Derivation of the Invariant Free-Energy Landscape Based on Langevin Dynamics.

A conventionally defined free-energy landscape (FEL) exhibits unphysical dependence on the choice of reaction coordinates and hence lacks universal predictive ability. We here show that three physically plausible requirements uniquely determine the FEL formula for a given reaction coordinate. Our FEL is expressed solely in terms of quantities obtained through time-series data analysis, namely, the probability distribution and the diffusion matrix. It is free from any unphysical coordinate dependence and coincides with the conventional FEL in special cases. The uniqueness and robustness of the formula strongly suggest that our FEL has universal predictive power.

Reproducing the Reaction Route Map on the Shape Space from Its Quotient by the Complete Nuclear Permutation-Inversion Group.

This study develops an algorithm to reproduce reaction route maps (RRMs) in the shape space from the outputs of potential search algorithms. To demonstrate the algorithm, global reaction route mapping is utilized as a potential search algorithm, but the proposed algorithm should work with other potential search algorithms in principle. The proposed algorithm does not require any encoding of the molecular configurations and is thus applicable to complicated realistic molecules for which efficient encoding is not readily available. We show that subgraphs of an RRM mapped to each other by the action of the symmetry group are isomorphic and also provide an algorithm to compute the set of feasible transformations in the sense of Longuet-Higgins. We demonstrate the proposed algorithm in toy models and in more realistic molecules. Finally, we remark on absolute rate theory from our perspective.

Characterizing Reaction Route Map of Realistic Molecular Reactions Based on Weight Rank Clique Filtration of Persistent Homology.

A reaction route map (RRM) constructed using the GRRM program is a collection of elementary reaction pathways, each of which comprises two equilibrium (EQ) geometries and one transition state (TS) geometry connected by an intrinsic reaction coordinate (IRC). An RRM can be mathematically represented by a graph with weights assigned to both vertices, corresponding to EQs, and edges, corresponding to TSs, representing the corresponding energies. In this study, we propose a method to extract topological descriptors of a weighted graph representing an RRM based on persistent homology (PH). The work of Mirth et al. [ J. Chem. Phys. 2021, 154, 114114], in which PH analysis was applied to the (3N - 6)-dimensional potential energy surface of an N atomic system, is related to the present method, but our method is practically applicable to realistic molecular reactions. Numerical assessments revealed that our method can extract the same information as the method proposed by Mirth et al. for the 0-th and 1-st PHs, except for the death of the 1-st PH. In addition, the information obtained from the 0-th PH corresponds to the analysis using the disconnectivity graph. The results of this study suggest that the descriptors obtained using the proposed method accurately reflect the characteristics of the chemical reactions and/or physicochemical properties of the system.

Development of Magnetocardiograph without Magnetically Shielded Room Using High-Detectivity TMR Sensors.

A magnetocardiograph that enables the clear observation of heart magnetic field mappings without magnetically shielded rooms at room temperatures has been successfully manufactured. Compared to widespread electrocardiographs, magnetocardiographs commonly have a higher spatial resolution, which is expected to lead to early diagnoses of ischemic heart disease and high diagnostic accuracy of ventricular arrhythmia, which involves the risk of sudden death. However, as the conventional superconducting quantum interference device (SQUID) magnetocardiographs require large magnetically shielded rooms and huge running costs to cool the SQUID sensors, magnetocardiography is still unfamiliar technology. Here, in order to achieve the heart field detectivity of 1.0 pT without magnetically shielded rooms and enough magnetocardiography accuracy, we aimed to improve the detectivity of tunneling magnetoresistance (TMR) sensors and to decrease the environmental and sensor noises with a mathematical algorithm. The magnetic detectivity of the TMR sensors was confirmed to be 14.1 pTrms on average in the frequency band between 0.2 and 100 Hz in uncooled states, thanks to the original multilayer structure and the innovative pattern of free layers. By constructing a sensor array using 288 TMR sensors and applying the mathematical magnetic shield technology of signal space separation (SSS), we confirmed that SSS reduces the environmental magnetic noise by -73 dB, which overtakes the general triple magnetically shielded rooms. Moreover, applying digital processing that combined the signal average of heart magnetic fields for one minute and the projection operation, we succeeded in reducing the sensor noise by about -23 dB. The heart magnetic field resolution measured on a subject in a laboratory in an office building was 0.99 pTrms and obtained magnetocardiograms and current arrow maps as clear as the SQUID magnetocardiograph does in the QRS and ST segments. Upon utilizing its superior spatial resolution, this magnetocardiograph has the potential to be an important tool for the early diagnosis of ischemic heart disease and the risk management of sudden death triggered by ventricular arrhythmia.

Effect of the cation on the stability of cation-glyme complexes and their interactions with the [TFSA]- anion.

The interactions of glymes with alkali or alkaline earth metal cations depend strongly on the metal cations. For example, the stabilization energies (Eform) calculated for the formation of cation-triglyme (G3) complexes with Li+, Na+, K+, Mg2+, and Ca2+ at the MP2/6-311G** level were -95.6, -66.4, -52.5, -255.0, and -185.0 kcal mol-1, respectively, and those for the cation-tetraglyme (G4) complexes were -107.7, -76.3, -60.9, -288.3 and -215.0 kcal mol-1, respectively. The electrostatic and induction interactions are the major source of the attraction in the complexes; the contribution of the induction interactions to the attraction is especially significant in the divalent cation-glyme complexes. The binding energies of the cation-G3 complexes with Li+, Na+, K+, Mg2+, and Ca2+ and the bis(trifluoromethylsulfonyl)amide anion ([TFSA]-) were -83.9, -86.6, -80.0, -196.1, and -189.5 kcal mol-1, respectively, and they are larger than the binding energies of the corresponding cation-G4 complexes (-73.6, -75.0, -77.4, -172.1, and -177.2 kcal mol-1, respectively). The binding energies and conformational flexibility of the cation-glyme complexes also affect the melting points of equimolar mixtures of glyme and TFSA salts. Furthermore, the interactions of the metal cations with the oxygen atoms of glymes significantly decrease the HOMO energy levels of glymes. The HOMO energy levels of glymes in the cation-glyme-TFSA complexes are lower than those of isolated glymes, although they are higher than those of the cation-glyme complexes.

Hierarchical structures of amorphous solids characterized by persistent homology.

This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the PDs is given by an atomic configuration and the output is expressed as 2D histograms. Then, specific distributions such as curves and islands in the PDs identify meaningful shape characteristics of the atomic configuration. Although the method can be applied to a wide variety of disordered systems, it is applied here to silica glass, the Lennard-Jones system, and Cu-Zr metallic glass as standard examples of continuous random network and random packing structures. In silica glass, the method classified the atomic rings as short-range and medium-range orders and unveiled hierarchical ring structures among them. These detailed geometric characterizations clarified a real space origin of the first sharp diffraction peak and also indicated that PDs contain information on elastic response. Even in the Lennard-Jones system and Cu-Zr metallic glass, the hierarchical structures in the atomic configurations were derived in a similar way using PDs, although the glass structures and properties substantially differ from silica glass. These results suggest that the PDs provide a unified method that extracts greater depth of geometric information in amorphous solids than conventional methods.

Persistent homology and many-body atomic structure for medium-range order in the glass.

The characterization of the medium-range (MRO) order in amorphous materials and its relation to the short-range order is discussed. A new topological approach to extract a hierarchical structure of amorphous materials is presented, which is robust against small perturbations and allows us to distinguish it from periodic or random configurations. This method is called the persistence diagram (PD) and introduces scales to many-body atomic structures to facilitate size and shape characterization. We first illustrate the representation of perfect crystalline and random structures in PDs. Then, the MRO in amorphous silica is characterized using the appropriate PD. The PD approach compresses the size of the data set significantly, to much smaller geometrical summaries, and has considerable potential for application to a wide range of materials, including complex molecular liquids, granular materials, and metallic glasses.

A guiding potential method for evaluating the bending rigidity of tensionless lipid membranes from molecular simulation.

A new method is proposed to estimate the bending rigidity of lipid membranes from molecular dynamics simulations. An external cylindrical guiding potential is used to impose a sinusoidal deformation to a planar membrane. The bending rigidity is obtained from the mean force acting on the cylinder by calibrating against a discretized Helfrich model that accounts for thermal fluctuations of the membrane surface. The method has been successfully applied to a dimyristoyl phosphatidylcholine bilayer simulated with a coarse-grained model. A well-converged bending rigidity was obtained for the tension-free membrane and showed reasonable agreement with that obtained from the height fluctuation spectrum.

Method of evaluating curvature-dependent elastic parameters for small unilamellar vesicles using molecular dynamics trajectory.

A numerical method is proposed for evaluating the curvature dependency of elastic parameters of a spherical vesicle based on a calculation of the pressure profile across the membrane. The proposed method is particularly useful for small unilamellar vesicles (SUVs), in which the internal structure of the membrane is asymmetric owing to the high curvature. In this case, the elastic energy is insufficiently described as a perturbation from a planar membrane. The calculated saddle-splay curvature modulus of SUVs, which is about 16 nm in diameter, is found to be much higher than that of a planar membrane. A comparison of the free energy change in the initial stage of vesicle-to-bicelle transformation with the Fromherz theory demonstrates that the elastic parameters estimated for SUVs provide better estimation of the free energy than those estimated for a planar membrane.

Novel numerical method for calculating the pressure tensor in spherical coordinates for molecular systems.

We propose a novel method for computing the pressure tensor along the radial axis of a molecular system with spherical symmetry. The proposed method uses the slice averaged pressure to improve the numerical stability and precision significantly. Simplified expressions of the local pressure are derived for a conventional molecular force field including non-bond, bond stretching, angle bending, and torsion interactions; these expressions are advantageous in terms of the computational cost. We also discuss an algorithm to avoid numerical singularity. Finally, the method is successfully applied to three different molecular systems, i.e., a water droplet in oil, a spherical micelle, and a liposome.

Fluctuation-response relation of many Brownian particles under nonequilibrium conditions.

We study many interacting Brownian particles under a tilted periodic potential. We numerically measure the linear response coefficient of the density field by applying a slowly varying potential transversal to the tilted direction. In equilibrium cases, the linear response coefficient is related to the intensity of density fluctuations in a universal manner, which is called a fluctuation-response relation. We then report numerical evidence that this relation holds even in nonequilibrium cases. This result suggests that Einstein's formula on density fluctuations can be extended to driven diffusive systems when the slowly varying potential is applied in a direction transversal to the driving force.

Experimental test of a new equality: measuring heat dissipation in an optically driven colloidal system.

Measurement of energy dissipation in small nonequilibrium systems is generally a difficult task. Recently, Harada and Sasa [Phys. Rev. Lett. 95, 130602 (2005)] derived an equality relating the energy dissipation rate to experimentally accessible quantities in nonequilibrium steady states described by the Langevin equation. Here, we show an experimental test of this new relation in an optically driven colloidal system. We find that this equality is validated to a fairly good extent, thus the irreversible work of a small system is estimated from readily obtainable quantities.

Systematic derivation of coarse-grained fluctuating hydrodynamic equations for many Brownian particles under nonequilibrium conditions.

We study the statistical properties of many Brownian particles under the influence of both a spatially homogeneous driving force and a periodic potential with period l in a two-dimensional space. In particular, we focus on two asymptotic cases lint<>l , where lint represents the interaction length between two particles. We derive fluctuating hydrodynamic equations describing the evolution of a coarse-grained density field defined on scales much larger than l for both cases. Using the obtained equations, we calculate the equal-time correlation functions of the density field to the lowest order of the interaction strength. We find that the system exhibits long-range correlation of the type r-d (d=2) for the case lint>>l , while no such behavior is observed for the case lint<

Anomalous time correlation in two-dimensional driven diffusive systems.

We study the time-correlation function of a density field in two-dimensional driven diffusive systems within the framework of fluctuating hydrodynamics. It is found that the time correlation exhibits power-law behavior in an intermediate time regime in the case that the fluctuation-dissipation relation is violated and that the power-law exponent depends on the extent of this violation. We obtain this result by employing a renormalization group method to treat a logarithmic divergence in time.