Erratum: Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation

Probing the range of applicability of structure- and energy-adjusted QM/MM link bonds III: QM/MM MD simulations of solid-state systems at the example of layered carbon structures

The previously introduced workflow to achieve an energetically and structurally optimized description of frontier bonds in quantum mechanical/molecular mechanics (QM/MM)-type applications was extended into the regime of computational material sciences at the example of a layered carbon model systems. Optimized QM/MM link bond parameters at HSEsol/6-311G(d,p) and self-consistent density functional tight binding (SCC-DFTB) were derived for graphitic systems, enabling detailed investigation of specific structure motifs occurring in graphene-derived structures v i a quantum-chemical calculations. Exemplary molecular dynamics (MD) simulations in the isochoric-isothermic (NVT) ensemble were carried out to study the intercalation of lithium and the properties of the Stone-Thrower-Wales defect. The diffusivity of lithium as well as hydrogen and proton adsorption on a defective graphene surface served as additional example. The results of the QM/MM MD simulations provide detailed insight into the applicability of the employed link-bond strategy when studying intercalation and adsorption properties of graphitic materials.

My life in science: Lessons for yours?

Because of an acquired obsession to understand as much as possible in a limited but important area of science and because of optimism, luck, and help from others, my life in science turned out to be much better than I or others could have expected or planned. This is the story of how that happened, and also the story of the groundstate density functional theory of electronic structure, told from a personal perspective.

Transmission of spin-polarization by π-orbitals: an approach to assessing its effect on NMR spin-spin coupling and EPR hyperfine structure

A new approach to assessing the effect of the transmission of spin-polarization by π-orbitals (π-TSP) is presented. In order to switch off the π-TSP effect, we artificially average the α- and β-densities of the valence π-orbitals when calculating the exchange-correlation contribution to the Fock matrix in the unrestricted Kohn-Sham framework. The π-TSP effect is then evaluated as the difference between the results obtained with switched-on and switched-off options. This approach is applied to estimate the π-TSP effect on the Fermi-contact contribution to spin-spin couplings and EPR hyperfine structure coupling constants. The π-TSP effect on the distribution of spin-density, spin-spin coupling pathways and pathways of EPR hyperfine couplings is demonstrated for benzene, naphthalene, 1,3,5,7,9-decapentaene and the 1,3,5,7,9-decapentaen-1-yl radical. The sign alternation of the spin-polarization transmitted by π-orbitals is explained in a theoretical framework based on perturbation theory. However, the delocalized nature of the π-system can interfere with the sign alternation in certain cases, two of which - the cyclobutadiene dication and the cyclooctatetraene dication - are examined, and an explanation for which is provided.

Density-functional theory vs density-functional fits

Kohn–Sham density-functional theory (DFT), the predominant framework for electronic structure computations in chemistry today, has undergone considerable evolution in the past few decades. The earliest DFT approximations were based on uniform electron gas models completely free of empirical parameters. Tremendous improvements were made by incorporating density gradients and a small number of parameters, typically one or two, obtained from fits to atomic data. Incorporation of exact exchange and fitting to molecular data, such as experimental heats of formation, allowed even further improvements. This, however, opened a Pandora’s Box of fitting possibilities, given the limitless choices of chemical reactions that can be fit. The result is a recent explosion of DFT approximations empirically fit to hundreds, or thousands, of chemical reference data. These fitted density functionals may contain several dozen empirical parameters. What has been lost in this fitting trend is physical modeling based on theory. In this work, we present a density functional comprising our best efforts to model exchange–correlation in DFT using good theory. We compare its performance to that of heavily fit density functionals using the GMTKN55 chemical reference data of Goerigk and co-workers [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. Our density-functional theory, using only a handful of physically motivated pre-factors, competes with the best heavily fit Kohn–Sham functionals in the literature.

Effect of Lattice Substitution on Adsorption of Hexavalent Chromium by Montmorillonite, Nontronite, and Beidellite

This work aims to evaluate the effect of lattice substitution on adsorption of hexavalent chromium by three kinds of typical clay minerals, and its common isomorph via experiments and calculations were performed based on density functional theory. The experiments (25 °C, 4 h, pH = 4 and without stirring) confirmed an order of adsorption capacity as follows: Montmorillonite (12 mg/g) > Nontronite (9 mg/g) > Beidellite (8 mg/g). Accordingly, the Mulliken populations, density of states, and band structures of the mineral models with the structural Al, Mg, Fe(II), Fe(III), and Al (in tetrahedrons) on behalf of five species of isomorph were calculated. The calculation results explain the differences between hexavalent chromium adsorption capacity of five kinds of isomorph by means of atom, key populations, overlapping valence electron orbitals, and the variation of energy band. However, no overlapping orbitals were observed in the adsorption system with structural Mg. It is implied that the structural Mg has little influence of hexavalent chromium adsorption. In conclusion, our study contributes to achieving a better understanding of modified clay minerals materials applications.

DFT Functionals for Modeling of Polyethylene Chains Cross-Linked by Metal Atoms. DLPNO-CCSD(T) Benchmark Calculations

Density functional theory (DFT) functionals for calculations of binding energies (BEs) of the polyethylene (PE) chains cross-linked by selected metal atoms (M) are benchmarked against DLPNO-CCSD(T) and DLPNO-CCSD(T1) data. PEX-M-PEX complexes as compared with plain parallel PEX···PEX chains with X = 3-9 carbon atoms are model species characterized by a cooperative effect of covalent C-M-C bonds and interchain dispersion interactions. The accuracy of DLPNO-CC methods was assessed by a comparison of BEs with the canonical CCSD(T) results for small PE3-M-PE3 complexes. Functionals for PEX···PEX and closed-shell PEX-M-PEX complexes (M = Be, Mg, Zn) were benchmarked against DLPNO-CCSD(T) BEs; open-shell complexes (M = Li, Ag, Au) were benchmarked against the DLPNO-CCSD(T1) method with iterative triples. Three dispersion corrections were combined with 25 DFT functionals for calculations of BEs with respect to PEX-M and PEX fragments employing def2-TZVPP and def2-QZVPP basis sets. Accuracy to within 5% for the closed-shell PEX-M-PEX complexes was achieved with five functionals. Less accurate are functionals for the open-shell PEX-M-PEX complexes; only two functionals deviate by less than 15% from DLPNO-CCSD(T1). Particularly problematic were PEX-Li-PEX complexes. A reasonable overall performance across all complexes in terms of the mean absolute percentage error is found for the range-separated hybrid functionals ωB97X-D3 and CAM-B3LYP/D3(BJ)-ABC.

Combining Raman Spectroscopy, DFT Calculations, and Atomic Force Microscopy in the Study of Clinker Materials

Raman spectroscopy and Raman mapping analysis, combined with density functional theory calculations were applied to the problem of differentiating similar clinker materials such as alite and belite. The Portland cement clinker 217 (further: clinker) was analysed using colocalised Raman mapping and atomic force microscopy mapping, which provided both spatial and chemical information simultaneously. The main constituents found in the clinker were alite, belite, portlandite, amorphous calcium carbonate, and gypsum. Since phonon bands of alite and belite greatly overlap, and their distinction is important for the hydration process during cement setting, we provided the calculated phonon density of states for alite Ca3SiO5 (Pc structure) and belite Ca2SiO4 (β P21/n structure) here for the first time. Both calculated phonon densities have similar distribution of phonon modes, with a gap between 560 and 810 cm-1. A comparison of the calculated phonon frequencies for Ca3SiO5 and Ca2SiO4 shows that the lowest calculated phonon frequency of β-Ca2SiO4 lies at 102 cm-1, while for Pc alite the lowest phonon frequency is predicted at 27 cm-1. Low frequency Raman spectroscopy could therefore be used for a clearer distinction of these two species in a clinker material.

Comparative Hybrid Hartree-Fock-DFT Calculations of WO2-Terminated Cubic WO3 as Well as SrTiO3, BaTiO3, PbTiO3 and CaTiO3 (001) Surfaces

We performed, to the best of our knowledge, the world’s first first-principles calculations for the WO2-terminated cubic WO3 (001) surface and analyzed the systematic trends in the WO3, SrTiO3, BaTiO3, PbTiO3 and CaTiO3 (001) surface ab initio calculations. According to our first principles calculations, all WO2 or TiO2-terminated WO3, SrTiO3, BaTiO3, PbTiO3 and CaZrO3 (001) surface upper-layer atoms relax inwards towards the crystal bulk, while all second-layer atoms relax upwards. The only two exceptions are outward relaxations of first layer WO2 and TiO2-terminated WO3 and PbTiO3 (001) surface O atoms. The WO2 or TiO2-terminated WO3, SrTiO3, BaTiO3, PbTiO3 and CaTiO3 (001) surface-band gaps at the Γ–Γ point are smaller than their respective bulk-band gaps. The Ti–O chemical bond populations in the SrTiO3, BaTiO3, PbTiO3 and CaTiO3 bulk are smaller than those near the TiO2-terminated (001) surfaces. Conversely, the W–O chemical bond population in the WO3 bulk is larger than near the WO2-terminated WO3 (001) surface.

B3LYP, M06 and B3PW91 DFT assignment of nd8 metal-bis-(N-heterocyclic carbene) complexes

This paper is focused on the examination of the bonding properties of a series of [M(NHC)₂X₂] (M = nd⁸ transition metal; X = Cl, Br and I) complexes in normal, abnormal and mixed C^∩C coordination modes. Structures have been optimised in gas phase using B3LYP, M06 and P3BW91 functionals. Two basis sets have been used: the LanL2DZ and a mixed basis set (LanL2DZ for nd⁸ transition metals as well as halogen atoms and 6-311+G(d,p) for other atoms). Results obtained indicate that the B3PW91 bond distances are closer to experimental data. The complexation energies obtained for each binding mode increase in the order: Ni²⁺ < Pd²⁺ < Pt²⁺, independently of the halogen atom adopted. From the Quantum Theory of Atoms in Molecule (QTAIM) approach, the instability has been found to follow this trend: M - X < M - C. The analysis of metal-ligand interactions using the natural bond orbital (NBO) revealed that the strongest metal-ligand interactions are observed in the normal binding mode. The NCH → MX₂ donation terms were found to be interestingly predominant compared with back donation ones in the complexes studied, except in Pt chloride ones. The contribution of electrostatic interaction energy between the above fragments (∆E_elstat term) is in the range 57.48-63.95% traducing the fact that the interactions are mostly electrostatic. Graphical abstract.

Fermi-crossing Type-II Dirac fermions and topological surface states in NiTe2

Transition-metal dichalcogenides (TMDs) offer an ideal platform to experimentally realize Dirac fermions. However, typically these exotic quasiparticles are located far away from the Fermi level, limiting the contribution of Dirac-like carriers to the transport properties. Here we show that NiTe₂ hosts both bulk Type-II Dirac points and topological surface states. The underlying mechanism is shared with other TMDs and based on the generic topological character of the Te p-orbital manifold. However, unique to NiTe₂, a significant contribution of Ni d orbital states shifts the energy of the Type-II Dirac point close to the Fermi level. In addition, one of the topological surface states intersects the Fermi energy and exhibits a remarkably large spin splitting of 120 meV. Our results establish NiTe₂ as an exciting candidate for next-generation spintronics devices.

Spin-Forbidden Reactivity of Transition Metal Oxo Species: Exploring the Potential Energy Surfaces

Spin-forbidden reactions are frequently encountered when transition metal oxo species are involved, particularly in oxygen transfer reactivity. The computational study of such reactions is challenging, because reactants and products are located on different spin potential energy surfaces (PESs). One possible approach to describe these reactions is the so-called minimum energy crossing point (MECP) between the diabatic reactants and products PESs. Alternatively, inclusion of spin-orbit coupling (SOC) effects allows to locate a saddle point on a single adiabatic PES (TS SOC). The TS SOC approach is rarely applied because of its high computational cost. Recently evidence for a TS SOC impact on significantly lowering the activation barrier in dioxygen addition to a carbene-gold(I)-hydride complex reaction (Chem. Sci. 2016, 7, 7034-7039) or even on predicting a qualitatively different reaction mechanism in mercury methylation by cobalt corrinoid (Angew. Chem. Int. Ed. 2016, 55, 11503-11506) has been put forward. Using MECP and TS SOC approaches a systematic analysis is provided here of three prototypical transition metal oxo spin-forbidden processes to investigate their implications on reactivity. Cycloaddition of ethylene to chromyl chloride (CrO₂ Cl₂ +C₂ H₄ ), iron oxide cation insertion into the hydrogen molecule (FeO⁺ +H₂ ) and H-abstraction from toluene by a Mn^V -oxo-porphyrin cation (MnOP(H₂ O)⁺ +C₆ H₅ CH₃ ) are case studies. For all these processes the MECP and TS SOC results are compared, which show that the spin-forbidden reactivity of transition metal oxo species can be safely described by a MECP approach, at least for the first-row transition metals investigated here, where the spin-orbit coupling is relatively weak. However, for the Mn-oxo reactivity, the MECP and TS SOC have been found to be crucial for a correct description of the reaction mechanism. In particular, the TS SOC approach allows to straightforwardly explore detailed features of the adiabatic potential energy surface which in principle could affect the overall reaction rate in cases where the involved diabatic PESs are tricky.

Computational study of the structures and photoelectron spectra of 12 azabenzenes

The molecular structures of 12 azabenzenes have been optimized with the Gaussian09 package at the level of coupled cluster singles and doubles with the basis set cc-pVTZ. The optimized geometry of each is used in the ADF13 program for the calculation of the vertical ionization energies of all the electrons. For both outer-shell and inner-shell valence electrons, the 2009 method of ΔPBE0(SAOP) is used, whereas the 1999 method of ΔPW86PW91 + Crel is employed for the core electrons. For degenerate orbitals, the alternative method chosen is to use localized orbitals, keeping the integer number of electrons, while giving up proper symmetry, rather than to keep symmetry with fractional electrons. The success of the computed results of valence ionization potentials of pyridine and the diazabenzenes gives confidence for the predicted values for the higher azabenzenes. The calculated results for core-electron binding energies provide incentive to experimentalists to measure them with X-ray photoelectron spectrometers and (or) synchrotron facilities.

van der Waals exchange-correlation functionals over bulk and surface properties of transition metals

The correct description of van der Waals (vdW) interaction forces is required for accurately describing dispersion bonded systems. Several approaches have been proposed to include London dispersion in density functional theory exchange-correlation functionals, where the family of so-called van der Waals (vdW-DF) exchange-correlation functionals have shown a better performance than local or semi local exchange-correlation functionals for describing molecular adsorption on metals. Despite the numerous benchmarks performed with these functionals, their performance in predicting bulk properties of transition metals has hitherto not been investigated in detail. We have therefore tested five vdW-DF exchange-correlation functionals, vdW-DF2, optPBE-vdW, BEEF-vdW, optB88-vdW and C09 _x -vdW to assess their performance in the prediction of lattice constants, bulk moduli, cohesive energies and surface energies of bulk Ni, Cu, Rh, Pd, Ag, Ir, Pt and Au (in fcc crystal structure). These transition metals are commonly used for benchmarking density functionals because they are important for applications in catalysis. The results are compared with experimental data and the PBE exchange-correlation functional. We found that both the optB88-vdW and the C09 _x -vdW exchange-correlation functionals estimate all properties with high accuracy, in better agreement with experimental data than PBE and other considered vdW functionals. The C09 _x -vdW functional clearly outperforms all other exchange-correlation functionals for surface energies for the (1 1 1) termination of different metals. We have also evaluated the interatomic electron density emerging from different functionals, and concluded that the observed differences are a result of the predicted lattice parameter, rather than a direct consequence of the functional form. Plane-wave and real-space grid-based expansions of the electron density are also compared, revealing good agreement between the two approaches for lattice parameters, cohesive energies, and surface energies, but more severe differences in bulk moduli. On the basis of our results, we recommend using the C09 _x -vdW for studying bulk properties and surface energies of transition metals.

Understanding the Reactivity of Mn-Oxo Porphyrins for Substrate Hydroxylation: Theoretical Predictions and Experimental Evidence Reconciled

The Mn-oxo porphyrin (MnOP) mechanism for substrate hydroxylation is computationally studied with the aim to better understand reactivity in these systems. Theoretical studies suggest Mn(V)OP species to be very reactive intermediates with thermally accessible reaction barriers represented by low-spin/high-spin-crossover occurring in the Mn(V)OP oxidant, and kinetics for selected Mn(V)OP species indeed find high reactivity. On the other hand, MnOP complexes lead to modest yields in hydroxylation reactions of several different substrates, implying low rate constants and high reaction barriers. The resolution of this inconsistency is very important to understand the reactivity of Mn-oxo porphyrins and to improve the catalytic conditions. In this work we use the toluene hydroxylation by the Mn(V)OP(H₂O)⁺ complex as a case study to gain deep insight into the reaction mechanism. Minimum energy crossing point (MECP) results on the H-abstraction process from toluene indicate a first crossover from a singlet to a triplet spin state of the Mn(V)OP(H₂O)⁺ species with a thermally accessible barrier, followed by a very facile H-abstraction by the triplet complex. Issues concerning (i) the validation of the level of the density functional theory employed (BP86) to describe the singlet-triplet energy gap in the Mn(V)OP(H₂O)⁺ system versus highly accurate DMRG-CASPT2/CC calculations, and (ii) the influence of the axial ligand (X = none, Cl^-, CH₃CN, OH^-, and O^2-) on MnOP reactivity, which models the different experimental conditions, are addressed. The ligand trans influence mainly controls the reactivity through the singlet-triplet energy gap modulation, with the porphyrin ruffling distortion also finely tuning it. Finally, a stepwise model for the H-abstraction process is proposed which allows a direct comparison between the calculated and experimentally measured Gibbs free activation energy barriers ( Zhang et al. J. Am. Chem. Soc. 2005 , 127 , 6573 - 6582 ). The low yields in catalysis are shown not to be due to low reactivity of Mn(V).

Thermodynamic stability of non-stoichiometric SrFeO3-δ: a hybrid DFT study

SrFeO3-δ is a mixed ionic-electronic conductor with a complex magnetic structure that reveals a colossal magnetoresistance effect. This material and its solid solutions are attractive for various spintronic, catalytic and electrochemical applications, including cathodes for solid oxide fuel cells and permeation membranes. Its properties strongly depend on oxygen non-stoichiometry. Ab initio hybrid functional approach was applied herein to study the thermodynamic stability of a series of SrFeO3-δ compositions with several non-stoichiometries δ, ranging from 0 to 0.5 (SrFeO3-SrFeO2.875-SrFeO2.75-SrFeO2.5) as a function of temperature and oxygen pressure. The results obtained by two approaches, in which either (i) all electrons at Fe atoms explicitly described or (ii) inner core electrons at Fe atoms are replaced by effective core potential, are compared. Based on our calculations, phase diagrams were constructed, allowing the determination of environmental conditions for the existence of stable phases. It is shown that (within an employed model) only the SrFeO2.5 phase appears to be stable. The stability region for this phase was re-drawn on the contour map of oxygen chemical potential, presented as a function of temperature and oxygen partial pressure. A similar analysis was also performed using experimental Gibbs energies of perovskite formation from the elements. The present modelling strongly suggest a significant attraction between neutral oxygen vacancies. These vacancies are created during a series of the abovementioned SrFeO3-δ mutual transformations accompanied by oxygen release.

Many-Body Spectral Functions from Steady State Density Functional Theory

We propose a scheme to extract the many-body spectral function of an interacting many-electron system from an equilibrium density functional theory (DFT) calculation. To this end we devise an ideal scanning tunneling microscope (STM) setup and employ the recently proposed steady-state DFT formalism (i-DFT) which allows one to calculate the steady current through a nanoscopic region coupled to two biased electrodes. In our setup, one of the electrodes serves as a probe ("STM tip"), which is weakly coupled to the system we want to measure. In the ideal STM limit of vanishing coupling to the tip, the system is restored to quasi-equilibrium and the normalized differential conductance yields the exact equilibrium many-body spectral function. Calculating this quantity from i-DFT, we derive an exact relation expressing the interacting spectral function in terms of the Kohn-Sham one. As illustrative examples, we apply our scheme to calculate the spectral functions of two nontrivial model systems, namely the single Anderson impurity model and the Constant Interaction Model.

First-principles calculations on Fe-Pt nanoclusters of various morphologies

Bimetallic FePt nanoparticles with L1₀ structure are attracting a lot of attention due to their high magnetocrystalline anisotropy and high coercivity what makes them potential material for storage of ultra-high density magnetic data. FePt nanoclusters are considered also as nanocatalysts for growth of carbon nanotubes of different chiralities. Using the DFT-LCAO CRYSTAL14 code, we have performed large-scale spin-polarized calculations on 19 different polyhedral structures of FePt nanoparticles in order to estimate which icosahedral or hcp-structured morphology is the energetically more preferable. Surface energy calculations of all aforementioned nanoparticles indicate that the global minimum corresponds to the nanocluster possessing the icosahedron “onion-like” structure and Fe₄₃Pt₁₀₄ morphology where the outer layer consists of Pt atoms. The presence of the Pt-enriched layer around FePt core explains high oxidation resistance and environmental stability, both observed experimentally.

Visualization of Electron Paramagnetic Resonance Hyperfine Structure Coupling Pathways

The close relation between the EPR hyperfine coupling constant and NMR indirect spin-spin coupling constant is well-known. For example, the Karplus-type dependence of hyperfine constants on the dihedral angle, originally proposed for NMR spin-spin coupling, is widely used in pNMR studies. In the present work we propose a new tool for visualization of hyperfine coupling pathways based on our experience with visualization of NMR indirect spin-spin couplings. The plotted 3D-function is the difference between the total electron densities when the magnetic moment of the nucleus of interest changes its sign and as such is an observable from the physical point of view. It has been shown that it is proportional to the linear response of the spin density to the nuclear spin (i.e., magnetic moment). In contrast to the widely used visualization of spin density, our new approach depicts only the part of the electron cloud of a molecule that is affected by the interaction of the unpaired electron(s) with the desired nuclear magnetic moment. Because visualization of NMR spin-spin couplings and hyperfine interaction is based on the same ideas and done using similar techniques, it allows a direct comparison of the corresponding pathways for the two phenomena so as to analyze their resemblance and/or dissimilarity.

Thermodynamic stability of stoichiometric LaFeO3 and BiFeO3: a hybrid DFT study

BiFeO₃ perovskite attracts great attention due to its multiferroic properties and potential use as a parent material for Bi_1-xSr_xFeO_3-δ and Bi_1-xSr_xFe_1-yCo_yO_3-δ solid solutions in intermediate temperature cathodes of oxide fuel cells. Another iron-based LaFeO₃ perovskite is the end member for well-known solid solutions (La_1-xSr_xFe_1-yCo_yO_3-δ) used for oxide fuel cells and other electrochemical devices. In this study an ab initio hybrid functional approach was used for the study of the thermodynamic stability of both LaFeO₃ and BiFeO₃ with respect to decompositions to binary oxides and to elements, as a function of temperature and oxygen pressure. The localized (LCAO) basis sets describing the crystalline electron wave functions were carefully re-optimized within the CRYSTAL09 computer code. The results obtained by considering Fe as an all-electron atom and within the effective core potential technique are compared in detail. Based on our calculations, the phase diagrams were constructed allowing us to predict the stability region of stoichiometric materials in terms of atomic chemical potentials. This permits determining the environmental conditions for the existence of stable BiFeO₃ and LaFeO₃. These conditions were presented as contour maps of oxygen atoms' chemical potential as a function of temperature and partial pressure of oxygen gas. A similar analysis was also performed using the experimental Gibbs energies of formation. The obtained phase diagrams and contour maps are compared with the calculated ones.

The ligand effect on the oxidative addition of dioxygen to gold(i)–hydride complexes

The activation energy barriers of the O₂ to [LAuH] oxidative addition, calculated by including spin–orbit coupling (SOC) effects, quantitatively correlate with the σ donation component of the L–AuH bond.

Ab Initio Study of BiFeO3: Thermodynamic Stability Conditions

BiFeO3 is investigated intensively, mainly as a multiferroic material. In this paper, the state-of-the-art ab initio hybrid functional approach with atomic basis sets was employed for a study of the stability range of BiFeO3 with respect to its decomposition into binary oxides and elementary metals, as a function of temperature and oxygen partial pressure. The calculated atomic and electronic structure of BiFeO3 was compared with previous LDA+U calculations using plane-wave basis sets. Based on performed calculations, the phase diagram was constructed, which allows us to predict the stability region of stoichiometric BiFeO3.

Perspective: Fifty years of density-functional theory in chemical physics

Since its formal inception in 1964-1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with well-developed wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development.

The effect of the Perdew-Zunger self-interaction correction to density functionals on the energetics of small molecules

Self-consistent calculations using the Perdew-Zunger self-interaction correction (PZ-SIC) to local density and gradient dependent energy functionals are presented for the binding energy and equilibrium geometry of small molecules as well as energy barriers of reactions. The effect of the correction is to reduce binding energy and bond lengths and increase activation energy barriers when bond breaking is involved. The accuracy of the corrected functionals varies strongly, the correction to the binding energy being too weak for the local density approximation but too strong for the gradient dependent functionals considered. For the Perdew, Burke, and Ernzerhof (PBE) functional, a scaling of the PZ-SIC by one half gives improved results on average for both binding energy and bond lengths. The PZ-SIC does not necessarily give more accurate total energy, but it can result in a better cancellation of errors. An essential aspect of these calculations is the use of complex orbitals. A restriction to real orbitals leads to less accurate results as was recently shown for atoms [S. Klüpfel, P. Klüpfel, and H. Jónsson, Phys. Rev. A 84, 050501 (2011)]. The molecular geometry of radicals can be strongly affected by PZ-SIC. An incorrect, non-linear structure of the C(2)H radical predicted by PBE is corrected by PZ-SIC. The CH(3) radical is correctly predicted to be planar when complex orbitals are used, while it is non-planar when the PZ-SIC calculation is restricted to real orbitals.

Improved semiconductor lattice parameters and band gaps from a middle-range screened hybrid exchange functional

We show that the middle-range exchange-correlation hybrid of Henderson, Izmaylov, Scuseria and Savin (HISS) performs extremely well for elemental and binary semiconductors with narrow or visible spectrum band gaps, as well as some wider gap or more ionic systems used in devices. The lattice parameters are superior to those predicted by the screened hybrid functional of Heyd, Scuseria and Ernzerhof (HSE), and provide a significant improvement over the geometries predicted by typical semilocal functionals, yielding results competitive with PBEsol, which was specially tuned for solids. HISS also yields band gaps superior to those produced by functionals developed specifically for the solid state. Timings indicate that HISS is more computationally efficient than HSE, implying that the high quality lattice constants coupled with improved optical band gap predictions render HISS a useful adjunct to HSE in the modeling of geometry-sensitive semiconductors.

Localization of dirac electrons in rotated graphene bilayers

For Dirac electrons the Klein paradox implies that the confinement is difficult to achieve with an electrostatic potential although it can be of great importance for graphene-based devices. Here, ab initio and tight-binding approaches are combined and show that the wave function of Dirac electrons can be localized in rotated graphene bilayers due to the Moire pattern. This localization of wave function is maximum in the limit of the small rotation angle between the two layers.

The atomic and electronic structure of CaF2 and BaF2 crystals with H centers: a hybrid DFT calculation study

Using the B3PW method we simulate the ground state of H center systems for CaF(2) and BaF(2) crystals. The energy difference between H centers with different orientations shows that the H center oriented in the [111] direction in alkaline earth fluorides is the most stable. We present the geometric relaxations of the neighboring atoms surrounding the H center. The combination energy of an H center and the formation energy of the related F-H pair in both alkaline earth fluorides are discussed. We also report the electronic structure of the H center systems. The effective charges and spins of the substitutional and interstitial fluorine atoms show that the hole is located at the interstitial fluorine. The band structures are presented. By studying the DOS sketches the constituents of the defect bands are clarified.

Range separation and local hybridization in density functional theory

Kohn-Sham density functional theory has become a standard method for modeling energetic, spectroscopic, and chemical reactivity properties of large molecules and solids. Density functional theory provides a rigorous theoretical framework for modeling the many-body exchange-correlation effects that dominate the computational cost of traditional wave function approaches. The advent of hybrid exchange-correlation functionals which incorporate a fraction of nonlocal exact exchange has solidified the prominence of density functional theory within computational chemistry. Hybrids provide accurate treatments of properties such as thermochemistry and molecular geometry. But they also exhibit some rather spectacular failures, and often contain multiple empirical parameters. This article reviews our work on developing novel exchange-correlation functionals that build upon the successes of global hybrids. We focus on more flexible functional forms, including local and range-separated hybrid functionals, constructed to obey known exact constraints and (ideally) to incorporate a minimum of empirical parametrization. The article places our work within the context of some other new approximate density functionals and discusses prospects for future work.