Transition metal diborides are ceramic materials with potential applications as hard protective thin films and electrical contact materials. We investigate the possibility to obtain age hardening through isostructural clustering, including spinodal decomposition, or ordering-induced precipitation in ternary diboride alloys. By means of first-principles mixing thermodynamics calculations, 45 ternary (M1-xMxB2)-M-1-B-2 alloys comprising (MB2)-B-i (M-i = Mg, Al, Sc, Y, Ti, Zr, Hf, V, Nb, Ta) with AlB2 type structure are studied. In particular Al1-xTixB2 is found to be of interest for coherent isostructural decomposition with a strong driving force for phase separation, while having almost concentration independent a and c lattice parameters. The results are explained by revealing the nature of the electronic structure in these alloys, and in particular, the origin of the pseudogap at E-F in TiB2, ZrB2, and HfB2.
Density functional theory using accepted semi-local exchange-correlation functionals is generally successful for structural properties. However, for electrical response calculations of extended molecular systems, like e.g. polyacetylene, they make large errors; for the hyperpolarizability the error can be several orders of magnitude. The errors can be traced to qualitative differences between the exchange potentials of semi-local and exact exchange methods. A recent effort has been successful in using a corrective term based on semi-local quantities to introduce the missing features directly into the exchange potential (as opposed to modeling the exchange-correlation energy). The resulting potential reproduces the derivative discontinuity, step structure, and counteracting field slope of exact exchange. It gives the polarizability of hydrogen chains with similar accuracy as exact exchange methods.
We present a large-scale density functional theory (DFT) investigation of the ABO(3) chemical space in the perovskite crystal structure, with the aim of identifying those that are relevant for forming piezoelectric materials. Screening criteria on the DFT results are used to select 49 compositions, which can be seen as the fundamental building blocks from which to create alloys with potentially good piezoelectric performance. This screening finds all the alloy end points used in three well-known high-performance piezoelectrics. The energy differences between different structural distortions, deformation, coupling between the displacement of the A and B sites, spontaneous polarization, Born effective charges, and stability is analyzed in each composition. We discuss the features that cause the high piezoelectric performance of the well-known piezoelectric lead zirconate titanate (PZT), and investigate to what extent these features occur in other compositions. We demonstrate how our results can be useful in the design of isovalent alloys with high piezoelectric performance.
We screen a large chemical space of perovskite alloys for systems with optimal properties to accommodate a morphotropic phase boundary (MPB) in their composition-temperature phase diagram, a crucial feature for high piezoelectric performance. We start from alloy end points previously identified in a high-throughput computational search. An interpolation scheme is used to estimate the relative energies between different perovskite distortions for alloy compositions with a minimum of computational effort. Suggested alloys are further screened for thermodynamic stability. The screening identifies alloy systems already known to host an MPB and suggests a few others that may be promising candidates for future experiments. Our method of investigation may be extended to other perovskite systems, e.g., (oxy-)nitrides, and provides a useful methodology for any application of high-throughput screening of isovalent alloy systems.
We derive an exchange energy functional of generalized gradient form with a corresponding potential that changes discontinuously at integer particle numbers. The functional is semilocal, yet incorporates key features that are connected to the derivative discontinuity of Kohn-Sham density-functional theory. We validate our construction for several paradigm systems and explain how it addresses central well-known deficiencies of antecedent semilocal methods, i.e., the description of charge transfer, properly localized orbitals, and band gaps. We find, e.g., an improved shell structure for atoms, eigenvalues that more closely correspond to ionization energies, and an improved description of band structure where localized states are lowered in energy.
An exchange potential functional is constructed from semi-local quantities and is shown to reproduce hydrogen chain polarizabilities with the same accuracy as exact exchange methods. We discuss the exchange potential features that are essential for accurate polarizability calculations, i.e., derivative discontinuities and the potential step structure. The possibility of a future generalization of the methods into a complete semi-local exchange-correlation functional is discussed.
It has recently been shown that local values of the conventional exchange energy per particle cannot be described by an analytic expansion in the density variation. Yet, it is known that the total exchange-correlation (XC) energy per particle does not show any corresponding nonanalyticity. Indeed, the nonanalyticity is here shown to be an effect of the separation into conventional exchange and correlation. We construct an alternative separation in which the exchange part is made well behaved by screening its long-ranged contributions, and the correlation part is adjusted accordingly. This alternative separation is as valid as the conventional one, and introduces no new approximations to the total XC energy. We demonstrate functional development based on this approach by creating and deploying a local-density-approximation-type XC functional. Hence, this work includes both the theory and the practical calculations needed to provide a starting point for an alternative approach towards improved approximations of the total XC energy.
We design a density-functional-theory (DFT) exchange-correlation functional that enables an accurate treatment of systems with electronic surfaces. Surface-specific approximations for both exchange and correlation energies are developed. A subsystem functional approach is then used: an interpolation index combines the surface functional with a functional for interior regions. When the local density approximation is used in the interior, the result is a straightforward functional for use in self-consistent DFT. The functional is validated for two metals (Al, Pt) and one semiconductor (Si) by calculations of (i) established bulk properties (lattice constants and bulk moduli) and (ii) a property where surface effects exist (the vacancy formation energy). Good and coherent results indicate that this functional may serve well as a universal first choice for solid-state systems and that yet improved functionals can be constructed by this approach.
A viable way of extending the successful use of density-functional theory into studies of even more complex systems than are addressed today has been suggested by Kohn and Mattsson [W. Kohn and A. E. Mattsson, Phys. Rev. Lett. 81, 3487 (1998); A. E. Mattsson and W. Kohn, J. Chem. Phys. 115, 3441 (2001)], and is further developed in this work. The scheme consists of dividing a system into subsystems and applying different approximations for the unknown (but general) exchange-correlation energy functional to the different subsystems. We discuss a basic requirement on approximative functionals used in this scheme; they must all adhere to a single explicit choice of the exchange-correlation energy per particle. From a numerical study of a model system with a cosine effective potential, the Mathieu gas, and one of its limiting cases, the harmonic oscillator model, we show that the conventional definition of the exchange energy per particle cannot be described by an analytical series expansion in the limit of slowly varying densities. This indicates that the conventional definition is not suitable in the context of subsystem functionals. We suggest alternative definitions and approaches to subsystem functionals for slowly varying densities and discuss the implications of our findings on the future of functional development.
The Becke-Johnson model potential [A. D. Becke and E. R. Johnson, J. Chem. Phys. 124, 221101 ( 2006)] and the potential of the AK13 functional [R. Armiento and S. Kummel, Phys. Rev. Lett. 111, 036402 ( 2013)] have been shown to mimic features of the exact Kohn-Sham exchange potential, such as step structures that are associated with shell closings and particle-number changes. A key element in the construction of these functionals is that the potential has a limiting value far outside a finite system that is a system-dependent constant rather than zero. We discuss a set of anomalous features in these functionals that are closely connected to the nonvanishing asymptotic potential. The findings constitute a formidable challenge for the future development of semilocal functionals based on the concept of a nonvanishing asymptotic constant.
Nodal surfaces of orbitals, in particular of the highest occupied one, play a special role in Kohn-Sham density-functional theory. The exact Kohn-Sham exchange potential, for example, shows a protruding ridge along such nodal surfaces, leading to the counterintuitive feature of a potential that goes to different asymptotic limits in different directions. We show here that nodal surfaces can heavily affect the potential of semilocal density-functional approximations. For the functional derivatives of the Armiento-Kummel (AK13) [Phys. Rev. Lett. 111, 036402 (2013)] and Becke88 [Phys. Rev. A 38, 3098 (1988)] energy functionals, i.e., the corresponding semilocal exchange potentials, as well as the Becke-Johnson [J. Chem. Phys. 124, 221101 (2006)] and van Leeuwen-Baerends (LB94) [Phys. Rev. A 49, 2421 (1994)] model potentials, we explicitly demonstrate exponential divergences in the vicinity of nodal surfaces. We further point out that many other semilocal potentials have similar features. Such divergences pose a challenge for the convergence of numerical solutions of the Kohn-Sham equations. We prove that for exchange functionals of the generalized gradient approximation (GGA) form, enforcing correct asymptotic behavior of the potential or energy density necessarily leads to irregular behavior on or near orbital nodal surfaces. We formulate constraints on the GGA exchange enhancement factor for avoiding such divergences.
The electronic properties of monolayer graphene grown epitaxially on SiC(0001) are known to be highly sensitive to the presence of NO2 molecules. The presence of small areas of bilayer graphene, on the other hand, considerably reduces the overall sensitivity of the surface. We investigate how NO2 molecules interact with monolayer and bilayer graphene, both free-standing and on a SiC(0001) substrate. We show that it is necessary to explicitly include the effect of the substrate in order to reproduce the experimental results. When monolayer graphene is present on SiC, there is a large charge transfer from the interface between the buffer layer and the SiC substrate to the molecule. As a result, the surface work function increases by 0.9 eV after molecular adsorption. A graphene bilayer is more effective at screening this interfacial charge, and so the charge transfer and change in work function after NO2 adsorption is much smaller.
We compare the accuracy of conventional semilocal density functional theory (DFT), the DFT+U method, and the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional for structural parameters, redox reaction energies, and formation energies of transition metal compounds. Conventional DFT functionals significantly underestimate redox potentials for these compounds. Zhou et al. [Phys. Rev. B 70, 235121 (2004)] addressed this issue with DFT+U and a linear-response scheme for calculating U values. We show that the Li intercalation potentials of prominent Li-ion intercalation battery materials, such as the layered Li(x)MO(2) (M=Co and Ni), Li(x)TiS(2); olivine Li(x)MPO(4) (M=Mn, Fe, Co, and Ni); and spinel-like Li(x)Mn(2)O(4), Li(x)Ti(2)O(4), are also well reproduced by HSE06, due to the self-interaction error correction from the partial inclusion of Hartree-Fock exchange. For formation energies, HSE06 performs well for transition metal compounds, which typically are not well reproduced by conventional DFT functionals but does not significantly improve the results of nontransition metal oxides. Hence, we find that hybrid functionals provide a good alternative to DFT+U for transition metal applications when the large extra computational effort is compensated by the benefits of (i) avoiding species-specific adjustable parameters and (ii) a more universal treatment of the self-interaction error that is not exclusive to specific atomic orbital projections on selected ions.
Study and design of magneto-optically active single point defects in semiconductors are rapidly growing fields due to their potential in quantum bit (qubit) and single photon emitter applications. Detailed understanding of the properties of candidate defects is essential for these applications, and requires the identification of the defects microscopic configuration and electronic structure. In multicomponent semiconductors point defects often exhibit several non-equivalent configurations of similar but different characteristics. The most relevant example of such point defect is the divacancy in silicon carbide, where some of the non-equivalent configurations implement room temperature qubits. Here, we identify four different configurations of the divacancy in 4H-SiC via the comparison of experimental measurements and results of first-principle calculations. In order to accomplish this challenging task, we carry out an exhaustive numerical accuracy investigation of zero-phonon line and hyperfine coupling parameter calculations. Based on these results, we discuss the possibility of systematic quantum bit search.
Point defects in semiconductors are relevant for use in quantum technologies as room temperature qubits and single photon emitters. Among suggested defects for these applications are the negatively charged silicon vacancy and the neutral divacancy in SiC. The possible nonequivalent configurations of these defects have been identified in 4H-SiC, but for 6H-SiC, the work is still in progress. In this paper, we identify the different configurations of the silicon vacancy and the divacancy defects to each of the V1-V3 and the QL1-QL6 color centers in 6H-SiC, respectively. We accomplish this by comparing the results from ab initio calculations with experimental measurements for the zero-phonon line, hyperfine tensor, and zero-field splitting. Published under license by AIP Publishing.
Elpasolite is the predominant quaternary crystal structure (AlNaK2F6 prototype) reported in the Inorganic Crystal Structure Database. We develop a machine learning model to calculate density functional theory quality formation energies of all ∼2×10^{6} pristine ABC_{2}D_{6} elpasolite crystals that can be made up from main-group elements (up to bismuth). Our model’s accuracy can be improved systematically, reaching a mean absolute error of 0.1 eV/atom for a training set consisting of 10×10^{3} crystals. Important bonding trends are revealed: fluoride is best suited to fit the coordination of the D site, which lowers the formation energy whereas the opposite is found for carbon. The bonding contribution of the elements A and B is very small on average. Low formation energies result from A and B being late elements from group II, C being a late (group I) element, and D being fluoride. Out of 2×10^{6} crystals, 90 unique structures are predicted to be on the convex hull—among which is NFAl_{2}C_{a6}, with a peculiar stoichiometry and a negative atomic oxidation state for Al.
We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb-like matrix that takes into account a number of neighboring unit cells; and (iii) an ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a dataset of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37eV/atom for the respective representations.
Certain excitations, especially ones of long-range charge transfer character, are poorly described by time-dependent density functional theory (TDDFT) when typical (semi-)local functionals are used. A proper description of these excitations would require an exchange-correlation response differing substantially from the usual (semi-) local one. It has recently been shown that functionals of the generalized gradient approximation (GGA) type can yield unusual potentials, mimicking features of the exact exchange derivative discontinuity and showing divergences on orbital nodal surfaces. We here investigate whether these unusual potential properties translate into beneficial response properties. Using the Sternheimer formalism we closely investigate the response obtained with the 2013 exchange approximation by Armiento and Kummel (AK13) and the 1988 exchange approximation by Becke (B88), both of which show divergences on orbital nodal planes. Numerical calculations for Na-2 as well as analytical and numerical calculations for the hydrogen atom show that the response of AK13 behaves qualitatively different from usual semi-local functionals. However, the AK13 functional leads to fundamental instabilities in the asymptotic region that prevent its practical application in TDDFT. Our findings may help the development of future improved functionals. They also corroborate that the frequency-dependent Sternheimer formalism is excellently suited for running and analyzing TDDFT calculations.
Scandium nitride has recently gained interest as a prospective compound for thermoelectric applications due to its high Seebeck coefficient. However, ScN also has a relatively high thermal conductivity, which limits its thermoelectric efficiency and figure of merit (zT). These properties motivate a search for other semiconductor materials that share the electronic structure features of ScN, but which have a lower thermal conductivity. Thus, the focus of our study is to predict the existence and stability of such materials among inherently layered equivalent ternaries that incorporate heavier atoms for enhanced phonon scattering and to calculate their thermoelectric properties. Using density functional theory calculations, the phase stability of TiMgN2, ZrMgN2 and HfMgN2 compounds has been calculated. From the computationally predicted phase diagrams for these materials, we conclude that all three compounds are stable in these stoichiometries. The stable compounds may have one of two competing crystal structures: a monoclinic structure (LiUN2 prototype) or a trigonal superstructure (NaCrS2 prototype; RmH). The band structure for the two competing structures for each ternary is also calculated and predicts semiconducting behavior for all three compounds in the NaCrS2 crystal structure with an indirect band gap and semiconducting behavior for ZrMgN2 and HfMgN2 in the monoclinic crystal structure with a direct band gap. Seebeck coefficient and power factors are also predicted, showing that all three compounds in both the NaCrS2 and the LiUN2 structures have large Seebeck coefficients. The predicted stability of these compounds suggests that they can be synthesized by, e.g., physical vapor deposition.
The subsystem functional scheme is a promising approach recently proposed for constructing exchange-correlation density functionals. In this scheme, the physics in each part of real materials is described by mapping to a characteristic model system. The "confinement physics," an essential physical ingredient that has been left out in present functionals, is studied by employing the harmonic-oscillator (HO) gas model. By performing the potential -greater than density and the density -greater than exchange energy per particle mappings based on two model systems characterizing the physics in the interior (uniform electron-gas model) and surface regions (Airy gas model) of materials for the HO gases, we show that the confinement physics emerges when only the lowest subband of the HO gas is occupied by electrons. We examine the approximations of the exchange energy by several state-of-the-art functionals for the HO gas, and none of them produces adequate accuracy in the confinement dominated cases. A generic functional that incorporates the description of the confinement physics is needed.
We have previously proposed that further improved functionals for density functional theory can be constructed based on the Armiento-Mattsson subsystem functional scheme if, in addition to the uniform electron gas and surface models used in the Armiento-Mattsson 2005 functional, a model for the strongly confined electron gas is also added. However, of central importance for this scheme is an index that identifies regions in space where the correction provided by the confined electron gas should be applied. The electron localization function (ELF) is a well-known indicator of strongly localized electrons. We use a model of a confined electron gas based on the harmonic oscillator to show that regions with high ELF directly coincide with regions where common exchange energy functionals have large errors. This suggests that the harmonic oscillator model together with an index based on the ELF provides the crucial ingredients for future improved semi-local functionals. For a practical illustration of how the proposed scheme is intended to work for a physical system we discuss monoclinic cupric oxide, CuO. A thorough discussion of this system leads us to promote the cell geometry of CuO as a useful benchmark for future semi-local functionals. Very high ELF values are found in a shell around the O ions, and take its maximum value along the Cu–O directions. An estimate of the exchange functional error from the effect of electron confinement in these regions suggests a magnitude and sign that could account for the error in cell geometry.
Hybrid functionals serve as a powerful practical tool in different fields of computational physics and quantum chemistry. On the other hand, their applicability for the case of correlated d and f orbitals is still questionable and needs more considerations. In this article we formulate the on-site occupation dependent exchange correlation energy and effective potential of hybrid functionals for localized states and connect them to the on-site correction term of the DFT+ U method. The resultant formula indicates that the screening of the onsite electron repulsion is governed by the ratio of the exact exchange in hybrid functionals. Our derivation provides a theoretical justification for adding a DFT+ U-like on-site potential in hybrid-DFT calculations to resolve issues caused by overscreening of localized states. The resulting scheme, hybrid DFT+ V-w, is tested for chromium impurity in wurtzite AlN and vanadium impurity in 4H-SiC, which are paradigm examples of systems with different degrees of localization between host and impurity orbitals.
Only a single linearly dispersing π-band cone, characteristic of monolayer graphene, has so far been observed in Angle Resolved Photoemission (ARPES) experiments on multilayer graphene grown on C-face SiC. A rotational disorder that effectively decouples adjacent layers has been suggested to explain this. However, the coexistence of μm-sized grains of single and multilayer graphene with different azimuthal orientations and no rotational disorder within the grains was recently revealed for C-face graphene, but conventional ARPES still resolved only a single π-band. Here we report detailed nano-ARPES band mappings of individual graphene grains that unambiguously show that multilayer C-face graphene exhibits multiple π-bands. The band dispersions obtained close to the K-point moreover clearly indicate, when compared to theoretical band dispersion calculated in the framework of the density functional method, Bernal (AB) stacking within the grains. Thus, contrary to earlier claims, our findings imply a similar interaction between graphene layers on C-face and Si-face SiC.
Constructing approximations for the exchange-correlation (xc) potential in density functional theory instead of the energy appears attractive because it may provide for a way of easily incorporating desirable features such as a particle number discontinuity into xc functionals. However, xc potentials that are constructed directly are problematic: An xc potential that is not a priori derived as a functional derivative of some xc energy functional is most likely not a functional derivative of any density functional at all. This severely limits the usefulness of directly constructed xc potentials, e.g., for calculating electronic excitations. For the explicit example of the Becke-Johnson (BJ) potential we discuss defining corresponding energy expressions by density path integrals. We show that taking the functional derivative of these energies does not lead back to potentials that are close to the BJ one, and the new potentials do not share the attractive features of the original BJ expression. With further examples we demonstrate that this is a general finding and not specific to the BJ potential form.
Predicting the polarizabilities of extended conjugated molecules with semilocal functionals has been a long-standing problem in density functional theory. These difficulties are due to the absence of a term in the typical semilocal Kohn-Sham exchange potentials that has been named "ultranonlocal". Such a term should develop in extended systems when an external electric field is applied, and it should counteract the field. We calculate the polarizabilities of polyacetylene molecules using the recently developed extended Becke-Johnson functional. Our results show that this functional predicts the polarizabilities with much better accuracy than typical semilocal functionals. Thus, the field-counteracting term in this functional, which is semilocal in the Kohn-Sham orbitals, can realistically describe real molecules. We discuss approaches of constructing an energy functional that corresponds to this potential functional, for example, via the Levy-Perdew virial relation.
To speed up the progress in the field of materials design, a number of challenges related to big data need to be addressed. This entry discusses these challenges and shows the semantic technologies that alleviate the problems related to variety, variability, and veracity.
Pyrite (FeS2), being a promising material for future solar technologies, has so far exhibited in experiments an open-circuit voltage (OCV) of around 0.2 V, which is much lower than the frequently quoted 'accepted' value for the fundamental bandgap of similar to 0.95 eV. Absorption experiments show large subgap absorption, commonly attributed to defects or structural disorder. However, computations using density functional theory with a semi-local functional predict that the bottom of the conduction band consists of a very low intensity sulfur p-band that may be easily overlooked in experiments because of the high intensity onset that appears 0.5 eV higher in energy. The intensity of absorption into the sulfur p-band is found to be of the same magnitude as contributions from defects and disorder. Our findings suggest the need to re-examine the value of the fundamental bandgap of pyrite presently in use in the literature. If the contribution from the p-band has so far been overlooked, the substantially lowered bandgap would partly explain the discrepancy with the OCV. Furthermore, we show that more states appear on the surface within the low energy sulfur p-band, which suggests a mechanism of thermalization into those states that would further prevent extracting electrons at higher energy levels through the surface. Finally, we speculate on whether misidentified states at the conduction band onset may be present in other materials.
The recent nonempirical semilocal exchange functional of Armiento and Kummel [Phys. Rev. Lett. 111, 036402 (2013)], AK13, incorporates a number of features reproduced by higher-order theory. The AK13 potential behaves analogously with the discontinuous jump associated with the derivative discontinuity at integer particle numbers. Recent works have established that AK13 gives a qualitatively improved orbital description compared to other semilocal methods, and reproduces a band structure closer to higher-order theory. However, its energies and energetics are inaccurate. The present work further investigates the deficiency in energetics. In addition to AK13 results, we find that applying the local-density approximation (LDA) non-self-consistently on the converged AK13 density gives very reasonable energetics with equilibrium lattice constants and bulk moduli well described across 13 systems. We also confirm that the attractive orbital features of AK13 are retained even after full structural relaxation. Hence, the deficient energetics cannot be a result of the AK13 orbitals having adversely affected the quality of the electron density compared to that of usual semilocal functionals; an improved orbital description and good energetics are not in opposition. This is also confirmed by direct calculation of the principal component of the electric field gradient. In addition, we prove that the non-self-consistent scheme is equivalent to using a single external-potential-dependent functional in an otherwise consistent, nonvariational Kohn-Sham density-functional theory (KS DFT) scheme. Furthermore, our results also demonstrate that, while an internally consistent KS functional is presently missing, non-self-consistent LDA on AK13 orbitals works as a practical nonempirical computational scheme to predict geometries, bulk moduli, while retaining the band structure features of AK13 at the computational cost of semi-local DFT.
We derive a closed-form expression for the quantum corrections to the kinetic energy density in the Thomas-Fermi limit of a linear potential model system in three dimensions (the Airy gas). The universality of the expression is tested numerically in a number of three-dimensional model systems: (i) jellium surfaces, (ii) confinement in a hydrogenlike potential (the Bohr atom), (iii) particles confined by a harmonic potential in one and (iv) all three dimensions, and (v) a system with a cosine potential (the Mathieu gas). Our results confirm that the usual gradient expansion of extended Thomas-Fermi theory does not describe the quantum oscillations for systems that incorporate surface regions where the electron density drops off to zero. We find that the correction derived from the Airy gas is universally applicable to relevant spatial regions of systems of types (i), (ii), and (iv), but somewhat surprisingly not (iii). We discuss possible implications of our findings to the development of functionals for the kinetic energy density.
We present exact-exchange calculations of the Kohn-Sham gap, as well as the fundamental gap resulting from it, using highly accurate grid-based all-electron and pseudopotential approaches for prototypical diatomic molecules. Results obtained with pseudopotentials that have been constructed in a manner consistent with the exact-exchange functional agree with the all electron results for the cases studied. This confirms the reliability of the pseudopotential approximation for orbital-dependent functionals such as exact exchange.
We show that the spin density generalization of the AM05 density functional [R. Armiento and A. E. Mattsson, Phys. Rev. B 72, 085108 (2005)] predicts the correct ground spin state for iron, a system known to be heavily dependent on proper spin treatment. Using the fundamental assumptions in the subsystem functional scheme, we resolve an ambiguity in how to treat the separate spin densities in AM05 but also show that the other less preferred treatments give no significantly different numerical outcome of the iron body-centered-cubic and face-centered-cubic test cases. Details and formulas are given to aid in the implementation of functionals in general, and the spin-resolved AM05 exchange-correlation potentials in particular, into different types of computer codes.
The subsystem functional scheme (Kohn and Mattsson, Phys Rev Lett 1998, 81, 3487; Armiento and Mattsson Phys Rev B 2002, 66, 165117) is a recently proposed framework for constructing exchange-correlation density-functionals for use in density functional theory based calculations. The fundamental principle is to describe the physics in a real material by mapping onto model systems that exhibit the characteristic physics in each separate part of the real system. The local density approximately (LDA) functional can be seen as a subsystem functional: in all parts of the real material the assumption is that the needed physics is well described by the uniform electron gas model system. It is well known that this assumption is very accurate for surprisingly large classes of materials. The Armiento Mattsson 2005 (AM05) (Armiento and Mattsson, Phys Rev B 2005, 72, 085108; Mattsson and Armiento, Phys Rev B 2009, 79, 155101) functional takes this a step further by distinguishing between two separate types of regions in a real material, one type that is assumed to be well described by the uniform electron gas, and the other type of region assumed to be well described by a surface model system. AM05 gives a consistent improvement over LDA. One important consequence of the subsystem functional scheme is that it is known what physics is included in a functional. Based on the performance of AM05 for a number of different systems, we discuss where the model systems included are enough and when additional physics need to be included in a new functional. Improvement of AM05 is possible by fine-tuning the details in the construction. But a new major step in accuracy improvement is only expected if new physics is integrated in a functional via an additional model system. We discuss what type of physics would be needed and what model systems could be used for this next step beyond AM05. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2274-2282, 2010
A Comment on the Letter by John P. Perdew , Phys. Rev. Lett. 100, 136406 (2008). The authors of the Letter offer a Reply.
We show that the AM05 functional [Armiento and Mattsson, Phys. Rev. B 72, 085108 (2005)] has the same excellent performance for solids as the hybrid density functionals tested in Paier et al. [J. Chem. Phys. 124, 154709 (2006); 125, 249901 (2006)]. This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. Hartree-Fock hybrid calculations are typically an order of magnitude slower than local or semilocal density functionals such as AM05, which is of a regular semilocal generalized gradient approximation form. The performance of AM05 is on average found to be superior to selecting the best of local density approximation and PBE for each solid. By comparing data from several different electronic-structure codes, we have determined that the numerical errors in this study are equal to or smaller than the corresponding experimental uncertainties. (C) 2008 American Institute of Physics.
Two of the most popular generalized gradient approximations used in the applications of the density functional theory, PW91 and PBE, are generally regarded as essentially equivalent. They produce similar numerical results for many simple properties, such as lattice constants, bulk moduli, and atomization energies. We examine more complex properties of systems with electronic surface regions, with the specific application of the monovacancy formation energies of Pt and Al. A surprisingly large and consistent discrepancy between PBE and PW91 results is obtained. This shows that despite similarities found between some simple material properties, PBE and PW91 are not equivalent. The differences obtained for the monovacancy formation energies are related to differences in surface intrinsic errors which are substantiated using the idealized, well-controlled, jellium surface model. In view of the differences obtained with the PW91 and PBE functionals we develop separate surface intrinsic error corrections for these and revisit some earlier results.
The results for Si interstitial formation energies differ substantially if calculated with quantum Monte Carlo (QMC) or density functional theory (DFT) techniques. In fact, not even DFT results using different exchange-correlation functionals agree well for these energies. We carefully quantify the differences between the DFT results by accurate calculations with large supercells. A similar discrepancy for vacancy formation energies in metals has previously been resolved by introducing the concept of an "electronic surface error," and this view is adopted and shown relevant also for the present DFT results for interstitials in semiconductors. The origin of the surface error for the Si interstitial is explained by careful examination of the electron density. A postcorrection for the surface error brings all the results obtained with the tested functionals close to the results of the AM05 functional. However, it remains an important puzzle that while the surface error correction aligns the DFT results, they are still in large disagreement with QMC results.
First-principles molecular-dynamics simulations based on a recently developed exchange-correlation functional show that self-diffusion in the refractory metal molybdenum is associated with strongly temperature-dependent activation energies for vacancy formation and migration. While static calculations of self-diffusion rates based on transition-state theory deviate systematically from experiments, with up to two orders of magnitude, the current results are accurate to within a mean deviation of 4 over the experimental range in temperature.
The electronic properties of epitaxial graphene grown on SiC(0001) are known to be impaired relative to those of freestanding graphene. This is due to the formation of a carbon buffer layer between the graphene layers and the substrate, which causes the graphene layers to become strongly n-doped. Charge neutrality can be achieved by completely passivating the dangling bonds of the clean SiC surface using atomic intercalation. So far, only one element, hydrogen, has been identified as a promising candidate. We show, using first-principles density functional calculations, how it can also be accomplished via the growth of a thin layer of silicon nitride on the SiC surface. The subsequently grown graphene layers display the electronic properties associated with charge neutral graphene. We show that the surface energy of this structure is considerably lower than that of others with intercalated atomic nitrogen and determine how its stability depends on the N-2 chemical potential.
We investigate the structural and electronic properties of Li-intercalated monolayer graphene on SiC(0001) using combined angle-resolved photoemission spectroscopy and first-principles density functional theory. Li intercalates at room temperature both at the interface between the buffer layer and SiC and between the two carbon layers. The graphene is strongly n-doped due to charge transfer from the Li atoms and two pi bands are visible at the (K) over bar point. After heating the sample to 300 degrees C, these pi bands become sharp and have a distinctly different dispersion to that of Bernal-stacked bilayer graphene. We suggest that the Li atoms intercalate between the two carbon layers with an ordered structure, similar to that of bulk LiC6. An AA stacking of these two layers becomes energetically favourable. The pi bands around the (K) over bar point closely resemble the calculated band structure of a C6LiC6 system, where the intercalated Li atoms impose a superpotential on the graphene electronic structure that opens gaps at the Dirac points of the two pi cones.
From a global perspective, the density of an atom is strongly inhomogeneous and not at all like the density of a uniform or nearly-uniform electron gas. But, from the semi-local or myopic perspective of standard density functional approximations to the exchange-correlation energy,it is not so easy to tell an atom from an electron gas. We address the following problem: Given the ground-state electron density n and orbital kinetic energy density in the neighborhood of a point r, can we construct an "inhomogeneity index" w(r) which approaches zero for weakly-inhomogeneous densities and unity for strongly-inhomogeneous ones? The solution requires not only the usual local ingredients of a meta-generalized gradient approximation (n,rn,r2n, ),but also r and r2 . The inhomogeneity index is displayed for atoms, and for model densities of metal surfaces and bulk metals. Scaling behavior and a possible application to functional interpolation are discussed.
The phase diagrams of the Ti-Zn-N, Zr-Zn-N, and Hf-Zn-N systems are determined using large-scale high-throughput density functional calculations. Thermodynamically stable ordered phases of TiZnN2, ZrZnN2, and HfZnN2 have been found to be promising candidates in piezoelectric devices/applications for energy harvesting. The identified stable phase of TiZnN2 is an ordered wurtzite superstructure, and the stable phases of ZrZnN2 and HfZnN2 have a layered structure with alternating tetrahedral ZnN and octahedral (Zr, Hf)N layers. All of the TMZnN2 (TM = Ti, Zn, Hf) structures exhibit electronic bandgaps and large piezoelectric constants, d(33)(TiZnN2) = 14.21; d(24)(ZrZnN2) = -26.15, and d(24)(HfZnN2) = -21.99 pC/N. The strong piezoelectric responses and their thermodynamical stability make materials with these phases promising candidates for piezoelectric applications. Published by AIP Publishing.
A recently published generalized gradient approximation functional within density functional theory (DFT) has shown, in a few paradigm tests, an improved KS orbital description over standard (semi) local approximations. The characteristic feature of this functional is an enhancement factor that diverges like s ln(s) for large reduced density gradients s which leads to unusual properties. We explore the improved orbital description of this functional more thoroughly by computing the electronic band structure, band gaps, and the optical dielectric constants in semiconductors, Mott insulators, and ionic crystals. Compared to standard semilocal functionals, we observe improvement in both the band gaps and the optical dielectric constants. In particular, the results are similar to those obtained with orbital functionals or by perturbation theory methods in that it opens band gaps in systems described as metallic by standard (semi) local density functionals, e. g., Ge, alpha-Sn, and CdO.
We propose a multi-body solver that extends the Material Point Method (MPM) to simulate cracks in computer animation. We define cracks as the intersection between pieces of bodies created by a pre-fracture process and held together by massless particle constraints (glue particles). These pieces are simulated using a MPM multi-body solver extended by us to efficiently handle N-body collisions. Benefits of the present work include (1) low computational overhead compared to a normal MPM algorithm; (2) good scaling in three dimensions due to our use of sparse grids for background computations; (3) allowing for an easy and controllable setup phase to simulate a desired material failure mode, which is especially useful for computer animation.
A Schrodinger eigenvalue problem is solved for the 2D quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, (i) an application of the Kelly error estimator, and (ii) a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver.
Band structure engineering for specific electronic or optical properties is essential for the further development of many important technologies including thermoelectrics, optoelectronics, and microelectronics. In this work, we report orbital interaction as a powerful tool to finetune the band structure and the transport properties of charge carriers in bulk crystalline semiconductors. The proposed mechanism of orbital interaction on band structure is demonstrated for IV-VI thermoelectric semiconductors. For IV-VI materials, we find that the convergence of multiple carrier pockets not only displays a strong correlation with the s-p and spin-orbit coupling but also coincides with the enhancement of power factor. Our results suggest a useful path to engineer the band structure and an enticing solid-solution design principle to enhance thermoelectric performance.