Configurational Averaging Research Articles

Modeling of the effect of the thickness of the antiferromagnetic layer on the energy of interfacial exchange interaction in Ferromagnetic/Antiferromagnet films

By means of thermodynamic and configuration averaging of the energy of the exchange interaction between the magnetic spin moments adjacent through the ferromagnetic/antiferromagnetic interphase boundary, the expression for the energy of the interphase exchange interaction Eex is obtained. The dependence of the energy Eex on the temperature and the characteristic dimensions of the ferromagnetic/antiferromagnetic two-phase film is modeled. The experimentally observed regularity of the growth of the energy of the interfacial exchange interaction due to the increase of the thickness of the antiferromagnetic layer is confirmed. A method for the estimation of the constants of the interfacial exchange interaction Jint and the exchange interaction in antiferromagnetics JAFM is proposed based on the agreement of the experimental and theoretical curves of the temperature dependence of the exchange bias field HebT.

Configuration average, state, orbital, Coulomb and exchange energies of confined beryllium atom

We have analysed the electronic structure for the ground and excited configurations of the confined beryllium atom under impenetrable spherical walls by using Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) methods. The wavefunction is built up from the one-electron wavefunctions which constitute the Slater-type basis sets. When the dot radius increases, all energies approach the corresponding values of free beryllium atom. In addition, in large dot radii, the ratio of the average potential energy to the total kinetic energy for each configuration approaches to the virial coefficients for free atoms (−2). It is found that the Coulomb interaction energy between the electrons occupying the 1s orbital is the biggest. For the 1s22s2p configuration, in small dot radii, while the 2s orbital energy is larger than the 2p orbital energy, the 2s orbital energy is smaller than that of 2p in large dot radii.

Acoustic Localization of an Intruder in a Strongly Scattering Medium

Localizing an intruder submerged in a strongly scattering medium, such as a dense granular suspension, is a practical challenge. Here we extract the coherent ultrasonic echo from a steel ball submerged in a dense glass-bead packing saturated by water, by using a standard single-element ultrasonic transducer thanks to a configuration averaging process. Different configurations of the granular packing are created by the nonaffine motion of the beads with a mixing blade, akin to the Brownian motion, in the vicinity of the intruder. We investigate the efficiency of this process to reduce the so-called material noise from multiply scattered ultrasound, as a function of the configuration number, the shear rate and the blade-intruder distance. Nonaffine motions of the beads in the shear zone induced by the blade are then analyzed on the basis of a split-bottom rotating shear cell. This method helps to develop not only ultrasonic imaging tools of buried objects in turbid marine sediments, but also the local rheology based on a ball falling monitored by ultrasonic tracking.

Influence of Number of Ligands and Point Group on the Electronic Structure of Co2+ Aqua-Complexes

The nucleation process of zeolitic imidazolate frameworks (ZIFs) is, to date, not yet completely understood, making the search for tailored materials very difficult. Recently, it has been shown that, during the formation process, the symmetry of the precursors is reduced by ligand elimination and substitution reactions. The octahedral precursors with simple ligands, such as water, methanol, and/or NO3-, are transformed to five- and finally four-coordinated complexes with imidazole ligands. This reduction of symmetry, caused both by the changing coordination environment and distortions from the perfect symmetry leading to another point group, will have a large influence on the electronic structure and more specifically on the d-orbital splitting. This, in turn, will affect the d-d electronic excitations, which can be followed using UV-vis spectroscopy and which can help to unravel the formation process. In this work, we systematically investigate how the lowering of the number of ligands affects the symmetry and thus the geometry and electronic structure of Co2+ complexes with six, five, and four aqua ligands. Therefore, we first resort to qualitative techniques, such as crystal field theory (CFT) and ligand field theory (LFT), which reveal that the orbital splitting is characteristic for the number of ligands. However, as these techniques are not capable of providing quantitative results without the use of experimental data as input, we perform various computational calculations. Both average of configuration (AOC) and unrestricted density functional theory (UDFT) are thoroughly investigated, and we will determine which technique is the best suited to properly describe the ground state of these systems. To investigate the dependency on the d-orbital occupation, we also investigated V2+, Mn2+, and Ni2+ hexa-aqua-complexes and compared them to the Co systems.

Towards stacking fault energy engineering in FCC high entropy alloys

Stacking Fault Energy (SFE) is an intrinsic alloy property that governs much of the plastic deformation mechanisms observed in fcc alloys. While SFE has been recognized for many years as a key intrinsic mechanical property, its inference via experimental observations or prediction using, for example, computationally intensive first-principles methods is challenging. This difficulty precludes the explicit use of SFE as an alloy design parameter. In this work, we combine DFT calculations (with necessary configurational averaging), machine-learning (ML) and physics-based models to predict the SFE in the fcc CoCrFeMnNiV-Al high-entropy alloy space. The best-performing ML model is capable of accurately predicting the SFE of arbitrary compositions within this 7-element system. This efficient model along with a recently developed model to estimate intrinsic strength of fcc HEAs is used to explore the strength–SFE Pareto front, predicting new-candidate alloys with particularly interesting mechanical behavior.

Multiple photoionization for the K shell in the Fe atom

Multiple photoionization for the K shell in the Fe atom is studied for all levels of the ground configuration. The study shows that sextuple-photoionization cross sections dominate for all levels of the 3d64s2configuration. The cross sections strongly depend on the initial level for which the photoionization is investigated. The partial photoionization cross sections to the configurations of the produced ions are determined. The main sequences of the radiative and Auger cascade following the photoionization of the K shell in the Fe atom are identified. Presented ion yields for subconfigurations and levels are compared with the previous calculations for configuration averages, revealing that they strongly overestimate ion yields for the Fe7+–Fe10+ions.

Molecular dynamics study of special quasirandom structure of Zr-Nb alloys

Irradiation damage to zirconium alloys (e.g., zirconium niobium (Zr-Nb) alloy) is the key to the design of fission-reactor structural materials and fuel rod cladding materials. Atomic scale computational simulations such as molecular dynamics and first principles are often needed to understand the physical mechanism of irradiation damage. For the simulation of randomly substitutional solid solution, it is necessary to construct large-sized supercells that can reflect the random distribution characteristics of alloy elements. However, it is not suitable to use large-size supercells (such as ≥ 200 atoms) for first principle calculation, due to the large computational cost. Special quasirandom supercells (SQS) are usually used for first principles calculation. The SQS can partly reflect the random distribution characteristics of alloy elements, but it only corresponds to one configuration for specific components, hence whether this model can reflect the statistical average of multiple local configurations in a real randomly substitutional solid solution is still an open question, and needs further studying and verifying. Molecular dynamics (MD) simulation can be carried out on the randomly substitutional solid solution with a larger scale based on random substitution (RSS) method, these supercells include more local configurations. Therefore, the MD studies of Zr-Nb alloy are carried out for the RSS and SQS-extended supercells. The critical size of RSS supercell which can truly reflect the statistical properties of solid solution alloy is determined. Then the lattice constant, formation energy and energy-volume relationship of SQS-extended supercell of Zr-Nb alloy and a series of RSS supercells are calculated and compared. The results show that the lattice constants, the formation energy and energy volume curves of the solid solution obtained by SQS supercell simulation are close to a series of corresponding statistical values of the physical properties of RSS supercells, so the SQS supercells can be used to study the random substitution of solid solution alloys.

Multiple photoionization cross sections for Fe2+ K shell

Multiple photoionization cross sections from the K shell are studied for all levels of the Fe2+ 3d6 configuration. The study shows that the quadruple photoionization leads to the largest cross sections. A large variation in the multiple photoionization cross sections is determined among the levels of the Fe2+ 3d6 configuration. Main decay branches of radiative and Auger cascades, following the photoionization of the K shell for the ground configuration of the Fe2+ ion, are identified. The radiative and Auger cascade is studied by considering transitions among energy levels and subconfigurations. The obtained data for ion yields are compared with previous calculations produced for configuration averages.

Configurational mean-field reduced transfer matrix method for Ising systems

A mean-field method for the hypercubic nearest-neighbor Ising system is introduced and applications to the method are demonstrated. The main idea of this work is to combine the Kadanoff’s mean-field approach with the model presented by one of us previously. The mean-field approximation is introduced with the replacement of the central spin in Ising Hamiltonian with an average value of particular spin configuration, i.e, the approximation is taken into account within each configuration. This approximation is used in two different mean-field-type approaches. The first consideration is a pure-mean-field-type treatment in which all the neighboring spins are replaced with the assumed configurational average. The second consideration is introduced by the reduced transfer matrix method. The estimations of critical coupling values of the systems are evaluated both numerically and also analytically by the using of saddle point approximation. The analytic estimation of critical values in the first and second considerations are [Formula: see text] and [Formula: see text] respectively. Obviously, both of the considerations have some significant deviation from the exact treatment. In this work, we conclude that the method introduced here is more appropriate physical picture than self-consistent mean-field-type models, because the method introduced here does not presume the presence of the phase transition from the outset. Consequently, the introduced approach potentially makes our research very valuable mean-field-type picture for phase transition treatment.

Shear viscosity of massless classical fields in scalar theory

Abstract We investigate the shear viscosity of massless classical scalar fields in the $\phi^4$ theory on a lattice by using the Green–Kubo formula. Based on the scaling property of the classical field, the shear viscosity is represented using a scaling function. The equilibrium expectation value of the time-correlation function of the energy–momentum tensor is evaluated as the ensemble average of the classical field configurations, whose time evolution is obtained by solving the classical equation of motion starting from the initial condition in thermal equilibrium. It is found that there are two distinct damping time scales in the time-correlation function, which is found to show damped oscillation behavior in the early stage around a slow monotonic decay with an exponential form, and the slow decay part is found to dominate the shear viscosity in the massless classical field theory. This kind of slow decay is also known to exist in molecular dynamics simulations, so it may be a generic feature of dense matter.

Ductile and brittle crack-tip response in equimolar refractory high-entropy alloys

Understanding the strengthening and deformation mechanisms in refractory high-entropy alloys (HEAs), proposed as new high-temperature material, is required for improving their typically insufficient room-temperature ductility. Here, density-functional theory simulations and a continuum mechanics analysis were conducted to systematically investigate the competition between cleavage decohesion and dislocation emission from a crack tip in the body-centered cubic refractory HEAs HfNbTiZr, MoNbTaVW, MoNbTaW, MoNbTiV, and NbTiVZr. This crack-tip competition is evaluated for tensile loading and a totality of 15 crack configurations and slip systems. Our results predict that dislocation plasticity at the crack tip is generally unfavorable – although the competition is close for some crack orientations, suggesting intrinsic brittleness and low crack-tip fracture toughness in these five HEAs at zero temperature. Fluctuations in local alloy composition, investigated for HfNbTiZr, can locally reduce the resistance to dislocation emission for a slip system relative to the configuration average of that slip system, but do not change the dominant crack-tip response. In the case of single-crystal MoNbTaW, where an experimental, room-temperature fracture-toughness value is available for a crack on a {100} plane, theoretical and experimental results agree favorably. Factors that may limit the agreement are discussed. We survey the effect of material anisotropy on preferred crack tip orientations, which are found to be alloy specific. Mixed-mode loadings are found to shift the competition in favor of cleavage or dislocation nucleation, depending on crack configuration and amplified by the effect of material anisotropy on crack tip stresses.

Critical evaluation of anharmonicity and configurational averaging in QM/MM modelling of equilibrium isotope effects.

Anharmonic effects upon vibrational frequencies and isotopic partition function ratios are modelled computationally by means of quantum mechanics/molecular mechanics (QM/MM) methods for two systems. First, the methyl cation in explicit water is considered using a B3LYP/6-31+G(d)/TIP3P method in order to check the previous prediction of an inverse equilibrium isotope effect (EIE) KH3/KD3 for transfer from vacuum to water at 298 K. A full QM/MM treatment including Lennard-Jones interactions predicts significantly inverse contributions from both internal (0.843 ± 0.001) and external (0.894 ± 0.001) modes of the solute. This treatment yields a much larger harmonic EIE (0.753 ± 0.002, averaged over 928 independent solvent configurations) than is obtained either by projecting out the translational and rotational contributions (0.853) or by treating the solvent by a point-charge representation (0.9360 ± 0.0006, harmonic; 0.9366 ± 0.0006, anharmonic). The contribution of anharmonicity to the EIE affects the value only in the 3rd significant figure. Second, anharmonicity is investigated by means of QM/MM potential-energy scans along 12 normal modes for internal and external vibrations of methyl cation in water and for three modes (one stretching and two bending) for the Hα atom at the carbenium-ion centre in cyclopentyl, cyclohexyl, tetrahydrofuranyl and tetrahydropyranyl cations in explicit water and cyclohexane solvents, as obtained by means of atomic Hessian analysis.

Ab initio theory of the spin-dependent conductivity tensor and the spin Hall effect in random alloys

We present an extension of the relativistic electron transport theory for the standard (charge) conductivity tensor of random alloys within the tight-binding linear muffin-tin orbital method to the so-called spin-dependent conductivity tensor, which describes the Kubo linear response of spin currents to external electric fields. The approach is based on effective charge- and spin-current operators, that correspond to intersite electron transport and that are nonrandom, which simplifies the configuration averaging by means of the coherent potential approximation. Special attention is paid to the Fermi sea term of the spin-dependent conductivity tensor, which contains a nonzero incoherent part, in contrast to the standard conductivity tensor. The developed formalism is applied to the spin Hall effect in binary random nonmagnetic alloys, both on a model level and for Pt-based alloys with an fcc structure. We show that the spin Hall conductivity consists of three contributions (one intrinsic and two extrinsic) which exhibit different concentration dependences in the dilute limit of an alloy. Results for selected Pt alloys (Pt-Re, Pt-Ta) lead to the spin Hall angles around 0.2; these sizable values are obtained for compositions that belong to thermodynamically equilibrium phases. These alloys can thus be considered as an alternative to other systems for efficient charge to spin conversion, which are often metastable crystalline or amorphous alloys.

Optimal stochastic unraveling of disordered open quantum systems: Application to driven-dissipative photonic lattices

We propose an efficient numerical method to compute configuration averages of observables in disordered open quantum systems whose dynamics can be unraveled via stochastic trajectories. We prove that the optimal sampling of trajectories and disorder configurations is simply achieved by considering one random disorder configuration for each individual trajectory. As a first application, we exploit the present method to the study the role of disorder on the physics of the driven-dissipative Bose-Hubbard model in two different regimes: (i) for strong interactions, we explore the dissipative physics of fermionized bosons in disordered one-dimensional chains; (ii) for weak interactions, we investigate the role of on-site inhomogeneities on a first-order dissipative phase transition in a two-dimensional square lattice.

Cluster expansion based configurational averaging approach to bandgaps of semiconductor alloys.

Configurationally disordered semiconducting materials including semiconductor alloys [e.g., (GaN)1-x(ZnO)x] and stoichiometric materials with fractional occupation (e.g., LaTiO2N) have attracted a lot of interest recently in search for efficient visible light photo-catalysts. First-principles modeling of such materials poses great challenges due to the difficulty in treating the configurational disorder efficiently. In this work, a configurational averaging approach based on the cluster expansion technique has been exploited to describe bandgaps of ordered, partially disordered (with short-range order), and fully disordered phases of semiconductor alloys on the same footing. We take three semiconductor alloys [Cd1-xZnxS, ZnO1-xSx, and (GaN)1-x(ZnO)x] as model systems and clearly demonstrate that semiconductor alloys can have a system-dependent short-range order that has significant effects on their electronic properties.

First-Principles Prediction of Incipient Order in Arbitrary High-Entropy Alloys: Exemplified in Ti <sub>0.25</sub>CrFeNiAl <sub>x</sub>

Multi-component solid-solution alloys, including high-entropy alloys, experience segregation or partially-ordering as they are cooled to lower temperatures. For Ti0.25CrFeNiAlx, experiments suggest a partially-ordered B2 phase, whereas CALculation of PHAse Diagrams (CALPHAD) predicts a region of L21+B2 coexistence. We employ first-principles KKR-CPA electronic-structure to assess stability of phases with arbitrary order having a specific Bravais lattice and composition, as it handles chemical disorder by direct configurational averaging during density-functional theory charge self-consistency. In addition, KKR-CPA linear-response theory is used to predict atomic short-range order (SRO) in the disorder phase, which reveals potentially competing long-range ordered (LRO) phases. With Warren-Cowley pair correlations defined relative to the diffraction lattice, SRO can be analyzed by concentration-waves (site-occupation probabilities) for any partially-ordered cells (including estimated energy gains) that can then be assess directly by KKR-CPA calculations. Our results are in good agreement with experiments and CALPHAD in Al-poor regions (x ≤0.75) and with CALPHAD in Al-rich region ($0.75 ≤x≤1), and they suggest more careful experiments in Al-rich region are needed. Our first-principles KKR-CPA electronic-structure and SRO predictions with additional concentration-wave analysis are shown to be a powerful and fast method to identify and assess competing phases in complex solid-solution alloys.

PySCF-NAO: An efficient and flexible implementation of linear response time-dependent density functional theory with numerical atomic orbitals

We present an algorithm and its implementation to calculate the propertiesof electronic excitations in molecules and clusters from first principles, using time-dependent density functional theory (TDDFT). The algorithm assumes the use of some localized functions as a basis set to represent the spatial degrees of freedom. It relies on an iterative computation of the induced density according to the Dyson-like equation for the linear response function. The current implementation is built upon so-called numerical atomic orbitals. It is suitable for a wide variety of density functional theory (DFT) software. In this work, we demonstrate TDDFT calculations starting from preceding DFT runs with SIESTA, GPAW and PySCF packages, while a coupling with the other DFT packages such as Fireball and OpenMX is planned. The mentioned packages are capable of performing ab initio molecular dynamics simulations, and the speed of our TDDFT implementation makes feasible to perform a configuration average of the optical absorption spectra. Our code is written mostly in Python language allowing for a quick and compact implementation of most numerical methods and data-managing tasks with the help of NumPy/SciPy libraries and Python intrinsic constructs. Part of the code is written in C and Fortran to achieve a competitive speed in particular sections of the algorithm. Many parts of the current algorithm and implementation are useful in other ab initio methods for electronic excited states, such as Hedin’s GW, Bethe–Salpeter equation and DFT with hybrid functionals. Corresponding proof-of-principles implementations are already part of the code. Program summaryProgram Title:PySCF-NAOProgram Files doi:http://dx.doi.org/10.17632/9wgp6255hn.1Licensing provisions: Apache License, Version 2.0Programming language: Python (2 or 3), Fortran90 and CSupplementary material: We provide the source code and input files to organize example and benchmark calculations discussed in the paper.Nature of the problem: The study of the interaction of photons and charged particles with matter depends upon understanding of electronic excitations in matter. A description of the electronic excitations within time-dependent density functional theory (TDDFT) is popular due to the combination of its reasonable accuracy and its relatively low computational cost. Despite the relative simplicity of TDDFT, its application becomes difficult for quantum systems containing several hundreds of atoms. Such microscopically small systems are relevant in organic electronics, plasmonics and surface science. Therefore, much work has been devoted to the development of adequate electronic structure methods. Moreover, thermal motion of atoms and the presence of solvents affects the properties of electronic excited states in a decisive manner. Modeling of the electronic excited states including the system’s dynamics within the Born–Oppenheimer approximation leads to even stronger efficiency requirements from the corresponding electronic structure methods.Solution method: We discretize the Kohn–Sham Hamiltonian using a basis of numerical atomic orbitals. The induced electronic density is determined in response to a dipolar external perturbation, according to linear response TDDFT, using an iterative algorithm. The method takes advantage of the sparsity generated by the finite support of the numerical atomic orbitals. This allows computing the dynamical polarizability of molecules and clusters containing up to several thousands of atoms.Additional comments including Restrictions and Unusual features: The current algorithm is formulated within the formalism of density response functions. Therefore, one needs to know explicitly an exchange–correlation kernel (second-derivative of energy with respect to variation of the density). The exchange–correlation kernel is analytically known for (semi-)local density functionals, but not for the hybrid density functionals. To date, we implemented only the local density approximation (LDA) for the exchange–correlation kernel to be used with the iterative TDDFT in PySCF-NAO. Spin-restricted formalism for finite systems is covered in the current implementation. Moreover, although our code is prepared to compute the electronic response of all-electron systems, our current implementation of an auxiliary product basis (density-fitting basis) is working best in combination with the use of pseudopotentials.

Relativistic calculations of x-ray transition energies and isotope shifts in heavy atoms

X-Ray transition energies and isotope shifts in heavy atoms are evaluated. The energy levels with vacancies in the inner shells are calculated within the approximation of the average of nonrelativistic configuration employing the Dirac-Fock-Sturm method. The obtained results are compared with other configuration-interaction theoretical calculations and with experimental data.

Importance of Accurate Structures for Quantum Chemistry Embedding Methods: Which Strategy Is Better?

Quantum chemistry embedding methods have become a popular approach to calculate molecular properties of larger systems. In order to account for finite temperature effects, including both configurational and conformational averaging, embedding methods are often combined with molecular dynamics (MD) simulations either in a direct or sequential manner. One of the decisive factors for a successful application of embedding methods is that that the underlying structures provided by the MD simulation are accurate, if not this will result in low-quality prediction of the molecular properties in question. Here we investigate different approaches for generating a set of molecular structures to be used in subsequent embedding calculations ranging from classical MD using a standard molecular mechanics (MM) force field to combined quantum mechanics/molecular mechanics (QM/MM) MD. Overall, we find an intermediate approach relying on classical MD followed by a constrained QM/MM geometry optimization to be a fairly accurate and very cost-effective approach, although this procedure naturally leads to underestimation of, for example, spectral bandwidths.

Symmetry Breaking Induced Activation of Nanocrystal Optical Transitions

ABSTRACTWe have analysed the effect of symmetry breaking on the optical properties of semiconductor nanocrystals due to doping by charged impurities. Using doped CdSe nanocrystals as an example, we show the effects of a Coulomb center on the exciton fine-structure and optical selection rules using symmetry theory and then quantify the effect of symmetry breaking on the exciton fine structure, modelling the charged center using a multipole expansion. The model shows that the presence of a Coulomb center breaks the nanocrystal symmetry and affects its optical properties through mixing and shifting of the hole spin and parity sublevels. This symmetry breaking, particularly for positively charged centers, shortens the radiative lifetime of CdSe nanocrystals even at room temperature, in qualitative agreement with the increase in PL efficiency observed in CdSe nanocrystals doped with positive Ag charge centers [A. Sahu et.al., Nano Lett. 12, 2587, (2012)]. The effect of the charged center on the photoluminescence and the absorption spectra is shown, with and without the presence of compensating charges on the nanocrystal surface. While spectra of individual nanocrystals are expected to shift and broaden with the introduction of a charged center, configuration averaging and inhomogeneous broadening are shown to wash out these effects. The presence of compensating charges at the NC surface also serves to stabilize the band edge transition energies relative to NCs with no charge centers.