Molecular density functional theory of solvation: From polar solvents to water

The orientational structure of a model patchy particle fluid: Simulations, integral equations, density functional theory, and machine learning

We investigate the orientational properties of a homogeneous and inhomogeneous tetrahedral four-patch fluid (Bol-Kern-Frenkel model). Using integral equations, either (i) HNC or (ii) a modified HNC scheme with a simulation input, the full orientational dependence of pair and direct correlation functions is determined. Density functionals for the inhomogeneous problem are constructed via two different methods. The first, molecular density functional theory, utilizes the full direct correlation function and an isotropic hard-sphere bridge functional. The second method, a machine learning approach, uses a decomposition of the functional into an isotropic reference part and a mean-field orientational part, where both parts are improved by machine learning techniques. A comparison with the simulation data at hard walls and around hard tracers shows a similar performance of the two functionals. Machine learning strategies are discussed to eliminate residual differences, with the goal of obtaining machine-learning enhanced functionals for the general anisotropic fluid.

A classical density functional theory for solvation across length scales

A central aim of multiscale modeling is to use results from the Schrödinger equation to predict phenomenology on length scales that far exceed those of typical molecular correlations. In this work, we present a new approach rooted in classical density functional theory (cDFT) that allows us to accurately describe the solvation of apolar solutes across length scales. Our approach builds on the Lum-Chandler-Weeks (LCW) theory of hydrophobicity [K. Lum et al., J. Phys. Chem. B 103, 4570 (1999)] by constructing a free energy functional that uses a slowly varying component of the density field as a reference. From a practical viewpoint, the theory we present is numerically simpler and generalizes to solutes with soft-core repulsion more easily than LCW theory. Furthermore, by assessing the local compressibility and its critical scaling behavior, we demonstrate that our LCW-style cDFT approach contains the physics of critical drying, which has been emphasized as an essential aspect of hydrophobicity by recent theories. As our approach is parameterized on the two-body direct correlation function of the uniform fluid and the liquid-vapor surface tension, it straightforwardly captures the temperature dependence of solvation. Moreover, we use our theory to describe solvation at a first-principles level on length scales that vastly exceed what is accessible to molecular simulations.

Repurposing of Drug Bank Compounds against Plasmodium falciparum Dihydroorotate Dehydrogenase as novel anti malarial drug candidates by Computational approaches

This study aimed to repurpose Drug Bank Compounds against P. falciparum Dihydroorotate dehydrogenase (Pf-DHODH)a potential molecular target for antimalarial drug development due to its vital role in P. falciparum survival. Initially, the MATGEN server was used to screen drugs against Pf-DHODH (PDB ID 6GJG), followed by revalidating the results through docking by Autodock Vina through PyRx. Based on the docking results, three drugs namely, Talnifumate, Sulfaphenazole, and (3S)-N-[(2S)-1-[2-(1H-indol-3-yl)ethylamino]-1-oxopropan-2-yl]-1-(4-methoxyphenyl)-5-oxopyrrolidine-3-carboxamide-were subjected to molecular dynamics simulation for 100 ns. Molecular dynamics simulation results indicate that (3S)-N-[(2S)-1-[2-(1H-indol-3-yl)ethylamino]-1-oxopropan-2-yl]-1-(4-methoxyphenyl)-5-oxopyrrolidine-3-carboxamide- and Sulfaphenazole may target Pf-DHODH by forming a stable protein-ligand complex as they showed better free binding energy -130.58 kJ/mol, and -79.84 kJ/mol, respectively as compared to the free binding energy 116.255 kJ/mol of the reference compound; 3,6-dimethyl- ~ {N}-[4-(trifluoromethyl)phenyl]-[1,2]oxazolo[5,4-d]pyrimidin-4-amine. Although the studied compounds are drugs, still we applied Lipinski's rules and ADMET analysis that reconfirmed that these drugs have favorable drug-like properties. In conclusion, the results of the study show that Talniflumate and Sulfaphenazole may be potential antimalarial drug candidates.The derivatives of these drugs could be designed and tested to develop better drugs against Plasmodium species.

Graphical Abstract

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.

Transferable Water Potentials Using Equivariant Neural Networks

Machine learning interatomic potentials (MLIPs) have emerged as a technique that promises quantum theory accuracy for reduced cost. It has been proposed [J. Chem. Phys. 2023, 158, 084111] that MLIPs trained on solely liquid water data cannot accurately transfer to the vapor-liquid equilibrium while recovering the many-body decomposition (MBD) analysis of gas-phase water clusters. This suggests that MLIPs do not directly learn the physically correct interactions of water molecules, limiting transferability. In this work, we show that MLIPs using equivariant architecture and trained on 3200 liquid water structures reproduces liquid-phase water properties (e.g., density within 0.003 g/cm3 between 230 and 365 K), vapor-liquid equilibrium properties up to 550 K, the MBD analysis of gas-phase water cluster up to six-body interactions, and the relative energy and the vibrational density of states of ice phases. We show that potentials developed using equivariant MLIPs allow transferability for arbitrary phases of water that remain stable in nanosecond long simulations.

Experimental Determination of the Standard Enthalpy of Formation of Trimellitic Acid and Its Prediction by Supervised Learning

The standard molar enthalpy of formation for trimellitic acid (TMAc) in the crystalline phase at 298.15 K, ΔfHm°(cr), was calculated experimentally from the enthalpy of combustion through combustion calorimetry experiments. Likewise, the standard molar enthalpy of sublimation was determined from the standard molar enthalpy of fusion and from the standard molar enthalpy of vaporization from differential scanning calorimetry and thermogravimetry, respectively. Subsequently, the standard molar enthalpies of formation in the gas-phase at 298.15 K, ΔfHm°(g), were calculated. The enthalpies of formation for TMAc, hemimellitic, and trimesic acids were predicted using multiple linear regression (MLR) with a nonreplacement evaluation technique. MLR was applied to the data set that allowed estimating these thermochemical properties with an R2 greater than 0.99. This model was used to compare the predicted and experimental results for benzene carboxylic acids.

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.

Noether-Constrained Correlations in Equilibrium Liquids

Liquid structure carries deep imprints of an inherent thermal invariance against a spatial transformation of the underlying classical many-body Hamiltonian. At first order in the transformation field Noether's theorem yields the local force balance. Three distinct two-body correlation functions emerge at second order, namely the standard two-body density, the localized force-force correlation function, and the localized force gradient. An exact Noether sum rule interrelates these correlators. Simulations of Lennard-Jones, Yukawa, soft-sphere dipolar, Stockmayer, Gay-Berne and Weeks-Chandler-Andersen liquids, of monatomic water and of a colloidal gel former demonstrate the fundamental role in the characterization of spatial structure.

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.

Accelerating the 3D reference interaction site model theory of molecular solvation with treecode summation and cut-offs

The 3D reference interaction site model (3D-RISM) of molecular solvation is a powerful tool for computing the equilibrium thermodynamics and density distributions of solvents, such as water and co-ions, around solute molecules. However, 3D-RISM solutions can be expensive to calculate, especially for proteins and other large molecules where calculating the potential energy between solute and solvent requires more than half the computation time. To address this problem, we have developed and implemented treecode summation for long-range interactions and analytically corrected cut-offs for short-range interactions to accelerate the potential energy and long-range asymptotics calculations in non-periodic 3D-RISM in the AmberTools molecular modeling suite. For the largest single protein considered in this work, tubulin, the total computation time was reduced by a factor of 4. In addition, parallel calculations with these new methods scale almost linearly and the iterative solver remains the largest impediment to parallel scaling. To demonstrate the utility of our approach for large systems, we used 3D-RISM to calculate the solvation thermodynamics and density distribution of 7-ring microtubule, consisting of 910 tubulin dimers, over 1.2 million atoms.

Implementation and Optimization of the Embedded Cluster Reference Interaction Site Model with Atomic Charges

In this work, we implemented the embedded cluster reference interaction site model (EC-RISM) originally developed by Kloss, Heil, and Kast (J. Phys. Chem. B2008, 112, 4337–4343). This method combines quantum mechanical calculations with the 3D reference interaction site model (3D-RISM). Numerous options, such as buffer, grid space, basis set, charge model, water model, closure relation, and so forth, were investigated to find the best settings. Additionally, the small point charges, which are derived from the solvent distribution from the 3D-RISM solution to represent the solvent in the QM calculation, were neglected to reduce the overhead without the loss of accuracy. On the MNSOL[a], MNSOL, and FreeSolv databases, our implemented and optimized method provides solvation free energies in water with 5.70, 6.32, and 6.44 kJ/mol root-mean-square deviations, respectively, but with different settings, 5.22, 6.08, and 6.63 kJ/mol can also be achieved. Only solvent models containing fitting parameters, like COSMO-RS and EC-RISM with universal correction and directly used electrostatic potential, perform better than our EC-RISM implementation with atomic charges.

Integral equation models for solvent in macromolecular crystals

The solvent can occupy up to ∼70% of macromolecular crystals, and hence, having models that predict solvent distributions in periodic systems could improve the interpretation of crystallographic data. Yet, there are few implicit solvent models applicable to periodic solutes, and crystallographic structures are commonly solved assuming a flat solvent model. Here, we present a newly developed periodic version of the 3D-reference interaction site model (RISM) integral equation method that is able to solve efficiently and describe accurately water and ion distributions in periodic systems; the code can compute accurate gradients that can be used in minimizations or molecular dynamics simulations. The new method includes an extension of the Ornstein–Zernike equation needed to yield charge neutrality for charged solutes, which requires an additional contribution to the excess chemical potential that has not been previously identified; this is an important consideration for nucleic acids or any other charged system where most or all the counter- and co-ions are part of the “disordered” solvent. We present several calculations of proteins, RNAs, and small molecule crystals to show that x-ray scattering intensities and the solvent structure predicted by the periodic 3D-RISM solvent model are in closer agreement with the experiment than are intensities computed using the default flat solvent model in the refmac5 or phenix refinement programs, with the greatest improvement in the 2 to 4 Å range. Prospects for incorporating integral equation models into crystallographic refinement are discussed.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Recent Progress toward Ab Initio Modeling of Electrocatalysis

Electrode potential is the key factor for controlling electrocatalytic reactions at electrochemical interfaces, and moreover, it is also known that the pH and solutes (e.g., cations) of the solution have prominent effects on electrocatalysis. Understanding these effects requires microscopic information on the electrochemical interfaces, in which theoretical simulations can play an important role. This Perspective summarizes the recent progress in method development for modeling electrochemical interfaces, including different methods for describing the electrolytes at the interfaces and different schemes for charging up the electrode surfaces. In the final section, we provide an outlook for future development in modeling methods and their applications to electrocatalysis.

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.

Thermodynamic Barrier for Nanoparticle Penetration into Nanotubes

It is promising yet challenging to develop efficient methods to separate nanoparticles (NPs) with nanochannel devices. Herein, in order to guide and develop the separation method, the thermodynamic mechanism of NP penetration into solvent-filled nanotubes is investigated by using classical density functional theory. The potential of mean force (PMF) is calculated to evaluate the thermodynamic energy barrier for NP penetration into nanotubes. The accuracy of the theory is validated by comparing it with parallel molecular dynamics simulation. By examining the effects of nanotube size, solvent density, and substrate wettability on the PMF, we find that a large tube, a low bulk solvent density, and a solvophilic substrate can boost the NP penetration into nanotubes. In addition, it is found that an hourglass-shaped entrance can effectively improve the NP penetration efficiency compared with a square-shaped entrance. Furthermore, the minimum separation density of NPs in solution is identified, below which the NP penetration into nanotubes requires an additional driving force. Our findings provide fundamental insights into the thermodynamic barrier for NP penetration into nanotubes, which may provide theoretical guidance for separating two components using microfluidics.

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.

Solvent Effects on the Symmetric and Asymmetric SN2 Reactions in the Acetonitrile Solution: A Reaction Density Functional Theory Study

Bimolecular nucleophilic substitution (S_N2) reactions are of great importance in chemistry and biochemistry due to their capability of constructing functional groups. In this work, we investigate the solvent effect on the free energy profiles of symmetric and asymmetric S_N2 reactions in the acetonitrile solution using the proposed reaction density functional theory (RxDFT) method. This multiscale method utilizes quantum density functional theory for calculating intrinsic reaction free energy coupled with classical density functional theory for addressing solvation contribution. We find that the presence of acetonitrile brings both the polarization effect and solvation effect on the reaction pathways. For the eight selected symmetric S_N2 reactions, the predicated reaction pathways agree well with the results from the direct and thermodynamic cycle (TC) methods with the SMD-M062X solvation model. In addition, the polarization effect reduces the free energy barriers by about 6 kcal/mol, while the solvation effect increases the barriers by about 18 kcal/mol. For the four selected asymmetric S_N2 reactions, the predicted reaction pathways agree well with the results from the Monte Carlo simulations and experiments. The polarization effect and the solvation effect mutually reduce the free energy barriers, and the solvation effect plays a dominant role.

Wetting Transition of Ionic Substrate by Modulating Surface Charge Distribution

Surface wettability regulation plays a crucial role in antifouling and related applications. For regulating surface wettability, one of the effective approaches is to modulate the surface charge distribution. Herein, we report a theoretical study for unraveling the mechanistic relation between surface charge distribution and ionic substrate wettability. Specifically, acetonitrile liquids at ambient condition in contact with various ionic substrates are considered. At different surface charge distributions, the interfacial thermodynamic properties are investigated by means of molecular density functional theory. We find that the variation of the spatial interval among the discrete charges strongly alters the substrate-acetonitrile interaction and leads to an oscillation in the interfacial tension, indicating that the substrate can be tuned from a solvophobic one to a solvophilic one. This trend can be further enhanced by increasing the charge quantity. The underlying mechanisms are extensively discussed and expatiated. Our work provides theoretical guidance to engineer and regulate surface wettability.

Nanoporous carbon for electrochemical capacitive energy storage

This review summarizes the recent advances of nanoporous carbon materials in the application of EDLCs, including a better understanding of the charge storage mechanisms by combining the advanced techniques and simulations methods.

Complex Coacervation in Asymmetric Solutions of Polycation and Polyanion

We study coacervation upon mixing two aqueous solutions of polyelectrolytes (PEs) with opposite charge, by considering asymmetric effects of PE composition and charge valency. The phase behavior, interfacial structure, and coacervate composition are investigated by a classical density-functional theory. We find two types of coacervation that are different in their density. Supernatant phase in low-density coacervation (LDCA) fully consists of small ions, while in high-density coacervation (HDCA) it contains a considerable amount of PE chains. Asymmetric PE composition could generate an electric double layer at the interface of coacervate. For HDCA, ion density changes monotonically, while for LDCA it shows a global minimum at the double layer, giving a low tension value. Charged species of high charge valency enhance the existence of double layer. Our results explained the coacervate structure of low interfacial tension, which is important for experiments and industrial applications.

Closure for the Ornstein-Zernike equation with pressure and free energy consistency

The Ornstein-Zernike (OZ) integral equation theory is a powerful approach to simple liquids due to its low computational cost and the fact that, when combined with an appropriate closure equation, the theory is thermodynamically complete. However, approximate closures proposed to date exhibit pressure or free energy inconsistencies that produce inaccurate or ambiguous results, limiting the usefulness of the Ornstein-Zernike approach. To address this problem, we combine methods to enforce both pressure and free energy consistency to create a new closure approximation and test it for a single-component Lennard-Jones fluid. The closure is a simple power series in the direct and total correlation functions for which we have derived analytical formulas for the excess Helmholtz free energy and chemical potential. These expressions contain a partial molar volumelike term, similar to excess chemical potential correction terms recently developed. Using our bridge approximation, we have calculated the pressure, Helmholtz free energy, and chemical potential for the Lennard-Jones fluid using the Kirkwood charging, thermodynamic integration techniques, and analytic expressions. These results are compared with those from the hypernetted chain equation and the Verlet-modified closure against Monte Carlo and equations-of-state data for reduced densities of ρ^{*}<1 and temperatures of T^{*}=1.5, 2.74, and 5. Our closure shows consistency among all thermodynamic paths, except for one expression of the Gibbs-Duhem relation, whereas the hypernetted chain equation and the Verlet-modified closure exhibit consistency between only a few relations. Accuracy of the closure is comparable to the Verlet-modified closure and a significant improvement to results obtained from the hypernetted chain equation.

Bubble Point Pressures of Hydrocarbon Mixtures in Multiscale Volumes from Density Functional Theory

Accurate characterization of the bubble point pressure of hydrocarbon mixtures under nanoconfinement is crucial to the prediction of ultimate oil recovery and well productivity of shale/tight oil reservoirs. Unlike conventional reservoirs, shale has an extensive network of tiny pores in the range of a few nanometers. In nanopores, the properties of hydrocarbon fluids deviate from those in bulk because of significant surface adsorption. Many previous theoretical works use a conventional equation of state model coupled with capillary pressure to study the nanoconfinement effect. Without including the inhomogeneous molecular density distributions in nanoconfinement, these previous approaches predict only slightly reduced bubble points. In this work, we use density functional theory to study the effect of nanoconfinement on the hydrocarbon mixture bubble point pressure by explicitly considering fluid-surface interactions and inhomogeneous density distributions in nanopores. We find that as system pressure decreases, while lighter components are continuously released from the nanopores, heavier components accumulate within. The bubble point pressure of nanoconfined hydrocarbon mixtures is thus significantly suppressed from the bulk bubble point to below the bulk dew point, in line with our previous experiments. When bulk fluids are in a two-phase, the confined hydrocarbon fluids are in a single liquid-like phase. As pore size increases, bubble point pressure of confined fluids increases and hydrocarbon average density in nanopores approaches the liquid-phase density in bulk when bulk is in a two-phase region. For a finite volume bulk bath, we find that because of the competitive adsorption in nanopores, the bulk bubble point pressure increases in line with a previous experimental work. Our work demonstrates how mixture dynamics and nanopore-bulk partitioning influence phase behavior in nanoconfinement and enables the accurate estimation of hydrocarbon mixture bubble point pressure in shale nanopores.

Confinement Effect on Molecular Conformation of Alkanes in Water-Filled Cavitands: A Combined Quantum/Classical Density Functional Theory Study

The depletion force exerted on an alkane molecule from surrounding solvent may greatly alter its conformation. Such a behavior is closely related to the selective molecular recognition, molecular sensors, self-assembly, and so on. Herein, we report a multiscale theoretical study on the conformational change of a single alkane molecule confined in water-filled cavitands, in which the quantum and classical density functional theories (DFTs) are combined to determine the grand potential of alkane-water system. Specifically, the intrinsic free energy of the alkane molecule is tackled by quantum DFT, while the solvent effect arising from the solvent density inhomogeneity in confined space is addressed by classical DFT. By varying the alkane chain length, pore size, and wettability of inner pore surface, we find that pore confinement and hydrophilic inner surface facilitate the alkane conformational change from extended state to helical state, which becomes more significant as the alkane chain length increases. Our findings, which are in line with previous experimental observations, provide not only the microscopic mechanism but also theoretical guidance for elaborately manipulating molecular conformation at the nanoscale.

Exact molecular direct, cavity, and bridge functions in water system

The exact molecular bridge function of the extended simple point charge model of liquid water at room temperature is extracted from Monte Carlo (MC) simulation data. The projections g_μν^mnl(r) onto rotational invariants of the highly directional pair distribution function g(r,Ω) are accumulated during simulation performed with N = 512 molecules (cubic box size L ≈ 25 Å). Making intensive use of anisotropic integral equation techniques, the molecular Ornstein-Zernike equation fed with the MC data available at short distances and completed beyond L/2 with the hypernetted chain closure valid at long distances is then inverted in order to derive on the whole r range the direct correlation function c_μν^mnl(r), the cavity function y_μν^mnl(r), the negative excess potential of mean force lny_μν^mnl(r), and, finally, the holy grail in such liquid state theory, the bridge function b_μν^mnl(r) projections. For completeness, the short distance domain inside the soft core can be reached, thanks to the use of a specially designed anisotropic finite potential which replaces the true one between a single pair of molecules in the simulation. The final bridge function b(r,Ω) of bulk water presents strong, non-universal directional features and can now serve as a reference for approximated bridge functions or functionals in liquid physics of aqueous solvents and solutions.

Tailoring the Variational Implicit Solvent Method for New Challenges: Biomolecular Recognition and Assembly

Predicting solvation free energies and describing the complex water behavior that plays an important role in essentially all biological processes is a major challenge from the computational standpoint. While an atomistic, explicit description of the solvent can turn out to be too expensive in large biomolecular systems, most implicit solvent methods fail to capture “dewetting” effects and heterogeneous hydration by relying on a pre-established (i.e., guessed) solvation interface. Here we focus on the Variational Implicit Solvent Method, an implicit solvent method that adds water “plasticity” back to the picture by formulating the solvation free energy as a functional of all possible solvation interfaces. We survey VISM's applications to the problem of molecular recognition and report some of the most recent efforts to tailor VISM for more challenging scenarios, with the ultimate goal of including thermal fluctuations into the framework. The advances reported herein pave the way to make VISM a uniquely successful approach to characterize complex solvation properties in the recognition and binding of large-scale biomolecular complexes.

The Role of Interfacial Water in Protein-Ligand Binding: Insights from the Indirect Solvent Mediated Potential of Mean Force

Classical density functional theory (DFT) can be used to relate the thermodynamic properties of solutions to the indirect solvent mediated part of the solute-solvent potential of mean force (PMF). Standard, but powerful numerical methods can be used to estimate the solute-solvent PMF from which the indirect part can be extracted. In this work we show how knowledge of the direct and indirect parts of the solute-solvent PMF for water at the interface of a protein receptor can be used to gain insights about how to design tighter binding ligands. As we show, the indirect part of the solute-solvent PMF is equal to the sum of the 1-body (energy + entropy) terms in the inhomogeneous solvation theory (IST) expansion of the solvation free energy. To illustrate the effect of displacing interfacial water molecules with particular direct/indirect PMF signatures on the binding of ligands, we carry out simulations of protein binding with several pairs of congeneric ligands. We show that interfacial water locations that contribute favorably or unfavorably at the 1-body level (energy + entropy) to the solvation free energy of the solute can be targeted as part of the ligand design process. Water locations where the indirect PMF is larger in magnitude provide better targets for displacement when adding a functional group to a ligand core.

Efficient Molecular Approach to Quantifying Solvent-Mediated Interactions

The solvent-mediated interaction, or equivalently the depletion force, play a pivotal role in the processes, by which two objects in solution such as lock and key particles, antibody and antigen, macromolecule and substrate, are attracted to each other. The quantification of this interaction is important yet challenging since it depends on the microscopic solvent structure in the surrounding. Here, we report an efficient molecular approach for predicting the solvent-mediated interaction by combining the classical density functional theory with a reversible solvation thermodynamic circle. For demonstration, the solvent-mediated interactions between two nanoparticles and between a nanoparticle and a rough wall are examined, and good agreements compared with the simulation results are illustrated. This approach is thereafter employed to interpret the reported self-assembly phenomena of lock and key colloidal particles. We show that the binding probability between the lock and key colloids can be successfully characterized at different depletant concentrations and system temperatures. This approach provides a potential route for identifying the coarse-graining interaction between two objects in fluid systems.