Divide-and-Conquer-Type Density-Functional Tight-Binding Simulations of Hydroxide Ion Diffusion in Bulk Water

Rotational Dynamics of Water near Osmolytes by Molecular Dynamics Simulations

The behavior of water molecules around organic molecules has attracted considerable attention as a crucial factor influencing the properties and functions of soft matter and biomolecules. Recently, it has been suggested that the change in protein stability upon the addition of small organic molecules (osmolytes) is dominated by the change in the water dynamics caused by the osmolyte, where the dynamics of not only the directly interacting water molecules but also the long-range hydration layer affect the protein stability. However, the relation between the long-range structure of hydration water in various solutions and the water dynamics remains unclear at the molecular level. We performed density-functional tight-binding molecular dynamics simulations to elucidate the varying rotational dynamics of water molecules in 15 osmolyte solutions. A positive correlation was observed between the rotational relaxation time and our proposed normalized parameter obtained by dividing the number of hydrogen bonds between water molecules by the number of nearest-neighbor water molecules. For the 15 osmolyte solutions, an increase or a decrease in the value of the normalized parameter for the second hydration shell tended to result in water molecules with slow and fast rotational dynamics, respectively, thus illustrating the importance of the second hydration shell for the rotational dynamics of water molecules. Our simulation results are anticipated to advance the current understanding of water dynamics around organic molecules and the long-range structure of water molecules.

Theoretical Examination of the Hydroxide Transport in Cobaltocenium-Containing Polyelectrolytes

Polymers incorporating cobaltocenium groups have received attention as promising components of anion-exchange membranes (AEMs), exhibiting a good balance of chemical stability and high ionic conductivity. In this work, we analyze the hydroxide diffusion in the presence of cobaltocenium cations in an aqueous environment based on the molecular dynamics of model systems confined in one dimension to mimic the AEM channels. In order to describe the proton hopping mechanism, the forces are obtained from the electronic structure computed at the density-functional tight-binding level. We find that the hydroxide diffusion depends on the channel size, modulation of the electrostatic interactions by the solvation shell, and its rearrangement ability. Hydroxide diffusion proceeds via both the vehicular and structural diffusion mechanisms with the latter playing a larger role at low diffusion coefficients. The highest diffusion coefficient is observed under moderate water densities (around half the density of liquid water) when there are enough water molecules to form the solvation shell, reducing the electrostatic interaction between ions, yet there is enough space for the water rearrangements during the proton hopping. The effects of cobaltocenium separation, orientation, chemical modifications, and the role of nuclear quantum effects are also discussed.

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

Fragmentation and embedding schemes are of great importance when applying quantum-chemical calculations to more complex and attractive targets. The divide-and-conquer (DC)-based quantum-chemical model is a fragmentation scheme that can be connected to embedding schemes. This feature article explains several DC-based schemes developed by the authors over the last two decades, which was inspired by the pioneering study of DC self-consistent field (SCF) method by Yang and Lee (J. Chem. Phys. 1995, 103, 5674-5678). First, the theoretical aspects of the DC-based SCF, electron correlation, excited-state, and nuclear orbital methods are described, followed by the two-component relativistic theory, quantum-mechanical molecular dynamics simulation, and the introduction of three programs, including DC-based schemes. Illustrative applications confirmed the accuracy and feasibility of the DC-based schemes.

Regularized Localized Molecular Orbitals in a Divide-and-Conquer Approach for Linear Scaling Calculations

Non-orthogonal localized molecular orbitals (NOLMOs) have been employed as building blocks for the divide-and-conquer (DC) linear scaling method. The NOLMOs are calculated from subsystems and used for constructing the density matrix (DM) of the entire system, instead of the subsystem DM in the original DC approach. Also, unlike the original DC method, the inverse electronic temperature parameter β is not needed anymore. Furthermore, a new regularized localization approach for NOLMOs has been developed, in which the localization cost function is a sum of the spatial spread function, as in the Boys method, and the kinetic energy, as a regularization measure to limit the oscillation of the NOLMOs. The optimal weight of the kinetic energy can be determined by optimization with analytical gradients. The resulting regularized NOLMOs have enhanced smoothness and better transferability because of reduced kinetic energies. Compared with the original DC, while NOLMO-DC has a similar computational linear scaling cost, the accuracy of NOLMO-DC is better by several orders of magnitude for large conjugated systems and by about 1 order of magnitude for other systems. The NOLMO-DC method is thus a promising development of the DC approach for linear scaling calculations.

Effects of Salt Concentration on the Water and Ion Self-Diffusion Coefficients of a Model Aqueous Sodium-Ion Battery Electrolyte

The aqueous sodium-ion battery is a promising alternative to the well-known lithium-ion battery owing to the large abundance of sodium ion resources. Although it is safer than the lithium-ion battery, the voltage window of the sodium-ion battery is narrower than that of the lithium-ion battery, thus limiting its practical implementation. Therefore, a highly concentrated electrolyte is required to address this issue. In the present work, the effect of the salt concentration on the transport properties of water molecules is investigated via theoretical analyses at the quantum mechanical level. A molecular dynamics simulation at the quantum mechanical level revealed that as the salt concentration increases, the ion-water interactions became stronger, leading to a lower diffusivity and a lower electronic band gap. These imply that the superconcentrated aqueous-based electrolytes have high potentials for the sodium-ion battery applications.

Rotational Dynamics of Water at the Phospholipid Bilayer Depending on the Head Groups Studied by Molecular Dynamics Simulations

Hydration states are a crucial factor that affect the self-assembly and properties of soft materials and biomolecules. Although previous experiments have revealed that the hydration state strongly depends on the chemical structure of lipid molecules, the mechanisms at the molecular level remain unknown. Classical and density-functional tight-binding (DFTB) molecular dynamics (MD) simulations are employed to determine the mechanisms underlying dissimilar water dynamics between lipid membranes with phosphatidylcholine (PC) and phosphatidylethanolamine (PE) head groups. The classical MD simulation shows that rotational relaxations of water are faster on the PE lipid than on the PC lipid, which is consistent with a previous experimental study using terahertz spectroscopy. Furthermore, DFTB-MD simulation of N(CH₃)₄⁺ and NH₄⁺ ions, which correspond to the different head groups in PC and PE, respectively, shows qualitative agreement with the classical MD simulation. Remarkably, the PE lipids and the NH₄⁺ ions break hydrogen bonds between water molecules in the secondary hydration shell. In contrast, the PC lipids and the N(CH₃)₄⁺ ions bind water molecules weakly in both the primary and secondary hydration shells and increase hydrogen bonds between water. Our atomistic simulations show that these changes in the hydrogen-bond network of water molecules cause the different rotational relaxation of water molecules between the two lipids.

Trajectory Surface Hopping Approach to Condensed-Phase Nonradiative Relaxation Dynamics Using Divide-and-Conquer Spin-Flip Time-Dependent Density-Functional Tight Binding

Nonradiative relaxation of excited molecules is central to many crucial issues in photochemistry. Condensed phases are typical contexts in which such problems are considered, and the nonradiative relaxation dynamics are expected to be significantly affected by interactions with the environment, for example, a solvent. We developed a nonadiabatic molecular dynamics simulation technique that can treat the nonradiative relaxation and explicitly include the environment in the calculations without a heavy computational burden. Specifically, we combined trajectory surface hopping with Tully's fewest-switches algorithm, a tight-binding approximated version of spin-flip time-dependent density-functional theory, and divide-and-conquer (DC) spatial fragmentation scheme. Numerical results showed that this method can treat systems with thousands of atoms within reasonable computational resources, and the error arising from DC fragmentation is negligibly small. Using this method, we obtained molecular insights into the solvent dependence of the photoexcited-state dynamics of trans-azobenzene, which demonstrate the importance of the environment for condensed-phase nonradiative relaxation.

Chemical Garden Membranes in Temperature-Controlled Microfluidic Devices

Thin-walled tubes that classically form when metal salts react with sodium silicate solution are known as chemical gardens. They share similarities with the porous, catalytic materials in hydrothermal vent chimneys, and both structures are exposed to steep pH gradients that, combined with thermal factors, might have provided the free energy for prebiotic chemistry on early Earth. We report temperature effects on the shape, composition, and opacity of chemical gardens. Tubes grown at high temperature are more opaque, indicating changes to the membrane structure or thickness. To study this dependence, we developed a temperature-controlled microfluidic device, which allows the formation of analogous membranes at the interface of two coflowing reactant solutions. For the case of Ni(OH)₂, membranes thicken according to a diffusion-controlled mechanism. In the studied range of 10-40 °C, the effective diffusion coefficient is independent of temperature. This suggests that counteracting processes are at play (including an increased solubility) and that the opacity of chemical garden tubes arises from changes in internal morphology. The latter could be linked to experimentally observed dendritic structures within the membranes.

ABEEM/MM OH- Models for OH-(H2O)n Clusters and Aqueous OH-: Structures, Charge Distributions, and Binding Energies

Based on the atom-bond electronegativity equalization method fused into molecular mechanics (ABEEM/MM), two fluctuating charge models of OH^--water system were proposed. The difference between these two models is whether there is charge transfer between OH^- and its first-shell water molecules. The structures, charge distributions, charge transfer, and binding energies of the OH^-(H₂O)_n (n = 1-8, 10, 15, 23) clusters were studied by these two ABEEM/MM models, the OPLS/AA force field, the OPLS-SMOOTH/AA force field, and the QM methods. The results demonstrate that two ABEEM/MM models can search out all stable structures just as the QM methods, and the structures and charge distributions agree well with those from the QM calculations. The structures, the charge transfer, and the strength of hydrogen bonds in the first hydration shell are closely related to the coordination number of OH^-. Molecular dynamics simulations on the aqueous OH^- solution are performed at 298 and 278 K using ABEEM/MM-I model. The MD results show that the populations of three-, four-, and five-coordinated OH^- are 29.6%, 67.1%, and 3.4% at 298 K, respectively, and those of two-, three-, four-, and five-coordinated OH^- are 10.8%, 44.9%, 39.2%, and 4.9% at 278 K, respectively; the average hydrogen bond lengths and the hydrogen bond angle in the first shell increase with the temperature decreasing.

Development of Divide-and-Conquer Density-Functional Tight-Binding Method for Theoretical Research on Li-Ion Battery

The density-functional tight-binding (DFTB) method is one of the useful quantum chemical methods, which provides a good balance between accuracy and computational efficiency. In this account, we reviewed the basis of the DFTB method, the linear-scaling divide-and-conquer (DC) technique, as well as the parameterization process. We also provide some refinement, modifications, and extension of the existing parameters that can be applicable for lithium-ion battery systems. The diffusion constants of common electrolyte molecules and LiTFSA salt in solution have been estimated using DC-DFTB molecular dynamics simulation with our new parameters. The resulting diffusion constants have good agreement to the experimental diffusion constants.

Development of Large-Scale Excited-State Calculations Based on the Divide-and-Conquer Time-Dependent Density Functional Tight-Binding Method

In this study, the divide-and-conquer (DC) method was extended to time-dependent density functional tight-binding (TDDFTB) theory to enable excited-state calculations of large systems and is denoted by DC-TDDFTB. The efficient diagonalization algorithms of TDDFTB and DC-TDDFTB methods were implemented into our in-house program. Test calculations of polyethylene aldehyde and p-coumaric acid, a pigment in photoactive yellow protein, in water demonstrate the high accuracy and efficiency of the developed DC-TDDFTB method. Furthermore, the (TD)DFTB metadynamics simulations of acridinium in the ground and excited states give reasonable p K_a values compared with the corresponding experimental values.

Performance of Density-Functional Tight-Binding in Comparison to Ab Initio and First-Principles Methods for Isomer Geometries and Energies of Glucose Epimers in Vacuo and Solution

Density functional theory (DFT) is a widely used methodology for the computation of molecular and electronic structure, and we confirm that B3LYP and the high-level ab initio G3B3 method are in excellent agreement for the lowest-energy isomers of the 16 glucose epimers. Density-functional tight-binding (DFTB) is an approximate version of DFT with typically comparable accuracy that is 2 to 3 orders of magnitude faster, therefore generally very suitable for processing large numbers of complex structures. Conformational isomerism in sugars is well known to give rise to a large number of isomer structures. On the basis of a comprehensive study of glucose epimers in vacuo and aqueous solution, we found that the performance of DFTB is on par to B3LYP in terms of geometrical parameters excluding hydrogen bonds and isomer energies. However, DFTB underestimates both hydrogen bonding interactions as well as torsional barriers associated with rotations of the hydroxy groups, resulting in a counterintuitive overemphasis of hydrogen bonding in both gas phase as well as in water. Although the associated root mean squared deviation from B3LYP within epimer isomer groups is only on the order of 1 kcal/mol, this deviation affects the correct assignment of major isomer ordering, which span less than 10 kcal/mol. Both second- as well as third-order DFTB methods are exhibiting similar deviations from B3LYP. Even after the inclusion of empirical dispersion corrections in vacuum, these deviations remain for a large majority of isomer energies and geometries when compared to dispersion-corrected B3LYP.