Adsorption of CO2 and CH4 in MIL-47 investigated by the 3D-RISM molecular theory of solvation

Metal-organic frameworks (MOFs) comprise a class of highly porous nanomaterials formed by the assembly of organic molecular templates connected by metal ions. These materials exhibit a large diversity of pore size and geometry, topology, surface area, and chemical functionality. MOFs are particularly promising materials for developing new technologies for capture and storage of greenhouse gases such as methane and carbon dioxide. Here we apply the three dimensional reference interaction site model (3D-RISM) molecular theory of solvation to study the interactions of CO₂ and CH₄ with the metal-organic material MIL-47. The 3D-RISM integral equations were solved to determine the three dimensional density correlation functions of the gas (solvent) relative to the atomic positions of the MIL-47 framework, treated as static solute sites. The computed solvent spatial distributions inside MIL-47 pores were used to identify whether or not there exist preferable binding sites and the binding free energy landscape for the gas of interest at low computational costs compared with other molecular modeling techniques, such as grand canonical Monte Carlo and molecular dynamics simulations. The 3D-RISM formalism was applied to pure CO₂, pure CH₄, and binary mixtures of these gases of various compositions under different pressure conditions. The results indicate that both gases bind very weakly to MIL-47 and that this material exhibits nearly vanishing CO₂/CH₄ selectivity. The 3D-RISM computations presented here can be extended to investigate the physical adsorption of gases on other MOFs and nanoporous materials, providing an alternative low-cost computational approach to study gas capture and storage in nanoporous materials in general and, in particular, to determine the binding free-energy landscape in these systems.

Integral equation study of soft-repulsive dimeric fluids

We study fluid structure and water-like anomalies of a system constituted by dimeric particles interacting via a purely repulsive core-softened potential by means of integral equation theories. In our model, dimers interact through a repulsive pair potential of inverse-power form with a softened repulsion strength. By employing the Ornstein-Zernike approach and the reference interaction site model (RISM) theory, we study the behavior of water-like anomalies upon progressively increasing the elongation λ of the dimers from the monomeric case ([Formula: see text]) to the tangent configuration ([Formula: see text]). For each value of the elongation we consider two different values of the interaction potential, corresponding to one and two length scales, with the aim to provide a comprehensive description of the possible fluid scenarios of this model. Our theoretical results are systematically compared with already existing or newly generated Monte Carlo data: we find that theories and simulations agree in providing the picture of a fluid exhibiting density and structural anomalies for low values of λ and for both the two values of the interaction potential. Integral equation theories give accurate predictions for pressure and radial distribution functions, whereas the temperatures where anomalies occur are underestimated. Upon increasing the elongation, the RISM theory still predicts the existence of anomalies; the latter are no longer observed in simulations, since their development is likely precluded by the onset of crystallization. We discuss our results in terms of the reliability of integral equation theories in predicting the existence of water-like anomalies in core-softened fluids.

MTS-MD of Biomolecules Steered with 3D-RISM-KH Mean Solvation Forces Accelerated with Generalized Solvation Force Extrapolation

We developed a generalized solvation force extrapolation (GSFE) approach to speed up multiple time step molecular dynamics (MTS-MD) of biomolecules steered with mean solvation forces obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model with the Kovalenko-Hirata closure). GSFE is based on a set of techniques including the non-Eckart-like transformation of coordinate space separately for each solute atom, extension of the force-coordinate pair basis set followed by selection of the best subset, balancing the normal equations by modified least-squares minimization of deviations, and incremental increase of outer time step in motion integration. Mean solvation forces acting on the biomolecule atoms in conformations at successive inner time steps are extrapolated using a relatively small number of best (closest) solute atomic coordinates and corresponding mean solvation forces obtained at previous outer time steps by converging the 3D-RISM-KH integral equations. The MTS-MD evolution steered with GSFE of 3D-RISM-KH mean solvation forces is efficiently stabilized with our optimized isokinetic Nosé-Hoover chain (OIN) thermostat. We validated the hybrid MTS-MD/OIN/GSFE/3D-RISM-KH integrator on solvated organic and biomolecules of different stiffness and complexity: asphaltene dimer in toluene solvent, hydrated alanine dipeptide, miniprotein 1L2Y, and protein G. The GSFE accuracy and the OIN efficiency allowed us to enlarge outer time steps up to huge values of 1-4 ps while accurately reproducing conformational properties. Quasidynamics steered with 3D-RISM-KH mean solvation forces achieves time scale compression of conformational changes coupled with solvent exchange, resulting in further significant acceleration of protein conformational sampling with respect to real time dynamics. Overall, this provided a 50- to 1000-fold effective speedup of conformational sampling for these systems, compared to conventional MD with explicit solvent. We have been able to fold the miniprotein from a fully denatured, extended state in about 60 ns of quasidynamics steered with 3D-RISM-KH mean solvation forces, compared to the average physical folding time of 4-9 μs observed in experiment.

Evaluation of the SCF Combination of KS-DFT and 3D-RISM-KH; Solvation Effect on Conformational Equilibria, Tautomerization Energies, and Activation Barriers

The effect of solvation on conformational equilibria, tautomerization energies, and activation barriers in simple SN2 reactions is reproduced by using the self-consistent field coupling of the Kohn-Sham density functional theory (KS-DFT) for electronic structure and the three-dimensional reference interaction site model with the closure approximation of Kovalenko and Hirata (3D-RISM-KH) for molecular solvation structure. These examples are used in order to validate the implementation of the 3D-RISM-KH method in the Amsterdam Density Functional package. The computations of the free energy difference in the trans/gauche conformational equilibrium for 1,2-dichloroethane in different solvents; the relative tautomerization free energy for cytosine, isocytosine, and guanine; and the free energy activation barrier for a CH3X-type (X = F, Cl, Br) SN2 reaction exhibit agreement with the experimental data. The method is also applied to the electronic and hydration structure of carbon single-wall nanotubes of different diameters, including the effect of water located in the inner space of the nanotubes. A comparison with continuum models of solvation (including COSMO) as well as with other more precise and computationally more expensive calculations is made to demonstrate the accuracy and predictive capability of the new KS-DFT/3D-RISM-KH method.

Electric Interfacial Layer of Modified Cellulose Nanocrystals in Aqueous Electrolyte Solution: Predictions by the Molecular Theory of Solvation

The X-ray crystal structure-based models of Iα cellulose nanocrystals (CNC), both pristine and containing surface sulfate groups with negative charge 0-0.34 e/nm(2) produced by sulfuric acid hydrolysis of softwood pulp, feature a highly polarized "crystal-like" charge distribution. We perform sampling using molecular dynamics (MD) of the structural relaxation of neutral pristine and negatively charged sulfated CNC of various lengths in explicit water solvent and then employ the statistical mechanical 3D-RISM-KH molecular theory of solvation to evaluate the solvation structure and thermodynamics of the relaxed CNC in ambient aqueous NaCl solution at a concentration of 0.0-0.25 mol/kg. The MD sampling induces a right-hand twist in CNC and rearranges its initially ordered structure with a macrodipole of high-density charges at the opposite faces into small local spots of alternating charge at each face. This surface charge rearrangement observed for both neutral and charged CNC significantly affects the distribution of ions around CNC in aqueous electrolyte solution. The solvation free energy (SFE) of charged sulfated CNC has a minimum at a particular electrolyte concentration depending on the surface charge density, whereas the SFE of neutral CNC increases linearly with NaCl concentration. The SFE contribution from Na(+) counterions exhibits behavior similar to the NaCl concentration dependence of the whole SFE. An analysis of the 3D maps of Na(+) density distributions shows that these model CNC particles exhibit the behavior of charged nanocolloids in aqueous electrolyte solution: an increase in electrolyte concentration shrinks the electric interfacial layer and weakens the effective repulsion between charged CNC particles. The 3D-RISM-KH method readily treats solvent and electrolyte of a given nature and concentration to predict effective interactions between CNC particles in electrolyte solution. We provide CNC structural models and a modeling procedure for studies of effective interactions and the formation of ordered phases of CNC suspensions in electrolyte solution.

Properties of a soft-core model of methanol: an integral equation theory and computer simulation study

Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations. The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed.

Multiple time step molecular dynamics in the optimized isokinetic ensemble steered with the molecular theory of solvation: accelerating with advanced extrapolation of effective solvation forces

We develop efficient handling of solvation forces in the multiscale method of multiple time step molecular dynamics (MTS-MD) of a biomolecule steered by the solvation free energy (effective solvation forces) obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model complemented with the Kovalenko-Hirata closure approximation). To reduce the computational expenses, we calculate the effective solvation forces acting on the biomolecule by using advanced solvation force extrapolation (ASFE) at inner time steps while converging the 3D-RISM-KH integral equations only at large outer time steps. The idea of ASFE consists in developing a discrete non-Eckart rotational transformation of atomic coordinates that minimizes the distances between the atomic positions of the biomolecule at different time moments. The effective solvation forces for the biomolecule in a current conformation at an inner time step are then extrapolated in the transformed subspace of those at outer time steps by using a modified least square fit approach applied to a relatively small number of the best force-coordinate pairs. The latter are selected from an extended set collecting the effective solvation forces obtained from 3D-RISM-KH at outer time steps over a broad time interval. The MTS-MD integration with effective solvation forces obtained by converging 3D-RISM-KH at outer time steps and applying ASFE at inner time steps is stabilized by employing the optimized isokinetic Nosé-Hoover chain (OIN) ensemble. Compared to the previous extrapolation schemes used in combination with the Langevin thermostat, the ASFE approach substantially improves the accuracy of evaluation of effective solvation forces and in combination with the OIN thermostat enables a dramatic increase of outer time steps. We demonstrate on a fully flexible model of alanine dipeptide in aqueous solution that the MTS-MD/OIN/ASFE/3D-RISM-KH multiscale method of molecular dynamics steered by effective solvation forces allows huge outer time steps up to tens of picoseconds without affecting the equilibrium and conformational properties, and thus provides a 100- to 500-fold effective speedup in comparison to conventional MD with explicit solvent. With the statistical-mechanical 3D-RISM-KH account for effective solvation forces, the method provides efficient sampling of biomolecular processes with slow and/or rare solvation events such as conformational transitions of hydrated alanine dipeptide with the mean life times ranging from 30 ps up to 10 ns for "flip-flop" conformations, and is particularly beneficial for biomolecular systems with exchange and localization of solvent and ions, ligand binding, and molecular recognition.

Multiscale modeling of solvation in chemical and biological nanosystems and in nanoporous materials

Statistical–mechanical, 3D-RISM-KH molecular theory of solvation (3D reference interaction site model with the Kovalenko–Hirata closure) is promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. 3D-RISM-KH explains the molecular mechanisms of self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), aggregation of prion proteins and β-sheet amyloid oligomers, protein-ligand binding, and function-related solvation properties of complexes as large as the Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) and GroEL/ES chaperone. Molecular mechanics/Poisson–Boltzmann (generalized Born) surface area [MM/PB(GB)SA] post-processing of molecular dynamics (MD) trajectories involving SA empirical nonpolar terms is replaced with MM/3D-RISM-KH statistical–mechanical evaluation of the solvation thermodynamics. 3D-RISM-KH has been coupled with multiple time-step (MTS) MD of the solute biomolecule driven by effective solvation forces, which are obtained analytically by converging the 3D-RISM-KH integral equations at outer time-steps and are calculated in between by using solvation force coordinate extrapolation (SFCE) in the subspace of previous solutions to 3D-RISM-KH. The procedure is stabilized by the optimized isokinetic Nosé–Hoover (OIN) chain thermostatting, which enables gigantic outer time-steps up to picoseconds to accurately calculate equilibrium properties. The multiscale OIN/SFCE/3D-RISM-KH algorithm is implemented in the Amber package and illustrated on a fully flexible model of alanine dipeptide in aqueous solution, exhibiting the computational rate of solvent sampling 20 times faster than standard MD with explicit solvent. Further substantial acceleration can be achieved with 3D-RISM-KH efficiently sampling essential events with rare statistics such as exchange and localization of solvent, ions, and ligands at binding sites and pockets of the biomolecule. 3D-RISM-KH was coupled with ab initio complete active space self-consistent field (CASSCF) and orbital-free embedding (OFE) Kohn–Sham (KS) density functional theory (DFT) quantum chemistry methods in an SCF description of electronic structure, optimized geometry, and chemical reactions in solution. The (OFE)KS-DFT/3D-RISM-KH multi-scale method is implemented in the Amsterdam Density Functional (ADF) package and extensively validated against experiment for solvation thermochemistry, photochemistry, conformational equilibria, and activation barriers of various nanosystems in solvents and ionic liquids (ILs). Finally, the replica RISM-KH-VM molecular theory for the solvation structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous materials reveals the molecular mechanisms of sorption and supercapacitance in nanoporous carbon electrodes, which is drastically different from a planar electrical double layer.

Calculation of local water densities in biological systems: a comparison of molecular dynamics simulations and the 3D-RISM-KH molecular theory of solvation

Water plays a unique role in all living organisms. Not only is it nature's ubiquitous solvent, but it also actively takes part in many cellular processes. In particular, the structure and properties of interfacial water near biomolecules such as proteins are often related to the function of the respective molecule. It can therefore be highly instructive to study the local water density around solutes in cellular systems, particularly when solvent-mediated forces such as the hydrophobic effect are relevant. Computational methods such as molecular dynamics (MD) simulations seem well suited to study these systems at the atomic level. However, due to sampling requirements, it is not clear that MD simulations are, indeed, the method of choice to obtain converged densities at a given level of precision. We here compare the calculation of local water densities with two different methods: MD simulations and the three-dimensional reference interaction site model with the Kovalenko-Hirata closure (3D-RISM-KH). In particular, we investigate the convergence of the local water density to assess the required simulation times for different levels of resolution. Moreover, we provide a quantitative comparison of the densities calculated with MD and with 3D-RISM-KH and investigate the effect of the choice of the water model for both methods. Our results show that 3D-RISM-KH yields density distributions that are very similar to those from MD up to a 0.5 Å resolution, but for significantly reduced computational cost. The combined use of MD and 3D-RISM-KH emerges as an auspicious perspective for efficient solvent sampling in dynamical systems.

A molecular theory of liquid interfaces

We propose a site site generalization of the Lovett-Mow-Buff-Wertheim integro-differential equation for the one-particle density distributions to polyatomic fluids. The method provides microscopic description of liquid interfaces of molecular fluids and solutions. It uses the inhomogeneous site-site direct correlation function of molecular fluid consistently constructed by nonlinear interpolation between the homogeneous ones. The site site correlations of the coexisting bulk phases are obtained from the reference interaction site model (RISM) integral equation with our closure approximation. For illustration, we calculated the structure of the planar liquid-vapor as well as liquid-liquid interfaces of n-hexane and methanol at ambient conditions.

Structure of electrolyte solutions sorbed in carbon nanospaces, studied by the replica RISM theory

The replica RISM theory is used to investigate the structure of electrolyte solutions confined in carbonized polyvinylidene chloride (PVDC) nanoporous material, compared to bulk electrolyte solution. Comparisons are made between the models of electrolyte solution sorbed in the carbonized PVDC material and a single carbon nanosphere in bulk electrolyte solution. Particular attention is paid to the chemical potential balance between the species of the sorbed electrolyte solution and the bulk solution in contact with the nanoporous material. As a result of the strong hydrophobicity of the carbonized PVDC material in the absence of activating chemical groups, the densities of water and ions sorbed in the material are remarkably low compared to those in the ambient bulk solution. The interaction between water molecules and cations becomes strong in nanospaces. It turns out that, in carbon nanopores, a cation adsorbed at the carbon surface is fully surrounded by the hydration shell of water molecules which separates the cation and the surface. Distinctively, an anion is adsorbed in direct contact with the carbon surface, which squeezes a part of its hydration shell out. The tendency increases toward smaller cations, which are characterized as "positive hydration" ions. In the bulk, cations are not hydrated so strongly and behave similarly to anions. The results suggest that the specific capacitance of an electric double-layer supercapacitor with nanoporous electrodes is intimately related to the solvation structure of electrolyte solution sorbed in nanopores, which is affected by the microscopic structure of the nanoporous electrode.

Self-consistent molecular theory of polymers in melts and solutions

We propose a self-consistent molecular theory of conformational properties of flexible polymers in melts and solutions. The method employs the polymer reference interaction site model for the intermolecular correlations and the Green function technique for the intramolecular correlations. We demonstrate this method on n-alkane molecules in different environments: water, hexane, and in melt, corresponding to poor, good, and theta condition, respectively. The numerical results of the intramolecular correlation function, the radius of gyration, and the characteristic ratio of a polymer chain are indicative of conformational changes from one environment to another and are in agreement with other findings in the literature. Scaling laws for the chain size with respect to the number of monomers are discussed. We show results for the intra- and intermolecular correlation functions and the medium-induced potential. We also extract the Kuhn length and the characteristic ratio for the infinite chain limit for melts. The latter is compared to the experimental results and computer simulation. The conformational free energy per monomer in different solvents is calculated. Our treatment can be generalized readily to other polymer-solvent systems, for example, those containing branched copolymers and polar solvents.

Molecular description of the collapse of hydrophobic polymer chains in water

We propose a self-consistent molecular theory of conformational properties of flexible polymers in solution. It is applied to the collapse of a hydrophobic polymer chain in water, and can be readily generalized to any polymer-solvent system (e.g., copolymers with high complexity). We stress the potential of this method for a variety of problems, such as protein folding.