Self-consistent Electron Densities Research Articles

A Critical Evaluation of the Hybrid KS DFT Functionals Based on the KS Exchange-Correlation Potentials.

We have developed a critical methodology for the evaluation of the quality of hybrid exchange-correlation (XC) density functional approximations (DFAs) based on very fundamental quantities, i.e., Kohn-Sham (KS) XC potentials, self-consistent electron densities, first ionization potentials (IPs), and total energies. Since the XC potentials, the primary objects in the current study, are not directly accessible for the hybrids, we calculate them by inverting the KS electron densities. Utilizing this methodology, we tested 155 hybrid DFAs available in the LIBXC library using FCI and CCSD(T) methods as a reference. We have found that a group of functionals produces very decent XC potentials, mainly those with a large mixture of Hartree-Fock exchange. Moreover, the value of IP strongly depends on the XC potential quality. On the other hand, we show that the XC energy is dominated by functional-driven error, which in some cases leads to substantial errors in electronic densities. The study shows new directions for constructing more accurate XC functionals within the KS-DFT framework.

Delta-doping modulation of three quantum wells under the influence of an electric field

The impact of delta-doping modulation and electric field influence within a nanostructure consisting of three GaAs quantum wells (QWs) separated by AlGaAs barriers was investigated. The quantized energy levels, Fermi energy, wavefunctions, self-consistent potential, and electron density distribution were evaluated by a self-consistent solution of the Schrödinger and Poisson equations using the finite element method within the FEniCS project in Python. The results indicate that increasing the electric field reduces energy levels and Fermi energy. In addition, the delta-doping position and electric field significantly affect the self-consistent potential and electron density distribution. This study provides a possibility to tailor optical properties, such as the linear absorption coefficient and photoluminescence, by adjusting geometrical and non-geometrical parameters, including donor density, enhancing the functionality of doped QWs in designing high electron mobility transistors.

Lagrangian of extended multiconfigurational self-consistent field second-order quasidegenerate perturbation theory combined with reference interaction site model self-consistent field constraint spatial electron density.

Lagrangians of the state-averaged multiconfigurational self-consistent field (SA-MCSCF) and multistate extended second-order quasidegenerate perturbation theory (MS-XMCQDPT2) coupled with the reference interaction site model self-consistent field constraint spatial electron density are defined. In addition, variational equations were derived to calculate the excitation energies of the target molecules dissolved in various solvents. The theory was applied to a phenol molecule in various solutions, and the gradients and Hessian matrices were calculated to evaluate the absorption spectral lines, including the broadening bandwidth. Numerical calculations revealed fine structures in any solvent surroundings. The main intramolecular vibrational modes related to such fine structures were stretching vibrations of the aromatic ring and the oxygen atom of the phenol molecule. The present theory plays an important role in predicting the structure of potential energy surfaces, such as Hessian matrices for various solvent types, during the photoexcitation process.

Daedalus Ionospheric Profile Continuation (DIPCont): Monte Carlo studies assessing the quality of in situ measurement extrapolation

Abstract. In situ satellite exploration of the lower thermosphere–ionosphere system (LTI) as anticipated in the recent Daedalus mission proposal to ESA will be essential to advance the understanding of the interface between the Earth's atmosphere and its space environment. To address physical processes also below perigee, in situ measurements are to be extrapolated using models of the LTI. Motivated by the need for assessing how cost-critical mission elements such as perigee and apogee distances as well as the number of spacecraft affect the accuracy of scientific inference in the LTI, the Daedalus Ionospheric Profile Continuation (DIPCont) project is concerned with the attainable quality of in situ measurement extrapolation for different mission parameters and configurations. This report introduces the methodological framework of the DIPCont approach. Once an LTI model is chosen, ensembles of model parameters are created by means of Monte Carlo simulations using synthetic measurements based on model predictions and relative uncertainties as specified in the Daedalus Report for Assessment. The parameter ensembles give rise to ensembles of model altitude profiles for LTI variables of interest. Extrapolation quality is quantified by statistics derived from the altitude profile ensembles. The vertical extent of meaningful profile continuation is captured by the concept of extrapolation horizons defined as the boundaries of regions where the deviations remain below a prescribed error threshold. To demonstrate the methodology, the initial version of the DIPCont package presented in this paper contains a simplified LTI model with a small number of parameters. As a major source of variability, the pronounced change in temperature across the LTI is captured by self-consistent non-isothermal neutral-density and electron density profiles, constructed from scale height profiles that increase linearly with altitude. The resulting extrapolation horizons are presented for dual-satellite measurements at different inter-spacecraft distances but also for the single-satellite case to compare the two basic mission scenarios under consideration. DIPCont models and procedures are implemented in a collection of Python modules and Jupyter notebooks supplementing this report.

Description of Solvatochromism of Peak Broadening in Absorption Spectra in Solution Using the Reference Interaction Site Model Self-Consistent Fields Spatial Electron Density Distribution.

We quantified and subsequently analyzed bandwidth of ultraviolet and visible photoabsorption spectral lines in solution by applying time-dependent first-order perturbation theory using the Born-Oppenheimer adiabatic potential calculated using the multistate extended-multi-configurational quasi-degenerated second-order perturbation theory (MS-XMCQDPT2) coupled with the reference interaction site model self-consistent field spatial electron density distribution (RISM-SCF-cSED). The proposed method was implemented for 2-thiocytosine in solution, and solvatochromism of the bandwidth of the πSπ* transition was clearly observed. The standard deviation of a characteristic electronic excitation was decomposed into the contributions of the characteristic vibrational mode of 2-thiocytosine. The main vibrational modes contributing to peak broadening were found to be for acetonitrile, methanol, and the aqueous phase. We concluded that the mechanism for peak broadening is qualitatively different for phases of protic and aprotic solvents because of the structural variation in 2-thiocytosine driven by the breakage of the resonance structures.

A wide-range semiclassical self-consistent average atom model

The discovery of material properties at extremes, which are essential for high energy density physics development, requires the most advanced experimental facilities, theories, and computations. Nowadays, it is possible to model properties of matter in such conditions using the state-of-the-art density functional theory (DFT) or path-integral Monte Carlo approaches with remarkable precision. However, fundamental and computational limitations of these methods impede their practical usage, while wide-range thermodynamic and transport models of plasma are required. As a consequence, an average atom (AA) framework is still relevant today and has been attracting more and more attention lately. The self-consistent field and electron density in an atomic cell is usually obtained using the Thomas–Fermi (TF), Hartree–Fock, Kohn–Sham approaches, or their extensions. In this study, we present the AA model, where semiclassical wave functions are used for bound states, while free electrons are approximated by the TF model with a thermodynamically consistent energy boundary. The model is compared in various regions of temperatures and pressures with the reference data: the Saha model for rarefied plasma, DFT for warm dense matter, and experimental shock Hugoniot data. It is demonstrated that a single AA model may provide a reasonable agreement with the established techniques at low computational cost and with stable convergence of the self-consistent field.

How Good Is the Density-Corrected SCAN Functional for Neutral and Ionic Aqueous Systems, and What Is So Right about the Hartree-Fock Density?

Density functional theory (DFT) is the most widely used electronic structure method, due to its simplicity and cost effectiveness. The accuracy of a DFT calculation depends not only on the choice of the density functional approximation (DFA) adopted but also on the electron density produced by the DFA. SCAN is a modern functional that satisfies all known constraints for meta-GGA functionals. The density-driven errors, defined as energy errors arising from errors of the self-consistent DFA electron density, can hinder SCAN from achieving chemical accuracy in some systems, including water. Density-corrected DFT (DC-DFT) can alleviate this shortcoming by adopting a more accurate electron density which, in most applications, is the electron density obtained at the Hartree-Fock level of theory due to its relatively low computational cost. In this work, we present extensive calculations aimed at determining the accuracy of the DC-SCAN functional for various aqueous systems. DC-SCAN (SCAN@HF) shows remarkable consistency in reproducing reference data obtained at the coupled cluster level of theory, with minimal loss of accuracy. Density-driven errors in the description of ionic aqueous clusters are thoroughly investigated. By comparison with the orbital-optimized CCD density in the water dimer, we find that the self-consistent SCAN density transfers a spurious fraction of an electron across the hydrogen bond to the hydrogen atom (H*, covalently bound to the donor oxygen atom) from the acceptor (OA) and donor (OD) oxygen atoms, while HF makes a much smaller spurious transfer in the opposite direction, consistent with DC-SCAN (SCAN@HF) reduction of SCAN overbinding due to delocalization error. While LDA seems to be the conventional extreme of density delocalization error, and HF the conventional extreme of (usually much smaller) density localization error, these two densities do not quite yield the conventional range of density-driven error in energy differences. Finally, comparisons of the DC-SCAN results with those obtained with the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method show that DC-SCAN represents a more accurate approach to reducing density-driven errors in SCAN calculations of ionic aqueous clusters. While the HF density is superior to that of SCAN for noncompact water clusters, the opposite is true for the compact water molecule with exactly 10 electrons.

Deep Density: Circumventing the Kohn-Sham equations via symmetry preserving neural networks

The recently developed Deep Potential [Phys. Rev. Lett. 120 (2018) 143001 [27]] is a powerful method to represent general inter-atomic potentials using deep neural networks. The success of Deep Potential rests on the proper treatment of locality and symmetry properties of each component of the network. In this paper, we leverage its network structure to effectively represent the mapping from the atomic configuration to the electron density in Kohn-Sham density function theory (KS-DFT). By directly targeting at the self-consistent electron density, we demonstrate that the adapted network architecture, called the Deep Density, can effectively represent the self-consistent electron density as the linear combination of contributions from many local clusters. The network is constructed to satisfy the translation, rotation, and permutation symmetries, and is designed to be transferable to different system sizes. We demonstrate that using a relatively small number of training snapshots, with each snapshot containing a modest amount of data-points, Deep Density achieves excellent performance for one-dimensional insulating and metallic systems, as well as systems with mixed insulating and metallic characters. We also demonstrate its performance for real three-dimensional systems, including small organic molecules, as well as extended systems such as water (up to 512 molecules) and aluminum (up to 256 atoms).

Predictive QM/MM Modeling of Modulations in Protein–Protein Binding by Lysine Methylation

Lysine methylation is a key regulator of protein–protein binding. The amine group of lysine can accept up to three methyl groups, and experiments show that protein–protein binding free energies are sensitive to the extent of methylation. These sensitivities have been rationalized in terms of chemical and structural features present in the binding pockets of methyllysine binding domains. However, understanding their specific roles requires an energetic analysis. Here we propose a theoretical framework to combine quantum and molecular mechanics methods, and compute the effect of methylation on protein–protein binding free energies. The advantages of this approach are that it derives contributions from all local non-trivial effects of methylation on induction, polarizability and dispersion directly from self-consistent electron densities, and at the same time determines contributions from well-characterized hydration effects using a computationally efficient classical mean field method. Limitations of the approach are discussed, and we note that predicted free energies of fourteen out of the sixteen cases agree with experiment. Critical assessment of these cases leads to the following overarching principles that drive methylation-state recognition by protein domains. Methylation typically reduces the pairwise interaction between proteins. This biases binding toward lower methylated states. Simultaneously, however, methylation also makes it easier to partially dehydrate proteins and place them in protein–protein complexes. This latter effect biases binding in favor of higher methylated states. The overall effect of methylation on protein–protein binding depends ultimately on the balance between these two effects, which is observed to be tuned via several combinations of local features.

Nuclear effects in proton transport and dose calculations

Interactions of protons with nuclei are modeled in a form that is suitable for Monte Carlo simulation of proton transport. The differential cross section (DCS) for elastic collisions of protons with neutral atoms is expressed as the product of the Rutherford DCS, which describes scattering by a bare point nucleus, and two correction factors that account for the screening of the nuclear charge by the atomic electrons and for the effect of the structure of the nucleus. The screening correction is obtained by considering the scattering of the projectile by an atom with a point nucleus and the atomic electron cloud described by a parameterization of the Dirac-Hartree-Fock-Slater self-consistent electron density. The DCS for scattering by this point nucleus atom is calculated by means of the eikonal approximation. The nuclear correction to the DCS for elastic collisions is calculated by conventional partial-wave analysis with a global optical-model potential that describes the interaction with the bare nucleus. Inelastic interactions of the projectile with target nuclei are described by using information from data files in ENDF-6 format, which provide cross sections, multiplicities, and angle-energy distributions of all reaction products: light ejectiles (neutrons, protons, …), gammas, as well as recoiling heavy residuals. These interaction models and data have been used in the Monte Carlo transport code penh, an extension of the electron-gamma code penelope, which originally accounted for electromagnetic interactions only. The combined code system penh/penelope performs simulations of coupled electron-photon-proton transport. A few examples of simulation results are presented to reveal the influence of nuclear interactions on proton transport processes and on the calculation of dose distributions from proton beams.

Dynamics of plasma confinement during ECR heating in the L-2M stellarator

Dynamics of plasma confinement was considered in the experiments on ECR plasma heating in the L-2M stellarator. It was ascertained that four stages can be distinguished in the process of plasma heating and further cooling. In each stage, plasma confinement has its own distinctive features. In the first stage, plasma confinement is determined by radiation loss. In the second stage, the self-consistent profiles of electron temperature and density form in plasma and the quasi-stationary confinement mode ensues. After ECRH switching off, the third stage begins. The plasma starts cooling and its parameters change in accordance with the scaling of the L-2M stellarator, the self-consistent electron temperature and density profiles being maintained. After the plasma periphery becomes cooled, the fourth stage of plasma confinement starts, and radiation loss becomes a determinative factor again.

Statistical Mechanics-Based Theoretical Investigation of Solvation Effects on Glucose Anomer Preferences.

The importance of solvation effects on the stability of glucose anomers has been studied by the combination of quantum mechanics and statistical mechanics, namely, the reference interaction site model self-consistent field spatial electron density distribution. The preferences of α- and β-glucose in H2O are well reproduced with the obtained ratio of 35:65 for α- and β-glucose, respectively. Indirect interactions and bulk effects, described by the Onsager model, are relatively small compared to the direct solute-solvent interactions, especially in [DMIM]Cl and dimethyl sulfoxide. From the decomposition of solvation free energy and solvation structures, it can be seen that the interactions with the solvent molecules greatly contribute to the anomer preferences.

Self-consistent mapping of the ab initio calculations to the multi-orbital p–d model: Magnetism in α-FeSi2 films as the effect of the local environment

To accurately translate the results obtained within density functional theory (DFT) to the language of many-body theory we suggest and test the following approach: the parameters of the formulated model are to be found from the requirement that the model self-consistent electron density and density of electron states are as close as possible to the ones found from the DFT-based calculations. The investigation of the phase diagram of the model allows us to find the critical regions in magnetic properties. Then the behavior of the real system in these regions is checked by the ab initio calculations. As an example, we studied the physics of magnetic moment (MM) formation due to substitutions of Si by Fe-atoms or vice versa in the otherwise non-magnetic alloy α-FeSi2. We find that the MM formation is essentially controlled by the interaction of Fe atoms with its next nearest atoms (NNN) and by their particular arrangement. The latter may result in different magnetic states at the same concentrations of constituents. Moreover, one of arrangements produces the counterintuitive result: a ferromagnetism arises due to an increase in Si concentration in Fe1−xSi2+x ordered alloy. The existing phenomenological models associate the destruction of magnetic moment only with the number of Fe–Si nearest neighbors. The presented results show that the crucial role in MM formation is played by the particular local NNN environment of the metal atom in the transition metal-metalloid alloy.

Ab-initio molecular characterization of nonclassical fullerenes cluster using two probe approach

Abstract

Modelling of free positron states in TiHx

Electron energy structure, positron spectrum and positron characteristics of α-Ti and α-TiH0.125 were calculated. Self-consistent calculations of the band structure were performed by the linear muffin-tin orbital method in the atomic sphere approximation. Modelling has been made on low content of hydrogen into α-Ti with expanded close-packed hexagonal cell inclusive 8 titanium atoms. Variation of sphere radiuses permitted to consider anisotropy and spherical symmetry of potential. Positron potential and positron wave function were calculated on a base of self-consistent electron density. Then positron probability of existence into TiHx lattice and lifetime were founded. Theoretical calculation indicated a satisfactory agreement of positron characteristics absolute values with the experimental data is achieved but the tendency of values with hydrogen defects increasing is not. The reason of divergence is discussed. On the basis of experimental data and theoretical calculations it was shown that different hydrogen atom states demonstrate the different influence in the lifetime spectra.

Reinvestigation of the ideal atomic shell structure and its application in orbital-free density functional theory

It is shown how to determine the ideal shell radii solely as a function of the nuclear charge. With the help of those ideal shell radii, an approximation to the Pauli potential for atoms in their groundstate can be constructed. The so-called SSB-ideal potential (shell structure-based) yields self-consistent orbital-free electron densities with proper atomic shell structure from Hohenberg–Kohn variational principle.

Local conditions for the Pauli potential in order to yield self-consistent electron densities exhibiting proper atomic shell structure.

The local conditions for the Pauli potential that are necessary in order to yield self-consistent electron densities from orbital-free calculations are investigated for approximations that are expressed with the help of a local position variable. It is shown that those local conditions also apply when the Pauli potential is given in terms of the electron density. An explicit formula for the Ne atom is given, preserving the local conditions during the iterative procedure. The resulting orbital-free electron density exhibits proper shell structure behavior and is in close agreement with the Kohn-Sham electron density. This study demonstrates that it is possible to obtain self-consistent orbital-free electron densities with proper atomic shell structure from simple one-point approximations for the Pauli potential at local density level.

Glucose transformation to 5-hydroxymethylfurfural in acidic ionic liquid: A quantum mechanical study.

Isomerization and transformation of glucose and fructose to 5-hydroxymethylfurfural (HMF) in both ionic liquids (ILs) and water has been studied by the reference interaction site model self-consistent field spatial electron density distribution (RISM-SCF-SEDD) method coupled with ab initio electronic structure theory, namely coupled cluster single, double, and perturbative triple excitation (CCSD(T)). Glucose isomerization to fructose has been investigated via cyclic and open chain mechanisms. In water, the calculations support the cyclic mechanism of glucose isomerization; with the predicted activation free energy is 23.8 kcal mol(-1) at experimental condition. Conversely, open ring mechanism is more favorable in ILs with the energy barrier is 32.4 kcal mol(-1) . Moreover, the transformation of fructose into HMF via cyclic mechanism is reasonable; the calculated activation barriers are 16.0 and 21.5 kcal mol(-1) in aqueous and ILs solutions, respectively. The solvent effects of ILs could be explained by the decomposition of free energies and radial distribution functions of solute-solvent that are produced by RISM-SCF-SEDD.

A simple approximation for the Pauli potential yielding self-consistent electron densities exhibiting proper atomic shell structure

A simple approximation for the Pauli potential for the groundstate of atomic systems is given, which in connection with Hohenberg-Kohn variational procedure yields self-consistent electron densities exhibiting proper atomic shell structure. (C) 2015 Wiley Periodicals, Inc.

Positron energy levels in zinc chalcogenides ZnS, ZnSe, and ZnTe

The self-consistent electron densities and the corresponding positron states are calculated for the zinc chalcogenides, ZnS, ZnSe and ZnTe, in the local-density approximation of the density-functional formalism. The calculations are performed with the full-potential linearized augmented plane-wave (FP-LAPW) method. The emphasis of this work is on the energy levels of the delocalized positron and the electron chemical potential. These energies determine quantities such as the positron and positronium work functions and the deformation potentials which are important parameters in slow-positron-beam experiments.