Understanding dynamics in coarse-grained models. III. Roles of rotational motion and translation-rotation coupling in coarse-grained dynamics.

This paper series aims to establish a complete correspondence between fine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I). While Paper II successfully captured translational motions in CG systems using a hard sphere mapping, the absence of rotational motions in single-site CG models introduces differences between FG and CG dynamics. In this third paper, our objective is to faithfully recover atomistic diffusion coefficients from CG dynamics by incorporating rotational dynamics. By extracting FG rotational diffusion, we unravel, for the first time reported to our knowledge, a universality in excess entropy scaling between the rotational and translational diffusion. Once the missing rotational dynamics are integrated into the CG translational dynamics, an effective translation-rotation coupling becomes essential. We propose two different approaches for estimating this coupling parameter: the rough hard sphere theory with acentric factor (temperature-independent) or the rough Lennard-Jones model with CG attractions (temperature-dependent). Altogether, we demonstrate that FG diffusion coefficients can be recovered from CG diffusion coefficients by (1) incorporating "entropy-free" rotational diffusion with translation-rotation coupling and (2) recapturing the missing entropy. Our findings shed light on the fundamental relationship between FG and CG dynamics in molecular fluids.

uMBD: A Materials-Ready Dispersion Correction That Uniformly Treats Metallic, Ionic, and van der Waals Bonding.

Materials design increasingly relies on first-principles calculations for screening important candidates and for understanding quantum mechanisms. Density functional theory (DFT) is by far the most popular first-principles approach due to its efficiency and accuracy. However, to accurately predict structures and thermodynamics, DFT must be paired with a van der Waals (vdW) dispersion correction. Therefore, such corrections have been the subject of intense scrutiny in recent years. Despite significant successes in organic molecules, no existing model can adequately cover the full range of common materials, from metals to ionic solids, hampering the applications of DFT for modern problems such as battery design. Here, we introduce a universally optimized vdW-corrected DFT method that demonstrates an unbiased reliability for predicting molecular, layered, ionic, metallic, and hybrid materials without incurring a large computational overhead. We use our method to accurately predict the intercalation potentials of layered electrode materials of a Li-ion battery system, a problem for which the existing state-of-the-art methods fail. Thus, we envisage broad use of our method in the design of chemo-physical processes of new materials.

Density-dependent finite system-size effects in equilibrium molecular dynamics estimation of shear viscosity: Hydrodynamic and configurational study.

We study the intrinsic nature of the finite system-size effect in estimating shear viscosity of dilute and dense fluids within the framework of the Green-Kubo approach. From extensive molecular dynamics simulations, we observe that the size effect on shear viscosity is characterized by an oscillatory behavior with respect to system size L at high density and by a scaling behavior with an L-1 correction term at low density. Analysis of the potential contribution in the shear-stress autocorrelation function reveals that the former is configurational and is attributed to the inaccurate description of the long-range spatial correlations in finite systems. Observation of the long-time inverse-power decay in the kinetic contribution confirms its hydrodynamic nature. The L-1 correction term of shear viscosity is explained by the sensitive change in the long-time tail obtained from a finite system.

Molecular hydrodynamics: Vortex formation and sound wave propagation.

In the present study, quantitative feasibility tests of the hydrodynamic description of a two-dimensional fluid at the molecular level are performed, both with respect to length and time scales. Using high-resolution fluid velocity data obtained from extensive molecular dynamics simulations, we computed the transverse and longitudinal components of the velocity field by the Helmholtz decomposition and compared them with those obtained from the linearized Navier-Stokes (LNS) equations with time-dependent transport coefficients. By investigating the vortex dynamics and the sound wave propagation in terms of these field components, we confirm the validity of the LNS description for times comparable to or larger than several mean collision times. The LNS description still reproduces the transverse velocity field accurately at smaller times, but it fails to predict characteristic patterns of molecular origin visible in the longitudinal velocity field. Based on these observations, we validate the main assumptions of the mode-coupling approach. The assumption that the velocity autocorrelation function can be expressed in terms of the fluid velocity field and the tagged particle distribution is found to be remarkably accurate even for times comparable to or smaller than the mean collision time. This suggests that the hydrodynamic-mode description remains valid down to the molecular scale.

Nature of intrinsic uncertainties in equilibrium molecular dynamics estimation of shear viscosity for simple and complex fluids.

We study two types of intrinsic uncertainties, statistical errors and system size effects, in estimating shear viscosity via equilibrium molecular dynamics simulations, and compare them with the corresponding uncertainties in evaluating the self-diffusion coefficient. Uncertainty quantification formulas for the statistical errors in the shear-stress autocorrelation function and shear viscosity are obtained under the assumption that shear stress follows a Gaussian process. Analyses of simulation results for simple and complex fluids reveal that the Gaussianity is more pronounced in the shear-stress process (related to shear viscosity estimation) compared with the velocity process of an individual molecule (related to self-diffusion coefficient). At relatively high densities corresponding to a liquid state, we observe that the shear viscosity exhibits complex size-dependent behavior unless the system is larger than a certain length scale, and beyond which, reliable shear viscosity values are obtained without any noticeable scaling behavior with respect to the system size. We verify that this size-dependent behavior is configurational and relate the characteristic length scale to the shear-stress correlation length.

Normal versus anomalous self-diffusion in two-dimensional fluids: memory function approach and generalized asymptotic Einstein relation.

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Threading Subunits for Polymers to Predict the Equilibrium Ensemble of Solid Polymer Electrolytes.

We present a computational method for polymer growth called "threading subunits for polymers (TSP)" that can efficiently sample solid polymer electrolyte structures with extended conformations. The TSP method involves equilibrating subunit (e.g., monomer) conformations that form favorable solvation ion shells, followed by consecutively connecting the subunits and minimizing the structures. The TSP method can sample polymers with good solvent-like conformations and from near-equilibrium structures in which ions are well-dispersed, avoiding unusual ion clustering under ambient conditions. Using the TSP method, the equilibration time can be reduced significantly by effectively sampling the polymer conformations near equilibrium. We anticipate that the TSP method can be applied to simulate various polymer electrolytes.

MolNet_Equi: A Chemically Intuitive, Rotation-Equivariant Graph Neural Network.

Although deep-learning (DL) models suggest unprecedented prediction capabilities in tackling various chemical problems, their demonstrated tasks have so far been limited to the scalar properties including the magnitude of vectorial properties, such as molecular dipole moments. A rotation-equivariant MolNet_Equi model, proposed in this paper, understands and recognizes the molecular rotation in the 3D Euclidean space, and exhibits the ability to predict directional dipole moments in the rotation-sensitive mode, as well as showing superior performance for the prediction of scalar properties. Three consecutive operations of molecular rotation R M ${\left(R\left(M\right)\right)}$ , dipole-moment prediction φ µ R M ${\left({\phi{} }_{\mu }\left(R\left(M\right)\right)\right)}$ , and dipole-moment inverse-rotation R - 1 φ µ R M ${\left({R}^{-1}\left({\phi{} }_{\mu }\left(R\left(M\right)\right)\right)\right)}$ do not alter the original prediction of the total dipole moment of a molecule φ µ M ${\left({\phi{} }_{\mu }\right(M\left)\right)}$ , assuring the rotational equivariance of MolNet_Equi. Furthermore, MolNet_Equi faithfully predicts the absolute direction of dipole moments given molecular poses, albeit the model has been trained only with the information on dipole-moment magnitudes, not directions. This work highlights the potential of incorporating fundamental yet crucial chemical rules and concepts into DL models, leading to the development of chemically intuitive models.

MolNet: A Chemically Intuitive Graph Neural Network for Prediction of Molecular Properties.

Most graph neural networks (GNNs) in deep-learning chemistry collect and update atom and molecule features from the fed atom (and, in some cases, bond) features, basically based on the two-dimensional (2D) graph representation of 3D molecules. However, the 2D-based models do not faithfully represent 3D molecules and their physicochemical properties, exemplified by the overlooked field effect that is a "through-space" effect, not a "through-bond" effect. We propose a GNN model, denoted as MolNet, which accommodates the 3D non-bond information in a molecule, via a noncovalent adjacency matrix A ‾ , and also bond-strength information from a weighted bond matrix B . Comparative studies show that MolNet outperforms various baseline GNN models and gives a state-of-the-art performance in the classification task of BACE dataset and regression task of ESOL dataset. This work suggests a future direction for the construction of deep-learning models that are chemically intuitive and compatible with the existing chemistry concepts and tools.

Thermodynamics of d-dimensional hard sphere fluids confined to micropores.

We derive an analytical expression of the second virial coefficient of d-dimensional hard sphere fluids confined to slit pores by applying Speedy and Reiss' interpretation of cavity space. We confirm that this coefficient is identical to the one obtained from the Mayer cluster expansion up to second order with respect to fugacity. The key step of both approaches is to evaluate either the surface area or the volume of the d-dimensional exclusion sphere confined to a slit pore. We, further, present an analytical form of thermodynamic functions such as entropy and pressure tensor as a function of the size of the slit pore. Molecular dynamics simulations are performed for d = 2 and d = 3, and the results are compared with analytically obtained equations of state. They agree satisfactorily in the low density regime, and, for given density, the agreement of the results becomes excellent as the width of the slit pore gets smaller, because the higher order virial coefficients become unimportant.

Rotational Variance-Based Data Augmentation in 3D Graph Convolutional Network.

This work proposes the data augmentation by molecular rotation, with consideration that the protein-ligand binding events are rotation-variant. As a proof-of-concept, known active (i. e., 1-labeled) ligands to human ß-secretase 1 (BACE-1) are rotated for the generation of 0-labeled data, and the rotation-dependent prediction accuracy of 3D graph convolutional network (3DGCN) is investigated after data augmentation. The data augmentation makes the orientation-recognizing ability of 3DGCN improved significantly in the classification task for BACE-1/ligand binding. Furthermore, the data-augmented 3DGCN has a capability for predicting active ligands from a candidate dataset, via improved performance of orientation recognition, which would be applied to virtual drug screening and discovery.

Layer-wise relevance propagation of InteractionNet explains protein-ligand interactions at the atom level.

Development of deep-learning models for intermolecular noncovalent (NC) interactions between proteins and ligands has great potential in the chemical and pharmaceutical tasks, including structure-activity relationship and drug design. It still remains an open question how to convert the three-dimensional, structural information of a protein-ligand complex into a graph representation in the graph neural networks (GNNs). It is also difficult to know whether a trained GNN model learns the NC interactions properly. Herein, we propose a GNN architecture that learns two distinct graphs-one for the intramolecular covalent bonds in a protein and a ligand, and the other for the intermolecular NC interactions between the protein and the ligand-separately by the corresponding covalent and NC convolutional layers. The graph separation has some advantages, such as independent evaluation on the contribution of each convolutional step to the prediction of dissociation constants, and facile analysis of graph-building strategies for the NC interactions. In addition to its prediction performance that is comparable to that of a state-of-the art model, the analysis with an explainability strategy of layer-wise relevance propagation shows that our model successfully predicts the important characteristics of the NC interactions, especially in the aspect of hydrogen bonding, in the chemical interpretation of protein-ligand binding.

Theoretical study of the microscopic origin of magnetocrystalline anisotropy in Fe16N2 and its alloys: comparison with the other L10 alloys.

We study the magnetocrystalline anisotropy (MCA) energy of Fe16-n X n N2 ([Formula: see text]), where X = Ti, V, Cr, Mn, Co, Ni, Cu. To understand the microscopic origin and basic mechanism controlling the MCA energy of Fe16-n X n N2, we first examined the behavior of the MCA energy of Fe16N2, focusing on the spin-orbit coupling (SOC), and compared the behavior with other alloy systems (FeCo, FePt and CoPt) with L10 structure. We find that whereas the MCA energy of FeCo is determined by the spin-conserved terms of the SOC energy, the MCA energy of Fe16N2 is determined by mutual competition between spin-conserved and spin-flip terms. We then studied the effect of the transition element X on the phase stability and MCA of Fe16-n X n N2. The MCA energy and cohesive energy are calculated to determine the most stable configuration for each choice of X and n, and compared with those of Fe16N2. For X = V and Cu, both the MCA and phase stability improved noticeably. For X = Co, the MCA energy improves, but Fe16-n Co n N2 is less stable than Fe16N2. The microscopic mechanism underlying the MCA energy enhancement due to X = V, Cu and Co in Fe16-n X n N2 was studied by examining the data for spin- and site-resolved projected density of states (PDOS), as well as each spin-conserved and spin-flip terms contributing to the SOC energy.

Effects of nonmagnetic impurities on the spin transport property of a graphene nanoribbon device.

Using a nonequilibrium density functional calculation, we investigated the electronic transport properties and fundamental mechanism of spin polarization as a function of the location of impurities from the center to an edge of a graphene nanoribbon device (GND) with zigzag edges. A center-located impurity enables both edges to be enhanced with respect to their spin transports whereas an edge-located impurity results in only the opposite edge channel being dominant. In the case of a center-located impurity, the ferromagnetic ground state induces new spin states near the Fermi level responsible for the spin-polarized current in the GND. We argue that the spin-polarized current can flow through the edge states induced by a nonmagnetic impurity around the Fermi level, especially on a GND with a center-located impurity.

Electronic Structure and Band Alignments of Various Phases of Titania Using the Self-Consistent Hybrid Density Functional and DFT+U Methods.

To understand, and thereby rationally optimize photoactive interfaces, it is of great importance to elucidate the electronic structures and band alignments of these interfaces. For the first-principles investigation of these properties, conventional density functional theory (DFT) requires a solution to mitigate its well-known bandgap underestimation problem. Hybrid functional and Hubbard U correction are computationally efficient methods to overcome this limitation, however, the results are largely dependent on the choice of parameters. In this study, we employed recently developed self-consistent approaches, which enable non-empirical determination of the parameters, to investigate TiO2 interfacial systems-the most prototypical photocatalytic systems. We investigated the structural, electronic, and optical properties of rutile and anatase phases of TiO2. We found that the self-consistent hybrid functional method predicts the most reliable structural and electronic properties that are comparable to the experimental and high-level GW results. Using the validated self-consistent hybrid functional method, we further investigated the band edge positions between rutile and anatase surfaces in a vacuum and electrolyte medium, by coupling it with the Poisson-Boltzmann theory. This suggests the possibility of a transition from the straddling-type to the staggered-type band alignment between rutile and anatase phases in the electrolyte medium, manifested by the formation of a Stern-like layer at the interfaces. Our study not only confirms the efficacy of the self-consistent hybrid functional method by reliably predicting the electronic structure of photoactive interfaces, but also elucidates a potentially dramatic change in the band edge positions of TiO2 in aqueous electrolyte medium which can extensively affect its photophysical properties.

Wall-mediated self-diffusion in slit and cylindrical pores.

Analytical and numerical simulation studies are performed on the diffusion of simple fluids in both thin slits and long cylindrical pores. In the region of large Knudsen numbers, where the wall-particle collisions outnumber the intermolecular collisions, we obtain analytical results for the self-diffusion coefficients for both slit and cylindrical pore shapes. The results show anomalous behavior of the mean square displacement and the velocity autocorrelation for the case of slits, unlike the case of cylindrical pores which shows standard Fick's law. Molecular dynamics simulations confirm the analytical results. We further study the wall-mediated diffusion behavior conducted by a Smoluchowski thermal wall and compare with our analytical results obtained from the stochastic thermal wall model proposed by Mon and Percus.

Spin transport in spin filtering magnetic tunneling junctions.

Taking into account spin-orbit coupling and s-d interaction, we investigate spin transport properties of the magnetic tunneling junctions with spin filtering barrier using Landauer-Büttiker formalism implemented with the recursive algorithm to calculate the real-space Green function. We predict completely different bias dependence of negative tunnel magnetoresistance (TMR) between the systems composed of nonmagnetic electrode (NM)/ferromagnetic barrier (FB)/ferromagnet (FM) and NM/FB/FM/NM spin filtering tunnel junctions (SFTJs). Analyses of the results provide us possible ways of designing the systems which modulate the TMR in the negative magnetoresistance regime.

Spin-polarized current of a transistor in single Mn12 molecular magnets.

Focusing on the framework of how to realize the molecular spintronics in a single molecular magnet, we present theoretical studies on the spin-polarized quantum transport behavior through a single Mn12 molecular magnet. Our theoretical results were obtained by carrying out density functional theoretical calculation within the Keldysh nonequilibrium Green function formalism. The ultimate goal of the molecular spintronics is to develop single molecule transistors which generate spin-polarized currents through the molecular magnet. We obtained the density of states, the transmission coefficients and the characteristic features of the current-voltage (I-V) on the spin-polarized transport properties of Mn12 by the theoretical calculation. These results show the possibility for the realization of molecular spintroinics using single molecular magnets.

Lyapunov instability of rigid diatomic molecules in three dimensions: a simpler method.

We present a method to calculate Lyapunov exponents of rigid diatomic molecules in three dimensions ( 12N -dimensional phase space). The spectra of Lyapunov exponents are obtained for 32 rigid diatomic molecules interacting through the Weeks-Chandler-Anderson potential for various bond length and densities, and compared with those of Shin [Phys. Rev. E 64, 041106 (2001)]. Our algorithm is easy to implement and total CPU time is relatively inexpensive.

Numerical method for solving stochastic differential equations with Poissonian white shot noise.

We propose a numerical integration scheme to solve stochastic differential equations driven by Poissonian white shot noise. Our formula, which is based on an integral equation, which is equivalent to the stochastic differential equation, utilizes a discrete time approximation with fixed integration time step. We show that our integration formula approaches the Euler formula if the Poissonian noise approaches the Gaussian white noise. The accuracy and efficiency of the proposed algorithm are examined by studying the dynamics of an overdamped particle driven by Poissonian white shot noise in a spatially periodic potential. We find that the accuracy of the proposed algorithm only weakly depends on the parameters characterizing the Poissonian white shot noise; this holds true even if the limit of Gaussian white noise is approached.