Self-consistent Implementation Research Articles

Self-Consistent Implementation of a Solvation Free Energy Framework to Predict the Salt Solubilities of Six Alkali Halides.

To assess the salt solubilities of six alkali halides in aqueous systems, we proposed a thermodynamic cycle and an efficient molecular modeling methodology. The Gibbs free energy changes for vaporization, dissociation, and dissolution were calculated using the experimental data of ionic thermodynamic properties obtained from the NBS tables. Additionally, the Marcus' and Tissandier's solvation free energy data for Li+, Na+, K+, Cl-, and Br- ions were compared with the conventional solvation free energies by substituting into our self-consistent thermodynamic cycle. Furthermore, Tissandier's absolute solvation free energy data were used as the training set to refit the Lennard-Jones parameters of OPLS-AA force field for ions. To predict salt solubilities, an assumption of a pseudo-solvent was proposed to characterize the coupling work of a solute with its environment from infinitely diluted to saturated solutions, indicating that the Gibbs energy change of solvation process is a function of ionic strength. Following the self-consistency of the cycle, the newly derived formulas were used to determine the salt solubilities by interpolating the intersection of Gibbs free energy of dissolution and the zero free energy line. The refined ion parameters can also predict the structure and thermodynamic properties of aqueous electrolyte solutions, such as densities, pair correlation functions, hydration numbers, mean activity coefficients, vapor pressures, and the radial dependences of the net charge at 298.15 K and 1 bar. Our method can be used to characterize the solid-liquid equilibria of ions or charged particles in aqueous systems. Furthermore, for highly concentrated strong electrolyte systems, it is essential to introduce accurate water models and polarizable force fields.

Challenges with the self-consistent implementation of closure models for anomalous electron transport in fluid simulations of Hall thrusters

The performance of closure models for the anomalous electron transport when self-consistently implemented in a fluid model for a Hall effect thruster is investigated. This cross-field transport, which is orders of magnitude higher than classical collisional transport, is represented as an effective collision frequency. The proposed closure models relate this transport coefficient to local fluid properties of the plasma. Before implementation, the models are calibrated against values of the collision frequency inferred empirically from a 9 kW Hall thruster at 300 V and 15 A. It is found that even though closure models match the empirical collision frequency values, they diverge from these values when implemented self-consistently in a Hall thruster code. Possible drivers of this behavior are examined, including the role of non-linearity in the governing equations of the Hall thruster fluid model, artifacts from using time-averaged calibration data, and the non-uniqueness of the empirically-inferred collision frequencies. These results are discussed in the context of their implications for discovering and validating new closures necessary for enabling fully-predictive Hall thruster models.

Generating Exchange–Correlation Functionals with a Simplified, Self-Consistent Correlation Factor Model

We focus on the spherically averaged exchange-correlation hole ρXC(r, u) of density functional theory, which describes the reduction in the electron density at a distance u due to the reference electron localized at position r. The correlation factor (CF) approach, where the model exchange hole ρXmodel(r, u) is multiplied by a CF (fC(r, u)) to yield an approximation to the exchange-correlation hole ρXC(r, u) = fC(r, u) ρXmodel(r, u), has proven to be a powerful tool for the development of new approximations. One of the remaining challenges within the CF approach is the self-consistent implementation of the resulting functionals. To address this issue, here we propose a simplification of the previously developed CFs such that self-consistent implementations become feasible. As an illustration of the simplified CF model, we develop a new meta-GGA functional, and using only a minimum of empiricism, we provide an easy derivation of an approximation that is of an accuracy similar to more involved meta-GGA functionals.

Self-consistent implementation of locally scaled self-interaction-correction method.

Recently proposed local self-interaction correction (LSIC) method [Zope et al., J. Chem. Phys. 151, 214108 (2019)] is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew-Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn-Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional [e.g., Perdew-Burke-Ernzerhof (PBE)] and barrier heights of the BH6 database better than some of the most widely used hybrid functionals (e.g., PBE0 and B3LYP). The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). This work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.

Development of an ensemble Monte Carlo simulator for high-power semiconductor devices with self-consistent electromagnetism and GPU implementation

The ensemble Monte Carlo (EMC) method is a powerful and widely used technique for modeling carrier transport in semiconductors in which one can easily take into account band structure and a variety of scattering mechanisms. In the usual implementations of EMC, the semiclassical electron dynamics is coupled self-consistently to the electrostatic field and this suffices for most devices. However, for high power, high current semiconductor device applications the electrostatic approximation is often not adequate and the full electromagnetic (EM) equations must be solved in fully-coupled fashion. We report on the development of a fully self-consistent, time-domain, EM-EMC simulator for two- and three-dimensional device simulations in which we also address a well known drawback of these methods, their computational intensiveness, by producing a GPU implementation.

Self-Consistent Implementation of Kohn-Sham Adiabatic Connection Models with Improved Treatment of the Strong-Interaction Limit.

Adiabatic connection models (ACMs), which interpolate between the limits of weak and strong interaction, are powerful tools to build accurate exchange–correlation functionals. If the exact weak-interaction expansion from the second-order perturbation theory is included, a self-consistent implementation of these functionals is challenging and still absent in the literature. In this work, we fill this gap by presenting a fully self-consistent-field (SCF) implementation of some popular ACM functionals. While using second-order perturbation theory at weak interactions, we have also introduced new generalized gradient approximations (GGAs), beyond the usual point-charge-plus-continuum model, for the first two leading terms at strong interactions, which are crucial to ensure robustness and reliability. We then assess the SCF–ACM functionals for molecular systems and for prototypical strong-correlation problems. We find that they perform well for both the total energy and the electronic density and that the impact of SCF orbitals is directly connected to the accuracy of the ACM functional form. For the H2 dissociation, the SCF–ACM functionals yield significant improvements with respect to standard functionals also thanks to the use of the new GGAs for the strong-coupling functionals.

Effect of the cosmological transition to metal-enriched star formation on the hydrogen 21-cm signal

ABSTRACT Mapping cosmic dawn with 21-cm tomography offers an exciting new window into the era of primordial star formation. However, self-consistent implementation of both the process of star formation and the related 21-cm signal is challenging, due to the multiscale nature of the problem. In this study, we develop a flexible semi-analytical model to follow the formation of the first stars and the process of gradual transition from primordial to metal-enriched star formation. For this transition, we use different scenarios with varying time-delays (or recovery times) between the first supernovae and the formation of the second generation of stars. We use recovery times between 10 and 100 Myr and find that these delays have a strong impact on the redshift at which the transition to metal-enriched star formation occurs. We then explore the effect of this transition on the 21-cm signal and find that the recovery time has a distinctive imprint in the signal. Together with an improved understanding of how this time-delay relates to the properties of Population III stars, future 21-cm observations can give independent constraints on the earliest epoch of star formation. As the transition away from the primordial star formation is expected to occur at high redshifts, here we ignore the impact of X-ray and ionizing radiation, focusing on the effect of Ly α photons on the 21-cm signal.

Implementation of self-consistent MGGA functionals in augmented plane wave based methods

The authors present the self-consistent implementation and validation of MGGA density functionals in the highly accurate all-electron augmented plane wave based (APW) method for the simulation of solid-state materials. MGGA functionals are the third level of density functional approximations on Jacob's ladder of exchange-correlation functionals. The implementation in the WIEN2k APW based code is discussed and validated using calculations of band gaps, lattice constants, magnetic properties, and electric field gradients.

Charge self-consistent electronic structure calculations with dynamical mean-field theory using Quantum ESPRESSO, Wannier 90 and TRIQS

We present a fully charge self-consistent implementation of dynamical mean field theory (DMFT) combined with density functional theory (DFT) for electronic structure calculations of materials with strong electronic correlations. The implementation uses the Quantum ESPRESSO package for the DFT calculations, the Wannier90 code for the up-/down-folding and the TRIQS software package for setting up and solving the DMFT equations. All components are available under open source licenses, are MPI-parallelized, fully integrated in the respective packages, and use an hdf5 archive interface to eliminate file parsing. We show benchmarks for three different systems that demonstrate excellent agreement with existing DFT + DMFT implementations in other ab initio electronic structure codes.

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.

Hybrid approach to accurate modeling of coupled vibrational-chemical kinetics in carbon dioxide

In the present study, a new hybrid approach is proposed to modeling coupled vibrational and chemical kinetics in carbon dioxide (CO2) and products of its decomposition. The study develops and completes our previous work carried out for a single-component CO2 gas. The model is based on self-consistent implementation of state-to-state chemical and energy production rates into the equations of multi-temperature CO2 kinetics. It distinguishes vibrational temperatures of all CO2 modes and diatomic species and thus takes into account multiple relaxation mechanisms including intra-mode, inter-mode, and inter-molecular energy transitions as well as state-specific dissociation and exchange reactions. Other advantages of the proposed full multi-temperature approach are the possibility of capturing strong non-equilibrium effects in a flow, straightforward implementation of the chemical-vibrational coupling terms, easy update for new models of state-specific reaction rates. Comparisons with the results obtained in the frame of a detailed but numerically demanding state-to-state approach for the problem of spatially homogeneous relaxation showed good accuracy of the new model under the wide range of initial conditions; at the same time, traditional multi-temperature approaches failed to provide accurate predictions of non-equilibrium flow parameters under arbitrary deviations from equilibrium. Effects of chemical reaction models and selective mode excitation are assessed. The numerical efficiency of the developed model is found acceptable compared to that of the state-to-state approach.

Modelling electrocatalytic reactions with a concerted treatment of multistep electron transfer kinetics and local reaction conditions

A physicochemical model is developed for electrocatalytic reactions involving multiple electron transfer steps occurring in the electric double layer (EDL). The local reaction conditions are calculated using a mean-field EDL model, which is derived from a comprehensive grand potential that considers the steric effects, solvent polarization, and chemisorption-induced surface dipoles. Macroscopic mass transport in the so-called diffusion layer is controlled by the same set of controlling equations of the EDL model, without imposing the electroneutrality assumption as usual. The Gerischer’s formulation of electron transfer theory, corrected with local reaction conditions, is used to describe the kinetics of elementary steps. Multistep kinetics of the electrocatalytic reaction is treated using microkinetics modelling, without resorting to the usual rate-determining step approximation. In formal analysis of the model, we retrieve canonical models with additional assumptions. Self-consistent numerical implementation of the model is demonstrated for oxygen reduction reaction (ORR) at Pt(111) in acidic solution, and the aptness of the model is verified by comparison with experimental data. A comparative study of the full model and its simplified versions allows us to examine how the ORR is influenced by asymmetric steric effects, finite concentration of ions, solvent polarization, surface charge effects, and metal electronic structure effects. We find that the difference in terms of the overpotential between the full model and the simplest model can be up to ∼0.1 V at a current density of −6 mA .

The Effect of Supernovae on the Turbulence and Dispersal of Molecular Clouds

Abstract We study the impact of supernovae on individual molecular clouds, using a high-resolution magnetohydrodynamic simulation of a 250 pc region where we resolve the formation of individual massive stars. The supernova feedback is implemented with real supernovae, meaning supernovae that are the natural evolution of the resolved massive stars, so their position and timing are self-consistent. We select a large sample of molecular clouds from the simulation to investigate the supernova energy injection and the resulting properties of molecular clouds. We find that molecular clouds have a lifetime of a few dynamical times, less than half of them contract to the point of becoming gravitationally bound, and the dispersal time of bound clouds of order one dynamical time is a factor of 2 shorter than that of unbound clouds. We stress the importance of internal supernovae, that is, massive stars that explode inside their parent cloud, in setting the cloud dispersal time, and their huge overdensity compared to models where the supernovae are randomly distributed. We also quantify the energy injection efficiency of supernovae as a function of supernova distance to the clouds. We conclude that intermittent driving by supernovae can maintain molecular cloud turbulence and may be the main process for cloud dispersal and that the full role of supernovae in the evolution of molecular clouds cannot be fully accounted for without a self-consistent implementation of the supernova feedback.

PWDFT.jl: A Julia package for electronic structure calculation using density functional theory and plane wave basis

We describe the implementation of PWDFT.jl, a package for electronic structure calculations written in Julia programming language using plane wave basis set and pseudopotentials. In this package, a typical Kohn–Sham density functional theory (KSDFT) is divided into three steps: initializing the molecular or crystalline structure, constructing the Kohn–Sham Hamiltonian, and solving the Kohn–Sham problem using self-consistent field (SCF) calculation. To facilitate various tasks involved in these steps, we provide several custom data types which are transparent and easy to be modified. Basic operations such as wave function orthogonalization, action of kinetic and potential operators to wave functions and iterative diagonalization of Hamiltonian have been implemented in pure Julia. Several algorithms to solve the Kohn–Sham problems such as self-consistent field and direct energy minimization have also been implemented in PWDFT.jl. To assess the validity of our implementation, we present the results of total energy calculations against the well-established ABINIT package. We also show how one can use PWDFT.jl to write a simple self-consistent field implementation. Program summaryProgram Title:PWDFT.jlCPC Library link to program files:http://dx.doi.org/10.17632/b87xzmzm2z.1Licensing provisions: GPL-v2Programming language: JuliaNature of problem: Electronic structure of interacting electrons in materialSolution method: Kohn–Sham density functional theory, using plane wave basis set and pseudopotentialsAdditional comments including restrictions and unusual features: Due to the precompilation step, the program may appear to be slow at the first call. Parallelization is not yet considered.

Self-Consistent Implementation of Hybrid Functionals with Local Range Separation.

Building on the previously introduced concept of local range separation (LRS) [ Krukau , A. V. ; Scuseria , G. E. ; Perdew , J. P. ; Savin , A. Hybrid functionals with local range separation J. Chem. Phys. 2008 129 124103 ], we report the first self-consistent implementation of hybrid exchange functionals with a position-dependent range-separation parameter. The two-electron integrals emerging from long-range exact exchange are calculated seminumerically. This avoids formerly suggested approximations to the exact exchange part and paves the way for applications to larger and chemically relevant systems. Additionally, we investigate the role of short-range exchange in this LRS scheme by comparing the local density approximation and PBE-type functionals. We propose a semiempirical approach for the range-separation function based on common ingredients of semilocal exchange-correlation functionals. Four parameters are optimized to a small training set of atomization energies and barrier heights. In comparison with established hybrid and semilocal functionals, the LRS functional performs well for basic chemical properties. In addition, our best functional yields outer-valence spectra comparable to optimally tuned approaches.

Multiscale Modeling of Thin-Wire Coupling Problems Using Hybridization of Finite Element and Dipole Moment Methods and GPU Acceleration

In this article, a hybrid numerical method, called finite element method (FEM) + dipole moment (DM), is presented for efficient solution of multiscale electromagnetic radiation and scattering problems that involve structures with fine features, such as thin-wire antennas or objects. In this method, the FEM is hybridized with the DM approach to help ease certain computational burdens, such as mesh refinement, ill-conditioning, memory overload, and long computation times, when solving multiscale problems with adequate numerical precision. Although the FEM+DM method is referred to as a single algorithm above, it is actually comprised of several different hybridization and/or implementation approaches. Two hybridization approaches are described, each tailored to the type of problem, e.g., radiation or scattering. Furthermore, both iterative and noniterative (self-consistent) implementations of the FEM+DM method are discussed. One of the important characteristics of the proposed method is that it can easily be parallelized to accelerate the speed of computation, thanks to the use of DMs for handling fine features as well as for modeling mutual interactions. The hybrid method with different hybridization/implementation approaches has been implemented in an in-house code by using graphics processing unit programming in MATLAB. Several numerical results are generated by the proposed method and are compared to those obtained from a commercial electromagnetic solver.

On the calculation of the bandgap of periodic solids with MGGA functionals using the total energy.

During the last few years, it has become more and more clear that functionals of the meta generalized gradient approximation (MGGA) are more accurate than GGA functionals for the geometry and energetics of electronic systems. However, MGGA functionals are also potentially more interesting for the electronic structure, in particular, when the potential is nonmultiplicative (i.e., when MGGAs are implemented in the generalized Kohn-Sham framework), which may help to get more accurate bandgaps. Here, we show that the calculation of bandgap of solids with MGGA functionals can also be done very accurately in a non-self-consistent manner. This scheme uses only the total energy and can, therefore, be very useful when the self-consistent implementation of a particular MGGA functional is not available. Since self-consistent MGGA calculations may be difficult to converge, the non-self-consistent scheme may also help to speed up the calculations. Furthermore, it can be applied to any other types of functionals, for which the implementation of the corresponding potential is not trivial.

Comparison between ad-hoc and instability-induced electron anomalous transport in a 1D fluid simulation of Hall-effect thruster

Anomalous electron transport is a long-standing problem in the understanding of Hall-effect thrusters. Recent results have suggested as a possible cause a kinetic instability, but few attempts have succeeded in implementing such phenomena in a fluid simulation of the thruster. The common approach in this case relies on including an ad-hoc model of the anomalous transport and so to fit experimental results. We propose here a comparison between the friction force and the anomalous heating arising from the ad-hoc model, with the corresponding effects coming from the use of the instability-induced transport. The results are obtained through a one-dimensional fluid simulation of the Hall-effect thruster with ad-hoc anomalous transport. The comparison shows good agreement between the two approaches, suggesting indeed that the instability-induced anomalous transport is the good candidate for reproducing the ad-hoc simulations and paving the way for a full self-consistent implementation of the phenomena in a fluid simulation.

Importance of van der Waals effects on the hydration of metal ions from the Hofmeister series.

The van der Waals (vdW) interaction plays a crucial role in the description of liquid water. Based on ab initio molecular dynamics simulations, including the non-local and fully self-consistent density-dependent implementation of the Tkatchenko-Scheffler dispersion correction, we systematically studied the aqueous solutions of metal ions (K+, Na+, and Ca2+) from the Hofmeister series. Similar to liquid water, the vdW interactions strengthen the attractions among water molecules in the long-range, leading to the hydrogen bond networks softened in all the ion solutions. However, the degree that the hydration structure is revised by the vdW interactions is distinct for different ions, depending on the strength of short-range interactions between the hydrated ion and surrounding water molecules. Such revisions by the vdW interactions are important for the understanding of biological functionalities of ion channels.

Correlation strength, Lifshitz transition, and the emergence of a two-dimensional to three-dimensional crossover in FeSe under pressure

We report a detailed theoretical study of the electronic structure, spectral properties, and lattice parameters of bulk FeSe under pressure using a fully charge self-consistent implementation of the density functional theory plus dynamical mean-field theory method (DFT+DMFT). In particular, we perform a structural optimization and compute the evolution of the lattice parameters (volume, $c/a$ ratio, and the internal $z$ position of Se) and the electronic structure of the tetragonal (space group $P4/nmm$) paramagnetic FeSe. Our results for the lattice parameters are in good quantitative agreement with experiment. The $c/a$ ratio is slightly overestimated by about $3$~\%, presumably due to the absence of the van der Waals interactions between the FeSe layers in our calculations. The lattice parameters determined within DFT are off the experimental values by a remarkable $\sim$$6$-$15$~\%, implying a crucial importance of electron correlations. Upon compression to $10$~GPa, the $c/a$ ratio and the lattice volume show a decrease by $2$ and $10$~\%, respectively, while the Se $z$ coordinate weakly increases by $\sim$$2$~\%. Most importantly, our results reveal a topological change of the Fermi surface (Lifshitz transition) which is accompanied by a two- to three-dimensional crossover. Our results indicate a small reduction of the quasiparticle mass renormalization $m^*/m$ by about $5$~\% for the $e$ and less than $1$~\% for the $t_2$ states, as compared to ambient pressure. The behavior of the momentum-resolved magnetic susceptibility $\chi({\bf q})$ shows no topological changes of magnetic correlations under pressure, but demonstrates a reduction of the degree of the in-plane $(\pi,\pi)$ stripe-type nesting. Our results for the electronic structure and lattice parameters of FeSe are in good qualitative agreement with recent experiments on its isoelectronic counterpart FeSe$_{1-x}$S$_x$.