4f fine‐structure levels as the dominant error in the electronic structures of binary lanthanide oxides

The ground‐state 4f fine‐structure levels in the intrinsic optical transition gaps between the 2p and 5d orbitals of lanthanide sesquioxides (Ln₂O₃, Ln = La…Lu) were calculated by a two‐way crossover search for the U parameters for DFT + U calculations. The original 4f‐shell potential perturbation in the linear response method were reformulated within the constraint volume of the given solids. The band structures were also calculated. This method yields nearly constant optical transition gaps between Ln‐5d and O‐2p orbitals, with magnitudes of 5.3 to 5.5 eV. This result verifies that the error in the band structure calculations for Ln₂O₃ is dominated by the inaccuracies in the predicted 4f levels in the 2p‐5d transition gaps, which strongly and non‐linearly depend on the on‐site Hubbard U. The relationship between the 4f occupancies and Hubbard U is non‐monotonic and is entirely different from that for materials with 3d or 4d orbitals, such as transition metal oxides. This new linear response DFT + U method can provide a simpler understanding of the electronic structure of Ln₂O₃ and enables a quick examination of the electronic structures of lanthanide solids before hybrid functional or GW calculations. © 2015 Wiley Periodicals, Inc.     

Critical Assessment of the DFT + U Approach for the Prediction of Vanadium Dioxide Properties

In a previous study (Stahl and Bredow, Chem. Phys. Lett. 2018, 695, 28–33), we have studied structural, energetic, and electronic properties of two vanadium dioxide VO₂ polymorphs with modified global and range-separated hybrid functionals. Since hybrid methods are computationally demanding, we evaluate the computationally more efficient DFT + U method in the present study. We assessed the widely used Dudarev PBE + U approach with a literature value of the effective Hubbard parameter U_eff = 3.4 eV. We compared the PBE + U results for the two VO₂ polymorphs with our previous results, a self-consistent hybrid functional sc-PBE0, and the meta-GGA functional SCAN. It was found that the PBE + U method yields a strongly distorted monoclinic phase and does not reproduce the metal-to-insulator transition of VO₂ correctly, even with modified values of U_eff. On the other hand, sc-PBE0 and SCAN describe the relative stability and the electronic structure of both polymorphs correctly and also provide reasonable lattice parameters. The functional SCAN yields the optimal balance between computational efficiency and accuracy. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

Magnetic ordering and metal‐atom site preference in tetragonal CrMnAs: Electronic correlation effects

The electronic and magnetic structures of tetragonal, Cu₂Sb‐type CrMnAs were examined using density functional theory. To obtain reasonable agreement with reported atomic and low‐temperature magnetic ordering in this compound, the intra‐atomic electron–electron correlation in term of Hubbard U on Mn atoms are necessary. Using GGA + U, calculations identify four low‐energy antiferromagnetically ordered structures, all of which adopt a magnetic unit cell that contains the same direct Cr Cr and Cr Mn magnetic interaction, as well as the same indirect Mn⋅⋅⋅Mn magnetic interaction across the Cr planes. One of these low‐energy configurations corresponds to the reported case. Effective exchange parameters for metal–metal contacts obtained from SPRKKR calculations indicate both direct and indirect exchange couplings play important roles in tetragonal CrMnAs. © 2018 Wiley Periodicals, Inc.     

Combined DFT and wave function theory approach to excited states of lanthanide luminescent materials: A case study of LaF3:Ce3+

Lanthanide luminescent materials play key roles in modern society, but their first-principles treatment remains a great challenge due to complex manifold of electronic excited states and the difficulty in performing excited state structural relaxations that is necessary to model luminescent properties. Herein, we propose a practical approach that combines embedded cluster model (ECM) based multi-configurational wave function theory (WFT) and occupancy constrained density-functional theory plus the Hubbard U correction (OC-DFT + U) to treat lanthanide doped luminescent materials, using LaF₃:Ce³⁺, a typical scintillator with low symmetry, as a case study. We show that the combined approach yields accurate absorption energies with an error on the order of 200 cm⁻¹, but the emission energies are significantly underestimated, the origin of which is further clarified by vibrationally resolved absorption and emission spectra calculation. This work demonstrates the possibility of combining ECM-based wave function theory and periodic DFT into a comprehensive computational scheme for lanthanide luminescent materials and highlights the limitations of the current implementation of OC-DFT + U for excited state structural optimization.     

The self‐consistent charge density functional tight‐binding theory study of carbon adatoms using tuned Hubbard U parameters

The self‐consistent charge density functional tight‐binding (DFTB) theory is a useful tool for realizing the electronic structures of large molecular complex systems. In this study, the electronic structure of C₆₁ formed by fullerene C₆₀ with a carbon adatom is analyzed, using the fully localized limit and pseudo self‐interaction correction methods of DFTB to adjust the Hubbard U parameter (DFTB + U). The results show that both the methods used to adjust U can significantly reduce the molecular orbital energy of occupied states localized on the defect carbon atom and improve the gap between highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital(LUMO) of C₆₁. This work will provide a methodological reference point for future DFTB calculations of the electronic structures of carbon materials.     

Metal–insulator transition in the Hubbard model on a triangular lattice with disorders: Renormalization group approach

A multistages block renormalization group approach to study the metal–insulator transition in the Hubbard model on a triangular lattice with hexagonal blocks is presented and implemented. A second‐order phase transition with a critical point at U/t = 12.5 is obtained (the coupling parameters U and t correspond to the repulsive charging energy and to the nearest‐neighbor exchange coupling terms, respectively). In the presence of disorder the phase diagram for the system exhibits a metallic phase, an insulating phase, and a domain‐localized phase that separates them in the Mott regime. The subtle influence of electron–electron interactions upon inverse participation rate in the Anderson regime is also investigated. The results are discussed in light of experimental evidence for arrays of metalic quantum dots and exact numerical diagonalization of the Hubbard Hamiltonian. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 360–374, 2003     

Electronic structure,magnetic properties,and mixed valence character of Ce2Ni3Si5 from first principles calculations

Cerium intermetallic compounds exhibit anomalous physical properties such as heavy fermion and Kondo behaviors. Here, an ab initio study of the electronic structure, magnetic properties, and mixed valence character of Ce₂Ni₃Si₅ using density functional theory (DFT) is presented. Two theoretical methods, including pure Perdew–Burke–Ernzerhof (PBE) and PBE + U , are used. In this study, Ce³⁺ and Ce⁴⁺ are considered as two different constituents in the unit cell. The formation energy calculations on the DFT level propose that Ce is in a stable mixed valence of 3.379 at 0 K. The calculated electronic structure shows that Ce₂Ni₃Si₅ is a metallic compound with a contribution at the Fermi level from Ce 4f and Ni 3d states. With the inclusion of the effective Hubbard parameter (U _eff), the five valence electrons of 5 Ce³⁺ ions are distributed only on Ce³⁺ 4f orbitals. Therefore, the occupied Ce³⁺ 4f band is located in the valence band (VB) while Ce⁴⁺ 4f orbitals are empty and Located at the Fermi level. The calculated magnetic moment in Ce₂Ni₃Si₅ is only due to cerium (Ce³⁺) in good agreement with the experimental results. The U _eff value of 5.4 eV provides a reasonable magnetic moment of 0.981 for the unpaired electron per Ce³⁺ ion. These results may serve as a guide for studying present mixed valence cerium‐based compounds. © 2017 Wiley Periodicals, Inc.     

Challenges in the use of density functional theory to examine catalysis by M‐doped ceria surfaces

For CeO₂ or M‐doped CeO₂ catalysts, reliable energetics associated with surface reactivity requires accurate representation of oxidized and reduced metal states. Density functional theory (DFT) is used extensively for metals and metal oxides; however, for strongly correlated electron materials, conventional DFT fails to predict both qualitative and quantitative properties. This is the result of a localized electron self‐interaction error that is inherit to DFT. DFT+U has shown promise in correcting energetic errors due to the self‐interaction error, however, its transferability across processes relevant to surface catalysis remains unclear. Hybrid functionals, such as HSE06, can also be used to correct this self‐interaction error. These hybrid functionals are computationally intensive, and especially demanding for periodic surface slab models. This perspective details the challenges in representing the energetics of M‐doped ceria catalyzed processes and examines using DFT extensions to model the localized electronic properties. © 2013 Wiley Periodicals, Inc.     

Magnetic Properties and Electronic Structure of Neptunyl(VI) Complexes: Wavefunctions,Orbitals, and Crystal‐Field Models

The electronic structure and magnetic properties of neptunyl(VI), NpO₂²⁺, and two neptunyl complexes, [NpO₂(NO₃)₃]^? and [NpO₂Cl₄]^2?, were studied with a combination of theoretical methods: ab initio relativistic wavefunction methods and density functional theory (DFT), as well as crystal‐field (CF) models with parameters extracted from the ab initio calculations. Natural orbitals for electron density and spin magnetization from wavefunctions including spin–orbit coupling were employed to analyze the connection between the electronic structure and magnetic properties, and to link the results from CF models to the ab initio data. Free complex ions and systems embedded in a crystal environment were studied. Of prime interest were the electron paramagnetic resonance g‐factors and their relation to the complex geometry, ligand coordination, and nature of the nonbonding 5f orbitals. The g‐factors were calculated for the ground and excited states. For [NpO₂Cl₄]^2?, a strong influence of the environment of the complex on its magnetic behavior was demonstrated. Kohn–Sham DFT with standard functionals can produce reasonable g‐factors as long as the calculation converges to a solution resembling the electronic state of interest. However, this is not always straightforward.     

GW-BSE Calculations of Electronic Band Gap and Optical Spectrum of ZnFe2O4: Effect of Cation Distribution and Spin Configuration

The G0W0, evGW0, evGW, and scGW0 approximations to many-body perturbation theory combined with the Bethe-Salpeter approach (BSE) are applied to calculate electronic and optical properties of the open-shell spinel ferrite ZnFe₂O₄. The effect of the various degrees of self-consistency is assessed by comparison to recent experimental results. Furthermore, the influence of the method for obtaining the ground-state wavefunction is studied, including the GGA functional PBE with and without an intermediate step using the COHSEX approximation, as well as PBE+U, where we try to minimize the influence of the Hubbard potential U. Best agreement for the optical band gap and the first maxima of the excitation spectrum is obtained with the evGW method based on a PBE+U wavefunction. This method is chosen and converged carefully to yield quantitative results for the optical spectra of four different magnetic structures and cation distributions of ZnFe₂O₄. With the results we provide a possible explanation for inconsistency in experimental results.     

Density Functional Theory Calculations of 95Mo NMR Parameters in Solid‐State Compounds

The application of periodic density functional theory‐based methods to the calculation of ⁹⁵Mo electric field gradient (EFG) and chemical shift (CS) tensors in solid‐state molybdenum compounds is presented. Calculations of EFG tensors are performed using the projector augmented‐wave (PAW) method. Comparison of the results with those obtained using the augmented plane wave + local orbitals (APW+lo) method and with available experimental values shows the reliability of the approach for ⁹⁵Mo EFG tensor calculation. CS tensors are calculated using the recently developed gauge‐including projector augmented‐wave (GIPAW) method. This work is the first application of the GIPAW method to a 4d transition‐metal nucleus. The effects of ultra‐soft pseudo‐potential parameters, exchange‐correlation functionals and structural parameters are precisely examined. Comparison with experimental results allows the validation of this computational formalism.     

Comprehensive SPHYB and B3LYP‐DFT Studies of Two Types of Ferrocene

Structural and optoelectronic properties of ferrocene (FeC₁₀H₁₀) using various exchange correlation potentials including Spin Polarized Generalized Gradient Approximation (SPGGA), Hybrid Density Functional Theory (SPHYB‐DFT), and hybrid density functional Becke3LYP are investigated. Obtained bandgap by the SPHYB‐DFT and SPGGA methods show consistency with the experiment, that are indirect and direct, respectively. The cell size effects on physical properties of ferrocene studied about two types of its lattice parameters ( I and II ). The calculated results reveal that the cell size and the lattice parameters have a remarkable effect on optoelectronic and magnetic properties of ferrocene. However, there is no significant difference between I and II within molecular, structural and charge transitions in calculating UV/Vis spectrum. The calculated electronic absorption spectrum is in good agreement with experiment, in which two major electron‐transition bands derived from d–d (n → n*) and n → π* metal to ligand. NBO analyses show that there are strong donor‐acceptor interactions between central Fe atoms and cyclopentadienyl (Cp) rings that these results are in close agreement with contour plots of charge densities for prediction of the strong covalent bond between C and Fe. The optoelectronic properties of ferrocene predict that it can be efficiently used in the semiconductor devices.     

Intermolecular Interactions in Weak Donor–Acceptor Complexes from Symmetry‐Adapted Perturbation and Coupled‐Cluster Theory: Tetracyanoethylene–Benzene and Tetracyanoethylene–p‐Xylene

The interactions in the complexes of tetracyanothylene (TCNE) with benzene and p‐xylene, often classified as weak electron donor–acceptor (EDA) complexes, are investigated by a range of quantum chemical methods including intermolecular perturbation theory at the DFT‐SAPT (symmetry‐adapted perturbation theory combined with density functional theory) level and explicitly correlated coupled‐cluster theory at the CCSD(T)‐F12 level. The DFT‐SAPT interaction energies for TCNE–benzene and TCNE–p‐xylene are estimated to be ?35.7 and ?44.9 kJ mol^?1, respectively, at the complete basis set limit. The best estimates for the CCSD(T) interaction energy are ?37.5 and ?46.0 kJ mol^?1, respectively. It is shown that the second‐order dispersion term provides the most important attractive contribution to the interaction energy, followed by the first‐order electrostatic term. The sum of second‐ and higher‐order induction and exchange–induction energies is found to provide nearly 40 % of the total interaction energy. After addition of vibrational, rigid‐rotor, and translational contributions, the computed internal energy changes on complex formation approach results from gas‐phase spectrophotometry at elevated temperatures within experimental uncertainties, while the corresponding entropy changes differ substantially.     

Applications of density functional theory methods in millimeter‐wave spectroscopy

Density functional theory (DFT), using the most common functionals, and ab initio quantum chemistry methods are used to calculate the rotational constants and dipole moments of the astrophysically important molecules HCN, CH₃CN, CH₃CNH⁺, HCCCN, and HCCNC. As far as millimeter‐wave spectroscopy is of interest the DFT methods performed well with most functionals, giving results within ±1% of experiments for rotational constants and ±3% for dipole moments. Analyzing the results obtained with all theoretical models, it may be concluded that the Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP) and Becke's three‐parameter functional with Perdew–Wang correlational functional [B3PW91/6‐31G(d, p)] give the best performances. A detailed analysis of the electron correlation effects shows that HCCCN is more stable than is HCCNC, by 1.16 eV, with important contribution arising from triple excitations. This result is also compared with those obtained with DFT methods. Despite occasional difficulties, DFT with the currently available functionals are of great utility in quickly assessing spectroscopic parameters of astrophysical interest. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003