Kirkwood–Buff integrals of finite systems: shape effects

The Kirkwood–Buff (KB) theory provides an important connection between microscopic density fluctuations in liquids and macroscopic properties. Recently, Krüger et al. derived equations for KB integrals for finite subvolumes embedded in a reservoir. Using molecular simulation of finite systems, KB integrals can be computed either from density fluctuations inside such subvolumes, or from integrals of radial distribution functions (RDFs). Here, based on the second approach, we establish a framework to compute KB integrals for subvolumes with arbitrary convex shapes. This requires a geometric function w(x) which depends on the shape of the subvolume, and the relative position inside the subvolume. We present a numerical method to compute w(x) based on Umbrella Sampling Monte Carlo (MC). We compute KB integrals of a liquid with a model RDF for subvolumes with different shapes. KB integrals approach the thermodynamic limit in the same way: for sufficiently large volumes, KB integrals are a linear function of area over volume, which is independent of the shape of the subvolume.     

Instability of a two-dimensional Bose–Einstein condensate with Rashba spin–orbit coupling at finite temperature

We prove that in a two-dimensional homogeneous boson system with Rashba spin–orbit coupling, Bose–Einstein condensate with plane-wave order is unstable at finite temperature. The calculations are based on a nonlinear sigma model scheme. The density wave contributions to the thermal deletions are divergent in the infrared limit. The behavior of the divergence is different from that without spin–orbit coupling.     

Simulation of laminar–turbulent transition in compressible Taylor–Green flow basing on quasi-gas dynamic equations

We report the results of numerical simulation of laminar–turbulent transition in the Taylor–Green vortex for viscous compressible gas flow basing on quasi-gas-dynamic (QGD) equations. Here the QGD system is obtained by a temporal averaging of the Navier–Stokes equations. The additional dissipative terms in QGD system serve to model the effects of the unresolved subgrid scales. Comparison with direct numerical simulation and large eddy simulation reference data demonstrates that QGD numerical algorithm provides a uniform and adequate simulation of both laminar and turbulent evolution of the vortex for Reynolds numbers from 100 up to 5000, including transition.     

The expanded triangular Kitaev–Heisenberg model in the full parameter space

The classical Kitaev–Heisenberg model on the triangular lattice is investigated by simulation in its full parameter space together with the next-nearest neighboring Heisenberg interaction or the single-ion anisotropy. The variation of the system is demonstrated directly by the joint density of states (DOS) depending on energy and magnetization obtained from Wang–Landau algorithm. The Metropolis Monte Carlo simulation and the zero-temperature Glauber dynamics are performed to show the internal energy, the correlation functions and spin configurations at zero temperature. It is revealed that two types of DOS (U and inverse U) divide the whole parameter range into two main parts with antiferromagnetic and ferromagnetic features respectively. In the parameter range of U type DOS, the mixed frustration from the triangular geometry and the Kitaev interaction produces rich phases, which are influenced in different ways by the next-nearest neighboring Heisenberg interaction and the single-ion anisotropy.     

On the performance of DFT/MRCI-R and MR-MP2 in spin–orbit coupling calculations on diatomics and polyatomic organic molecules

ABSTRACT

We have investigated the performance of different multi-reference quantum chemical methods with regard to electronic excitation energies and spin–orbit matrix elements (SOMES). Among these methods are two variants of the combined density functional theory and multi-reference configuration interaction method (DFT/MRCI and DFT/MRCI-R) and a multi-reference second-order Møller–Plesset perturbation theory (MR-MP2) approach. Two variants of MR-MP2 have been tested based on either Hartree–Fock orbitals or Kohn–Sham orbitals of the BH-LYP density functional. In connection with the MR-MP2 approaches, the first-order perturbed wave functions have been employed in the evaluation of spin–orbit coupling. To validate our results, we assembled experimental excitation energies and SOMES of eight diatomic and fifteen polyatomic molecules. For some of the smaller molecules, we carried out calculations at the complete active space self-consistent field (CASSCF) level to obtain SOMEs to compare with. Excitation energies of the experimentally unknown states were assessed with respect to second-order perturbation theory corrected (CASPT2) values where available. Overall, we find a very satisfactory agreement between the excitation energies and the SOMEs obtained with the four approaches. For a few states, outliers with regard to the excitation energies and/or SOMEs are observed. These outliers are carefully analysed and traced back to the wave function composition.     

Reynolds-averaged Navier–Stokes initialization and benchmarking in shock-driven turbulent mixing

We investigate a strategy for benchmarking Reynolds-averaged Navier–Stokes (RANS) models by comparing moments extracted from averaged large eddy simulation (LES) data and those predicted directly by RANS. We consider the Besnard–Harlow–Rauenzahn (BHR) RANS approach designed for variable-density compressible flows, which has been previously applied to a wide variety of turbulence problems of interest. We focus on the model's ability to predict moments relevant to shock-driven material mixing. A prototypical inverse chevron shock tube configuration is considered, for which laboratory and previous LES studies are available for comparison and validation. We show that when appropriately initialized, BHR is capable of accurately capturing various characteristic integral measures of the flow; strategies for initialization are demonstrated while addressing sensitivity of BHR predictions to closure and initialization specifics, initial material interface conditions, and grid resolution. The reference simulations are performed using implicit LES based on the Los Alamos National Laboratory RAGE hydrodynamics code.     

Dynamical current–current correlation in two-dimensional parabolic Dirac systems

We theoretically investigate the current–current correlation of the two-dimensional (2D) parabolic Dirac system in hexogonal lattice. The analytical expressions of the random phase approximation (RPA) susceptibility, Ruderman–Kittel–Kasuya–Yosida (RKKY) Hamiltonian, and the diamagnetic orbital susceptibility in noninteracting case base on the density–density or current–current correlation function are derived and quantitatively analyzed. In noninteracting case, the dynamical polarization within RPA, and spin transverse susceptibility as well as the RKKY interaction (when close to the half-filling) are related to the current–current response in the 2D parabolic Dirac systems. Both the cases of anisotropic dispersion and isotropic dispersion are discussed.     

Analysis of the composition of Ti-based thin films deposited on silicon by means of self-ion assisted deposition

The composition of Ti-based thin films deposited on silicon using a self-ion assisted deposition (SIAD) method was investigated by utilising the Rutherford backscattering spectrometry technique and RUMP simulation code. The hydrogen affinity of the coatings produced by means of SIAD was investigated using the ¹H(¹⁵N, αγ)¹²C nuclear resonance reaction. The titanium–based films on silicon were found to have a high content of oxygen, carbon, hydrogen and substantial concentration of the substrate. Near 10% H content enrichment was found at the surface of coatings but no hydrogen enrichment at the coating–substrate interfaces was observed.     

Thermodynamic properties for the triangular-well fluid

The thermodynamic properties of the triangular-well fluid with a well range of up to twice the hard sphere diameter were studied by means of a new developed equation of state and molecular simulation. This EoS is based on the perturbation theory of Barker and Henderson with the first and second-order perturbation terms evaluated by molecular simulation and then a fit with a simple function based on the radial distribution function of the reference fluid. The thermodynamic properties for the triangular-well fluid were also obtained directly by Gibbs ensemble and NPT Monte Carlo simulations. Good agreement is observed between the proposed EoS and the molecular simulation results. A model for the triangular-well solid is also presented; this has been used to calculate the solid–liquid transition line. Very good agreement is obtained with previously report values for this line and for the triple point temperature and pressure.     

Density and bond-orientational relaxations in supercooled water

ABSTRACT

Recent computational studies have reported evidence of a metastable liquid–liquid phase transition (LLPT) in molecular models of water under deeply supercooled conditions. A competing hypothesis suggests, however, that non-equilibrium artefacts associated with coarsening of the stable crystal phase have been mistaken for an LLPT in these models. Such artefacts are posited to arise due to a separation of time scales in which density fluctuations in the supercooled liquid relax orders of magnitude faster than those associated with bond-orientational order. Here, we use molecular simulation to investigate the relaxation of density and bond-orientational fluctuations in three molecular models of water (ST2, TIP5P and TIP4P/2005) in the vicinity of their reported LLPT. For each model, we find that density is the slowly relaxing variable under such conditions. We also observe similar behaviour in the coarse-grained mW model of water. Our findings, therefore, challenge the key physical assumption underlying the competing hypothesis.     

The reassessment of the structural transition regions along the liquidus of Fe–Si alloys and a possible liquid–liquid structural transition in FeSi2 alloy

We reassessed the structural transition regions along the liquidus of Fe–Si alloys by using ab initio molecular dynamics simulation. Except for 50 at.% Si, structural transition compositions are found at both 30 at.% Si and 67 at.% Si (FeSi₂) which are eutectic alloys. We demonstrated that the liquid structure in the sub-region of 0～30 at.% Si is close-packed, and in the sub-region of 67～100 at.% Si liquid alloys have very open structure. From 30 at.% Si to 67 at.% Si, the close-packed structure gradually change into open one. These structure transition sub-regions are also supported by the formation enthalpy of liquid alloys. Furthermore, the predicted enthalpy change between 1585 K and 1873 K is so large that there is probably liquid–liquid transition with temperature at FeSi₂ alloy which is an important thermoelectric material. Discussions have been made on the materials phenomenon of several Fe–Si alloys based on the structural information.     

Solvation force in hard ellipsoid fluids with HNW interaction

In present work, using density functional theory and extended restricted orientation model, the one particle density of hard Gaussian overlap fluid near the colloid walls is calculated. The hard needle–wall interaction between molecules and colloids are considered. Using non-linear equation, proposed by Grimson–Rickyazen, the solvation force of hard ellipsoidal molecular fluid with hard Gaussian overlap interaction is calculated. We could not find the exact or simulation results for comparison. The results in the case k = 2.0 are compared with the solvation force of one-dimensional hard rod fluids. The results are corresponded, qualitatively.     

Convergence acceleration for the multilevel Hartree–Fock model

In the previously introduced multilevel Hartree–Fock (HF) model, the electronic density is optimised in a given region of the molecular system. The approach is based on generating an active occupied and active virtual space by decomposing a start guess density for the entire system. In this work, a diagonalisation based implementation for Roothaan–Hall (RH) with direct inversion in iterative subspace (DIIS) and a quasi-Newton minimisation procedure using the augmented RH (ARH) approach are described for accelerating convergence for the multilevel HF model. The equations are derived to be consistent with convergence acceleration for traditional atomic orbital based HF calculations. The main idea is to formulate all quantities in the molecular orbital basis to exploit that the active molecular orbital basis is significantly smaller than the atomic orbital basis, and thus enable the application of wave function approaches that are well-studied for small molecular systems to large molecular systems. Thus, all equations are formulated such that no atomic orbital density or Fock matrices are needed for the DIIS and ARH algorithms. Results show that the acceleration schemes yield efficient optimisation of the multilevel HF wave function.     

Electronic structures of Stone–Wales defective chiral (6,2) silicon carbide nanotubes: First-principles calculations

By using first-principle calculations based on density functional theory, the geometries and electronic structures of the Stone–Wales defective chiral (6,2) silicon carbide nanotubes (SiCNTs) are investigated. Independent on their orientations, Stone–Wales defects form two asymmetric pentagons and heptagons coupled in pairs (5-7-7-5) and a defect energy level in the band gap of the SiCNT. By applying transverse electric fields, significant differences in the electronic structures of the defective (6,2) SiCNTs are achieved, which may provide the foundation of identifying the orientation of Stone–Wales defects in chiral SiCNTs.     

Quantum analysis of fluctuations of electromagnetic fields in heavy-ion collisions

We perform quantum calculations of fluctuations of the electromagnetic fields in AA collisions at RHIC and LHC energies. The analysis is based on the fluctuation–dissipation theorem. We find that in the quantum picture the field fluctuations are very small. They turn out to be much smaller than the predictions of the classical Monte Carlo simulation with the Woods–Saxon nuclear density.     

A temperature-related boundary Cauchy–Born method for multi-scale modeling of silicon nano-structures

The surface, edge and corner effects have significant influences in the electrical and optical properties of silicon nano-structures. In this paper, a novel hierarchical temperature-related multi-scale model is presented based on the boundary Cauchy–Born method to investigate not only the surface but also the edge and corner effects in thermal properties of diamond-like structures such as silicon nano-structures at finite temperature. A combined finite element method and molecular dynamics are respectively employed in macro- and micro-scale levels. The temperature-related Cauchy–Born rule is applied using the Helmholtz free energy, as the energy density of equivalent continua relating to the Tersoff inter-atomic potential. The model employs radial quadratures at the surface, edge and corner elements as an indicator of material behavior. The capability of computational algorithm is illustrated by numerical simulation of a nano-scale cube at finite temperature and the results are compared with the atomistic model.     

Identification of Rhubarb Samples by Using NIR Spectrometry and Takagi–Sugeno Fuzzy System

Abstract

The Takagi–Sugeno fuzzy system is implemented based on several back‐propagation neural networks (BP‐NNs) and has been applied to identification of official and unofficial rhubarb samples based on their near‐infrared spectra. Rhubarb is one of the most important Chinese medical herbs. It is of importance to identify official and unofficial rhubarb samples based on nondestructive near‐infrared spectrometry for quality control in Chinese herbal products. Near‐infrared diffuse reflectance spectrometry and the Takagi–Sugeno fuzzy system were used to classify 52 rhubarb samples, and the effects of the number of hidden neurons and of momentum parameters on prediction were investigated. The results obtained by using the Takagi–Sugeno fuzzy system were better than those by commonly used BP networks. With proper network training parameters, 100% correctness can be obtained by using the Takagi–Sugeno fuzzy system.     

Defining donor and acceptor strength in conjugated copolymers

ABSTRACT

The progress in efficiency of organic photovoltaic devices is largely driven by the development of new donor–acceptor (D–A) copolymers. The number of possible D–A combinations escalates rapidly with the ever-increasing number of donor and acceptor units, and the design process often involves a trial-and-error approach. We here present a computationally efficient methodology for the prediction of optical and electronic properties of D–A copolymers based on density functional theory calculations of donor- and acceptor-only homopolymers. Ten donors and eight acceptors are studied, as well as all of their 80 D–A copolymer combinations, showing absorption energies of 1.3–2.3 eV, and absorption strengths varying by up to a factor of 2.5. Focus lies on exhibited trends in frontier orbital energies, optical band gaps, and absorption intensities, as well as their relation to the molecular structure. Based on the results, we define the concept of donor and acceptor strength, and calculate this quantity for all investigated units. The light-harvesting capabilities of the 80 D–A copolymers were also assessed. This gives a valuable theoretical guideline to the design of D–A copolymers with the potential to reduce the synthesis efforts in the development of new polymers.