Tackling Solvent Effects by Coupling Electronic and Molecular Density Functional Theory

Coupling molecular density functional theory with converged selected configuration interaction methods to study excited states in aqueous solution

This paper presents the first implementation of a coupling between advanced wavefunction theories and molecular density functional theory (MDFT). This method enables the modeling of solvent effect into quantum mechanical (QM) calculations by incorporating an electrostatic potential generated by solvent charges into the electronic Hamiltonian. Solvent charges are deduced from the spatially and angularly dependent solvent particle density. Such a density is obtained through the minimization of the functional associated with the molecular mechanics (MM) Hamiltonian describing the interaction between the fluid particles. The introduced QM/MDFT framework belongs to QM/MM family of methods, but its originality lies in the use of MDFT as the MM solver, offering two main advantages. First, its functional formulation makes it competitive with respect to sampling-based molecular mechanics. Second, it preserves a molecular-level description lost in macroscopic continuum approaches. The excited state properties of water and formaldehyde molecules solvated into water have been computed at the selected configuration interaction (SCI) level. The excitation energies and dipole moments have been compared with experimental data and previous theoretical work. A key finding is that using the Hartree-Fock method to describe the solute allows for predicting the solvent charge around the ground state with sufficient precision for the subsequent SCI calculations of excited states. This significantly reduces the computational cost of the described procedure, paving the way for the study of more complex molecules.

Predicting Solvation Free Energies from the Minnesota Solvation Database Using Classical Density Functional Theory Based on the PC-SAFT Equation of State

We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.

Solvent effects in anion recognition

Anion recognition is pertinent to a range of environmental, medicinal and industrial applications. Recent progress in the field has relied on advances in synthetic host design to afford a broad range of potent recognition motifs and novel supramolecular structures capable of effective binding both in solution and at derived molecular films. However, performance in aqueous media remains a critical challenge. Understanding the effects of bulk and local solvent on anion recognition by host scaffolds is imperative if effective and selective detection in real-world media is to be viable. This Review seeks to provide a framework within which these effects can be considered both experimentally and theoretically. We highlight proposed models for solvation effects on anion binding and discuss approaches to retain strong anion binding in highly competitive (polar) solvents. The synthetic design principles for exploiting the aforementioned solvent effects are explored.

Recent developments and applications of reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED): A hybrid model of quantum chemistry and integral equation theory of molecular liquids

The significance of solvent effects in electronic structure calculations has long been noted, and various methods have been developed to consider this effect. The reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED) is a hybrid model that combines the integral equation theory of molecular liquids with quantum chemistry. This method can consider the statistically convergent solvent distribution at a significantly lower cost than molecular dynamics simulations. Because the RISM theory explicitly considers the solvent structure, it performs well for systems where hydrogen bonds are formed between the solute and solvent molecules, which is a challenge for continuum solvent models. Taking advantage of being founded on the variational principle, theoretical developments have been made in calculating various properties and incorporating electron correlation effects. In this review, we organize the theoretical aspects of RISM-SCF-cSED and its distinctions from other hybrid methods involving integral equation theories. Furthermore, we carefully present its progress in terms of theoretical developments and recent applications.

An Electrostatically Embedded QM/MM Scheme for Electrified Interfaces

Atomistic modeling of electrified interfaces remains a major issue for detailed insights in electrocatalysis, corrosion, electrodeposition, batteries, and related devices such as pseudocapacitors. In these domains, the use of grand-canonical density functional theory (GC-DFT) in combination with implicit solvation models has become popular. GC-DFT can be conveniently applied not only to metallic surfaces but also to semiconducting oxides and sulfides and is, furthermore, sufficiently robust to achieve a consistent description of reaction pathways. However, the accuracy of implicit solvation models for solvation effects at interfaces is in general unknown. One promising way to overcome the limitations of implicit solvents is going toward hybrid quantum mechanical (QM)/molecular mechanics (MM) models. For capturing the electrochemical potential dependence, the key quantity is the capacitance, i.e., the relation between the surface charge and the electrochemical potential. In order to retrieve the electrochemical potential from a QM/MM hybrid scheme, an electrostatic embedding is required. Furthermore, the charge of the surface and of the solvent regions has to be strictly opposite in order to consistently simulate charge-neutral unit cells in MM and in QM. To achieve such a QM/MM scheme, we present the implementation of electrostatic embedding in the VASP code. This scheme is broadly applicable to any neutral or charged solid/liquid interface. Here, we demonstrate its use in the context of GC-DFT for the hydrogen evolution reaction (HER) over a noble-metal-free electrocatalyst, MoS₂. We investigate the effect of electrostatic embedding compared to the implicit solvent model for three contrasting active sites on MoS₂: (i) the sulfur vacancy defect, which is rather apolar; (ii) a Mo antisite defect, where the active site is a surface bound highly polar OH group; and (iii) a reconstructed edge site, which is generally believed to be responsible for most of the catalytic activity. According to our results, the electrostatic embedding leads to almost indistinguishable results compared to the implicit solvent for the apolar system but has a significant effect on polar sites. This demonstrates the reliability of the hybrid QM/MM, electrostatically embedded solvation model for electrified interfaces.

Comparative study of force-based classical density functional theory

We reexamine results obtained with the recently proposed density functional theory framework based on forces (force-DFT) [S. M. Tschopp et al., Phys. Rev. E 106, 014115 (2022)2470-004510.1103/PhysRevE.106.014115]. We compare inhomogeneous density profiles for hard sphere fluids to results from both standard density functional theory and from computer simulations. Test situations include the equilibrium hard sphere fluid adsorbed against a planar hard wall and the dynamical relaxation of hard spheres in a switched harmonic potential. The comparison to grand canonical Monte Carlo simulation profiles shows that equilibrium force-DFT alone does not improve upon results obtained with the standard Rosenfeld functional. Similar behavior holds for the relaxation dynamics, where we use our event-driven Brownian dynamics data as benchmark. Based on an appropriate linear combination of standard and force-DFT results, we investigate a simple hybrid scheme which rectifies these deficiencies in both the equilibrium and the dynamical case. We explicitly demonstrate that although the hybrid method is based on the original Rosenfeld fundamental measure functional, its performance is comparable to that of the more advanced White Bear theory.

Molecular reaction and dynamic mechanism of iodate reduction to molecular iodine by nitrogen(III) in aqueous solution

This work studies the molecular reaction and dynamic mechanism of iodate reduction by nitrogen(III) in aqueous solution using the ab initio molecular dynamics (AIMD) method based on density functional theory (DFT). Two possible reaction pathways (without and with H⁺) are proposed. The thermodynamic parameters of the proposed reaction pathways are calculated. The theoretical calculation aspects of iodate reduction, including the atomic dipole moment corrected Hirshfeld population (ADCH) atomic charge values, the intrinsic reaction coordinate (IRC) curves, the calculated interaction regional indicator (IRI) isosurfaces with the corresponding sign(λ₂)ρ scatter plots, electrostatic potential (ESP) analysis and molecular reaction dynamics are discussed in-depth. The results show that the reaction pathway with H⁺ is confirmed based on the Gibbs free energy analysis. The transition state proved that the iodate reduction with nitrous acid undergoes four steps according to oxygen-atom deprivation. The IRC curves describe the energy change of the chemical bonds of the reactant conformations in the four steps, with an energy reduction of 71.95, 69.35, 130.15, and 125.87 kJ mol^-1, respectively. The ESP interpenetration diagram and IRI isosurfaces provide detailed information on the nucleophilicity and electrophilicity of the reactant conformations. By decreasing the O atom number in HIO_x (x = 1, 2, 3), the maximum positive charge decreases, and the positive charge coverage area increases, thus resulting in energy reduction and consequently a more stable conformation. Molecular reaction dynamics analytical results indicated that a relatively stable status of the reactants of the four steps was achieved after around 200 fs, and that the HIO₃-HNO₂ reaction released the highest energy.

Solvent Control of Chemical Identity Can Change Photodissociation into Photoisomerization

In solution-phase chemistry, the solvent is often considered to be merely a medium that allows reacting solutes to encounter each other. In this work, however, we show that moderate locally specific solute-solvent interactions can affect not only the nature of the solute but also the types of reactive chemistry. We use quantum simulation methods to explore how solvent participation in solute chemical identity alters reactions involving the breaking of chemical bonds. In particular, we explore the photoexcitation dynamics of Na₂⁺ dissolved in liquid tetrahydrofuran. In the gas phase, excitation of Na₂⁺ directly leads to dissociation, but in solution, photoexcitation leads to an isomerization reaction involving rearrangement of the first-shell solvent molecules; this isomerization must go to completion before the solute can dissociate. Despite the complexity, the solution-phase reaction dynamics can be captured by a two-dimensional energy surface where one dimension involves only the isomerization of the first-shell solvent molecules.

Electron Transfer of Functionalised Quinones in Acetonitrile

Quinones are redox active organic molecules that have been proposed as an alternative choice to metal-based materials in electrochemical energy storage devices. Functionalization allows to fine tune not only their chemical stability but also the redox potential and the kinetics of the electron transfer reaction. However, reaction rate constant is not solely determined by the redox species but is also impacted by solvent effects. In this work, we show how the functionalization of benzoquinone with different functional groups impacts the solvent reorganization free energies of electron transfer half-reactions in acetonitrile. The use of molecular density functional theory, whose computational cost for studying electron transfer reaction is considerably reduced compared to state-of-the art molecular dynamics simulations, enables to perform a systematic study. We validate the method by comparing the predictions of the solvation shell structure and the free energy profiles for electron transfer reaction to reference classical molecular dynamics simulations in the case of anthraquinone solvated in acetonitrile. We show that all the studied electron transfer half-reactions follow Marcus' description, regardless of functional groups. Consequently, the solvent reorganization free energy decreases as the molecular size increases.

Multiscale molecular modelling: from electronic structure to dynamics of nanosystems and beyond

Important contemporary biological and materials problems often depend on interactions that span orders of magnitude differences in spatial and temporal dimensions. This Tutorial Review attempts to provide an introduction to such fascinating problems through a series of case studies, aimed at beginning researchers, graduate students, postdocs and more senior colleagues who are changing direction to focus on multiscale aspects of their research. The choice of specific examples is highly personal, with examples either chosen from our own work or outstanding multiscale efforts from the literature. I start with various embedding schemes, as exemplified by polarizable continuum models, 3-D RISM, molecular DFT and frozen-density embedding. Next, QM/MM (quantum mechanical/molecular mechanical) techniques are the workhorse of pm-to-nm/ps-to-ns simulations; examples are drawn from enzymes and from nanocatalysis for oil-sands upgrading. Using polarizable force-fields in the QM/MM framework represents a burgeoning subfield; with examples from ion channels and electron dynamics in molecules subject to strong external fields, probing the atto-second dynamics of the electrons with RT-TDDFT (real-time - time-dependent density functional theory) eventually coupled with nuclear motion through the Ehrenfest approximation. This is followed by a section on coarse graining, bridging dimensions from atoms to cells. The penultimate chapter gives a quick overview of multiscale approaches that extend into the meso- and macro-scales, building on atomistic and coarse-grained techniques to enter the world of materials engineering, on the one hand, and cell biology, on the other. A final chapter gives just a glimpse of the burgeoning impact of machine learning on the structure-dynamics front. I aim to capture the excitement of contemporary leading-edge breakthroughs in the description of physico-chemical systems and processes in complex environments, with only enough historical content to provide context and aid the next generation of methodological development. While I aim also for a clear description of the essence of methodological breakthroughs, equations are kept to a minimum and detailed formalism and implementation details are left to the references. My approach is very selective (case studies) rather than exhaustive. I think that these case studies should provide fodder to build as complete a reference tree on multiscale modelling as the reader may wish, through forward and backward citation analysis. I hope that my choices of cases will excite interest in newcomers and help to fuel the growth of multiscale modelling in general.

Anion Recognition by a Pincer-Type Host Constructed from Two Polyamide Macrocyclic Frameworks Jointed by a Photo-Addressable Azobenzene Switch

A sterically crowded light-responsive host 1 was synthetized with a 93% yield by applying a post-functionalization protocol utilizing the double amidation of 4,4'-azodibenzoyl dichloride with a readily available 26-membered macrocyclic amine. X-ray structures of two hydrates of trans-1 demonstrate a very different alignment of the azobenzene linkage, which is involved in T-shape or parallel-displaced π⋯π stacking interactions with the pyridine-2,6-dicarboxamide moieties from the macrocyclic backbone. Despite the rigidity of the macrocyclic framework, which generates a large steric hindrance around the azobenzene chromophore, the host 1 retains the ability to undergo a reversible cis⟷trans isomerization upon irradiation with UVA (368 nm) and blue (410 nm) light. Moreover, thermal cis→trans back-isomerization (ΔG0 = 106.5 kJ∙mol-1, t½ = 141 h) is markedly slowed down as compared to the non-macrocyclic analog. 1H NMR titration experiments in DMSO-d6/0.5% water solution reveal that trans-1 exhibits a strong preference for dihydrogenphosphate (H2PO4-) over other anions (Cl-, MeCO2-, and PhCO2-), whereas the photogenerated metastable cis-1 shows lower affinity for the H2PO4- anion.

Effect of Solvents on Proline Modified at the Secondary Sphere: A Multivariate Exploration

The critical influence of solvent effects on proline-catalyzed aldol reactions has been extensively described. Herein, we apply multivariate regression strategies to probe the influence of different solvents on an aldol reaction catalyzed by proline modified at its secondary sphere with boronic acids. In this system, both in situ binding of the boronic acid to proline and the outcome of the aldol reaction are impacted by the solvent-controlled microenvironment. Thus, with the aim of uncovering mechanistic insight and an ancillary aim of identifying methodological improvements, we designed a set of experiments, spanning 15 boronic acids in five different solvents. Based on hypothesized intermediates or interactions that could be responsible for the selectivity in these reactions, we proposed several structural configurations for the library of boronic acids. Subsequently, we compared the statistical models correlating the outcome of the reaction in different solvents with molecular descriptors produced for each of these proposed configurations. The models allude to the importance of different interactions in controlling selectivity in each of the studied solvents. As a proof-of-concept for the practicality of our approach, the models in chloroform ultimately led to lowering the ketone loading to only two equivalents while retaining excellent yield and enantio- and diastereo-selectivity.

Rationalizing the Mechanism of Peroxyformate Decomposition: Computational Insights To Understand Solvent Influence

The heterolytic decomposition of tert‐butyl peroxyformate to tert‐butanol and carbon dioxide, catalyzed by pyridine, is a long‐known example of a reaction whose kinetics are strongly affected by solvent polarity. From DFT and ab initio methods together with the SMD implicit solvation model, an extension on the formerly accepted mechanism is proposed. This novel proposal involves the formation of a carbonic acid ester intermediate and its further decomposition, through an unreported pyridine‐mediated stepwise route. Computed barriers for this mechanism at DLPNO/CCSD(T)‐def2‐TZVP are in excellent agreement with experimental kinetic data across different solvents. Furthermore, the strong relationships between activation energies, geometric parameters in the transition state and the characteristics of the different solvents are also analyzed in depth.

Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional

This paper assesses the ability of molecular density functional theory to predict efficiently and accurately the hydration free energies of molecular solutes and the surrounding microscopic water structure. A wide range of solutes were investigated, including hydrophobes, water as a solute, and the FreeSolv database containing 642 drug-like molecules having a variety of shapes and sizes. The usual second-order approximation of the theory is corrected by a third-order, angular-independent bridge functional. The overall functional is parameter-free in the sense that the only inputs are bulk water properties, independent of the solutes considered. These inputs are the direct correlation function, compressibility, liquid-gas surface tension, and excess chemical potential of the solvent. Compared to molecular simulations with the same force field and the same fixed solute geometries, the present theory is shown to describe accurately the solvation free energy and structure of both hydrophobic and hydrophilic solutes. Overall, the method yields a precision of order 0.5 k_BT for the hydration free energies of the FreeSolv database, with a computer speedup of 3 orders of magnitude. The theory remains to be improved for a better description of the H-bonding structure and the hydration free energy of charged solutes.

Predicting solvation free energies in non-polar solvents using classical density functional theory based on the PC-SAFT equation of state

We propose a predictive Density Functional Theory (DFT) for the calculation of solvation free energies. Our approach is based on a Helmholtz free-energy functional that is consistent with the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. This allows for a coarse-grained description of the solvent based on an inhomogeneous density of PC-SAFT segments. The solute, on the other hand, is described in full detail by atomistic Lennard-Jones interaction sites. The approach is entirely predictive as it only takes the PC-SAFT parameters of the solvent and the force-field parameters of the solute as input. No adjustable parameters or empirical corrections are involved. The framework is applied to study self-solvation of n-alkanes and to the calculation of residual chemical potentials in binary solvent mixtures. Our DFT approach accurately predicts solvation free energies of small molecular solutes in three different non-polar solvents, namely n-hexane, cyclohexane, and benzene. Additionally, we show that the calculated solvation free energies agree well with those obtained by molecular dynamics simulations and with the residual chemical potential calculated by the bulk PC-SAFT equation of state. We observe higher deviations for the solvation free energy of systems with significant solute-solvent Coulomb interactions.