactone Hydrolysis in Alkaline and Acidic Conditions

Searching for functional polyesters with stability and degradability is important due to their potential applications in biomedical supplies, biomass fuel, and environmental protection. Recently, a cyclobutane-fused lactone (CBL) polymer was experimentally found to have superior stability and controllable degradability through hydrolysis reactions after activation by mechanical force. In order to provide a theoretical basis for developing new functional degradable polyesters, in this work, we performed a detailed quantum chemical study of the alkaline and acidic hydrolysis of CBL using dispersion-corrected density functional theory (DFT-D3) and mixed implicit/explicit solvent models. Various possible hydrolysis mechanisms were found: B_AC2 and B_AL2 in the alkaline condition and A_AC2, A_AL2, and A_AL1 in the acidic condition. Our calculations indicated that CBL favors the B_AC2 and A_AC2 mechanisms in alkaline and acidic conditions, respectively. In addition, we found that incorporating explicit water solvent molecules is highly necessary because of their strong hydrogen-bonding with reactant/intermediate/product molecules.