Approaching chemical accuracy with density functional calculations: Diatomic energy corrections
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Native defects in Tl{sub 6}SI{sub 4}: Density functional calculations
Tl{sub 6}SI{sub 4} is a promising room-temperature semiconductor radiation detection material. Here, we report density functional calculations of native defects and dielectric properties of Tl{sub 6}SI{sub 4}. Formation energies and defect levels of native point defects and defect complexes are calculated. Donor-acceptor defect complexes are shown to be abundant in Tl{sub 6}SI{sub 4}. High resistivity can be obtained by Fermi level pinning by native donor and acceptor defects. Deep donors that are detrimental to electron transport are identified and methods to mitigate such problem are discussed. Furthermore, we show that mixed ionic-covalent character of Tl{sub 6}SI{sub 4} gives rise to enhanced Born effective charges and large static dielectric constant, which provides effective screening of charged defects and impurities.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Localized orbital corrections for density functional calculations on transition metal containing systems
Not Available
Friesner, Richard A.↗
Charge compensation and electrostatic transferability in three entropy-stabilized oxides: Results from density functional theory calculations
Density functional theory calculations were carried out for three entropic rocksalt oxides, (Mg{sub 0.1}Co{sub 0.1}Ni{sub 0.1}Cu{sub 0.1}Zn{sub 0.1})O{sub 0.5}, termed J14, and J14 + Li and J14 + Sc, to understand the role of charge neutrality and electronic states on their properties, and to probe whether simple expressions may exist that predict stability. The calculations predict that the average lattice constants of the ternary structures provide good approximations to that of the random structures. For J14, Bader charges are transferable between the binary, ternary, and random structures. For J14 + Sc and J14 + Li, average Bader charges in the entropic structures can be estimated from the ternary compositions. Addition of Sc to J14 reduces the majority of Cu, which show large displacements from ideal lattice sites, along with reduction of a few Co and Ni cations. Addition of Li to J14 reduces the lattice constant, consistent with experiment, and oxidizes some of Co as well as some of Ni and Cu. The Bader charges and spin-resolved density of states (DOS) for Co{sup +3} in J14 + Li are very different from Co{sup +2}, while for Cu and Ni the Bader charges form continuous distributions and the two DOS are similar for the two oxidation states. Experimental detection of different oxidation states may therefore be challenging for Cu and Ni compared to Co. Based on these results, empirical stability parameters for these entropic oxides may be more complicated than those for non-oxide entropic solids.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Electronic Structure, Phonon Dynamical Properties, and CO 2 Capture Capability of Na 2 - x M x Zr O 3 ( M = Li ,K): Density-Functional Calculations and Experimental Validations
The electronic structural and phonon properties of Na 2-α M α ZrO 3 (M ¼ Li,K, α = ¼ 0.0,0.5,1.0,1.5,2.0) are investigated by first-principles density-functional theory and phonon dynamics. The thermodynamic properties of CO 2 absorption and desorption in these materials are also analyzed. With increasing doping level α, the binding energies of Na 2-α Li α ZrO 3 are increased while the binding energies of Na 2-α K α ZrO 3 are decreased to destabilize the structures. The calculated band structures and density of states also show that, at the same doping level, the doping sites play a significant role in the electronic properties. The phonon dispersion results show that few soft modes are found in several doped configurations, which indicates that these structures are less stable than other configurations with different doping levels. From the calculated relationships among the chemical-potential change, the CO 2 pressure, and the temperature of the CO 2 capture reactions by Na 2-α M α ZrO 3 , and from thermogravimetric-analysis experimental measurements, the Li- and K-doped mixtures Na 2-α M α ZrO 3 have lower turnover temperatures (T t ) and higher CO 2 capture capacities, compared to pure Na 2 ZrO 3 . The Li-doped systems have a larger T t decrease than the K-doped systems. When increasing the Li-doping level α, the T t of the corresponding mixture Na 2-α Li α ZrO 3 decreases further to a low-temperature range. However, in the case of K-doped systems Na 2-α K α ZrO 3 , although doping K into Na 2 ZrO 3 initially shifts its T t to lower temperatures, further increases of the K-doping level α causes T t to increase. Therefore, doping Li into Na 2 ZrO 3 has a larger influence on its CO 2 capture performance than the K-doped Na 2 ZrO 3 . Compared with pure solidsM 2 ZrO 3 , after doping with other elements, these doped systems’ CO 2 capture performances are improved.
Duan, Yuhua↗
Antisites in III-V semiconductors: Density functional theory calculations
Density functional based simulation, corrected for finite size effects, is used to investigate systematically the formation of antisite defects in III-V semiconductors (III = Al, Ga, and In and V = P, As, and Sb). Different charge states are modelled as a function of the Fermi level and under different growth conditions. The formation energies of group III antisites (III{sub V}{sup q}) decrease with increasing covalent radius of the group V atom though not group III radius, whereas group V antisites (V{sub III}{sup q}) show a consistent decrease in formation energies with increase in group III and group V covalent radii. In general, III{sub V}{sup q} defects dominate under III-rich conditions and V{sub III}{sup q} under V-rich conditions. Comparison with equivalent vacancy formation energy simulations shows that while antisite concentrations are always dominant under stoichiometric conditions, modest variation in growth or doping conditions can lead to a significantly higher concentration of vacancies.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Interaction of TiO{sub 2}{sup −} with water: Photoelectron spectroscopy and density functional calculations
The interactions of titania with water molecules were studied via photoelectron spectroscopy and density functional calculations of TiO(OH){sub 2}{sup −} and Ti(OH){sub 4}(H{sub 2}O){sub n}{sup −} (n = 0–5) clusters which are corresponding to the TiO{sub 2}(H{sub 2}O){sup −} and TiO{sub 2}(H{sub 2}O){sub n+2}{sup −} (n = 0–5) systems, respectively. Experimental observation and theoretical calculations confirmed that TiO(OH){sub 2}{sup −} was produced when TiO{sub 2}{sup −} interacts with one water molecule, and Ti(OH){sub 4}(H{sub 2}O){sub n}{sup −} (n = 0–5) were produced successively when TiO{sub 2}{sup −} interacts with two or more water molecules. The structures of Ti(OH){sub 4}(H{sub 2}O){sub n}{sup −} with n = 4, 5 are slightly different from those of n = 1–3. The structures of Ti(OH){sub 4}(H{sub 2}O){sub 1-3}{sup −} can be viewed as the water molecules interacting with the Ti(OH){sub 4}{sup −} core through hydrogen bonds; however, in Ti(OH){sub 4}(H{sub 2}O){sub 4,5}{sup −}, one of the water molecules interacts directly with the Ti atom via its oxygen atom instead of a hydrogen bond and distorted the Ti(OH){sub 4}{sup −} core.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Large-scale real-space density-functional calculations: Moiré-induced electron localization in graphene
We show that our real-space finite-difference scheme allows us to perform density-functional calculations for nanometer-scale targets containing more than 100 000 atoms. This real-space scheme is applied to twisted bilayer graphene, clarifying that Moiré pattern induced in the slightly twisted bilayer graphene drastically modifies the atomic and electronic structures.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Adaptively Compressed Exchange Operator for Large-Scale Hybrid Density Functional Calculations with Applications to the Adsorption of Water on Silicene
Density functional theory (DFT) calculations using hybrid exchange-correlation functionals have been shown to provide an accurate description of the electronic structures of nanosystems. However, such calculations are often limited to small system sizes due to the high computational cost associated with the construction and application of the Hartree-Fock (HF) exchange operator. Here, we demonstrate that the recently developed adaptively compressed exchange (ACE) operator formulation [J. Chem. Theory Comput. 2016, 12, 2242-2249] can enable hybrid functional DFT calculations for nanosystems with thousands of atoms. The cost of constructing the ACE operator is the same as that of applying the exchange operator to the occupied orbitals once, while the cost of applying the Hamiltonian operator with a hybrid functional (after construction of the ACE operator) is only marginally higher than that associated with applying a Hamiltonian constructed from local and semilocal exchange-correlation functionals. Therefore, this new development significantly lowers the computational barrier for using hybrid functionals in large-scale DFT calculations. We demonstrate that a parallel planewave implementation of this method can be used to compute the ground-state electronic structure of a 1000-atom bulk silicon system in less than 30 wall clock minutes and that this method scales beyond 8000 computational cores for a bulk silicon system containing about 4000 atoms. The efficiency of the present methodology in treating large systems enables us to investigate adsorption properties of water molecules on Ag-supported two-dimensional silicene. Our computational results show that water monomer, dimer, and trimer configurations exhibit distinct adsorption behaviors on silicene. In particular, the presence of additional water molecules in the dimer and trimer configurations induces a transition from physisorption to chemisorption, followed by dissociation on Ag-supported silicene. This is caused by the enhanced effect of hydrogen bonds on charge transfer and proton transfer processes. Lastly, such a hydrogen bond autocatalytic effect is expected to have broad applications for silicene as an efficient surface catalyst for oxygen reduction reactions and water dissociation.
36 MATERIALS SCIENCE↗
Linear Scaling Density Functional Calculations with Gaussian Orbitals
Recent advances in linear scaling algorithms that circumvent the computational bottlenecks of large-scale electronic structure simulations make it possible to carry out density functional calculations with Gaussian orbitals on molecules containing more than 1000 atoms and 15000 basis functions using current workstations and personal computers. This paper discusses the recent theoretical developments that have led to these advances and demonstrates in a series of benchmark calculations the present capabilities of state-of-the-art computational quantum chemistry programs for the prediction of molecular structure and properties.
Scuseria, Gustavo E.↗
Electronic bands and excited states of III-V semiconductor polytypes with screened-exchange density functional calculations
The electronic band structures and excited states of III-V semiconductors such as GaP, AlP, AlAs, and AlSb for various polytypes are determined employing the screened-exchange density functional calculations implemented in the full-potential linearized augmented plane-wave methods. We demonstrate that GaP and AlSb in the wurtzite (WZ) structure have direct gap while III-V semiconductors in the zinc blende, 4H, and 6H structures considered in this study exhibit an indirect gap. Furthermore, we find that inclusion of Al atoms less than 17% and 83% in the hexagonal Al{sub x}Ga{sub 1−x}P and Al{sub x}Ga{sub 1−x}As alloys, respectively, leads to a direct transition with a gap energy of ∼2.3 eV. The feasibility of III-V semiconductors with a direct gap in WZ structure offers a possible crystal structure engineering to tune the optical properties of semiconductor materials.
36 MATERIALS SCIENCE↗
Accurate Hellmann–Feynman forces from density functional calculations with augmented Gaussian basis sets
The Hellmann–Feynman (HF) theorem provides a way to compute forces directly from the electron density, enabling efficient force calculations for large systems through machine learning (ML) models for the electron density. The main issue holding back the general acceptance of the HF approach for atom-centered basis sets is the well-known Pulay force which, if naively discarded, typically constitutes an error upward of 10 eV/Å in forces. In this work, we demonstrate that if a suitably augmented Gaussian basis set is used for density functional calculations, the Pulay force can be suppressed, and HF forces can be computed as accurately as analytical forces with state-of-the-art basis sets, allowing geometry optimization and molecular dynamics to be reliably performed with HF forces. Our results pave a clear path forward for the accurate and efficient simulation of large systems using ML densities and the HF theorem.
Pathak, Shivesh (ORCID:0000000172798195)↗
Accurate double excitations from ensemble density functional calculations
The recent use of a new ensemble in density functional theory (DFT) to produce direct corrections to the Kohn-Sham transitions yields the elusive double excitations that are missed by time-dependent DFT (TDDFT) with the standard adiabatic approximation. But accuracies are lower than for single excitations, and formal arguments about TDDFT suggest that a correction kernel is needed. In principle, ensemble DFT with direct corrections at the exchange level must yield accurate doubles in the weakly correlated limit. We illustrate with exact calculations and analytic results on the Hubbard dimer. Lastly, we also explain the error in formal arguments in TDDFT.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Broken symmetry approach to density functional calculation of zero field splittings including anisotropic exchange interactions
The broken symmetry approach to the calculation of zero field splittings (or magnetic anisotropies) of multinuclear transition metal complexes is further developed. A procedure is suggested how to extract spin Hamiltonian parameters for anisotropic exchange from a set of broken symmetry density functional calculations. For isotropic exchange coupling constants J{sub ij}, the established procedure is retrieved, and anisotropic (or pseudodipolar) exchange coupling tensors D{sub ij} are obtained analogously. This procedure only yields the sum of the individual single-ion zero field splitting tensors D{sub i}. Therefore, a procedure based on localized orbitals has been developed to extract the individual single-ion contributions. With spin Hamiltonian parameters at hand, the zero field splittings of the individual spin multiplets are calculated by an exact diagonalization of the isotropic part, followed by a spin projection done numerically. The method is applied to the binuclear cation [LCr(OH){sub 3}CrL]{sup 3+} (L = 1,4,7-trimethyl-1,4,7-triazanonane) for which experimental zero field splittings for all low-energy spin states are known, and to the single-molecule magnet [Fe{sub 4}(CH{sub 3}C(CH{sub 2}O){sub 3}){sub 2}(dpm){sub 6}] (Hdpm = 2,2,6,6-tetramethylheptane-3,5-dione). In both these 3d compounds, the single-ion tensors mainly come from the spin-orbit interaction. Anisotropic exchange is dominated by the spin-dipolar interaction only for the chromium compound. Despite the rather small isotropic exchange couplings in the iron compound, spin-orbit and spin-dipolar contributions to anisotropic exchange are of similar size here.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Density Functional Calculations of Native Defects in CH 3 NH 3 PbI 3 : Effects of Spin–Orbit Coupling and Self-Interaction Error
We know that native point defects play an important role in carrier transport properties of CH3NH3PbI3. However, the nature of many important defects remains controversial due partly to the conflicting results reported by recent density functional theory (DFT) calculations. In this Letter, we show that self-interaction error and the neglect of spin–orbit coupling (SOC) in many previous DFT calculations resulted in incorrect positions of valence and conduction band edges, although their difference, which is the band gap, is in good agreement with the experimental value. Moreover, this problem has led to incorrect predictions of defect-level positions. Hybrid density functional calculations, which partially correct the self-interaction error and include the SOC, show that, among native point defects (including vacancies, interstitials, and antisites), only the iodine vacancy and its complexes induce deep electron and hole trapping levels inside of the band gap, acting as nonradiative recombination centers.
36 MATERIALS SCIENCE↗
Molecular NMR shieldings, J -couplings, and magnetizabilities from numeric atom-centered orbital based density-functional calculations
This paper reports and benchmarks a new implementation of nuclear magnetic resonance shieldings, magnetizabilities, and J-couplings for molecules within semilocal density functional theory, based on numeric atom-centered orbital (NAO) basis sets. NAO basis sets are attractive for the calculation of these nuclear magnetic resonance (NMR) parameters because NAOs provide accurate atomic orbital representations especially near the nucleus, enabling high-quality results at modest computational cost. Moreover, NAOs are readily adaptable for linear scaling methods, enabling efficient calculations of large systems. Here, the paper has five main parts: (1) It reviews the formalism of density functional calculations of NMR parameters in one comprehensive text to make the mathematical background available in a self-contained way. (2) The paper quantifies the attainable precision of NAO basis sets for shieldings in comparison to specialized Gaussian basis sets, showing similar performance for similar basis set size. (3) The paper quantifies the precision of calculated magnetizabilities, where the NAO basis sets appear to outperform several established Gaussian basis sets of similar size. (4) The paper quantifies the precision of computed J-couplings, for which a group of customized NAO basis sets achieves precision of ~Hz for smaller basis set sizes than some established Gaussian basis sets. (5) The paper demonstrates that the implementation is applicable to systems beyond 1000 atoms in size.
74 ATOMIC AND MOLECULAR PHYSICS↗
GPU acceleration of local and semilocal density functional calculations in the SPARC electronic structure code
We present a Graphics Processing Unit (GPU)-accelerated version of the real-space SPARC electronic structure code for performing Kohn–Sham density functional theory calculations within the local density and generalized gradient approximations. In particular, we develop a modular math-kernel based implementation for NVIDIA architectures wherein the computationally expensive operations are carried out on the GPUs, with the remainder of the workload retained on the central processing units (CPUs). Here, using representative bulk and slab examples, we show that relative to CPU-only execution, GPUs enable speedups of up to 6× and 60× in node and core hours, respectively, bringing time to solution down to less than 30 s for a metallic system with over 14 000 electrons and enabling significant reductions in computational resources required for a given wall time.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon
We present a new efficient way to perform hybrid density functional theory (DFT)-based electronic structure calculations. The new method uses an interpolative separable density fitting (ISDF) procedure to construct a set of numerical auxiliary basis vectors and a compact approximation of the matrix consisting of products of occupied orbitals represented in a large basis set such as the planewave basis. Such an approximation allows us to reduce the number of Poisson solves from O ($N$ $^{2}_{ϵ}$) to O ( N ϵ ) when we apply the exchange operator to occupied orbitals in an iterative method for solving the Kohn–Sham equations, where Ne is the number of electrons in the system to be studied. We show that the ISDF procedure can be carried out in O ($N$ $^{3}_{ϵ}$) operations, with a much smaller preconstant compared to methods used in existing approaches. When combined with the recently developed adaptively compressed exchange (ACE) operator formalism, which reduces the number of times the exchange operator needs to be updated, the resulting ACE-ISDF method significantly reduces the computational cost associated with the exchange operator by nearly 2 orders of magnitude compared to existing approaches for a large silicon system with 1000 atoms. We demonstrate that the ACE-ISDF method can produce accurate energies and forces for insulating and metallic systems and that it is possible to obtain converged hybrid functional calculation results for a 1000-atom bulk silicon within 10 min on 2000 computational cores. We also show that ACE-ISDF can scale to 8192 computational cores for a 4096-atom bulk silicon system. We use the ACE-ISDF method to geometrically optimize a 1000-atom silicon system with a vacancy defect using the HSE06 functional and computes its electronic structure. Here, we find that that the computed energy gap from the HSE06 functional is much closer to the experimental value compared to that produced by semilocal functionals in the DFT calculations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗