Machine Learning-Guided Approach for Studying Solvation Environments

The Stability of Hydrogen-Bonded Ion-Pair Complex Unexpectedly Increases with Increasing Solvent Polarity

The generally observed decrease of the electrostatic energy in the complex with increasing solvent polarity has led to the assumption that the stability of the complexes with ion-pair hydrogen bonds decreases with increasing solvent polarity. Besides, the smaller solvent-accessible surface area (SASA) of the complex in comparison with the isolated subsystems results in a smaller solvation energy of the latter, leading to a destabilization of the complex in the solvent compared to the gas phase. In our study, which combines Nuclear Magnetic Resonance, Infrared Spectroscopy experiments, quantum chemical calculations, and molecular dynamics (MD) simulations, we question the general validity of this statement. We demonstrate that the binding free energy of the ion-pair hydrogen-bonded complex between 2-fluoropropionic acid and n-butylamine (CH3CHFCOO-…NH3But+) increases with increased solvent polarity. This phenomenon is rationalized by a substantial charge transfer between the subsystems that constitute the ion-pair hydrogen-bonded complex. This unexpected finding introduces a new perspective to our understanding of solvation dynamics, emphasizing the interplay between solvent polarity and molecular stability within hydrogen-bonded systems.

Role of Explicit Solvation in Computational Modeling of Chemical Reactions: Mechanism of Cu(I) Transfer Between Thiolate-Based Chelators in Water

Solvation plays important roles in controlling the thermodynamic and kinetic aspects of chemical reactions. The conventional approaches to treat solvation via electronic structure methods are likely to become inadequate, when the reacting solutes have strong electrostatic and hydrogen bonding interactions with the solvent and undergo significant structural changes during the course of the reaction. In this article, we present evidence of such solvent and structural effects in the computational study of the Cu(I) transfer reaction between thiolate-based chelators dithiobutylamine (DTBA) and dithiotheritol (DTT) in water, inspired from biological copper trafficking phenomena. We propose a general solution to the problem by combining classical molecular dynamics (MD) simulations of the bulk system and static quantum chemistry calculations. The fluctuating solvation shell was estimated from MD, and energetics was assessed by averaging QM energies of a series of molecular clusters constructed from the MD snapshots. Applying this approach, we propose a reaction pathway with estimates of relative intermediate stabilities and barriers, which suggest the overall reaction to be reversible in nature and likely to go through both two and three coordinated intermediates, confirming previous studies of similar protein analogues. An interesting fact that emerged from our study was the strong indication that the rate-determining step is the deprotonation of initial thiol bound Cu(I) complex, without involving any Cu(I)-S bonds. The proposed method will lead to a better treatment of solvations, and these mechanistic insights will aid our understanding of biological copper(I) trafficking.

Discovering Molecular Coordination Environment Trends for Selective Ion Binding to Molecular Complexes Using Machine Learning

The design of ion-selective materials with improved separation efficacy and efficiency is paramount, as current technologies fail to meet real-world deployment challenges. Selectivity in these materials can be informed by local ion binding in confined membrane ion channels. In this study, we utilize a data-driven approach to investigate design features in small molecular complexes coordinating ions as simplified models of ion channels. We curate a data set of 563 alkali metal coordinating molecular complexes (i.e., with Li+, Na+, or K+) from the Cambridge Structural Database and calculate differential ion binding energies using density functional theory. Using this information, we probe when and why structures favor exchange with alternate ions. Our analysis reveals that energetic preferences are related to ion size but are largely due to chemical interactions rather than structural reorganization. We identify unique trends in the selectivity for Li+ over other alkali ions, including the presence of N coordination atoms, planar coordination geometry, and small coordinating ring sizes. We use machine learning models to identify the key contributions of both geometric and electronic features in predicting selective ion binding. These physical insights offer preliminary guidance into the design of optimal membranes for ion selectivity.

Machine Learning Methods for Small Data Challenges in Molecular Science

Small data are often used in scientific and engineering research due to the presence of various constraints, such as time, cost, ethics, privacy, security, and technical limitations in data acquisition. However, big data have been the focus for the past decade, small data and their challenges have received little attention, even though they are technically more severe in machine learning (ML) and deep learning (DL) studies. Overall, the small data challenge is often compounded by issues, such as data diversity, imputation, noise, imbalance, and high-dimensionality. Fortunately, the current big data era is characterized by technological breakthroughs in ML, DL, and artificial intelligence (AI), which enable data-driven scientific discovery, and many advanced ML and DL technologies developed for big data have inadvertently provided solutions for small data problems. As a result, significant progress has been made in ML and DL for small data challenges in the past decade. In this review, we summarize and analyze several emerging potential solutions to small data challenges in molecular science, including chemical and biological sciences. We review both basic machine learning algorithms, such as linear regression, logistic regression (LR), k-nearest neighbor (KNN), support vector machine (SVM), kernel learning (KL), random forest (RF), and gradient boosting trees (GBT), and more advanced techniques, including artificial neural network (ANN), convolutional neural network (CNN), U-Net, graph neural network (GNN), Generative Adversarial Network (GAN), long short-term memory (LSTM), autoencoder, transformer, transfer learning, active learning, graph-based semi-supervised learning, combining deep learning with traditional machine learning, and physical model-based data augmentation. We also briefly discuss the latest advances in these methods. Finally, we conclude the survey with a discussion of promising trends in small data challenges in molecular science.

Solv: An Alternative Continuum Model Implementation Based on Fixed Atomic Charges, Scaled Particle Theory, and the Atom-Atom Potential Method

An alternative continuum model implementation is reported. The electrostatic contribution to the solvation Gibbs free energy utilizes the noniterative conductor-like screening model of Vyboishchikov and Voityuk (DOI: 10.1002/jcc.26531) based on the fixed partial atomic charges. The nonelectrostatic solute-solvent dispersion-repulsion energy is calculated through the Caillet-Claverie atom-atom potential method employing the grid-based approach. The nonelectrostatic cavitation energy is computed within the scaled particle theory (SPT) formalism with the solute hard-sphere radius obtained via the Pierotti-Claverie (PC) scheme, from the solute molecular surface (SPT-S) or volume (SPT-V). The solvent hard-sphere radius is derived through the fitting to the experimental total solvation free energies of 2530 neutral species in 92 solvents. Application of the model to reproduce both the absolute and relative (reaction net) solvation free energies indicates that the SPT-V approach based on the CM5 charges is the best performer. The method is suggested for the solvation free energy calculation in the nonaqueous solvents.

Data-Driven Machine Learning for Understanding Surface Structures of Heterogeneous Catalysts

The design of heterogeneous catalysts is necessarily surface-focused, generally achieved via optimization of adsorption energy and microkinetic modelling. A prerequisite is to ensure the adsorption energy is physically meaningful is the stable existence of the conceived active-site structure on the surface. The development of improved understanding of the catalyst surface, however, is challenging practically because of the complex nature of dynamic surface formation and evolution under in-situ reactions. We propose therefore data-driven machine-learning (ML) approaches as a solution. In this Minireview we summarize recent progress in using machine-learning to search and predict (meta)stable structures, assist operando simulation under reaction conditions and micro-environments, and critically analyze experimental characterization data. We conclude that ML will become the new norm to lower costs associated with discovery and design of optimal heterogeneous catalysts.

Machine learning based implicit solvent model for aqueous-solution alanine dipeptide molecular dynamics simulations

Inspired by the recent work from Noé and coworkers on the development of machine learning based implicit solvent model for the simulation of solvated peptides [Chen et al., J. Chem. Phys., 2021, 155, 084101], here we report another investigation of the possibility of using machine learning (ML) techniques to "derive" an implicit solvent model directly from explicit solvent molecular dynamics (MD) simulations. For alanine dipeptide, a machine learning potential (MLP) based on the DeepPot-SE representation of the molecule was trained to capture its interactions with its average solvent environment configuration (ASEC). The predicted forces on the solute deviated only by an RMSD of 0.4 kcal mol-1 Å-1 from the reference values, and the MLP-based free energy surface differed from that obtained from explicit solvent MD simulations by an RMSD of less than 0.9 kcal mol-1. Our MLP training protocol could also accurately reproduce combined quantum mechanical molecular mechanical (QM/MM) forces on the quantum mechanical (QM) solute in ASEC environment, thus enabling the development of accurate ML-based implicit solvent models for ab initio-QM MD simulations. Such ML-based implicit solvent models for QM calculations are cost-effective in both the training stage, where the use of ASEC reduces the number of data points to be labelled, and the inference stage, where the MLP can be evaluated at a relatively small additional cost on top of the QM calculation of the solute.

Physical and numerical aspects of sodium ion solvation free energies via the cluster-continuum model

Sodium cation solvation Gibbs free energies (ΔG_solv(Na⁺)) have been obtained in water, dimethylformamide, dimethyl sulfoxide, ethanol, acetone, acetonitrile, and methanol through the "monomer cycle" cluster-continuum approach where a solvent reference state is described by infinitely separated molecules. The following steps are vital for obtaining reliable ΔG_solv(Na⁺) values: (a) a meticulous conformational search involving dispersion corrected density functional theory (DFT-D) and the continuum solvation model (CSM); (b) gas-phase DFT-D geometry optimization followed by single-point (SP) domain-based local pair natural orbital coupled clusters including single, double, and partly triple excitation (DLPNO-CCSD(T)) calculations in conjunction with the complete basis set extrapolation; (c) advanced statistical thermodynamic treatment of the low harmonic frequencies (<100 cm^-1) to obtain the robust gas-phase Gibbs free energy correction; (d) gas-phase and dielectric continuum SP with non-electrostatic contributions included in the CSM; (e) an evaluation of the relative thermodynamic stability of the Na⁺(S)_n clusters to identify the number of explicit solvent molecules n to be considered. Our refined computational protocol is promising with a Pearson correlation coefficient between the predicted and experimental data, ρ, of 0.82, and the mean signed and mean unsigned errors of 0.3 and 1.4 kcal mol^-1, respectively.

Molecular design of redox carriers for electrochemical CO2 capture and concentration

Developing improved methods for CO₂ capture and concentration (CCC) is essential to mitigating the impact of our current emissions and can lead to carbon net negative technologies. Electrochemical approaches for CCC can achieve much higher theoretical efficiencies compared to the thermal methods that have been more commonly pursued. The use of redox carriers, or molecular species that can bind and release CO₂ depending on their oxidation state, is an increasingly popular approach as carrier properties can be tailored for different applications. The key requirements for stable and efficient redox carriers are discussed in the context of chemical scaling relationships and operational conditions. Computational and experimental approaches towards developing redox carriers with optimal properties are also described.

Conformational energies of microsolvated Na+ clusters with protic and aprotic solvents from GFNn-xTB methods

Performance of contemporary tight-binding semiempirical GFNn-xTB methods for the conformational energies of singly charged sodium clusters Na⁺ (S)_n (n = 4-8) with 3 protic and 8 aprotic solvents is examined against the reference RI-MP2/CBS method. The median Pearson correlation coefficients of ρ = 0.84 (GFN2-xTB) and ρ = 0.82 (GFN1-xTB) do not give the clear preference to any tested approach. GFN1-xTB method demonstrates more stable performance than its GFN2-xTB successor with the average mean absolute errors (MAEs)/mean signed errors (MSEs) of 1.2/0.2 and 2.3/1.6 kcal mol^-1 , respectively. Conformational energies produced by the computationally efficient DFT functional PBE and double-ζ basis set complemented with -D3(BJ) dispersion correction are suitable for the preliminary sampling (median ρ = 0.93), but should be used with a caution for the calculations of the average ensemble properties (MAE/MSE = 1.7/1.1 kcal mol^-1 ). Higher-ranking PBE0-D3(BJ) and ωB97M-V with triple-ζ basis sets yield significantly lower MAEs/MSEs of 0.55/0.20 and 0.51/0.23 kcal mol^-1 , respectively.

Hydrated Anions: From Clusters to Bulk Solution with Quasi-Chemical Theory

The interactions of hydrated ions with molecular and macromolecular solution and interface partners are strong on a chemical energy scale. Here, we recount the foremost ab initio theory for the evaluation of the hydration free energies of ions, namely, quasi-chemical theory (QCT). We focus on anions, particularly halides but also the hydroxide anion, because they have been outstanding challenges for all theories. For example, this work supports understanding the high selectivity for F^- over Cl^- in fluoride-selective ion channels despite the identical charge and the size similarity of these ions. QCT is built by the identification of inner-shell clusters, separate treatment of those clusters, and then the integration of those results into the broader-scale solution environment. Recent work has focused on a close comparison with mass-spectrometric measurements of ion-hydration equilibria. We delineate how ab initio molecular dynamics (AIMD) calculations on ion-hydration clusters, elementary statistical thermodynamics, and electronic structure calculations on cluster structures sampled from the AIMD calculations obtain just the free energies extracted from the cluster experiments. That theory-experiment comparison has not been attempted before the work discussed here, but the agreement is excellent with moderate computational effort. This agreement reinforces both theory and experiment and provides a numerically accurate inner-shell contribution to QCT. The inner-shell complexes involving heavier halides display strikingly asymmetric hydration clusters. Asymmetric hydration structures can be problematic for the evaluation of the QCT outer-shell contribution with the polarizable continuum model (PCM). Nevertheless, QCT provides a favorable setting for the exploitation of PCM when the inner-shell material shields the ion from the outer solution environment. For the more asymmetrically hydrated, and thus less effectively shielded, heavier halide ions clustered with waters, the PCM is less satisfactory. We therefore investigate an inverse procedure in which the inner-shell structures are sampled from readily available AIMD calculations on the bulk solutions. This inverse procedure is a remarkable improvement; our final results are in close agreement with a standard tabulation of hydration free energies, and the final composite results are independent of the coordination number on the chemical energy scale of relevance, as they should be. Finally, a comparison of anion hydration structure in clusters and bulk solutions from AIMD simulations emphasize some differences: the asymmetries of bulk solution inner-shell structures are moderated compared with clusters but are still present, and inner hydration shells fill to slightly higher average coordination numbers in bulk solution than in clusters.

Inverse molecular design of alkoxides and phenoxides for aqueous direct air capture of CO2

Aqueous direct air capture (DAC) is a key technology toward a carbon negative infrastructure. Developing sorbent molecules with water and oxygen tolerance and high CO₂ binding capacity is therefore highly desired. We analyze the CO₂ absorption chemistries on amines, alkoxides, and phenoxides with density functional theory calculations, and perform inverse molecular design of the optimal sorbent. The alkoxides and phenoxides are found to be more suitable for aqueous DAC than amines thanks to their water tolerance (lower pK_a prevents protonation by water) and capture stoichiometry of 1:1 (2:1 for amines). All three molecular systems are found to generally obey the same linear scaling relationship (LSR) between [Formula: see text] and [Formula: see text], since both CO₂ and proton are bonded to the nucleophilic (alkoxy or amine) binding site through a majorly [Formula: see text] bonding orbital. Several high-performance alkoxides are proposed from the computational screening. Phenoxides have comparatively poorer correlation between [Formula: see text] and [Formula: see text], showing promise for optimization. We apply a genetic algorithm to search the chemical space of substituted phenoxides for the optimal sorbent. Several promising off-LSR candidates are discovered. The most promising one features bulky ortho substituents forcing the CO₂ adduct into a perpendicular configuration with respect to the aromatic ring. In this configuration, the phenoxide binds CO₂ and a proton using different molecular orbitals, thereby decoupling the [Formula: see text] and [Formula: see text]. The [Formula: see text] trend and off-LSR behaviors are then confirmed by experiments, validating the inverse molecular design framework. This work not only extensively studies the chemistry of the aqueous DAC, but also presents a transferrable computational workflow for understanding and optimization of other functional molecules.

Bridging the Experiment-Calculation Divide: Machine Learning Corrections to Redox Potential Calculations in Implicit and Explicit Solvent Models

Prediction of redox potentials is essential for catalysis and energy storage. Although density functional theory (DFT) calculations have enabled rapid redox potential predictions for numerous compounds, prominent errors persist compared to experimental measurements. In this work, we develop machine learning (ML) models to reduce the errors of redox potential calculations in both implicit and explicit solvent models. Training and testing of the ML correction models are based on the diverse ROP313 data set with experimental redox potentials measured for organic and organometallic compounds in a variety of solvents. For the implicit solvent approach, our ML models can reduce both the systematic bias and the number of outliers. ML corrected redox potentials also demonstrate less sensitivity to DFT functional choice. For the explicit solvent approach, we significantly reduce the computational costs by embedding the microsolvated cluster in implicit bulk solvent, obtaining converged redox potential results with a smaller solvation shell. This combined implicit-explicit solvent model, together with GPU-accelerated quantum chemistry methods, enabled rapid generation of a large data set of explicit-solvent-calculated redox potentials for 165 organic compounds, allowing detailed investigation of the error sources in explicit solvent redox potential calculations.

Dynamics of Heterogeneous Catalytic Processes at Operando Conditions

The rational design of high-performance catalysts is hindered by the lack of knowledge of the structures of active sites and the reaction pathways under reaction conditions, which can be ideally addressed by an in situ/operando characterization. Besides the experimental insights, a theoretical investigation that simulates reaction conditions-so-called operando modeling-is necessary for a plausible understanding of a working catalyst system at the atomic scale. However, there is still a huge gap between the current widely used computational model and the concept of operando modeling, which should be achieved through multiscale computational modeling. This Perspective describes various modeling approaches and machine learning techniques that step toward operando modeling, followed by selected experimental examples that present an operando understanding in the thermo- and electrocatalytic processes. At last, the remaining challenges in this area are outlined.

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.

Elastic Collision Based Dynamic Partitioning Scheme for Hybrid Simulations

In hybrid simulations, such as the QM/MM approach, the system is partitioned into regions that are treated at different levels of theory. The key question then becomes how to evaluate the interactions between particles on opposite sides of the boundary. One approach is to place the boundary in such a way that particles near the boundary on both sides are of the same type, thus simplifying the evaluation of the interactions. If mobile particles are present, such as solvent molecules, and particles are allowed to cross the boundary, the conservation of energy and atomic forces is problematic unless the computational effort is increased significantly. By preventing particles from crossing the boundary but allowing the boundary to be flexible, an accurate estimate of average thermodynamic properties is obtained in principle as illustrated by the flexible inner region ensemble separator (FIRES) method [C. Rowley and B. Roux, J. Chem. Theory Comput. 2012, 8, 3526]. In FIRES, a harmonic restraint is applied to particles near the boundary. Therefore, it can occur that particle cross the boundary to some extent resulting in anomalies in the particle density. Here, a constraint approach is presented where particles instantaneously scatter from the boundary. This scattering-adapted FIRES (SAFIRES) implementation makes use of a variable-time-step propagation algorithm where the time step is scaled automatically to identify the moment a collision should occur. If the length of the time step is kept constant, this propagator reduces to a regular Langevin dynamics algorithm, and to the velocity Verlet algorithm for conservative dynamics if the friction coefficient is set to zero. Correct average ensemble statistics are obtained as demonstrated in simulations where, for testing purposes, the particles in the two regions are treated at the same level of theory, namely, a homogeneous Lennard-Jones (LJ) liquid and liquid water based on the TIP4P potential function. In order to illustrate this approach in solid-liquid interface simulations, a LJ liquid in contact with the surface of a crystal is also simulated. The simulations using SAFIRES are shown to reproduce the unconstrained reference simulations without significant deviations in the particle density and the dynamics are shown to conserve energy when coupling to the heat bath is turned off.

Machine learning implicit solvation for molecular dynamics

Accurate modeling of the solvent environment for biological molecules is crucial for computational biology and drug design. A popular approach to achieve long simulation time scales for large system sizes is to incorporate the effect of the solvent in a mean-field fashion with implicit solvent models. However, a challenge with existing implicit solvent models is that they often lack accuracy or certain physical properties compared to explicit solvent models as the many-body effects of the neglected solvent molecules are difficult to model as a mean field. Here, we leverage machine learning (ML) and multi-scale coarse graining (CG) in order to learn implicit solvent models that can approximate the energetic and thermodynamic properties of a given explicit solvent model with arbitrary accuracy, given enough training data. Following the previous ML-CG models CGnet and CGSchnet, we introduce ISSNet, a graph neural network, to model the implicit solvent potential of mean force. ISSNet can learn from explicit solvent simulation data and be readily applied to molecular dynamics simulations. We compare the solute conformational distributions under different solvation treatments for two peptide systems. The results indicate that ISSNet models can outperform widely used generalized Born and surface area models in reproducing the thermodynamics of small protein systems with respect to explicit solvent. The success of this novel method demonstrates the potential benefit of applying machine learning methods in accurate modeling of solvent effects for in silico research and biomedical applications.

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.

MLSolvA: solvation free energy prediction from pairwise atomistic interactions by machine learning

Recent advances in machine learning technologies and their applications have led to the development of diverse structure-property relationship models for crucial chemical properties. The solvation free energy is one of them. Here, we introduce a novel ML-based solvation model, which calculates the solvation energy from pairwise atomistic interactions. The novelty of the proposed model consists of a simple architecture: two encoding functions extract atomic feature vectors from the given chemical structure, while the inner product between the two atomistic feature vectors calculates their interactions. The results of 6239 experimental measurements achieve outstanding performance and transferability for enlarging training data owing to its solvent-non-specific nature. An analysis of the interaction map shows that our model has significant potential for producing group contributions on the solvation energy, which indicates that the model provides not only predictions of target properties but also more detailed physicochemical insights.

Physics-Inspired Structural Representations for Molecules and Materials

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

Revisiting conformations of methyl lactate in water and methanol

The recently developed efficient protocols to implicit [Grimme et al., J. Phys. Chem. A 125, 4039-4054 (2021)] and explicit quantum mechanical modeling of non-rigid molecules in solution [Katsyuba et al., J. Phys. Chem. B 124, 6664-6670 (2020)] are applied to methyl lactate (ML). Building upon this work, a new combination scheme is proposed to incorporate solvation effects for the computation of infrared (IR) absorption spectra. Herein, Boltzmann populations calculated for implicitly solvated single conformers are used to weight the IR spectra of explicitly solvated clusters with a size of typically ten solvent molecules, i.e., accounting for the first solvation shell. It is found that in water and methanol, the most abundant conformers of ML are structurally modified relative to the gas phase, where the major form is ML1, in which the syn conformation of the -OH moiety is stabilized by a OH⋯O=C intramolecular hydrogen bond (HB). In solution, this syn conformation transforms to the gauche form because the intramolecular HB is disrupted by explicit water molecules that form intermolecular HBs with the hydroxyl and carbonyl groups. Similar changes induced by the gas-solution transition are observed for the minor conformers, ML2 and/or ML3, characterized by OH⋯OCH₃ intramolecular HB in the gas phase. The relative abundance of ML1 is shown to decrease from ∼96% in gas to ∼51% in water and ∼92% in methanol. The solvent strongly influences frequencies, IR intensities, and normal modes, resulting in qualitatively different spectra compared to the gas phase. Some liquid-state conformational markers in the fingerprint region of IR spectra are revealed.

Machine Learning for Chemical Reactions

Machine learning (ML) techniques applied to chemical reactions have a long history. The present contribution discusses applications ranging from small molecule reaction dynamics to computational platforms for reaction planning. ML-based techniques can be particularly relevant for problems involving both computation and experiments. For one, Bayesian inference is a powerful approach to develop models consistent with knowledge from experiments. Second, ML-based methods can also be used to handle problems that are formally intractable using conventional approaches, such as exhaustive characterization of state-to-state information in reactive collisions. Finally, the explicit simulation of reactive networks as they occur in combustion has become possible using machine-learned neural network potentials. This review provides an overview of the questions that can and have been addressed using machine learning techniques, and an outlook discusses challenges in this diverse and stimulating field. It is concluded that ML applied to chemistry problems as practiced and conceived today has the potential to transform the way with which the field approaches problems involving chemical reactions, in both research and academic teaching.

Free Energies of Hydrated Halide Anions: High Through-Put Computations on Clusters to Treat Rough Energy-Landscapes

With a longer-term goal of addressing the comparative behavior of the aqueous halides F−, Cl−, Br−, and I− on the basis of quasi-chemical theory (QCT), here we study structures and free energies of hydration clusters for those anions. We confirm that energetically optimal (H2O)nX clusters, with X = Cl−, Br−, and I−, exhibit surface hydration structures. Computed free energies, based on optimized surface hydration structures utilizing a harmonic approximation, typically (but not always) disagree with experimental free energies. To remedy the harmonic approximation, we utilize single-point electronic structure calculations on cluster geometries sampled from an AIMD (ab initio molecular dynamics) simulation stream. This rough-landscape procedure is broadly satisfactory and suggests unfavorable ligand crowding as the physical effect addressed. Nevertheless, this procedure can break down when n≳4, with the characteristic discrepancy resulting from a relaxed definition of clustering in the identification of (H2O)nX clusters, including ramified structures natural in physical cluster theories. With ramified structures, the central equation for the present rough-landscape approach can acquire some inconsistency. Extension of these physical cluster theories in the direction of QCT should remedy that issue, and should be the next step in this research direction.

Computational predictions of metal-macrocycle stability constants require accurate treatments of local solvent and pH effects

Rational design of molecular chelating agents requires a detailed understanding of physicochemical ligand-metal interactions in solvent phase. Computational quantum chemistry methods should be able to provide this, but computational reports have shown poor accuracy when determining absolute binding constants for many chelating molecules. To understand why, we compare and benchmark static- and dynamics-based computational procedures for a range of monovalent and divalent cations binding to a conventional cryptand molecule: 2.2.2-cryptand ([2.2.2]). The benchmarking comparison shows that dynamics simulations using standard OPLS-AA classical potentials can reasonably predict binding constants for monovalent cations, but these procedures fail for divalent cations. We also consider computationally efficient static procedure using Kohn-Sham density functional theory (DFT) and cluster-continuum modeling that accounts for local microsolvation and pH effects. This approach accurately predicts binding energies for monovalent and divalent cations with an average error of 3.2 kcal mol-1 compared to experiment. This static procedure thus should be useful for future molecular screening efforts, and high absolute errors in the literature may be due to inadequate modeling of local solvent and pH effects.

Machine learning of free energies in chemical compound space using ensemble representations: Reaching experimental uncertainty for solvation

Free energies govern the behavior of soft and liquid matter, and improving their predictions could have a large impact on the development of drugs, electrolytes, or homogeneous catalysts. Unfortunately, it is challenging to devise an accurate description of effects governing solvation such as hydrogen-bonding, van der Waals interactions, or conformational sampling. We present a Free energy Machine Learning (FML) model applicable throughout chemical compound space and based on a representation that employs Boltzmann averages to account for an approximated sampling of configurational space. Using the FreeSolv database, FML's out-of-sample prediction errors of experimental hydration free energies decay systematically with training set size, and experimental uncertainty (0.6 kcal/mol) is reached after training on 490 molecules (80% of FreeSolv). Corresponding FML model errors are on par with state-of-the art physics based approaches. To generate the input representation for a new query compound, FML requires approximate and short molecular dynamics runs. We showcase its usefulness through analysis of solvation free energies for 116k organic molecules (all force-field compatible molecules in the QM9 database), identifying the most and least solvated systems and rediscovering quasi-linear structure-property relationships in terms of simple descriptors such as hydrogen-bond donors, number of NH or OH groups, number of oxygen atoms in hydrocarbons, and number of heavy atoms. FML's accuracy is maximal when the temperature used for the molecular dynamics simulation to generate averaged input representation samples in training is the same as for the query compounds. The sampling time for the representation converges rapidly with respect to the prediction error.

Quantum Chemical Microsolvation by Automated Water Placement

We developed a quantitative approach to quantum chemical microsolvation. Key in our methodology is the automatic placement of individual solvent molecules based on the free energy solvation thermodynamics derived from molecular dynamics (MD) simulations and grid inhomogeneous solvation theory (GIST). This protocol enabled us to rigorously define the number, position, and orientation of individual solvent molecules and to determine their interaction with the solute based on physical quantities. The generated solute-solvent clusters served as an input for subsequent quantum chemical investigations. We showcased the applicability, scope, and limitations of this computational approach for a number of small molecules, including urea, 2-aminobenzothiazole, (+)-syn-benzotriborneol, benzoic acid, and helicene. Our results show excellent agreement with the available ab initio molecular dynamics data and experimental results.

Modeling microsolvation clusters with electronic-structure calculations guided by analytical potentials and predictive machine learning techniques

We propose a new methodology to study, at the density functional theory (DFT) level, the clusters resulting from the microsolvation of alkali-metal ions with rare-gas atoms. The workflow begins with a global optimization search to generate a pool of low-energy minimum structures for different cluster sizes. This is achieved by employing an analytical potential energy surface (PES) and an evolutionary algorithm (EA). The next main stage of the methodology is devoted to establish an adequate DFT approach to treat the microsolvation system, through a systematic benchmark study involving several combinations of functionals and basis sets, in order to characterize the global minimum structures of the smaller clusters. In the next stage, we apply machine learning (ML) classification algorithms to predict how the low-energy minima of the analytical PES map to the DFT ones. An early and accurate detection of likely DFT local minima is extremely important to guide the choice of the most promising low-energy minima of large clusters to be re-optimized at the DFT level of theory. In this work, the methodology was applied to the Li+Krn (n = 2-14 and 16) microsolvation clusters for which the most competitive DFT approach was found to be the B3LYP-D3/aug-pcseg-1. Additionally, the ML classifier was able to accurately predict most of the solutions to be re-optimized at the DFT level of theory, thereby greatly enhancing the efficiency of the process and allowing its applicability to larger clusters.

Computing Potential of the Mean Force Profiles for Ion Permeation Through Channelrhodopsin Chimera, C1C2

Umbrella sampling, coupled with a weighted histogram analysis method (US-WHAM), can be used to construct potentials of mean force (PMFs) for studying the complex ion permeation pathways of membrane transport proteins. Despite the widespread use of US-WHAM, obtaining a physically meaningful PMF can be challenging. Here, we provide a protocol to resolve that issue. Then, we apply that protocol to compute a meaningful PMF for sodium ion permeation through channelrhodopsin chimera, C1C2, for illustration.

Computational Methods in Heterogeneous Catalysis

The unprecedented ability of computations to probe atomic-level details of catalytic systems holds immense promise for the fundamentals-based bottom-up design of novel heterogeneous catalysts, which are at the heart of the chemical and energy sectors of industry. Here, we critically analyze recent advances in computational heterogeneous catalysis. First, we will survey the progress in electronic structure methods and atomistic catalyst models employed, which have enabled the catalysis community to build increasingly intricate, realistic, and accurate models of the active sites of supported transition-metal catalysts. We then review developments in microkinetic modeling, specifically mean-field microkinetic models and kinetic Monte Carlo simulations, which bridge the gap between nanoscale computational insights and macroscale experimental kinetics data with increasing fidelity. We finally review the advancements in theoretical methods for accelerating catalyst design and discovery. Throughout the review, we provide ample examples of applications, discuss remaining challenges, and provide our outlook for the near future.

First-principles modeling of chemistry in mixed solvents: Where to go from here?

Mixed solvents (i.e., binary or higher order mixtures of ionic or nonionic liquids) play crucial roles in chemical syntheses, separations, and electrochemical devices because they can be tuned for specific reactions and applications. Apart from fully explicit solvation treatments that can be difficult to parameterize or computationally expensive, there is currently no well-established first-principles regimen for reliably modeling atomic-scale chemistry in mixed solvent environments. We offer our perspective on how this process could be achieved in the near future as mixed solvent systems become more explored using theoretical and computational chemistry. We first outline what makes mixed solvent systems far more complex compared to single-component solvents. An overview of current and promising techniques for modeling mixed solvent environments is provided. We focus on so-called hybrid solvation treatments such as the conductor-like screening model for real solvents and the reference interaction site model, which are far less computationally demanding than explicit simulations. We also propose that cluster-continuum approaches rooted in physically rigorous quasi-chemical theory provide a robust, yet practical, route for studying chemical processes in mixed solvents.