Kinetic Energy Density Research Articles

Laplacian-level meta-generalized gradient approximation for solid and liquid metals

Modern meta-GGAs based on the local kinetic energy density can predict properties of diverse systems with near experimental accuracy, but unexpectedly describe properties of metallic solids poorly due to their underestimation of screening in metals. In this work, the authors replace the kinetic energy dependence of a sophisticated meta-GGA with an approximation based on the electronic density gradient and Laplacian. This Laplacian-level meta-GGA is tested on a diverse set of solid-state properties: geometries, cohesive energies, bulk moduli, ferromagnetic moments, monovacancy formation energies, and formation enthalpies. Most deficiencies of the parent meta-GGA in describing metals are remedied with its Laplacian-level variant.

Constraint‐based analysis of a physics‐guided kinetic energy density expansion

AbstractAn approach guided by physical consistency in determining the general forms of D‐dimensional kinetic energy density functionals (KEDF) has been demonstrated previously, producing an expansion which contains the majority of the known one‐point KEDF forms. It has also been shown that any noninteracting KEDF must necessarily have a homogeneity degree of 2 in coordinate scaling, and that the ratio of the collective KED to electron density must approach the ionization energy as . This article demonstrates that the scaling condition is already satisfied in the general expansion despite not being conceived with the scaling as a constraint, and that the second condition places a restriction on the expansion terms of the KED. The discussion is extended as well for some known KEDs for comparison.

Correct and Accurate Polymorphic Energy Ordering of Transition-Metal Monoxides Obtained from Semilocal and Onsite-Hybrid Exchange-Correlation Approximations

The relative energetic stability of the structural phases of common antiferromagnetic transition-metal oxides (MnO, FeO, CoO, and NiO) within the semilocal and hybrid density functionals are fraught with difficulties. In particular, MnO is known to be the most difficult case for almost all common semilocal and hybrid density approximations. Here, we show that the meta-generalized gradient approximation (meta-GGA) constructed from the cuspless hydrogen model and Pauli kinetic energy density (MGGAC) can lead to the correct phase as the ground-state of MnO. The relative energy differences of zinc blende (zb) and rock salt (rs) structures as computed using MGGAC are found to be in nice agreement with those obtained from high-level correlation methods like the random phase approximation or quantum Monte Carlo techniques. Besides, we have also applied the onsite hybrid functionals (closely related to DFT+U) based on GGA and meta-GGA functionals, and it is shown that a relatively high amount of Hartree–Fock exchange is necessary to obtain rs as the ground-state phase. Our present investigation suggests the semilocal MGGAC and onsite hybrids, both being computationally cheap, as methods of choice for the calculation of the relative stability of antiferromagnetic transition-metal oxides having potential applications in solid-state physics and structural chemistry.

Development of Kinetic Energy Density Functional Using Response Function Defined on the Energy Coordinate

Development of Kinetic Energy Density Functional Using Response Function Defined on the Energy Coordinate

Kinetically driven ekpyrosis

We explore the possibility of a scalar field driving ekpyrotic contraction through a noncanonical kinetic energy density rather than a negative potential. We find that this kinetically driven ekpyrosis (``k-ekpyrosis'') can be achieved in a variety of models, including scalar field theories with power-law, polynomial, or Dirac-Born-Infeld (DBI-)like kinetic terms in the action. Of these examples, the ekpyrotic phase is best sustained in power-law models, which can generate large and constant equation-of-state parameters, followed by DBI-like models, which can exhibit dynamical attractors toward similarly large equations of state. We show that for a broad class of theories including these examples, phases of k-ekpyrosis are accompanied by preceding or concurrent phases of superluminality.

Theoretical insights into the nature of the bonding between carbon monoxide and iron(II) phthalocyanine: How do QTAIM descriptors change as a function of the Fe–CO distance?

The nature of the bonding in the complex between iron(II) phthalocyanine and carbon monoxide is theoretically investigated using density functional theory calculations in combination with the quantum theory of atoms in molecules (QTAIM). The QTAIM results indicate that the interaction between Fe and CO corresponds to a coordination covalent bonding with a significant ionic character. The stepwise elongation of the Fe–C bond produces a linear decrease in both the charge density and its Laplacian, both evaluated at the bond critical point, whereas the corresponding kinetic, potential, and total energy densities display a non-linear change in the same elongation range.

The Distance between Minima of Electron Density and Electrostatic Potential as a Measure of Halogen Bond Strength.

In this study, we present results of a detailed topological analysis of electron density (ED) of 145 halogen-bonded complexes formed by various fluorine-, chlorine-, bromine-, and iodine-containing compounds with trimethylphosphine oxide, Me3PO. To characterize the halogen bond (XB) strength, we used the complexation enthalpy, the interatomic distance between oxygen and halogen, as well as the typical set of electron density properties at the bond critical points calculated at B3LYP/jorge-ATZP level of theory. We show for the first time that it is possible to predict the XB strength based on the distance between the minima of ED and molecular electrostatic potential (ESP) along the XB path. The gap between ED and ESP minima exponentially depends on local electronic kinetic energy density at the bond critical point and tends to be a common limiting value for the strongest halogen bond.

Impact of the current density on paramagnetic NMR properties.

Meta-generalized gradient approximations (meta-GGAs) and local hybrid functionals generally depend on the kinetic energy density τ. For magnetic properties, this necessitates generalizations to ensure gauge invariance. In most implementations, τ is generalized by incorporating the external magnetic field. However, this introduces artifacts in the response of the density matrix and does not satisfy the iso-orbital constraint. Here, we extend previous approaches based on the current density to paramagnetic nuclear magnetic resonance (NMR) shieldings and electron paramagnetic resonance (EPR) g-tensors. The impact is assessed for main-group compounds and transition-metal complexes considering 25 density functional approximations. It is shown that the current density leads to substantial improvements-especially for the popular Minnesota and strongly constrained and appropriately normed (SCAN) functional families. Thus, we strongly recommend to use the current density generalized τ in paramagnetic NMR and EPR calculations with meta-GGAs.

Vertical Structure and Seasonal Variability of Shear on the Southwestern Continental Slope of the East China Sea

The vertical structure and seasonal variability of shear were examined using nearly three years of mooring ADCP (acoustic Doppler current profiler) data on the southwestern continental slope of the East China Sea (ECS). Shear spectra suggest that the sub-inertial currents (SICs); near-inertial waves (NIWs); and diurnal (D1), semidiurnal (D2), and tridiurnal (D3) internal tides (ITs) dominate the local shear field. The shear exhibits a remarkable surface-intensified pattern with high values occurring mostly in the upper 200 m. Significant seasonal variations can be found in the shear, but with differences between the upper (50–200 m averaged) and lower layers (210–570 m averaged). Satellite altimeter data indicate that the meander of the Kuroshio mainstream and the Kuroshio intrusion affect the seasonal variation of total shear by mainly influencing the shear caused by SICs. In addition, the shear efficiency (SE) of D2 ITs is obviously less than that of NIWs and that of D1 and D3 ITs via analyzing the kinetic energy (KE) densities and shear caused by these motions, since the predominant mode of the former is the first baroclinic mode, while the latter is dominated by higher baroclinic modes with large vertical wavenumbers. Moreover, the SE of incoherent ITs is relatively stronger than that of coherent ITs as a result of a larger proportion of high baroclinic modes in the incoherent component compared to the coherent component, based on modal decomposition.

Eigenvalue asymptotics for the one-particle kinetic energy density operator

The kinetic energy of a multi-particle system is described by the one-particle kinetic energy density matrix τ(x,y). Alongside the one-particle density matrix γ(x,y) it is one of the key objects in the quantum-mechanical approximation schemes. We prove the asymptotic formula λk∼(Bk)−2, B⩾0, as k→∞, for the eigenvalues λk of the self-adjoint operator T⩾0 with kernel τ(x,y).

Linear Response of Current-Dependent Density Functional Approximations in Magnetic Fields.

This Letter outlines the steps and derivations that are necessary to apply density functional approximations that depend on the current and kinetic energy density rigorously within the framework of linear-response methods, including adiabatic time-dependent current density functional theory. This includes systems with a non-zero current density in the ground state. The necessary exchange-correlation kernel for these density functional approximations is derived, and the matrix elements are given explicitly. Due to the gauge variance of the kinetic energy density in an external magnetic field, having access to the proper current-dependent exchange-correlation kernel is necessary to recover gauge invariance for excited states. As a proof of principle application, the excited states of two small molecules in strong external magnetic fields are calculated using linear-response time-dependent current density functional theory. Finally, the implications of the derived current density-dependent exchange-correlation kernel for systems with strong spin-orbit coupling are discussed.

A new methodology for the simulation of tunnel rockburst due to far-field seismic event

Dynamic disturbance from far-field seismic events is one of the main causes for triggering rockbursts in underground excavations. In this study, a comprehensive methodology for the simulation of a remote seismic source is proposed. The methodology encompasses the processing of raw seismic waveform based on the synchro-squeezing transform (SST) method and numerical modelling using finite-difference code FLAC3D. The main contributions of this study are as follows. First, the raw waveform is processed and reconstructed into P- and S- waveforms using the SST method, which is superior to applying synthetic waveforms in seismic modelling. Secondly, an innovative source waveform and material damping calibration procedure is put forward based on the empirical scaling law, producing a generalized seismic source waveform with input level of energy. Furthermore, a seismic loading scheme in numerical modelling is proposed; a spherical point source is created for applying P- and S- waveforms in different theoretical directions. Numerical modelling results show that the theoretical directionalities of P- and S- waves are well differentiated and reflected using the proposed dynamic loading method. The peak particle velocity (PPV) and peak kinetic energy density distributions around openings are interpreted, demonstrating that the proposed methodology could assist in rockburst risk assessment and dynamic rock support design

Numerical investigation on cavitating wake dynamic of a propeller with bionic tubercle leading-edge

The effects of the bionic tubercle leading-edge on the cavitating wake dynamic with cavitaion number σ = 1.76, 2.016 is calculated and discussed using numerical techniques based on the detached eddy simulation method. The propeller loads, cavitation extents, instantaneous wake topology, and the kinetic energy spectra are analyzed to investigate the influence mechanism of the bionic tubercles on propeller performance and wake flow field. The results indicated that the effect of bionic tubercle comes from the formation of the counter-rotating vortex pairs which change the distribution of streamlines on leading edge. The bionic tubercles are conductive to the cavitation and blade shed vortex reduction independent of advance coefficient. Analysis of power spectral density of kinetic energy demonstrates that the mean values of propeller with bionic leading-edge are generally smaller than those of original one, especially in the far field.

Retraction Note: Quasi-dimensional models applied to kinetic and exchange energy density functionals

Retraction Note: Quasi-dimensional models applied to kinetic and exchange energy density functionals

A Search for Correlations between Turbulence and Star Formation in THINGS Galaxies

Abstract The spatial range for feedback from star formation varies from molecular cloud disruption on parsec scales to supershells and disk blowout on kiloparsec scales. The relative amounts of energy and momentum given to these scales are important for understanding the termination of star formation in any one region and the origin of interstellar turbulence and disk stability in galaxies as a whole. Here, we measure, for 11 THINGS galaxies, the excess kinetic energy, velocity dispersion, and surface density of H i gas associated with regions of excess star formation, where the excess is determined from the difference between the observed local value and the azimuthal average. We find small decreases in the excess kinetic energy and velocity dispersion in regions of excess star formation rate density, suggesting that most of the feedback energy does not go into local H i motion. Most likely, it disrupts molecular clouds and dissipates rapidly at high gas density. Some could also be distributed over larger regions, filling in spaces between the peaks of star formation and contributing to other energy sources from self-gravity and spiral arm shocks.

Numerical study on the influence of pre-swirl angle on internal flow characteristics of centrifugal pumps

The effect of inlet pre-swirl on the performance of a centrifugal pump is studied by numerical simulation. The governing equations are Navier–Stokes equations and the shear stress transport k–ω turbulence model. The numerical results show that the optimal operating point moves from the low flow region to the high flow region as the pre-swirl angle shifts from positive to negative. It is found by contours of Omega–Liutex that the positive pre-swirl angle is able to weaken the vortex on the blade suction and reduce the energy dissipation. On both the 0.5Q0 and 1.2Q0 operating conditions, the proportion of entropy production loss in the impeller and volute is about 60% and 30%, respectively. As the pre-swirl angle changes from negative to positive, the entropy production loss in the inlet and outlet pipes increases slowly, and the entropy production loss in the volute and impeller shows a decreasing trend and the peak area of entropy loss moves toward the outlet. Under the four pre-swirl angles, the main frequency is always the passing frequency of the blade. The pre-swirl angle affects the pressure fluctuation at the main frequency but has little effect at the secondary frequency. The change in velocity pulsation amplitude in the impeller in the positive pre-swirl angle is smaller than that in the negative pre-swirl angle. As a result, for the positive pre-swirl angle, the turbulent kinetic energy density in the impeller is low, and the energy loss is low, compared with negative pre-swirl. Under the low flow condition (0.5Q0), the change in velocity pulsation amplitude in the inertial range of the energy spectrum under negative pre-swirl is greater than that under positive pre-swirl.

Cubic spline solver for generalized density functional treatments of atoms and generation of atomic datasets for use with exchange-correlation functionals including meta-GGA

Within generalized density functional theory, recent developments of functionals which depend upon the kinetic energy density, such as the r2SCAN form, show significant improvement in the computational representation of real material properties. In order to implement these forms within plane-wave codes, it is necessary to use pseudopotentials, ideally constructed with the same exchange-correlation functional as has been implemented for the projector augmented-wave (PAW) formalism in the atompaw code. This was accomplished with the help of an efficient solver for the self-consistent radial bound states of each atom, based on cubic spline interpolation. Details of the formalism are presented, and preliminary results for several simple materials are encouraging.

Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods.

We examine the role of self-interaction error (SIE) removal on the evaluation of magnetic exchange coupling constants. In particular, we analyze the effect of scaling down the self-interaction correction (SIC) for three nonempirical density functional approximations (DFAs) namely, the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and the recent SCAN family of meta-GGA functionals. To this end, we employ three one-electron SIC methods: Perdew-Zunger SIC [Perdew, J. P.; Zunger, A. Phys. Rev. B, 1981, 23, 5048.], the orbitalwise scaled SIC method [Vydrov, O. A. et al. J. Chem. Phys. 2006, 124, 094108.], and the recent local scaling method [Zope, R. R. et al. J. Chem. Phys. 2019, 151, 214108.]. We compute the magnetic exchange coupling constants using the spin projection and nonprojection approaches for sets of molecules composed of dinuclear and polynuclear H···He models, organic radical molecules, and chlorocuprate and compare these results against accurate theories and experiment. Our results show that for the systems that mainly consist of single-electron regions, PZSIC performs well, but for more complex organic systems and the chlorocuprates, an overcorrecting tendency of PZSIC combined with the DFAs utilized in this work is more pronounced, and in such cases, LSIC with kinetic energy density ratio performs better than PZSIC. Analysis of the results in terms of SIC corrections to the density and to the total energy shows that both density and energy correction are required to obtain an improved prediction of magnetic exchange couplings.

Hybrid functionals with local range separation: Accurate atomization energies and reaction barrier heights.

Range-separated hybrid approximations to the exchange-correlation density functional mix exact and semi-local exchange in a position-dependent manner. In their conventional form, the range separation is controlled by a constant parameter. Turning this constant into a density functional leads to a locally space-dependent range-separation function and thus a more powerful and flexible range-separation approach. In this work, we explore the self-consistent implementation of a local range-separated hybrid, taking into account a one-electron self-interaction correction and the behavior under uniform density scaling. We discuss different forms of the local range-separation function that depend on the electron density, its gradient, and the kinetic energy density. For test sets of atomization energies, reaction barrier heights, and total energies of atoms, we demonstrate that our best model is a clear improvement over common global range-separated hybrid functionals and can compete with density functionals that contain multiple empirical parameters. Promising results for equilibrium bond lengths, harmonic vibrational frequencies, and vertical ionization potentials further underline the potential and flexibility of our approach.

Mean fields and fluctuations in compressible magnetohydrodynamic flows

We apply Gaussian smoothing to obtain mean magnetic field, density, velocity, and magnetic and kinetic energy densities from our numerical model of the interstellar medium, based on three-dimensional magnetohydrodynamic equations in a shearing box in size. The interstellar medium is highly compressible, as the turbulence is transonic or supersonic; it is thus an excellent context in which to explore the use of smoothing to represent physical variables in a compressible medium in terms of their mean and fluctuating parts. Unlike alternative averaging procedures, such as horizontal averaging, Gaussian smoothing retains the three-dimensional structure of the mean fields. Although Gaussian smoothing does not obey the Reynolds rules of averaging, physically meaningful and mathematically sound central statistical moments are defined as suggested by Germano [Turbulence – The filtering approach. J. Fluid Mech. 1992, 238, 325–336]. We discuss methods to identify an optimal smoothing scale ℓ and the effects of this choice on the results. From spectral analysis of the magnetic, density and velocity fields, we find a suitable smoothing length for all three fields, of . Such a smoothing scale is likely to be sensitive to the choice of simulation parameters; this may be considered in future work, but here we just explore the methodology. We discuss the properties of third-order statistical moments in fluctuations of kinetic energy density in compressible flows, and suggest their physical interpretation. The mean magnetic field, amplified by a mean-field dynamo, significantly alters the distribution of kinetic energy in space and between scales, reducing the magnitude of kinetic energy at intermediate scales. This intermediate-scale kinetic energy is a useful diagnostic of the importance of SN-driven outflows.