Dielectric response of confined water films from a classical density functional theory perspective.

We re-examine the problem of the dielectric response of highly polar liquids such as water in confinement between two walls using simple two-variable density functional theory involving number and polarisation densities. In the longitudinal polarisation case where a perturbing field is applied perpendicularly to the walls, we show that the notion of the local dielectric constant, although ill-defined at a microscopic level, makes sense when coarse-graining over the typical size of a particle is introduced. The approach makes it possible to study the effective dielectric response of thin liquid films of various thicknesses in connection with the recent experiments of Fumagalli et al., [Science, 2018, 360, 1339-1342], and to discuss the notion of the interfacial dielectric constant. We argue that the observed properties as a function of slab dimensions, in particular the very low dielectric constants of the order of 2-3 measured for thin slabs of ∼1 nm thickness do not highlight any special properties of water but can be recovered for a generic polar solvent having similar particle size and the same high dielectric constant. Regarding the transverse polarisation case where the perturbing field is parallel to the walls, the associated effective dielectric constant as a function of slab dimensions reaches bulk-like values at much shorter widths than in the longitudinal case. In both cases, we find an oscillatory behaviour for slab thicknesses in the one nanometer range due to packing effects.

Quantifying Fluctuations of Average Solvent Environments for Embedding Calculations.

The viability and effectiveness of replacing an ensemble of embedded solute calculations by a single calculation using an average description of the solvent environment are evaluated. This work explores the fluctuations of the average description of the system obtained in two ways: from calculations on an ensemble of geometries and from an average environment constructed from the same ensemble. To this end, classical molecular dynamics simulations of a rigid acetone solute in SPCE water are performed in order to generate an ensemble of solvent environments. From this ensemble of solvent configurations, a number of different approaches for constructing an average solvent environment are employed. We perform a thorough numerical analysis of the fluctuations of the electrostatic potential experienced by the solute, as well as the resulting fluctuations of the solute's electronic density, measured through its dipole moment and fitted atomic point charges. At the same time, we inspect the accuracy of the methods used to construct average environments. Finally, the proposed method for generating the embedding potential from an average environment density is applied to estimate the solvatochromic shift of the first excitation of acetone. In order to account for quantum confinement effects, which may be important in certain cases, the fluctuations in the shift due to the interaction with the solvent are evaluated using frozen-density-embedding theory. Our results demonstrate that, for normally distributed environments, the constructed average environment is a reasonably good representation of a fluctuating molecular solvent environment. We then provide guidance for future comparisons between these theoretical treatments of solute/solvent systems to experimental measurements.

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 kBT 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.

Tackling Solvent Effects by Coupling Electronic and Molecular Density Functional Theory.

Solvation effects can have a tremendous influence on chemical reactions. However, precise quantum chemistry calculations are most often done either in vacuum neglecting the role of the solvent or using continuum solvent model ignoring its molecular nature. We propose a new method coupling a quantum description of the solute using electronic density functional theory with a classical grand-canonical treatment of the solvent using molecular density functional theory. Unlike a previous work, both densities are minimized self-consistently, accounting for mutual polarization of the molecular solvent and the solute. The electrostatic interaction is accounted using the full electron density of the solute rather than fitted point charges. The introduced methodology represents a good compromise between the two main strategies to tackle solvation effects in quantum calculation. It is computationally more effective than a direct quantum mechanics/molecular mechanics coupling, requiring the exploration of many solvent configurations. Compared to continuum methods, it retains the full molecular-level description of the solvent. We validate this new framework onto two usual benchmark systems: a water solvated in water and the symmetrical nucleophilic substitution between chloromethane and chloride in water. The prediction for the free energy profiles are not yet fully quantitative compared to experimental data, but the most important features are qualitatively recovered. The method provides a detailed molecular picture of the evolution of the solvent structure along the reaction pathway.

Simple Parameter-Free Bridge Functionals for Molecular Density Functional Theory. Application to Hydrophobic Solvation.

Computer simulations have been fundamental in understanding the fine details of hydrophobic solvation and hydrophobic interactions. Alternative approaches based on liquid-state theories have been proposed, but are not yet at the same degree of completeness and accuracy. In this vein, a classical, molecular density functional theory approach to hydrophobic solvation is introduced. The lowest, second-order approximation of the theory, equivalent to the hypernetted chain approximation in integral equations, fails in describing correctly cavitation free-energies. It is corrected here by two simple, angular-independent, so-called bridge functionals; they are parameter-free in the sense that all variables can be fixed unambiguously from the water bulk properties, including pressure, isothermal compressibility, and liquid-gas surface tension. A hard-sphere bridge functional, based on the known functional of a reference hard fluid system, turns out to face strong limitations for water. A simpler weighted density approximation is shown to properly reproduce the solvation free energy of hydrophobes of various sizes, from microscopic ones to the nanoscale, and predicting the solvation free energy of a data set of more than 600 model hydrophobic molecules having a variety of shapes and sizes with an accuracy of a quarter of kBT compared to Monte Carlo simulations values. It constitutes an excellent starting point for a general functional describing accurately both hydrophobic and hydrophilic solvation, and making it possible to study nonidealized hydrophobic interactions.

Predicting Hydration Free Energies of the FreeSolv Database of Drug-like Molecules with Molecular Density Functional Theory.

We assess the performance of molecular density functional theory (MDFT) to predict hydration free energies of the small drug-like molecules benchmark, FreeSolv. The MDFT in the hypernetted chain approximation (HNC) coupled with a pressure correction predicts experimental hydration free energies of the FreeSolv database within 1 kcal/mol with an average computation time of 2 cpu·min per molecule. This is the same accuracy as for simulation-based free energy calculations that typically require hundreds of cpu·h or tens of gpu·h per molecule.

Hydration free energies and solvation structures with molecular density functional theory in the hypernetted chain approximation.

The capability of molecular density functional theory in its lowest, second-order approximation, equivalent to the hypernetted chain approximation in integral equations, to predict accurately the hydration free-energies and microscopic structure of molecular solutes is explored for a variety of systems: spherical hydrophobic solutes, ions, water as a solute, and the Mobley's dataset of organic molecules. The successes and the caveats of the approach are carefully pinpointed. Compared to molecular simulations with the same force field and the same fixed solute geometries, the theory describes accurately the solvation of cations, less so that of anions or generally H-bond acceptors. Overall, the electrostatic contribution to solvation free-energies of neutral molecules is correctly reproduced. On the other hand, the cavity contribution is poorly described but can be corrected using scaled-particle theory ideas. Addition of a physically motivated, one-parameter cavity correction accounting for both pressure and surface effects in the nonpolar solvation contribution yields a precision of 0.8 kcal/mol for the overall hydration free energies of the whole Mobley's dataset. Inclusion of another one-parameter cavity correction for the electrostatics brings it to 0.6 kcal/mol, that is, kBT. This is accomplished with a three-orders of magnitude numerical speed-up with respect to molecular simulations.

Study of a water-graphene capacitor with molecular density functional theory.

Most of the performances of electrochemical devices are governed by molecular processes taking place at the solution-electrode interfaces, and molecular simulation is the main way to study these processes. Aqueous electrochemical systems have often been studied using classical density functional theory (DFT) but with too crude approximations to consider the system description to be realistic. We study the interface between graphene electrodes and liquid water at different applied voltages using molecular DFT, improving the state of the art by the following key points: (1) electrodes have a realistic atomic resolution, (2) classical DFT calculations are carried out at a fixed imposed potential difference, and (3) water is described by a molecular model. This allows us to reveal the structural modification of water adsorbed at the graphene interface and the evolution of water dielectric permittivity when a voltage is applied. The computed capacitance of this device is in agreement with molecular dynamics simulations. This demonstrates the relevance of molecular DFT to study electrochemical systems at the molecular level.

A molecular density functional theory approach to electron transfer reactions.

Beyond the dielectric continuum description initiated by Marcus theory, the standard theoretical approach to study electron transfer (ET) reactions in solution or at interfaces is to use classical force field or ab initio molecular dynamics simulations. We present here an alternative method based on liquid-state theory, namely molecular density functional theory, which is numerically much more efficient than simulations while still retaining the molecular nature of the solvent. We begin by reformulating molecular ET theory in a density functional language and show how to compute the various observables characterizing ET reactions from an ensemble of density functional minimizations. In particular, we define within that formulation the relevant order parameter of the reaction, the so-called vertical energy gap, and determine the Marcus free energy curves of both reactant and product states along that coordinate. Important thermodynamic quantities such as the reaction free energy and the reorganization free energies follow. We assess the validity of the method by studying the model Cl0 → Cl+ and Cl0 → Cl- ET reactions in bulk water for which molecular dynamics results are available. The anionic case is found to violate the standard Marcus theory. Finally, we take advantage of the computational efficiency of the method to study the influence of a solid-solvent interface on the ET, by investigating the evolution of the reorganization free energy of the Cl0 → Cl+ reaction when the atom approaches an atomistically resolved wall.

What Does Second-Harmonic Scattering Measure in Diluted Electrolytes?

We derive a theoretical expression of the second harmonic scattering signal in diluted electrolytes compared with bulk water. We show that the enhancement of the signal with respect to pure water observed recently for electrolytes at very low dilution in the micromolar range is a mere manifestation of the Debye screening that makes the infinite-range dipole-dipole solvent correlations in 1/ r3 disappear as soon as the ionic concentration becomes finite. In q space, this translates into a correlation function having a well known singular behavior around q = 0, which drives the observed ionic effects. We find that the signal is independent of the ion-induced long-range behavior of the function ⟨cos ϕ( r)⟩ that has been recently discussed. We find also that the enhancement depends on the experimental geometry and occurs only for in-plane polarization detection, as observed experimentally. On the contrary, the measured isotope effect between light and heavy water cannot be fully explained.

Screened Coulombic Orientational Correlations in Dilute Aqueous Electrolytes.

The ion-induced long-range orientational order between water molecules recently observed in second harmonic scattering experiments and illustrated with large scale molecular dynamics simulations is quantitatively explained using the Ornstein-Zernike integral equation approach of liquid physics. This general effect, not specific to hydrogen-bonding solvents, is controlled by electroneutrality conditions, dipolar interactions, and dielectric+ionic screening. As expected, all numerical theories recover the well-known analytical expressions established 40 years ago.

Efficient molecular density functional theory using generalized spherical harmonics expansions.

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.

Electronic Excited State Lifetimes of Anionic Water Clusters: Dependence on Charge Solvation Motif.

An ongoing controversy about water cluster anions concerns the electron-binding motif, whether the charge center is localized at the surface or within the cluster interior. Here, mixed quantum-classical dynamics simulations have been carried out for a wide range of cluster sizes (n ≤ 1000) for (H2O)n- and (D2O)n-, based on a nonequilibrium first-order rate constant approach. The computed data are in good general agreement with time-resolved photoelectron imaging results (n ≤ 200). The analysis reveals that, for surface state electrons, the cluster size dependence of the excited state electronic energy gap and the magnitude of the nonadiabatic couplings have compensating influences on the excited state lifetimes: the excited state lifetime for surface states reaches a minimum for n ∼ 150 and then increases for larger clusters. It is concluded that the electron resides in a surface-localized motif in all of these measured clusters, dominating at least up to n = 200.

Molecular density functional theory of water including density-polarization coupling.

We present a three-dimensional molecular density functional theory of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.

Solvation free-energy pressure corrections in the three dimensional reference interaction site model.

Solvation free energies are efficiently predicted by molecular density functional theory if one corrects the overpressure introduced by the usual homogeneous reference fluid approximation. Sergiievskyi et al. [J. Phys. Chem. Lett. 5, 1935-1942 (2014)] recently derived the rigorous compensation of this excess of pressure (referred as "pressure correction" or PC) and proposed an empirical "ideal gas" supplementary correction (referred as "advanced pressure correction" or PC+) that further enhances the calculated solvation free energies. In a recent paper [M. Misin, M. V. Fedorov, and D. S. Palmer, J. Chem. Phys. 142, 091105 (2015)], those corrections were applied to solvation free energy calculations using the three-dimensional reference interaction site model (3D-RISM). As for classical DFT, PC and PC+ improve greatly the predictions of 3D-RISM, but PC+ is described as decreasing the accuracy. In this article, we derive rigorously the expression of the pressure in 3D-RISM as well as the associated PC and PC+. This provides a consistent way to correct the solvation free-energies calculated by 3D-RISM method.

Molecular density functional theory for water with liquid-gas coexistence and correct pressure.

The solvation of hydrophobic solutes in water is special because liquid and gas are almost at coexistence. In the common hypernetted chain approximation to integral equations, or equivalently in the homogenous reference fluid of molecular density functional theory, coexistence is not taken into account. Hydration structures and energies of nanometer-scale hydrophobic solutes are thus incorrect. In this article, we propose a bridge functional that corrects this thermodynamic inconsistency by introducing a metastable gas phase for the homogeneous solvent. We show how this can be done by a third order expansion of the functional around the bulk liquid density that imposes the right pressure and the correct second order derivatives. Although this theory is not limited to water, we apply it to study hydrophobic solvation in water at room temperature and pressure and compare the results to all-atom simulations. The solvation free energy of small molecular solutes like n-alkanes and hard sphere solutes whose radii range from angstroms to nanometers is now in quantitative agreement with reference all atom simulations. The macroscopic liquid-gas surface tension predicted by the theory is comparable to experiments. This theory gives an alternative to the empirical hard sphere bridge correction used so far by several authors.

Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections.

Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2-3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently.

Molecular density functional theory of water describing hydrophobicity at short and long length scales.

We present an extension of our recently introduced molecular density functional theory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619 (2013)] to the solvation of hydrophobic solutes of various sizes, going from angstroms to nanometers. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields: the particle density and the multipolar polarization density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric susceptibilities. The fine three-dimensional water structure around small hydrophobic molecules is found to be well reproduced. In contrast, the computed solvation free-energies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by complementing the functional with a truncated hard-sphere functional acting beyond quadratic order in density, and making the resulting functional compatible with the Van-der-Waals theory of liquid-vapor coexistence at long range. Compared to available molecular simulations, the approach yields reasonable solvation structure and free energy of hard or soft spheres of increasing size, with a correct qualitative transition from a volume-driven to a surface-driven regime at the nanometer scale.

Accurate evaluation of the angular-dependent direct correlation function of water.

The direct correlation function (DCF) plays a pivotal role in addressing the thermodynamic properties with non-mean-field statistical theories of liquid state. This work provides an accurate yet efficient calculation procedure for evaluating the angular-dependent DCF of bulk SPC∕E water. The DCF here represented in a discrete angles basis is computed with two typical steps: the first step involves solving the molecular Ornstein-Zernike equation with the input of total correlation function extracted from simulation; the resultant DCF is then polished in second step at small wavelength for all orientations in order to match correct thermodynamic properties. This function is also discussed in terms of its rotational invariant components. In particular, we show that the component c112(r) that accounts for dipolar symmetry reaches already its long-range asymptotic behavior at a short distance of 4 Å. With the knowledge of DCF, the angular-dependent bridge function of bulk water is thereafter computed and discussed in comparison with referenced hard-sphere bridge functions. We conclude that, even though such hard-sphere bridge functions may be relevant to improve the calculation of Helmholtz free energies in integral equations or density functional theory, they are doomed to fail at a structural level.

Computing Wigner distributions and time correlation functions using the quantum thermal bath method: application to proton transfer spectroscopy.

Langevin dynamics coupled to a quantum thermal bath (QTB) allows for the inclusion of vibrational quantum effects in molecular dynamics simulations at virtually no additional computer cost. We investigate here the ability of the QTB method to reproduce the quantum Wigner distribution of a variety of model potentials, designed to assess the performances and limits of the method. We further compute the infrared spectrum of a multidimensional model of proton transfer in the gas phase and in solution, using classical trajectories sampled initially from the Wigner distribution. It is shown that for this type of system involving large anharmonicities and strong nonlinear coupling to the environment, the quantum thermal bath is able to sample the Wigner distribution satisfactorily and to account for both zero point energy and tunneling effects. It leads to quantum time correlation functions having the correct short-time behavior, and the correct associated spectral frequencies, but that are slightly too overdamped. This is attributed to the classical propagation approximation rather than the generation of the quantized initial conditions themselves.