All-electron Density Functional Theory Research Articles

Accurate frozen core approximation for all-electron density-functional theory.

We implement and benchmark the frozen core approximation, a technique commonly adopted in electronic structure theory to reduce the computational cost by means of mathematically fixing the chemically inactive core electron states. The accuracy and efficiency of this approach are well controlled by a single parameter, the number of frozen orbitals. Explicit corrections for the frozen core orbitals and the unfrozen valence orbitals are introduced, safeguarding against seemingly minor numerical deviations from the assumed orthonormality conditions of the basis functions. A speedup of over twofold can be achieved for the diagonalization step in all-electron density-functional theory simulations containing heavy elements, without any accuracy degradation in terms of the electron density, total energy, and atomic forces. This is demonstrated in a benchmark study covering 103 materials across the Periodic Table and a large-scale simulation of CsPbBr3 with 2560 atoms. Our study provides a rigorous benchmark of the precision of the frozen core approximation (sub-meV per atom for frozen core orbitals below -200 eV) for a wide range of test cases and for chemical elements ranging from Li to Po. The algorithms discussed here are implemented in the open-source Electronic Structure Infrastructure software package.

Treecode-accelerated Green iteration for Kohn-Sham density functional theory

We present a real-space computational method called treecode-accelerated Green Iteration (TAGI) for all-electron Kohn-Sham Density Functional Theory. TAGI is based on a reformulation of the Kohn-Sham equations in which the eigenvalue problem in differential form is converted into a fixed-point problem in integral form by convolution with the modified Helmholtz Green's function. In each self-consistent field (SCF) iteration, the fixed-points are computed by Green Iteration, where the discrete convolution sums are efficiently evaluated by a GPU-accelerated barycentric Lagrange treecode. Other techniques used in TAGI include a-priori adaptive mesh refinement, Fejér quadrature, singularity subtraction, gradient-free eigenvalue update, and Anderson mixing to accelerate convergence of the SCF and Green Iterations. Ground state energy computations of several atoms (Li, Be, O) and small molecules (H2, CO, C6H6) demonstrate TAGI's ability to efficiently achieve chemical accuracy.

Orthogonalized Enriched Finite Elements - A Robust, Accurate and Efficient Basis for All-Electron Density Functional Theory Calculations

Orthogonalized Enriched Finite Elements - A Robust, Accurate and Efficient Basis for All-Electron Density Functional Theory Calculations

Perturbation approach to ab initio effective mass calculations

A degenerate perturbation k⋅p approach for effective mass calculations is implemented in the all-electron density functional theory (DFT) package WIEN2k. The accuracy is tested on major group IVA, IIIA–VA, and IIB–VIA semiconductor materials. Then, the effective mass in graphene and CuI with defects is presented as illustrative applications. For states with significant Cu-d character additional local orbitals with higher principal quantum numbers (more radial nodes) have to be added to the basis set in order to converge the results of the perturbation theory. Caveats related to a difference between velocity and momentum matrix elements are discussed in the context of application of the method to non-local potentials, such as Hartree–Fock/DFT hybrid functionals and DFT+U.

Role of opacity at the 9 keV back lighter energy used in measuring the equation of state of boron at pressures up to a Gbar

Many experiments have been conducted at the National Ignition Facility to measure the equation of state Hugoniot of plastic, boron, and diamond at extreme pressures up to a Gbar. The “Gbar” design employs a strong spherically converging shock launched through a solid ball of material using a hohlraum radiation drive. The shock front conditions are characterized using X-ray radiography, typically at energies near 9 keV. In this paper we examine how the opacity of boron at 9 keV changes at high pressures and temperatures. Understanding this is vital to unfolding the density in the shock front as pressures exceed 100 Mbar. We compare opacity calculations from a number of methods including the legacy XSN opacity tables, super transition array (STA), average atom (AVAT), and detailed configuration accounting (DCA) methods. We examine how the changing opacity is correlated with the K-shell occupation calculated using the opacity methods as well as other electronic structure methods such as MECCA, Purgatorio, and an all-electron Kohn-Sham density functional theory calculation that uses optimized all-electron norm-conserving Vanderbilt pseudopotentials (ONCV). We also examine the relative contribution of free-free opacity to the overall opacity, which is dominated by bound-free absorption.

Influence of Polymorphism on the Electronic Structure of Ga2O3

The search for new wide band gap materials is intensifying to satisfy the need for more advanced and energy efficient power electronic devices. Ga$_2$O$_3$ has emerged as an alternative to SiC and GaN, sparking a renewed interest in its fundamental properties beyond the main $\beta$-phase. Here, three polymorphs of Ga$_2$O$_3$, $\alpha$, $\beta$ and $\varepsilon$, are investigated using X-ray diffraction, X-ray photoelectron and absorption spectroscopy, and ab initio theoretical approaches to gain insights into their structure - electronic structure relationships. Valence and conduction electronic structure as well as semi-core and core states are probed, providing a complete picture of the influence of local coordination environments on the electronic structure. State-of-the-art electronic structure theory, including all-electron density functional theory and many-body perturbation theory, provide detailed understanding of the spectroscopic results. The calculated spectra provide very accurate descriptions of all experimental spectra and additionally illuminate the origin of observed spectral features. This work provides a strong basis for the exploration of the Ga$_2$O$_3$ polymorphs as materials at the heart of future electronic device generations.

Pentacene and tetracene molecules and films on H/Si(111): level alignment from hybrid density functional theory

The electronic properties of hybrid organic–inorganic semiconductor interfaces depend strongly on the alignment of the electronic carrier levels in the organic/inorganic components. In the present work, we address this energy level alignment from first principles theory for two paradigmatic organic–inorganic semiconductor interfaces, the singlet fission materials tetracene and pentacene on H/Si(111), using all-electron density functional theory calculations with a hybrid exchange–correlation functional. For isolated tetracene on H/Si(111), a type I-like heterojunction (lowest-energy electron and hole states on Si) is found. For isolated pentacene, the molecular and semiconductor valence band edges are degenerate. For monolayer films, we show how to construct supercell geometries with up to 1192 atoms, which minimize the strain between the inorganic surface and an organic monolayer film. Based on these models, we predict the formation of type II heterojunctions (electron states on Si, hole-like states on the organic species) for both acenes, indicating that charge separation at the interface between the organic and inorganic components is favored. The paper discusses the steps needed to find appropriate low-energy interface geometries for weakly bonded organic molecules and films on inorganic substrates from first principles, a necessary prerequisite for any computational level alignment prediction.

Density functional theory plane-wave/pseudopotential calculations of the equation of state of rhenium in the terapascal regime

The equation of state (EOS) of hexagonal close-packed rhenium has been previously determined up to 1.5 TPa (V/V0 = 0.46) using all-electron (AE) density functional theory (DFT) including core relativistic effects [Phys. Rev. B 100, 174107 (2019)]. This work focuses on assessing the validity of pseudopotentials at such high-pressures, above 1 terapascal (TPa), by comparing the EOS obtained using plane-wave/pseudopotentials (PW/PPs) with previous AE calculations. Both ONCV pseudopotentials tested (PBE and PBEsol) yield results in good agreement with all-electron calculations. The fitted parameters of the Rose-Vinet EOS, the bulk modulus, B0 (380(2) GPa and 379(3) GPa for the PBE and PBEsol PPs), and its pressure derivative, B0’(4.58(2) and 4.59(3) for the PBE and PBEsol PPs), are in good agreement with previous all-electron results (B0=367(5) GPa and B0’=4.64(3)). The agreement is worse for the equilibrium volume at zero pressure, V0 (199.9(2) Bohr3 and 199.2(2) Bohr3 for PBE and PBEsol PPs, versus 196.7(3) Bohr3 for AE). Even so, for a given V/V0 ratio, the pressures estimated using the EOS derived from the PPs and AE calculations are in very good agreement, thus suggesting that the PPs used in this study are valid even at such high compression regime.

Theoretical insights into the performance of graphene derivatives, h-BN and BNC heterostructures in the adsorption and elimination of atrazine: An all-electron DFT study

The emergence of nanostructures with tunable chemical properties has triggered a great deal of interests in exploring their potential capabilities in adsorption processes. In this study, density functional theory (DFT) based calculations have been carried out to investigate the capability of three different hexagonal sheets namely: graphene and its defected form, h-BN and C-doped h-BN in the adsorption of atrazine molecule. These structures have been subjected to various analysis including molecular orbital interactions and energy calculations to unveil their affinity towards atrazine molecule and to understand the types as well as magnitude of their interactions with the guest molecule. The obtained results based on the adsorption energies and rotational as well as the translational energy barriers reveled that despite the existence of strong physical interactions between the involved fragments, however the mobility of adsorbed atrazine is strongly affected by the relatively low translational and rotational energy barriers for graphene monolayers while the polar bonds in hexagonal boron-nitride help in limiting the movement of atrazine. The nature of interactions between the involved molecules has also been taken into consideration and it was found that dispersion interactions play the main role in stabilizing the atrazine above the substrates. In addition, electrostatic attractions have also been found between the electronegative atoms of atrazine and electropositive boron atoms of boron-nitride. This favorable interaction further augments the stabilization of atrazine through compensating for the repulsive interactions between the highly localized electrons of N in the boron-nitride and the ring of atrazine.

GPU acceleration of all-electron electronic structure theory using localized numeric atom-centered basis functions

We present an implementation of all-electron density-functional theory for massively parallel GPU-based platforms, using localized atom-centered basis functions and real-space integration grids. Special attention is paid to domain decomposition of the problem on non-uniform grids, which enables compute- and memory-parallel execution across thousands of nodes for real-space operations, e.g. the update of the electron density, the integration of the real-space Hamiltonian matrix, and calculation of Pulay forces. To assess the performance of our GPU implementation, we performed benchmarks on three different architectures using a 103-material test set. We find that operations which rely on dense serial linear algebra show dramatic speedups from GPU acceleration: in particular, SCF iterations including force and stress calculations exhibit speedups ranging from 4.5 to 6.6. For the architectures and problem types investigated here, this translates to an expected overall speedup between 3–4 for the entire calculation (including non-GPU accelerated parts), for problems featuring several tens to hundreds of atoms. Additional calculations for a 375-atom Bi2Se3 bilayer show that the present GPU strategy scales for large-scale distributed-parallel simulations.

Theoretical study of the electronic structure and electrical properties of Al-doped niobium clusters

A methodology previously suggested for niobium clusters is here applied to the prediction of the ground spin-state of the niobium clusters doped with aluminum atoms. By using all-electron density functional theory with Douglas-Kroll-Hess correction, the spin-state, geometry, hardness, binding energy, ionization potential, electron affinity, and mean static dipole polarizability of the NbxAly clusters are examined. The ground spin-states obtained from the energy minimization were confronted with the results provided by the maximum hardness principle (MHP) and by the minimum polarizability principle (MPP). In general, the MHP and MPP have yielded the expected results, i.e., in agreement with the ones obtained from the minimum energy. Additionally, were compared the theoretical results for polarizability, ionization potential, and reactivity with the available experimental values.

Large-Z limit in atoms and solids from first principles.

We present density functional theory (DFT) calculations of atomic ionization potentials and lattice constants of simple solids from low atomic numbers Z to the large-Z limit. We compare different kinetic energy functional approximations [Kohn-Sham (KS) vs simple orbital-free functionals] and, in the case of orbital free, also different methods for including the nuclear potential (all-electron with the projector augmented wave method vs local pseudopotentials). For both ionization potentials and lattice constants, all-electron orbital-free DFT does yield the general trend of KS DFT for moderate values of the atomic number Z. For large values of Z, all-electron orbital-free DFT deviates from the KS DFT results. Local pseudopotentials give a better qualitative description by adding shell oscillations to the orbital-free DFT model. We show that both all-electron orbital-free DFT and KS DFT have a finite value for nonrelativistic lattice constants in the large-Z limit.

Substitution Effects on the Optoelectronic Properties of Coumarin Derivatives

Coumarin derivatives have gathered major attention largely due to their versatile utility in a wide range of applications. In this framework, we report a comparative computational investigation on the optoelectronic properties of 3-phenylcoumarin and 3-heteroarylcoumarin derivatives established as enzyme inhibitors. Specifically, we concentrate on the variation in the optoelectronic characteristics for the hydroxyl group substitutions within the coumarin moiety. In order to realize our aims, all-electron density functional theory and time dependent density functional theory calculations were performed with a localized Gaussian basis-set matched with a hybrid exchange–correlation functionals. Molecular properties such as highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, vertical ionization (IEV) and electron affinity energies, absorption spectra, quasi-particle gap, and exciton binding energy values are examined. Furthermore, the influence of solvent on the optical properties of the molecules is considered. We found a good agreement between the experimental (8.72 eV) and calculated (8.71 eV) IEV energy values for coumarin. The computed exciton binding energy of the investigated molecules indicated their potential optoelectronics application.

Electronic structure and core electron fingerprints of caesium-based multi-alkali antimonides for ultra-bright electron sources

The development of novel photocathode materials for ultra-bright electron sources demands efficient and cost-effective strategies that provide insight and understanding of the intrinsic material properties given the constraints of growth and operational conditions. To address this question, we propose a viable way to establish correlations between calculated and measured data on core electronic states of Cs-K-Sb materials. To do so, we combine first-principles calculations based on all-electron density-functional theory on the three alkali antimonides Cs3Sb, Cs2KSb, and CsK2Sb with x-ray photoemission spectroscopy (XPS) on Cs-K-Sb photocathode samples. Within the GW approximation of many-body perturbation theory, we obtain quantitative predictions of the band gaps of these materials, which range from 0.57 eV in Cs2KSb to 1.62 eV in CsK2Sb and manifest direct or indirect character depending on the relative potassium content. Our theoretical electronic-structure analysis also reveals that the core states of these systems have binding energies that depend only on the atomic species and their crystallographic sites, with largest shifts of the order of 2 eV and 0.5 eV associated to K 2p and Sb 3d states, respectively. This information can be correlated to the maxima in the XPS survey spectra, where such peaks are clearly visible. In this way, core-level shifts can be used as fingerprints to identify specific compositions of Cs-K-Sb materials and their relation with the measured values of quantum efficiency. Our results represent the first step towards establishing a robust connection between the experimental preparation and characterization of photocathodes, the ab initio prediction of their electronic structure, and the modeling of emission and beam formation processes.

DFT study of [Pt(Cl)2L] complex (L = rubeanic acid) and its derived compounds with DNA purine bases

In this study, we present a systematic computational investigation on the electronic properties of cisplatin (cis-[Pt(Cl)2(NH3)2] (CP) and complex [Pt(Cl)2L] (1) (L = rubeanic acid) employing all-electron density functional theory. In detail, we analyzed essential molecular properties such as geometrical parameters, ionization energies, electron affinity, highest occupied molecular orbital, and lowest unoccupied molecular orbital energies. Concerning CP, molecule 1 exhibited improved lipophilicity and a pronounced electrophilic property. Furthermore, to investigate and compare the DNA binding capability between CP and molecule 1, we extended the investigation to the guanine and adenine derived complexes, respectively. Complexes of molecule 1 with the adenine and guanine bases followed a similar trend of stability found for CP systems, with the highest affinity found for guanine complexes. Altogether, molecule 1 displayed promising physicochemical and druglikeness features to serve as a starting point for developing a drug-like enough that could be therapeutically useful.

Equation of state of hexagonal-close-packed rhenium in the terapascal regime

All-electron density functional theory calculations were performed aiming to determine the equation of state and the dependence with pressure of the $c/a$ ratio and the anisotropic compressibility for hexagonal-close-packed rhenium. Calculations were carried out up to maximum compression of 0.46, and the resulting total energy versus volume is well described by a Vinet equation of state with ${B}_{0}$ = 367(5) GPa and ${B}_{0}^{\ensuremath{'}}$ = 4.64(3), valid up to 1.5 TPa. The agreement with two recent experimental studies [S. Anzellini et al., Equation of state of rhenium and application for ultra high pressure calibration, J. Appl. Phys. 115, 043511 (2014); T. Sakai et al., High pressure generation using double-stage diamond anvil technique: Problems and equations of state of rhenium, High Pressure Res. 38, 107 (2018)] supports their conclusion that the pressure in previous experiments with a double-stage diamond-anvil cell [L. Dubrovinsky et al., Implementation of micro-ball nanodiamond anvils for high-pressure studies above 6 Mbar, Nat. Commun. 3, 1163 (2012)] was significantly overestimated.

Iron(II) Corrole Anions.

Reduction of [Fe(TPC)(THF)] (TPC = trianion of 5,10,15-triphenylcorrole) with KC8 generates the iron(II) corrole anion, K(THF)2[FeII(TPC)] (3a). Compound 3a represents the first example of an isolated and crystallographically characterized corrole complex of divalent iron. The compound adopts an intermediate-spin state (S = 1), displaying square-planar geometry about the iron atom. All-electron density functional theory (OLYP and B3LYP) calculations with STO-TZP basis sets indicate two essentially equienergetic d electron configurations, dxy2dz22dxz1dyz1 (occupation 1) and dxy2dz21dxz1dyz2 (occupation 2), as likely contenders for the ground state of [FeII(TPC)]-, with the optimized geometry of the former in slightly better agreement with the low-temperature X-ray structure. Solutions of 3a react with carbon monoxide to afford the low-spin (S = 0) complex, [Fe(TPC)(CO)]-, whereas introduction of oxygen at -78 °C leads to a putative O2 adduct, [Fe(TPC)(O2)]-, which decays rapidly even at low temperatures. Treatment of 3a with organic electrophiles results in formal oxidative addition to give both iron(III) and iron(IV) corrole species. With iodomethane, [Fe(TPC)Me] is produced, illustrating the first instance of alkyl ligand coordination in an iron corrole complex.

Energy-Level Alignment at Organic/Inorganic Interfaces from First Principles: Example of Poly(para-phenylene)/Rock-Salt ZnO(100)

By means of full-potential all-electron density-functional theory and many-body perturbation theory, we compute the band alignment at a prototypical hybrid inorganic/organic interface. The electron...

Structural transition of C6−nSinNH7 at n = 0–6 clusters upon substitution of carbon by silicon

The structural and energetic properties of C6−nSinNH7 (n = 0–6) clusters are examined using quantum chemical methods. Global minimum and low-lying isomers are generated by Molclus program, which is an optimization strategy combining semi-empirical quantum chemistry search with all-electron density functional theory, and optimized at DFT-B3LYP/6–311++G(d,p) level of theory. The electronic, optical and reactivity properties are investigated in detail. UV–vis spectra and AdNDP analyses are also performed to evaluate absorption properties and molecular orbitals. It found that a structural transition occurs at n = 2 (C4Si2NH7) where the aniline-like isomer is less stable than the global minimum. The calculated properties are compared with experimental parameters. The results are in good agreement with most available experimental findings.

SinC13-n (n = 1 – 12) Clusters: An All-electron DFT Investigation

The geometrical and electronic structures of SinC13-n (n = 1 – 12) nanoclusters have been investigated using all-electron density functional theory (DFT) with the generalized gradient approximation (GGA). The binding energies, highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps, and the vibrational frequencies have been computed. We note that the binary clusters have a number of isomeric structures with lower symmetries and the stability of the clusters increases as the number of carbon atoms increases. As the number of silicon atoms increases, the lowest-energy structures of the SinC13-n (n = 1 – 12) clusters transform from planar structures to three-dimensional structures. The HOMO-LUMO gaps of the lowest-energy structures indicate that with the exception of Si6C7 and Si12C, the ground states are of high chemical stability and have the characteristics of semiconductors. In addition, the Mulliken populations show that there is significant charge transfer from the silicon atoms to the carbon atoms.