Combining a Dissociative Water Model with a Hybrid QM/MM Approach—A Simulation Strategy for the Study of Proton Transfer Reactions in Solution

Reshaping the QM Region On-the-Fly: Adaptive-Shape QM/MM Dynamic Simulations of a Hydrated Proton in Bulk Water

Adaptive quantum mechanics/molecular mechanics (QM/MM) reclassifies on-the-fly a molecule or molecular fragment as QM or MM during dynamics simulations without abrupt changes in the energy or forces. Notably, the permuted adaptive-partitioning (PAP) algorithms have been applied to simulate a hydrated proton, with a mobile QM zone anchored at a pseudoatom called a proton indicator. The position of the proton indicator approximates the location of the delocalized excess proton, yielding a smooth trajectory of the proton diffusing via the Grotthuss mechanism in aqueous solutions. The mobile QM zone, which has been taken to be a sphere with a preset radius, follows the proton wherever it goes. Although the simulations are successful, the use of a spherical QM zone has one disadvantage: A large preset radius must be utilized to minimize the chance of missing water molecules that are important to proton translocation. A large radius leads to a large QM zone, which is computationally expensive. In this work, we report a new way to set up the QM zone, where one includes only the water molecules important to proton transfer. The importance of a given water molecule is quantified by its "weight" that depends on its relation to the reaction path of proton transfer. The weight varies smoothly, ensuring that a water molecule gradually appears in or disappears from the QM zone without abrupt changes, as required by the PAP method. Consequently, the shape of the QM zone evolves on-the-fly, keeping the QM zone as small as possible and as large as necessary. Test simulations demonstrate that the new algorithm significantly improves the computation efficiency while maintaining the proper descriptions of proton transfer in bulk water.

Recent advances on graphyne and its family members as membrane materials for water purification and desalination

Graphyne and its family members (GFMs) are allotropes of carbon (a class of 2D materials) having unique properties in form of structures, pores and atom hybridizations. Owing to their unique properties, GFMs have been widely utilized in various practical and theoretical applications. In the past decade, GFMs have received considerable attention in the area of water purification and desalination, especially in theoretical and computational aspects. More recently, GFMs have shown greater prospects in achieving optimal separation performance than the experimentally derived commercial polyamide membranes. In this review, recent theoretical and computational advances made in the GFMs research as it relates to water purification and desalination are summarized. Brief details on the properties of GFMs and the commonly used computational methods were described. More specifically, we systematically reviewed the various computational approaches employed with emphasis on the predicted permeability and selectivity of the GFM membranes. Finally, the current challenges limiting their large-scale practical applications coupled with the possible research directions for overcoming the challenges are proposed.

Tracking the Delocalized Proton in Concerted Proton Transfer in Bulk Water

A solvated proton in water is often characterized as a charge or structural defect, and it is important to track its evolution on-the-fly in certain dynamics simulations. Previously, we introduced the proton indicator, a pseudo-atom, whose position approximates the location of the excess proton modeled as a structural defect. The proton indicator generally yields a smooth trajectory of a hydrated proton diffusing in aqueous solutions, including in the events of stepwise proton transfer via the Grotthuss mechanism; however, the proton indicator did not perform well in the events of concerted proton transfer, for which it occasionally yielded large position displacements between two successive time steps. To overcome this hurdle, we develop a new algorithm of a proton indicator with greatly enhanced performance for concerted proton transfer in bulk water. A protocol is proposed to exhaustively explore the hydrogen-bonding network of the water wires over which the excess proton is delocalized and to properly account for the contributions of the water molecules in this network as the geometry evolves. The new proton indicator (called Indicator 2.0) is assessed in dynamics simulations of an excess proton in bulk water and in specially constructed model systems of more complex architectures. The results demonstrate that the new indicator yields a smooth trajectory in both stepwise and concerted proton transfers.

Improved Indicator Algorithms for Tracking a Hydrated Proton as A Local Structural Defect in Grotthuss Diffusion in Aqueous Solutions

Keeping track of a hydrated proton in dynamics simulations is important and nontrivial. Here, we report two revised algorithms for the proton indicator, a pseudo-atom whose position approximates the location of an excess proton diffusing via the Grotthuss mechanism in aqueous solution. The new methods describe the delocalized proton as a structural defect. Encouragingly, in test simulations of a hydrated proton in bulk water, the new algorithms substantially outperform the original scheme by significantly reducing large displacements in the indicator positions upon donor switch, yielding smoother trajectories that effectively track the movement of the solvated proton.

Formation and migration of H3O+ and OH− ions at the water/silica and water/vapor interfaces under the influence of a static electric field: a molecular dynamics study

Water ‘layers’ 1 and 2 in pink; ‘layer’ 3 in blue and green over portion of glass surface (grey). +90° field causes water migration and clustering.

An effective partial charge model for bulk and surface properties of cubic ZrO2, Y2O3 and yttrium-stabilised zirconia

In this work a newly parametrised Coulomb plus Buckingham potential formulation for cubic ZrO₂, Y₂O₃ and yttrium-stabilised zirconia (YSZ) is presented. The density and pair distributions obtained for neat ZrO₂ and Y₂O₃ under ambient conditions are in excellent agreement with experimental data, while the vibrational power spectra are highly similar compared to those obtained via ab initio molecular dynamics simulations at the PBEsol level. In addition, it is shown that the use of effective partial charges has several advantages compared to interaction potentials employing the oxidation states in the evaluation of the coulombic interactions: (i) the diffusion coefficient and the associated activation energy of oxygen ions evaluated for YSZn (n = 4 to 12) display the best agreement with experimental data; (ii) no unphysical reorganisation of the interface and the bulk are observed in simulations of the (110) and (111) surfaces of cubic ZrO₂ and Y₂O₃, while due to the strong coulombic contributions in the case of the tested full-charge models a pronounced restructuring of the interface and the bulk is observed in the ZrO₂ case, and (iii) the use of effective partial charges ensures compatibility with existing solvent models and force-fields for the treatment of molecular compounds.

Role of the hydrogen bond lifetimes and rotations at the water/amorphous silica interface on proton transport

Using a highly robust and reactive all-atom potential, molecular dynamics computer simulations have been used to provide detailed analysis of the behavior of water and protons at a large-scale amorphous silica surface that offers the heterogeneity of surface sites and water/silica interactions. Structural data of the H-O distances as a function of distance from the glass surface showed variation in hydrogen bond (H-bond) lengths to second and third nearest oxygen neighbors that play an important role in H-bond lifetimes, rotations, and proton transfer, especially at the glass surface. The higher density and inherently closer average spacing between oxygens in the glass surface (2.6 Å) in comparison to that in water (2.8 Å) create a significantly different environment for H-bond lifetimes and proton transfers. Continuous H-bond lifetime autocorrelation functions for water H-bonded to the surface are considerably shorter than those of bulk water, whereas the intermittent lifetime autocorrelation functions are longer. Such results affect proton transfers that are over an order of magnitude higher at the surface than farther from the surface or in bulk water. However, most of these transfers are rattling events between the participating oxygens, one of which is the newly formed H₃O⁺ ion adjacent to the interface. Such a H₃O⁺ ion has an extremely low barrier to proton transfer back to the surface site in comparison to a H₃O⁺ ion in bulk water. Nonetheless, the simulations showed that rotation of the H₃O⁺ ion away from the initial transfer site allowed for structural diffusion of an excess proton away from the surface. Proton conduction from such rotations could be enhanced by external forces.

Towards a dissociative SPC-like water model II. The impact of Lennard-Jones and Buckingham non-coulombic forces

The dissociative water potential by Garofalini and coworkers has been re-formulated in the framework of the widely employed Lennard-Jones and Buckingham potentials, enhancing the transferability of the model to third party simulation programs.

Stability of hydrolytic arsenic species in aqueous solutions: As3+vs. As5+

By combining ab initio molecular dynamics simulations and experiments, the stable hydrolytic species formed by As³⁺ and As⁵⁺ have been identified both in natural waters and in biologically relevant systems.

Structural aspects of the topological model of the hydrogen bond in water on auto-dissociation via proton transfer

Different H-bond structures of donor and acceptor water molecules significantly affect structure, H-bond lifetimes, and autodissociation via proton transfer.

Square planar or octahedral after all? The indistinct solvation of platinum(ii)

The solvation structures of Pd(ii) and Pt(ii) are typically reduced to the well-known square-planar structural motif, although it has been shown, in both experimental and theoretical investigations, that these solutes demonstrate the affinity to bind ligand molecules at elongated distance in axial coordination sites.

Restrained Proton Indicator in Combined Quantum-Mechanics/Molecular-Mechanics Dynamics Simulations of Proton Transfer through a Carbon Nanotube

Recently, a collective variable "proton indicator" was purposed for tracking an excess proton solvated in bulk water in molecular dynamics simulations. In this work, we demonstrate the feasibility of utilizing the position of this proton indicator as a reaction coordinate to model an excess proton migrating through a hydrophobic carbon nanotube in combined quantum-mechanics/molecular-mechanics simulations. Our results indicate that applying a harmonic restraint to the proton indicator in the bulk solvent near the nanotube pore entrance leads to the recruitment of water molecules into the pore. This is consistent with an earlier study that employed a multistate empirical valence bond potential and a different representation (center of excess charge) of the proton. We attribute this water recruitment to the delocalized nature of the solvated proton, which prefers to be in high-dielectric bulk solvent. While water recruitment into the pore is considered an artifact in the present simulations (because of the artificially imposed restraint on the proton), if the proton were naturally restrained, it could assist in building water wires prior to proton transfer through the pore. The potential of mean force for a proton translocation through the water-filled pore was computed by umbrella sampling, where the bias potentials were applied to the proton indicator. The free energy curve and barrier heights agree reasonably with those in the literature. The results suggest that the proton indicator can be used as a reaction coordinate in simulations of proton transport in confined environments.

Towards a dissociative SPC-like water model – probing the impact of intramolecular Coulombic contributions

A modification of the dissociative Garofalini water model towards an SPC-like Coulombic formulation proved to enhance accuracy and transferability of this successful force field approach.

Proton transfer in a short hydrogen bond caused by solvation shell fluctuations: an ab initio MD and NMR/UV study of an (OHO)(-) bonded system

We present a joint experimental and quantum chemical study on the influence of solvent dynamics on the protonation equilibrium in a strongly hydrogen bonded phenol-acetate complex in CD2Cl2. Particular attention is given to the correlation of the proton position distribution with the internal conformation of the complex itself and with fluctuations of the aprotic solvent. Specifically, we have focused on a complex formed by 4-nitrophenol and tetraalkylammonium-acetate in CD2Cl2. Experimentally we have used combined low-temperature (1)H and (13)C NMR and UV-vis spectroscopy and showed that a very strong OHO hydrogen bond is formed with proton tautomerism (PhOH···(-)OAc and PhO(-)···HOAc forms, both strongly hydrogen bonded). Computationally, we have employed ab initio molecular dynamics (70 and 71 solvent molecules, with and without the presence of a counter-cation, respectively). We demonstrate that the relative motion of the counter-cation and the "free" carbonyl group of the acid plays the major role in the OHO bond geometry and causes proton "jumps", i.e. interconversion of PhOH···(-)OAc and PhO(-)···HOAc tautomers. Weak H-bonds between CH(CD) groups of the solvent and the oxygen atom of carbonyl stabilize the PhOH···(-)OAc type of structures. Breaking of CH···O bonds shifts the equilibrium towards PhO(-)···HOAc form.

Tuning the reactivity of a dissociative force field: proton transfer properties of aqueous H3O+ and their dependence on the three-body interaction

Selective adjustment of the three-body interaction of a dissociative water potential results in a significant improvement in the description of proton transport properties.

The zero-multipole summation method for estimating electrostatic interactions in molecular dynamics: analysis of the accuracy and application to liquid systems

In the preceding paper [I. Fukuda, J. Chem. Phys. 139, 174107 (2013)], the zero-multipole (ZM) summation method was proposed for efficiently evaluating the electrostatic Coulombic interactions of a classical point charge system. The summation takes a simple pairwise form, but prevents the electrically non-neutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large energetic noises and significant artifacts. The purpose of this paper is to judge the ability of the ZM method by investigating the accuracy, parameter dependencies, and stability in applications to liquid systems. To conduct this, first, the energy-functional error was divided into three terms and each term was analyzed by a theoretical error-bound estimation. This estimation gave us a clear basis of the discussions on the numerical investigations. It also gave a new viewpoint between the excess energy error and the damping effect by the damping parameter. Second, with the aid of these analyses, the ZM method was evaluated based on molecular dynamics (MD) simulations of two fundamental liquid systems, a molten sodium-chlorine ion system and a pure water molecule system. In the ion system, the energy accuracy, compared with the Ewald summation, was better for a larger value of multipole moment l currently induced until l ≲ 3 on average. This accuracy improvement with increasing l is due to the enhancement of the excess-energy accuracy. However, this improvement is wholly effective in the total accuracy if the theoretical moment l is smaller than or equal to a system intrinsic moment L. The simulation results thus indicate L ∼ 3 in this system, and we observed less accuracy in l = 4. We demonstrated the origins of parameter dependencies appearing in the crossing behavior and the oscillations of the energy error curves. With raising the moment l we observed, smaller values of the damping parameter provided more accurate results and smoother behaviors with respect to cutoff length were obtained. These features can be explained, on the basis of the theoretical error analyses, such that the excess energy accuracy is improved with increasing l and that the total accuracy improvement within l ⩽ L is facilitated by a small damping parameter. Although the accuracy was fundamentally similar to the ion system, the bulk water system exhibited distinguishable quantitative behaviors. A smaller damping parameter was effective in all the practical cutoff distance, and this fact can be interpreted by the reduction of the excess subset. A lower moment was advantageous in the energy accuracy, where l = 1 was slightly superior to l = 2 in this system. However, the method with l = 2 (viz., the zero-quadrupole sum) gave accurate results for the radial distribution function. We confirmed the stability in the numerical integration for MD simulations employing the ZM scheme. This result is supported by the sufficient smoothness of the energy function. Along with the smoothness, the pairwise feature and the allowance of the atom-based cutoff mode on the energy formula lead to the exact zero total-force, ensuring the total-momentum conservations for typical MD equations of motion.

Perspectives for hybrid ab initio/molecular mechanical simulations of solutions: from complex chemistry to proton-transfer reactions and interfaces

As a consequence of the ongoing development of enhanced computational resources, theoretical chemistry has become an increasingly valuable field for the investigation of a variety of chemical systems. Simulations employing a hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) technique have been shown to be a particularly promising approach, whenever ultrafast (i.e., picosecond) dynamical properties are to be studied, which are in many cases difficult to access via experimental techniques. Details of the quantum mechanical charge field (QMCF) ansatz, an advanced QM/MM protocol, are discussed and simulation results for various systems ranging from simple ionic hydrates to solvated organic molecules and coordination complexes in solution are presented. A particularly challenging application is the description of proton-transfer reactions in chemical simulations, which is a prerequisite to study acidified and basic systems. The methodical requirements for a combination of the QMCF methodology with a dissociative potential model for the description of the solvent are discussed. Furthermore, the possible extension of QM/MM approaches to solid/liquid interfaces is outlined.

Specific Reaction Path Hamiltonian for Proton Transfer in Water: Reparameterized Semiempirical Models

The semiempirical MNDO-based AM1 and PM3 methods and the orthogonalization-corrected OM1, OM2, and OM3 models were reparameterized to improve their description of bulk water and of proton transfer in water. Reference data included the gas-phase geometries and energies of the water molecule, small water clusters, the hydronium ion, and small hydronium ion-water clusters, as well as the gas-phase potential energy surface for proton transfer between the two water molecules in a Zundel ion, all calculated at the MP2/aug-cc-pVTZ level of theory. Combined QM/MM molecular dynamics simulations were carried out for bulk water and for a proton solvated in water using large cluster models. Both the authentic and reparameterized semiempirical models were employed in the simulations. The reparameterization led to significantly better results in all cases. The new set of OM3 parameters gave the best overall results for the structural and dynamic properties of water and the hydrated proton, with a small but finite barrier of 0.1-0.2 kcal/mol in the potential of mean force for proton transfer, in agreement with ab initio path-integral molecular dynamics simulations. The reparameterized OM3 model is expected to be useful for efficient modeling of proton transfer in aqueous solution.

Lifetimes of excess protons in water using a dissociative water potential

Molecular dynamics simulations using a dissociative water potential were applied to study transport of excess protons in water and determine the applicability of this potential to describe such behavior. While originally developed for gas-phase molecules and bulk liquid water, the potential is transferrable to nanoconfinement and interface scenarios. Applied here, it shows proton behavior consistent with ab initio calculations and empirical models specifically designed to describe proton transport. Both Eigen and Zundel complexes are observed in the simulations showing the Eigen-Zundel-Eigen-type mechanism. In addition to reproducing the short-time rattling of the excess proton between the two oxygens of Zundel complexes, a picosecond-scale lifetime was also found. These longer-lived H3O(+) ions are caused by the rapid conversion of the local solvation structure around the transferring proton from a Zundel-like form to an Eigen-like form following the transfer, effectively severing the path along which the proton can rattle. The migration of H(+) over long times (>100 ps) deviates from the conventional short-time multiexponentially decaying lifetime autocorrelation model and follows the t(-3/2) power-law behavior. The potential function employed here matches many of the features of proton transport observed in ab initio molecular dynamics simulations as well as the highly developed empirical valence bond models, yet is computationally very efficient, enabling longer time and larger systems to be studied.