Ground-state Charge Density Research Articles

Linear Jacobi-Legendre expansion of the charge density for machine learning-accelerated electronic structure calculations

Kohn–Sham density functional theory (KS-DFT) is a powerful method to obtain key materials’ properties, but the iterative solution of the KS equations is a numerically intensive task, which limits its application to complex systems. To address this issue, machine learning (ML) models can be used as surrogates to find the ground-state charge density and reduce the computational overheads. We develop a grid-centred structural representation, based on Jacobi and Legendre polynomials combined with a linear regression, to accurately learn the converged DFT charge density. This integrates into a ML pipeline that can return any density-dependent observable, including energy and forces, at the quality of a converged DFT calculation, but at a fraction of the computational cost. Fast scanning of energy landscapes and producing starting densities for the DFT self-consistent cycle are among the applications of our scheme.

Realizing the potentials of density functional theory (DFT) and of the materials genome initiative (MGI)

From 1964 and 1965 to present, the wide spread utilization of an incomplete density functional theory (DFT) has led to mixed results: The second theorem of the theory asserts that the energy functional reaches its minimum if the calculation employs the ground state charge density—without providing a mechanism for finding this density. Calculations purporting to employ DFT have mostly assumed that results obtained with a judiciously selected basis set, following self-consistent iterations, are those of the ground state. The state obtained with a single basis set is a stationary one, among an infinite number of such states, with no proven relation to the actual ground state of the material. Most failures or limitations of the incomplete DFT can be traced to this error. We present results from calculations using the completed DFT. They are in excellent agreement with experiment and portend the realization of the Materials Genome Initiative.

DeePKS-kit: A package for developing machine learning-based chemically accurate energy and density functional models

We introduce DeePKS-kit, an open-source software package for developing machine learning based energy and density functional models. DeePKS-kit is interfaced with PyTorch, an open-source machine learning library, and PySCF, an ab initio computational chemistry program that provides simple and customized tools for developing quantum chemistry codes. It supports the DeePHF and DeePKS methods. In addition to explaining the details in the methodology and the software, we also provide an example of developing a chemically accurate model for water clusters. Program summaryProgram Title: DeePKS-kitCPC Library link to program files:https://doi.org/10.17632/x54bnz5vxk.1Developer's repository link:https://github.com/deepmodeling/deepks-kitLicensing provisions: LGPLProgramming language: PythonNature of problem: Modeling the energy and density functional in electronic structure problems with high accuracy by neural network models. Solving electronic ground state energy and charge density using the learned model.Solution method: DeePHS and DeePKS methods are implemented, interfaced with PyTorch and PySCF for neural network training and self-consistent field calculations. An iterative learning procedure is included to train the model self-consistently.

Excited-state charge polarization and electronic structure of mixed-cation halide perovskites: the role of mixed inorganic-organic cations in CsFAPbI3.

Mixed-cation perovskite materials have shown great potential for sunlight harvesting and have surpassed unmixed perovskite materials in solar cell efficiency and stability. The role of mixed monovalent cations in the enhanced optoelectronic properties and excited state response, however, are still elusive from a theoretical perspective. Herein, through time dependent density functional theory calculations of mixed cation perovskites, we report the electronic structure of Cs formamidinium (FA) mixed cationic lead iodide (Cs0.17FA0.87PbI3) in comparison to the corresponding single monovalent cation hybrid perovskite. The results show that the Cs0.17FA0.87PbI3 and FAPbI3 had negligible differences in the optical band gap, and partial and total density of states in comparison to a single cation perovskite, while the effective mass of carriers, the local atomic density of states, the directional transport, and the structural distortions were significantly different. A lattice-distortion-induced asymmetry in the ground-state charge density is found, and originates from the co-location of caesium atoms in the lattice and signifies the effect on the charge density upon cation mixing and corresponding symmetry breaking. The excited-state charge response and induced polarizabilities are quantified, and discussed in terms of their importance for effective light absorption, charge separation, and final solar cell performance. We also quantify the impact of such polarizabilities on the dynamics of the structure of the perovskites and the implications this has for hot carrier cooling. The results shed light on the mechanism and origin of the enhanced performance in mixed-cation perovskite-based devices and their merits in comparison to single cation perovskites.

Elastic and inelastic C2 form factors of nickel isotopes and two-body correlations

The inelastic form factors for C2 transition have been studied for even nickel isotopes ([Formula: see text]Ni) using the form of Tassie shape for ground state charge density distribution. The charge density distribution is investigated using the one- and two-body terms in the cluster expansion. The effect of short-range correlations is included using Jastrow-type correlation function into the two-body density term of the cluster expansion. This concludes that the inserting of the influence of short-range correlations is required for reaching an important adjustment in the calculated elastic and inelastic form factors which explain the data very well at the high momentum transfers ([Formula: see text][Formula: see text]fm[Formula: see text].

Effectively improving the quick-repair characteristics of epoxy coatings for the SF6-inflate metal tubes through molecular modifications

Four crosslinked epoxies, agented by ODA, SDA, DDS, and SSDDS, were constructed, followed by DFT calculations and MD simulations to assist the selection of coatings for the quick repairment of GIL. The DFT-based ground-state charge density results indicate that the core group and molecular length impact the reactivity of diamine curing agents. Based on the MD simulations, the key physical properties were predicted. The glass transition temperatures, in the narrow range from 374 to 396 K, of epoxies crosslinked by various agents, are close, owing to the similar polymer network-determine crystallinity. SDA cured epoxy model with the lowest Young’s module, which is only 1.877 GPa, shows the best elastic behaviors under the action of axial mechanical stresses. The fractional free volume of the crosslinked epoxies, no more than 10−5 Pa cm2/s, is small enough to forbid the motion of SF6 inside, leading to low permeability. Furthermore, the results indicated that the SDA crosslinked epoxy model had the most prominent effects. Therefore, the SDA may be an effective curing agent for the epoxy coating in the GIL quick repairing application.

Charged surfaces and slabs in periodic boundary conditions

Plane wave density functional theory codes generally assume periodicity in all three dimensions. This causes difficulties when studying charged systems, for instance energies per unit cell become infinite, and, even after being renormalised by the introduction of a uniform neutralising background, are very slow to converge with cell size. The periodicity introduces spurious electric fields which decay slowly with cell size and which also slow the convergence of other properties relating to the ground state charge density. This paper presents a simple self-consistent technique for producing rapid convergence of both energies and charge distribution in the particular geometry of 2D periodicity, as used for studying surfaces.

Ground state charge density prediction in C-BN nanoflakes using rotation equivariant feature-free artificial neural networks

Ab initio methods have been the workhorse for the computational investigation of new materials during the past few decades. In spite of the improvements regarding the efficiency and scalability achieved by various implementations, the self-consistent solution of the Konhn-Sham equations remains challenging as the size of the system increases. We propose here machine learning methods based on a feature-free deep ANN approach that are able to predict the ground state charge density by starting from readily accessible free-atom charge densities, thus bypassing the usual Hamiltonian diagonalization. We validate our approach on hybrid C-BN nanoflakes with random atomic configurations by comparing the predicted charge density to that computed by DFT. The ANN architecture is optimized in order to reach the high prediction accuracy required to extract ground state based material properties. In order to correlate the effect of spatial rotations in the input-output mapping, we introduce a novel rotational equivariant network (RE-ANN), by properly symmetrizing the synaptic weights during training. This regularization procedure enhances the prediction accuracy, provides consistent results under rotation operations and also increases the sparsity of the weight matrix. These methods have the potential to speed-up DFT simulations and can be used as high throughput investigation tools.

A first-principles Quantum Monte Carlo study of two-dimensional (2D) GaSe

Two-dimensional (2D) post-transition metal chalcogenides (PTMCs) have attracted attention due to their suitable bandgaps and lower exciton binding energies, making them more appropriate for electronic, optical, and water-splitting devices than graphene and monolayer transition metal dichalcogenides. Of the predicted 2D PTMCs, GaSe has been reliably synthesized and experimentally characterized. Despite this fact, quantities such as lattice parameters and band character vary significantly depending on which density functional theory (DFT) functional is used. Although many-body perturbation theory (GW approximation) has been used to correct the electronic structure and obtain the excited state properties of 2D GaSe, and solving the Bethe-Salpeter equation (BSE) has been used to find the optical gap, we find that the results depend strongly on the starting wavefunction. In an attempt to correct these discrepancies, we employed the many-body Diffusion Monte Carlo (DMC) method to calculate the ground and excited state properties of GaSe because DMC has a weaker dependence on the trial wavefunction. We benchmark these results with available experimental data, DFT [local-density approximation, Perdew-Burke-Ernzerhof (PBE), strongly constrained and appropriately normed (SCAN) meta-GGA, and hybrid (HSE06) functionals] and GW-BSE (using PBE and SCAN wavefunctions) results. Our findings confirm that monolayer GaSe is an indirect gap semiconductor (Γ-M) with a quasiparticle electronic gap in close agreement with experiment and low exciton binding energy. We also benchmark the optimal lattice parameter, cohesive energy, and ground state charge density with DMC and various DFT methods. We aim to present a terminal theoretical benchmark for pristine monolayer GaSe, which will aid in the further study of 2D PTMCs using DMC methods.

Compton profile of few-layer graphene investigated by electron energy-loss spectroscopy

In this paper, acquisition of the valence Compton profile of few-layer graphene using electron energy-loss spectroscopy at large scattering angle is reported. The experimental Compton profile is compared with the corresponding theoretical profile, calculated using the full-potential linearized augmented plane wave method based on the local-density approximation. Good agreement exists between the theoretical calculation and experiment. The graphene profile indicates a substantially greater delocalization of the ground state charge density compared to that of graphite.

Systematic Study of the Nuclear Structure for Some Exotic Nuclei Using Skyrme–Hartree–Fock Method

The ground state charge, neutron, proton and matter densities, the associated nuclear radii and the binding energy per nucleon of 8B, 17Ne, 23Al and 27P halo nuclei have been investigated using the Skyrme–Hartree–Fock (SHF) model with the new SKxs25 parameters. According to the calculated results, it is found that the SHF model with these Skyrme parameters provides a good description on the nuclear structure of above proton-rich halo nuclei. The elastic charge form factors of 8B and 17Ne halo nuclei and those of their stable isotopes 10B and 20Ne are calculated using plane-wave Born approximation with the charge density distributions obtained by SHF model to investigate the effect of the extended charge distributions of proton-rich nuclei on the elastic electron scattering. Calculations show that the major difference between the elastic charge form factors of halo nuclei and those of their stable isotopes is caused by the variation in the charge density distributions, especially the details of the outer parts.

Investigation of Electron Momentum Density in Carbon Nanotubes Using Transmission Electron Microscopy.

Valence Compton profiles (CPs) of multiwall (MWCNTs) and single-wall carbon nanotubes (SWCNTs) were obtained by recording electron energy-loss spectra at large momentum transfer in the transmission electron microscope, a technique known as electron Compton scattering from solids (ECOSS). The experimental MWCNT/SWCNT results were compared with that of graphite. Differences between the valence CPs of MWCNTs and SWCNTs were observed, and the SWCNT CPs indicate a greater delocalization of the ground-state charge density compared to graphite. The results clearly demonstrate the feasibility and potential of the ECOSS technique as a complementary tool for studying the electronic structure of materials with nanoscale spatial resolution.

Nuclear Structure Investigation of Some Ni-Isotopes Using Skyrme-Hartree-Fock Method

The nuclear ground-state structure of some Nickel (58-66Ni) isotopes has been investigated within the framework of the mean field approach using the self-consist Hartree-Fock calculations (HF) including the effective interactions of Skyrme. The Skyrme parameterizations SKM, SKM*, SI, SIII, SKO, SKE, SLY4, SKxs15, SKxs20 and SKxs25 have been utilized with HF method to study the nuclear ground state charge, mass, neutron and proton densities with the corresponding root mean square radii, charge form factors, binding energies and neutron skin thickness. The deduced results led to specifying one set or more of Skyrme parameterizations that used to achieve the best agreement with the available experimental data.

Investigation of the Static Nuclear Properties of Some Cr-Isotopes Using Skyrme-Hartree-Fock Method

The self-consistent Hartree-Fock (HF) calculations with several Skyrme parameterizations; SKM, SKM*, SLY4, SKxs25, MSK7, SKO, SKxta, and SKxtb have been used to investigate some static nuclear ground-state properties of some Chromium (50-54Cr) isotopes. The nuclear ground state charge, mass, neutron and proton densities with the corresponding root mean square radii, the charge form factors, the total binding energies and the neutron skin thickness can be calculated. The calculations are performed using NuShellX@MSU code, where the deduced results led to specifying one set or more of Skyrme parameterizations that used to achieve the best agreement with the available experimental data.

The effect of short range correlation on the inelastic C4 form factors of 18O nucleus

The effect of short range correlations on the inelastic longitudinalCoulomb form factors for different states of J   4 , T  1withexcitation energies 3.553,7.114, 8.960 and 10.310 MeV in 18O isanalyzed. This effect (which depends on the correlation parameter )is inserted into the ground state charge density distribution throughthe Jastrow type correlation function. The single particle harmonicoscillator wave function is used with an oscillator size parameter b.The parameters  and b are considered as free parameters, adjustedfor each excited state separately so as to reproduce the experimentalroot mean square charge radius of 18O. The model space of 18O doesnot contribute to the transition charge density. As a result, theinelastic Coulomb form factors of 18O comes absolutely from thecore polarization transition charge density. According to thecollective modes of nuclei, the core polarization transition chargedensity is assumed to have the form of Tassie shape. It is found thatthe introduction of the effect of short range correlations is necessaryfor obtaining a remarkable modification in the calculated inelasticlongitudinal Coulomb form factors and considered as an essential forexplanation the data amazingly throughout the whole range ofconsidered momentum transfer.

The effect of short range correlation on the inelastic C2 and C4 form factors of 18O nucleus

The effect of short range correlations on the inelastic Coulomb form factors for excited +2 states (1.982, 3.919, 5.250 and 8.210MeV) and +4 states (3.553, 7.114, 8.960 and 10.310 MeV) in O18 is analyzed. This effect (which depends on the correlation parameterβ) is inserted into the ground state charge density distribution through the Jastrow type correlation function. The single particle harmonic oscillator wave function is used with an oscillator size parameter .b The parameters β and b are adjusted for each excited state separately so as to reproduce the experimental root mean square charge radius of .18O The nucleusO18 is considered as an inert core of C12 with two protons and four neutrons distributed over 212521211sdp−− active orbits. The total transition charge density comes from both the model space and core polarization transition charge densities. The realistic effective interaction of Reehal–Wildenthal (REWIL) is used for this model space. It is found that the introduction of the effect of short range correlations is necessary for obtaining a remarkable improvement for the calculated inelastic Coulomb form factors and considered as an essential for explanation the data amazingly throughout the whole range of considered momentum transfer.

The study of nuclear structure for some nuclei

An analytical form of the ground state charge density distributionsfor the low mass fp shell nuclei ( 40  A  56 ) is derived from asimple method based on the use of the single particle wave functionsof the harmonic oscillator potential and the occupation numbers ofthe states, which are determined from the comparison between theoryand experiment.For investigating the inelastic longitudinal electron scattering formfactors, an expression for the transition charge density is studiedwhere the deformation in nuclear collective modes is taken intoconsideration besides the shell model space transition density. Thecore polarization transition density is evaluated by adopting theshape of Tassie model together with the derived form of the groundstate charge density distribution. In this work, we devote ourinvestigation on 0 3 2 3 1 1   transition of Ti 50 , 0 1 2 1 1 1   transitionof Cr 50 and 0 2 2 2 1 1   of Cr 52 nuclei. It is found that the corepolarization effects, which represent the collective modes, areessential for reproducing a remarkable agreement between thecalculated inelastic longitudinal C2 form factors and those ofexperimental data.

Inelastic Longitudinal C2 Form Factors with Core-Polarization Effects for 10B Nucleus

An effective two-body density operator for point nucleon system folded with the full two-body correlations (which include the tensor correlations and short-range correlations), which take account of the effect of the strong tensor force and the strong short-range repulsion in the nucleon–nucleon forces, is produced and used to derive an explicit form for ground-state two-body charge density distributions. The inelastic longitudinal form factors C2 are calculated using this transition charge density with excitation of the levels in 10B (J π , T):(1+, 0) at E x = 0.718 MeV, (1+, 0) at E x = 2.154 MeV, (2+, 0) at E x = 3.587 MeV, (3+, 0) at E x = 4.774 MeV, (2+, 0) at E x = 5.920 MeV, and (4+, 0) at E x = 6.025 MeV. In this work, the core-polarization transition density is evaluated by adopting the shape of Tassie model together with the derived form of the ground-state two-body charge density distributions with the effect of higher occupation probabilities η. It is noticed that the core-polarization effects which represent the collective modes are essential in obtaining a remarkable agreement between the calculated inelastic longitudinal F(q)s and those of the experimental data.

Communication: Investigation of the electron momentum density distribution of nanodiamonds by electron energy-loss spectroscopy.

The electron momentum distribution of detonation nanodiamonds (DND) was investigated by recording electron energy-loss spectra at large momentum transfer in the transmission electron microscope (TEM), which is known as electron Compton scattering from solid (ECOSS). Compton profile of diamond film obtained by ECOSS was found in good agreement with prior photon experimental measurement and theoretical calculation that for bulk diamond. Compared to the diamond film, the valence Compton profile of DND was found to be narrower, which indicates a more delocalization of the ground-state charge density for the latter. Combining with other TEM characterizations such as high-resolution transmission electron spectroscopy, diffraction, and energy dispersive X-ray spectroscopy measurements, ECOSS was shown to be a great potential technique to study ground-state electronic properties of nanomaterials.

Multicomponent Skyrmion Lattices and Their Excitations

We study quantum Hall ferromagnets with a finite density of topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrized by a d-component spinor field. In the absence of anisotropies we find a hexagonal Skyrmion lattice that completely breaks the underlying SU(d) symmetry with the low-lying excitation spectrum separating into d(2) - 1 gapless acoustic magnetic modes and a magnetophonon. The ground state charge density modulations, which inevitably exist in these lattices, vanish exponentially in d. We discuss the role of effective mass anisotropy for SU(3)-valley Skyrmions relevant to experiments with AlAs quantum wells. Here we find a transition which breaks a sixfold rotational symmetry of the triangular lattice, followed by the formation of a square lattice at large values of anisotropy strength.