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.

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.

Electron transfer of functionalized 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 one to fine tune not only their chemical stability but also the redox potential and kinetics of the electron transfer reaction. However, the reaction rate constant is not only determined by the redox species but 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 the electron transfer reaction is considerably reduced compared to the state-of-the-art molecular dynamics simulations, enables us 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 the reference classical molecular dynamics simulations in the case of anthraquinone solvated in acetonitrile. We show that all the studied electron transfer half-reactions follow the Marcus theory, regardless of functional groups. Consequently, the solvent reorganization free energy decreases as the molecular size increases.

Microscopic Simulations of Electrochemical Double-Layer Capacitors.

Electrochemical double-layer capacitors (EDLCs) are devices allowing the storage or production of electricity. They function through the adsorption of ions from an electrolyte on high-surface-area electrodes and are characterized by short charging/discharging times and long cycle-life compared to batteries. Microscopic simulations are now widely used to characterize the structural, dynamical, and adsorption properties of these devices, complementing electrochemical experiments and in situ spectroscopic analyses. In this review, we discuss the main families of simulation methods that have been developed and their application to the main family of EDLCs, which include nanoporous carbon electrodes. We focus on the adsorption of organic ions for electricity storage applications as well as aqueous systems in the context of blue energy harvesting and desalination. We finally provide perspectives for further improvement of the predictive power of simulations, in particular for future devices with complex electrode compositions.

Multi-scale simulation of the adsorption of lithium ion on graphite surface: From quantum Monte Carlo to molecular density functional theory.

The structure of the double-layer formed at the surface of carbon electrodes is governed by the interactions between the electrode and the electrolyte species. However, carbon is notoriously difficult to simulate accurately, even with well-established methods such as electronic density functional theory and molecular dynamics. Here, we focus on the important case of a lithium ion in contact with the surface of graphite, and we perform a series of reference quantum Monte Carlo calculations that allow us to benchmark various electronic density functional theory functionals. We then fit an accurate carbon-lithium pair potential, which is used in molecular density functional theory calculations to determine the free energy of the adsorption of the ion on the surface in the presence of water. The adsorption profile in aqueous solution differs markedly from the gas phase results, which emphasize the role of the solvent on the properties of the double-layer.

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.

Assessing the correctness of pressure correction to solvation theories in the study of electron transfer reactions.

Liquid state theories have emerged as a numerically efficient alternative to costly molecular dynamics simulations of electron transfer reactions in solution. In a recent paper [Jeanmairet et al., Chem. Sci. 10, 2130-2143 (2019)], we introduced the framework to compute the energy gap, free energy profile, and reorganization free energy using molecular density functional theory. However, this technique, as other molecular liquid state theories, overestimates the bulk pressure of the fluid. Because of the very high pressure, the predicted free energy is dramatically exaggerated. Several attempts were made to fix this issue, either based on simple a posteriori correction or by introducing bridge terms. By studying two model half reactions in water, Cl → Cl+ and Cl → Cl-, we assess the correctness of these two types of corrections to study electron transfer reactions. We found that a posteriori correction, because it violates the Variational principle, leads to an inconsistency in the definition of the reorganization free energy and should not be used to study electron transfer reactions. The bridge approach, because it is theoretically well grounded, is perfectly suitable for this type of systems.

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.

A first-principles investigation of the structural and electrochemical properties of biredox ionic species in acetonitrile.

Biredox ionic liquids are a new class of functionalized electrolytes that may play an important role in future capacitive energy storage devices. By allowing additional storage of electrons inside the liquids, they can improve device performance significantly. However current devices employ nanoporous carbons in which the diffusion of the liquid and the adsorption of the ions could be affected by the occurrence of electron-transfer reactions. It is therefore necessary to understand better the thermodynamics and the kinetics of such reactions in biredox ionic liquids. Here we perform ab initio molecular dynamics simulations of both the oxidized and reduced species of several redox-active ionic molecules (used in biredox ionic liquids) dissolved in acetonitrile solvent and compare them with the bare redox molecules. We show that in all the cases, it is necessary to introduce a two Gaussian state model to calculate the reaction free energies accurately. These reaction free energies are only slightly affected by the presence of the IL group on the molecule. We characterize the structure of the solvation shell around the redox active part of the molecules and show that in the case of TEMPO-based molecules strong reorientation effects occur during the oxidation reaction.

Simulating Electrochemical Systems by Combining the Finite Field Method with a Constant Potential Electrode.

A better understanding of interfacial mechanisms is needed to improve the performances of electrochemical devices. Yet, simulating an electrode surface at fixed electrolyte composition remains a challenge. Here, we apply a finite electric field to a single electrode held at constant potential and in contact with an aqueous ionic solution, using classical molecular dynamics. The polarization yields two electrochemical interfaces on opposite sides of the same metal slab. The net charge on one electrode surface is the opposite of the net charge on the other, maintaining overall charge neutrality of the metal. The electrode surface charge fluctuations are compensated by the adsorption of ions from the electrolyte, forming a pair of electric double layers with aligned dipoles. This opens the way towards the efficient simulation of electrochemical interfaces using any flavor of molecular dynamics, from classical to first-principles-based methods.

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.

Confinement Effects on an Electron Transfer Reaction in Nanoporous Carbon Electrodes.

Nanoconfinement generally leads to a drastic effect on the physical and chemical properties of ionic liquids. Here we investigate how the electrochemical reactivity in such media may be impacted inside of nanoporous carbon electrodes. To this end, we study a simple electron transfer reaction using molecular dynamics simulations. The electrodes are held at constant electric potential by allowing the atomic charges on the carbon atoms to fluctuate. We show that the Fe3+/Fe2+ couple dissolved in an ionic liquid exhibits a deviation with respect to Marcus theory. This behavior is rationalized by the stabilization of a solvation state of the Fe3+ cation in the disordered nanoporous electrode that is not observed in the bulk. The simulation results are fitted with a recently proposed two solvation state model, which allows us to estimate the effect of such a deviation on the kinetics of electron transfer inside of nanoporous electrodes.

Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory.

We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 2016, 12, 3674], by introducing a semistochastic algorithm for performing multireference Epstein-Nesbet perturbation theory, in order to completely eliminate the severe memory bottleneck of the original method. The proposed algorithm has several attractive features. First, there is no sign problem that plagues several quantum Monte Carlo methods. Second, instead of using Metropolis-Hastings sampling, we use the Alias method to directly sample determinants from the reference wave function, thus avoiding correlations between consecutive samples. Third, in addition to removing the memory bottleneck, semistochastic HCI (SHCI) is faster than the deterministic variant for many systems if a stochastic error of 0.1 mHa is acceptable. Fourth, within the SHCI algorithm one can trade memory for a modest increase in computer time. Fifth, the perturbative calculation is embarrassingly parallel. The SHCI algorithm extends the range of applicability of the original algorithm, allowing us to calculate the correlation energy of very large active spaces. We demonstrate this by performing calculations on several first row dimers including F2 with an active space of (14e, 108o), Mn-Salen cluster with an active space of (28e, 22o), and Cr2 dimer with up to a quadruple-ζ basis set with an active space of (12e, 190o). For these systems we were able to obtain better than 1 mHa accuracy with a wall time of merely 55 s, 37 s, and 56 min on 1, 1, and 4 nodes, respectively.

Stochastic multi-reference perturbation theory with application to the linearized coupled cluster method.

In this article we report a stochastic evaluation of the recently proposed multireference linearized coupled cluster theory [S. Sharma and A. Alavi, J. Chem. Phys. 143, 102815 (2015)]. In this method, both the zeroth-order and first-order wavefunctions are sampled stochastically by propagating simultaneously two populations of signed walkers. The sampling of the zeroth-order wavefunction follows a set of stochastic processes identical to the one used in the full configuration interaction quantum Monte Carlo (FCIQMC) method. To sample the first-order wavefunction, the usual FCIQMC algorithm is augmented with a source term that spawns walkers in the sampled first-order wavefunction from the zeroth-order wavefunction. The second-order energy is also computed stochastically but requires no additional overhead outside of the added cost of sampling the first-order wavefunction. This fully stochastic method opens up the possibility of simultaneously treating large active spaces to account for static correlation and recovering the dynamical correlation using perturbation theory. The method is used to study a few benchmark systems including the carbon dimer and aromatic molecules. We have computed the singlet-triplet gaps of benzene and m-xylylene. For m-xylylene, which has proved difficult for standard complete active space self consistent field theory with perturbative correction, we find the singlet-triplet gap to be in good agreement with the experimental values.

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.

Quasi-degenerate perturbation theory using matrix product states.

In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner's 2n + 1 rule. Further, our formulation satisfies Granovsky's requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

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.