Time-dependent principal component analysis: A unified approach to high-dimensional data reduction using adiabatic dynamics.

Systematic reduction of the dimensionality is highly demanded in making a comprehensive interpretation of experimental and simulation data. Principal component analysis (PCA) is a widely used technique for reducing the dimensionality of molecular dynamics (MD) trajectories, which assists our understanding of MD simulation data. Here, we propose an approach that incorporates time dependence in the PCA algorithm. In the standard PCA, the eigenvectors obtained by diagonalizing the covariance matrix are time independent. In contrast, they are functions of time in our new approach, and their time evolution is implemented in the framework of Car-Parrinello or Born-Oppenheimer type adiabatic dynamics. Thanks to the time dependence, each of the step-by-step structural changes or intermittent collective fluctuations is clearly identified, which are often keys to provoking a drastic structural transformation but are easily masked in the standard PCA. The time dependence also allows for reoptimization of the principal components (PCs) according to the structural development, which can be exploited for enhanced sampling in MD simulations. The present approach is applied to phase transitions of a water model and conformational changes of a coarse-grained protein model. In the former, collective dynamics associated with the dihedral-motion in the tetrahedral network structure is found to play a key role in crystallization. In the latter, various conformations of the protein model were successfully sampled by enhancing structural fluctuation along the periodically optimized PC. Both applications clearly demonstrate the virtue of the new approach, which we refer to as time-dependent PCA.

Adsorption of toxic gases on silicene/Ag(111).

Silicene is a two-dimensional nanomaterial, composed of Si atoms arranged into a buckled honeycomb network. It has become of great interest in recent years due to its remarkable properties such as its natural compatibility with current silicon-based technology. Due to its extreme thinness on the nanoscale, and large lateral dimensions, it has potential applications in gas sensing, gas storage and components in modern electronic devices. In this work, density functional theory calculations and ab initio molecular dynamics simulations are used to examine the reaction of SO2, NO2 and H2S on the Si/Ag(111) surface. It was shown that each gas will adsorb on the surface in different orientations and adsorption sites. SO2 and NO2 were found to chemisorb on the surface, whereas H2S was found to physisorb. SO2 and H2S adsorb associatively, whereas NO2 readily dissociates, producing adsorbed oxygen, and gaseous NO. At elevated temperatures, the SO2 and NO2 remain strongly bound to the surface, resulting in poisoning of the silicene, while H2S readily desorbs. Ab initio molecular dynamics also show that NO2 will selectively bind before SO2 when both gases are present in the same environment. This work shows that Si/Ag(111) may provide useful properties for gas sensing and storage applications.

Tuning the work function of the silicene/4 × 4 Ag(111) surface.

Silicene, the silicon analog of graphene, is an atomically thin two-dimensional material with promising applications in gas sensing, storage and as components in modern electronic devices. Silicene epitaxially grown on the Ag(111) surface can expand the utility of the silver surface by enabling the tuning of its work function through the functionalisation of silicene. Here we examine the electronic and structural properties and the thermodynamic stability of functionalised silicene/4 × 4 Ag(111) using density functional theory calculations coupled with ab initio molecular dynamics (AIMD) simulations. We focus on 11 functional groups, namely phenyl, methyl, hydroxyl, cyano, methoxyl, amino and ethylmethylamine, in addition to 4 halogen atoms. These functional groups are shown to endow the Si/Ag(111) surface with a large variation in the work function. Our AIMD simulations confirm the thermodynamic stability of these 11 functionalised structures. This work shows the possibility of tuning the electronic structure of silicene by functionalisation, which could then be utilized in polymer solar cells and nanoelectronic circuit components.

Chemical modification of group IV graphene analogs.

Mono-elemental two-dimensional (2D) crystals (graphene, silicene, germanene, stanene, and so on), termed 2D-Xenes, have been brought to the forefront of scientific research. The stability and electronic properties of 2D-Xenes are main challenges in developing practical devices. Therefore, in this review, we focus on 2D free-standing group-IV graphene analogs (graphene quantum dots, silicane, and germanane) and the functionalization of these sheets with organic moieties, which could be handled under ambient conditions. We highlight the present results and future opportunities, functions and applications, and novel device concepts.

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.

Tuning the band gap of silicene by functionalisation with naphthyl and anthracyl groups.

Silicene is a relatively new material consisting of a two-dimensional sheet of silicon atoms. Functionalisation of silicene with different chemical groups has been suggested as a way to tune its electronic properties. In this work, density functional theory calculations and ab initio molecular dynamics simulations are used to examine the effects of functionalisation with naphthyl or anthracyl groups, which are two examples of small polycyclic aromatic hydrocarbons (PAHs). Different attachment positions on the naphthyl and anthracyl groups were compared, as well as different thicknesses of the silicene nanosheet. It was found that the carbon attachment position farthest from the bond fusing the aromatic rings gave the more stable structures for both functional groups. All structures showed direct band gaps, with tuning of the band gap being achievable by increasing the length of the PAH or the thickness of the silicene. Hence, modifying the functional group or thickness of the silicene can both be used to alter the electronic properties of silicene making it a highly promising material for use in future electronic devices and sensors.

An ab initio approach to free-energy reconstruction using logarithmic mean force dynamics.

We present an ab initio approach for evaluating a free energy profile along a reaction coordinate by combining logarithmic mean force dynamics (LogMFD) and first-principles molecular dynamics. The mean force, which is the derivative of the free energy with respect to the reaction coordinate, is estimated using density functional theory (DFT) in the present approach, which is expected to provide an accurate free energy profile along the reaction coordinate. We apply this new method, first-principles LogMFD (FP-LogMFD), to a glycine dipeptide molecule and reconstruct one- and two-dimensional free energy profiles in the framework of DFT. The resultant free energy profile is compared with that obtained by the thermodynamic integration method and by the previous LogMFD calculation using an empirical force-field, showing that FP-LogMFD is a promising method to calculate free energy without empirical force-fields.

Ab Initio Characterization of the CO2-Water Interface Using Unsupervised Machine Learning for Dimensionality Reduction.

Precise characterization of the supercritical CO2-water interface under high pressure and temperature conditions is crucial for the geological storage of carbon dioxide (CO2) in deep saline aquifers. Molecular dynamics (MD) simulations offer a valuable approach to gaining insight into the CO2-water interface at a microscopic level. However, no attempt has been made to characterize the CO2-water interface with the accuracy afforded by ab initio calculations. In this study, we performed ab initio MD (AIMD) simulations to investigate the structural and dynamical properties of the CO2-water interface, comparing the results with those obtained from classical force-field MD (FF-MD) simulations. Molecular orientation at the interface was well reproduced in both AIMD and FF-MD simulations. Characteristic structural fluctuations of water at the interface were unveiled by applying multidimensional scaling and time-dependent principal component analysis to the AIMD trajectories; however, they were not prominent in the FF-MD simulations. Furthermore, our study demonstrated a marked difference in the residence time of molecules in the interface region between AIMD and FF-MD simulations, indicating that time-dependent properties of the CO2-water interface strongly depend on the description of the intermolecular forces.

Atomic-Scale Insights into the Phase Behavior of Carbon Dioxide and Water from 313 to 573 K and 8 to 30 MPa.

We performed molecular dynamics (MD) simulations of CO2 + H2O systems by employing widely used force fields (EPM2, TraPPE, and PPL models for CO2; SPC/E and TIP4P/2005 models for H2O). The phase behavior observed in our MD simulations is consistent with the coexistence lines obtained from previous experiments and SAFT-based theoretical models for the equations of state. Our structural analysis reveals a pronounced correlation between phase transitions and the structural orderliness. Specifically, the coordination number of Ow (oxygen in H2O) around other Ow significantly correlates with phase changes. In contrast, coordination numbers pertaining to the CO2 molecules show less sensitivity to the thermodynamic state of the system. Furthermore, our data indicate that a predominant number of H2O molecules exist as monomers without forming hydrogen bonds, particularly in a CO2-rich mixture, signaling a breakdown in the hydrogen bond network's orderliness, as evidenced by a marked decrease in tetrahedrality. These insights are crucial for a deeper atomic-level understanding of phase behaviors, contributing to the well-grounded design of CO2 injection under high-pressure and high-temperature conditions, where an atomic-scale perspective of the phase behavior is still lacking.

On-the-fly reconstruction of free-energy profiles using logarithmic mean-force dynamics.

Mean-force dynamics (MFD), which is a fictitious dynamics for a set of collective variables on a potential of mean-force, is a powerful algorithm to efficiently explore free-energy landscapes. Recently, we have introduced logarithmic MFD (LogMFD) (Morishita et al., Phys. Rev. E 2012, 85, 066702) which overcomes difficulties encounterd in free-energy calculations using standard approaches such as thermodynamic integration. Here, we present a guide to implementing LogMFD calculations paying attention to the practical issues in choosing the parameters in LogMFD. A primary focus is given to the effect of the parameters on the accuracy of the reconstructed free-energy profiles. A recipe for reducing the errors due to energy dissipation is presented. We also demonstrate that multidimensional free-energy landscapes can be reconstructed on-the-fly using LogMFD, which cannot be accomplished using any other free-energy calculation techniques.

Decomposition-order effects of time integrator on ensemble averages for the Nosé-Hoover thermostat.

Decomposition-order dependence of time development integrator on ensemble averages for the Nosé-Hoover dynamics is discussed. Six integrators were employed for comparison, which were extensions of the velocity-Verlet or position-Verlet algorithm. Molecular dynamics simulations by these integrators were performed for liquid-argon systems with several different time steps and system sizes. The obtained ensemble averages of temperature and potential energy were shifted from correct values depending on the integrators. These shifts increased in proportion to the square of the time step. Furthermore, the shifts could not be removed by increasing the number of argon atoms. We show the origin of these ensemble-average shifts analytically. Our discussion can be applied not only to the liquid-argon system but also to all MD simulations with the Nosé-Hoover thermostat. Our recommended integrators among the six integrators are presented to obtain correct ensemble averages.

First-principles molecular dynamics at a constant electrode potential.

A simulation scheme for performing first-principles molecular dynamics at a constant electrode potential is presented, opening the way for a more realistic modeling of voltage-driven devices. The system is allowed to exchange electrons with a reservoir at fixed potential, and dynamical equations for the total electronic charge are derived by using the potential energy of the extended system. In combination with a thermostat, this potentiostat scheme reproduces thermal fluctuations of the charge with the correct statistics, implying a realistic treatment of the potential as a control variable. Practically, the dynamics of the charge are decoupled from the electronic structure calculations, making the scheme easily implementable in existing first-principles molecular dynamics codes. Our approach is demonstrated on a test system by considering various test cases.

Compressed exponential relaxation in liquid silicon: universal feature of the crossover from ballistic to diffusive behavior in single-particle dynamics.

We report a first-principles molecular-dynamics study of the relaxation dynamics in liquid silicon (l-Si) over a wide temperature range (1000-2200 K). We find that the intermediate scattering function for l-Si exhibits a compressed exponential decay above 1200 K including the supercooled regime, which is in stark contrast to that for normal "dense" liquids which typically show stretched exponential decay in the supercooled regime. The coexistence of particles having ballistic-like motion and those having diffusive-like motion is demonstrated, which accounts for the compressed exponential decay in l-Si. An attempt to elucidate the crossover from the ballistic to the diffusive regime in the "time-dependent" diffusion coefficient is made and the temperature-independent universal feature of the crossover is disclosed.

The electronic and structural properties of novel organomodified Si nanosheets.

We show that the properties of a new class of functional materials, silicon nanosheets modified with phenyl groups and H atoms, are highly promising for applications such as electronic devices. This novel material retains the sp(3) structure after functionalisation, resulting in a wide (direct) band gap of 1.92 eV.

Relationship between diffraction peak, network topology, and amorphous-forming ability in silicon and silica.

The network topology in disordered materials is an important structural descriptor for understanding the nature of disorder that is usually hidden in pairwise correlations. Here, we compare the covalent network topology of liquid and solidified silicon (Si) with that of silica (SiO2) on the basis of the analyses of the ring size and cavity distributions and tetrahedral order. We discover that the ring size distributions in amorphous (a)-Si are narrower and the cavity volume ratio is smaller than those in a-SiO2, which is a signature of poor amorphous-forming ability in a-Si. Moreover, a significant difference is found between the liquid topology of Si and that of SiO2. These topological features, which are reflected in diffraction patterns, explain why silica is an amorphous former, whereas it is impossible to prepare bulk a-Si. We conclude that the tetrahedral corner-sharing network of AX2, in which A is a fourfold cation and X is a twofold anion, as indicated by the first sharp diffraction peak, is an important motif for the amorphous-forming ability that can rule out a-Si as an amorphous former. This concept is consistent with the fact that an elemental material cannot form a bulk amorphous phase using melt quenching technique.

Structural, electronic, and vibrational properties of high-density amorphous silicon: a first-principles molecular-dynamics study.

We report a first-principles study of the structural, electronic, and dynamical properties of high-density amorphous (HDA) silicon, which was found to be formed by pressurizing low-density amorphous (LDA) silicon (a normal amorphous Si) [T. Morishita, Phys. Rev. Lett. 93, 055503 (2004); P. F. McMillan, M. Wilson, D. Daisenberger, and D. Machon, Nature Mater. 4, 680 (2005)]. Striking structural differences between HDA and LDA are revealed. The LDA structure holds a tetrahedral network, while the HDA structure contains a highly distorted tetrahedral network. The fifth neighboring atom in HDA tends to be located at an interstitial position of a distorted tetrahedron composed of the first four neighboring atoms. Consequently, the coordination number of HDA is calculated to be approximately 5 unlike that of LDA. The electronic density of state (EDOS) shows that HDA is metallic, which is consistent with a recent experimental measurement of the electronic resistance of HDA Si. We find from local EDOS that highly distorted tetrahedral configurations enhance the metallic nature of HDA. The vibrational density of state (VDOS) also reflects the structural differences between HDA and LDA. Some of the characteristic vibrational modes of LDA are dematerialized in HDA, indicating the degradation of covalent bonds. The overall profile of the VDOS for HDA is found to be an intermediate between that for LDA and liquid Si under pressure (high-density liquid Si).

Structural and dynamical heterogeneity in deeply supercooled liquid silicon.

We report on a first-principles molecular-dynamics study of structural and dynamical heterogeneity in supercooled liquid silicon. We find that highly tetrahedral configurations are intermittently formed and that spatially heterogeneous dynamics is concurrently induced in the deeply supercooled state (1000 K). This heterogeneity is responsible for the anomalous structural relaxation characterized by the stretched-exponential function. The temporal structural fluctuation is found to give rise to the 1/f dependence in the corresponding power spectral density. In a moderately supercooled state (1600 K), the structural and dynamical heterogeneity is quite weak, in contrast to the deeply supercooled state. The applicability of the Stillinger-Weber potential to the deeply supercooled state is also discussed.

Free Energy Reconstruction from Logarithmic Mean-Force Dynamics Using Multiple Nonequilibrium Trajectories.

Efficient and reliable estimation of the mean force (MF), the derivatives of the free energy with respect to a set of collective variables (CVs), has been a challenging problem because free energy differences are often computed by integrating the MF. Among various methods for computing free energy differences, logarithmic mean-force dynamics (LogMFD) [ Morishita et al., Phys. Rev. E 2012 , 85 , 066702 ] invokes the conservation law in classical mechanics to integrate the MF, which allows us to estimate the free energy profile along the CVs on-the-fly. Here, we present a method called parallel dynamics, which improves the estimation of the MF by employing multiple replicas of the system and is straightforwardly incorporated in LogMFD or a related method. In the parallel dynamics, the MF is evaluated by a nonequilibrium path-ensemble using the multiple replicas based on the Crooks-Jarzynski nonequilibrium work relation. Thanks to the Crooks relation, realizing full-equilibrium states is no longer mandatory for estimating the MF. Additionally, sampling in the hidden subspace orthogonal to the CV space is highly improved with appropriate weights for each metastable state (if any), which is hardly achievable by typical free energy computational methods. We illustrate how to implement parallel dynamics by combining it with LogMFD, which we call logarithmic parallel dynamics (LogPD). Biosystems of alanine dipeptide and adenylate kinase in explicit water are employed as benchmark systems to which LogPD is applied to demonstrate the effect of multiple replicas on the accuracy and efficiency in estimating the free energy profiles using parallel dynamics.

[A case of spontaneous epidural emphysema occurring during sleep].

A 19-year-old man consulted a doctor for swelling of his neck and shortness of breath. The day before, he woke up with a slight cough and upper chest pain early in the morning. He went to school and spent the day as usual. He did not have a history of asthma or violent cough. The next day, chest radiography showed subcutaneous emphysema and pneumomediastinum. Computed tomography not only confirmed the presence of mediastinal and subcutaneous air, but also demonstrated a linear radiolucent stripe in the spinal canal corresponding to epidural emphysema. The patient did not have any neurologic findings. His general condition remained good except that his arterial blood oxygen saturation slightly decreased to 95%. Laboratory data were normal, except for serum IgE, which was elevated (2072 IU/ml). He stayed at rest and was treated conservatively and his symptoms improved within a few days. Seven days later, the intraspinal air and pneumomediastinum had resolved spontaneously on follow-up chest computed tomography (CT).

Monolayer-to-bilayer transformation of silicenes and their structural analysis.

Silicene, a two-dimensional honeycomb network of silicon atoms like graphene, holds great potential as a key material in the next generation of electronics; however, its use in more demanding applications is prevented because of its instability under ambient conditions. Here we report three types of bilayer silicenes that form after treating calcium-intercalated monolayer silicene (CaSi2) with a BF4(-) -based ionic liquid. The bilayer silicenes that are obtained are sandwiched between planar crystals of CaF2 and/or CaSi2, with one of the bilayer silicenes being a new allotrope of silicon, containing four-, five- and six-membered sp(3) silicon rings. The number of unsaturated silicon bonds in the structure is reduced compared with monolayer silicene. Additionally, the bandgap opens to 1.08 eV and is indirect; this is in contrast to monolayer silicene which is a zero-gap semiconductor.