Density-functional calculation of the parameters in the Anderson model: Application to Mn in CdTe

Orbital-Resolved DFT+U for Molecules and Solids

We present an orbital-resolved extension of the Hubbard U correction to density-functional theory (DFT). Compared to the conventional shell-averaged approach, the prediction of energetic, electronic and structural properties is strongly improved, particularly for compounds characterized by both localized and hybridized states in the Hubbard manifold. The numerical values of all Hubbard parameters are readily obtained from linear-response calculations. The relevance of this more refined approach is showcased by its application to bulk solids pyrite (FeS2) and pyrolusite (β-MnO2), as well as to six Fe(II) molecular complexes. Our findings indicate that a careful definition of Hubbard manifolds is indispensable for extending the applicability of DFT+U beyond its current boundaries. The present orbital-resolved scheme aims to provide a computationally undemanding yet accurate tool for electronic structure calculations of charge-transfer insulators, transition-metal (TM) complexes and other compounds displaying significant orbital hybridization.

First-Principles Calculations of Magnetite (Fe3O4) above the Verwey Temperature by Using Self-Consistent DFT + U + V

In this report, we have used the DFT + U + V approach, an extension of the DFT + U approach that takes into account both on-site and intersite interactions, to simulate structural, magnetic, and electronic properties together with the Fe and O K-edge XAS spectra of Fe3O4 above the Verwey temperature (Tv). Moreover, we compared the simulated XAS spectra with experimental XAS data. We examined both orthogonalized and nonorthogonalized atomic orbital projectors and compared DFT + U + V to DFT, DFT + U, and HSE as a hybrid functional. It is noteworthy that, despite the widespread use of the same Hubbard U value for Feoct and Fetet at the DFT + U level in the literature, the HP code identified two distinct values for them using the Hubbard approaches (DFT + U and DFT + U + V). The resulting Hubbard U and V parameters are strongly dependent on the chosen orbital projectors. This study demonstrates how DFT + U + V can improve the structural, magnetic, and electronic properties of Fe3O4 compared to approximate DFT and DFT + U. In this context, DFT + U + V supports the half-metallic character of the bulk crystal Fe3O4 above Tv, since the Fermi level is found in the t2g band with a Feoct down-spin. Thus, the observations in the current study emphasize the significance of intersite interactions in the theoretical analysis of Fe3O4 above the Tv.

Ab initio methods for the computation of physical properties and performance parameters of electrochemical energy storage devices

With the rapid development of electric vehicles and mobile technologies, there is a high demand for electrochemical energy storage devices and electrochemical energy conversion devices. Devices meeting these needs include metal-ion batteries (MIBs), supercapacitors (SCs), electrochromic devices (ECDs), and multifunctional devices such as electrochromic batteries and supercapatteries. Currently, the goal has been the enhancement of operational parameters and physical properties that results in a higher performance of these devices. In the case of batteries, SCs, and supercapatteries, scientists seek to improve the equilibrium voltage, energy density, power, capacitance, and charge rate. In the case of ECDs, the focus is on improvement of the optical modulation and coloration efficiency. However, synthesis and characterization of new materials, or of materials with optimized properties, is time consuming and highly expensive. Computational simulation of materials can expedite the experimental endeavor by modelling novel atomic structures and predicting device performance. This is possible using ab initio theories and applying physical principles that allow us to understand the underlying mechanisms governing the behavior of materials in these devices. Taking as a point of departure density functional theory (DFT), in this review, we discuss the first principles methods used for the computation of physical properties and performance parameters of electrochemical energy storage devices. A wide coverage of DFT is given, dealing with the strengths and weaknesses of the most popular functionals used in the field of electrochemical energy storage. With these tools, ab initio methods for the computation of basic properties such as effective mass, mobility, optical band gap, transmissivity, conductivity (ionic and electronic), and criteria for structure stability (cohesive energy, formation energy, adsorption energy, and phonon frequency) are addressed. We also highlight the first principles techniques for the calculation of performance parameters in MIBs, SCs, and ECDs.

Role of the Magnetic Anisotropy in Atomic-Spin Sensing of 1D Molecular Chains

One-dimensional metal-organic chains often possess a complex magnetic structure susceptible to modification by alteration of their chemical composition. The possibility to tune their magnetic properties provides an interesting playground to explore quasi-particle interactions in low-dimensional systems. Despite the great effort invested so far, a detailed understanding of the interactions governing the electronic and magnetic properties of the low-dimensional systems is still incomplete. One of the reasons is the limited ability to characterize their magnetic properties at the atomic scale. Here, we provide a comprehensive study of the magnetic properties of metal-organic one-dimensional (1D) coordination polymers consisting of 2,5-diamino-1,4-benzoquinonediimine ligands coordinated with Co or Cr atoms synthesized under ultrahigh-vacuum conditions on a Au(111) surface. A combination of integral X-ray spectroscopy with local-probe inelastic electron tunneling spectroscopy corroborated by multiplet analysis, density functional theory, and inelastic electron tunneling simulations enables us to obtain essential information about their magnetic structures, including the spin magnitude and orientation at the magnetic atoms, as well as the magnetic anisotropy.

DFT+U within the framework of linear combination of numerical atomic orbitals

We present a formulation and implementation of the density functional theory (DFT)+U method within the framework of linear combination of numerical atomic orbitals (NAO). Our implementation not only enables single-point total energy and electronic-structure calculations but also provides access to atomic forces and cell stresses, hence allowing for full structure relaxations of periodic systems. Furthermore, our implementation allows one to deal with non-collinear spin texture, with the spin-orbit coupling (SOC) effect treated self-consistently. The key aspect behind our implementation is a suitable definition of the correlated subspace when multiple atomic orbitals with the same angular momentum are used, and this is addressed via the "Mulliken charge projector" constructed in terms of the first (most localized) atomic orbital within the d/f angular momentum channel. The important Hubbard U and Hund J parameters can be estimated from a screened Coulomb potential of the Yukawa type, with the screening parameter either chosen semi-empirically or determined from the Thomas-Fermi screening model. Benchmark calculations are performed for four late transition metal monoxide bulk systems, i.e., MnO, FeO, CoO, and NiO, and for the 5d-electron compounds IrO₂. For the former type of systems, we check the performance of our DFT+U implementation for calculating bandgaps, magnetic moments, electronic band structures, as well as forces and stresses; for the latter, the efficacy of our DFT+U+SOC implementation is assessed. Systematic comparisons with available experimental results, especially with the results from other implementation schemes, are carried out, which demonstrate the validity of our NAO-based DFT+U formalism and implementation.

Electronic and thermoelectric properties of Nd-doped Ce-filled skutterudites

The electronic and thermoelectric properties of Nd-doped Ce-filled skutterudites (CeFe₄P₁₂, CeFe₄As₁₂, and CeOs₄P₁₂) were explored using full-potential linearized augmented plane waves (FP-LAPW). The exchange-correlation between the electrons was treated with the generalized gradient approximation of Perdew-Burke-Ernzerhof (PBE) and the Coulomb repulsion term (U) between the electrons for the highly correlated system was also considered. The energy band structures revealed the semiconducting nature with energy gaps of 0.42 eV, 0.25 eV and 0.22 eV for CeFe₄P₁₂, CeFe₄As₁₂, and CeOs₄P₁₂, respectively. The phonon dispersion curve displayed the forbidden gap between the optical and acoustic modes in CeFe₄P₁₂ and CeOs₄P₁₂. The analysis of n-type and p-type doping on pure alloys suggest enhanced thermoelectric behavior in p-type doping on pure alloys and hence the addition of Nd at the central cage atomic site generates flat and dense bands at E_F and also opens an optical band gap in doped CeOs₄P₁₂. Moreover, the Nd atom introduces strong phonon scattering and hence reduces the lattice thermal conductivity (K_L) substantially from 6.79 W m^-1 K^-1 to 3.47 W m^-1 K^-1 for CeFe₄P₁₂, 3.63 W m^-1 K^-1 to 1.97 W m^-1 K^-1 for CeFe₄As₁₂ and 6.43 W m^-1 K^-1 to 2.58 W m^-1 K^-1 for CeOs₄P₁₂ at room temperature. A considerably amplified figure of merit has been observed for the doped sample materials with the highest value of 0.72 at 800 K for doped CeFe₄P₁₂ with the highest Seebeck coefficient of 215.51 μV K^-1.

Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps

Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+U can be interpreted as an approximate spectral-potential method when U is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+U to predict band gaps. However, it is still frequent in the literature to determine the Hubbard U parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other total-energy characteristics. Here, we present an extensive assessment of DFT+U band gaps computed using self-consistent ab initio U parameters obtained from density-functional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transition-metal or p-block (group III-IV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides. By comparing DFT+U results obtained using nonorthogonalized and orthogonalized atomic orbitals as Hubbard projectors, we find that the predicted band gaps are extremely sensitive to the type of projector functions and that the orthogonalized projectors give the most accurate band gaps, in satisfactory agreement with experimental data. This work demonstrates that DFT+U may serve as a useful method for high-throughput workflows that require reliable band gap predictions at moderate computational cost.

Spin Hamiltonians in Magnets: Theories and Computations

The effective spin Hamiltonian method has drawn considerable attention for its power to explain and predict magnetic properties in various intriguing materials. In this review, we summarize different types of interactions between spins (hereafter, spin interactions, for short) that may be used in effective spin Hamiltonians as well as the various methods of computing the interaction parameters. A detailed discussion about the merits and possible pitfalls of each technique of computing interaction parameters is provided.

Half-metallicity in new Heusler alloys Mn2ScZ (Z = Si, Ge, Sn)

Study of half-metallicity has been performed in a new series of Mn₂ScZ (Z = Si, Ge and Sn) full Heusler alloys using density functional theory with the calculation and implementation of a Hubbard correction term (U). Volume optimization in magnetic and non-magnetic phases for both the Cu₂MnAl and Hg₂CuTi type structures was done to predict the stable ground state configuration. The stability was determined by calculating their formation energy as well as from elastic constants under ambient conditions. A half-metal is predicted for Mn₂ScSi and Mn₂ScGe with a narrow band gap in the minority spin whereas Mn₂ScSn shows a metallic nature. The magnetic moments of Mn and Sc are coupled in opposite directions with different strengths indicating that the ferrimagnetic order and the total magnetic moment per formula unit for half-metals follows the Slater Pauling rule. And a strong effect was shown by the size of the Z element in the electronic and magnetic properties.

Study of half-metallicity has been performed in a new series of Mn₂ScZ (Z = Si, Ge and Sn) full Heusler alloys using density functional theory with the calculation and implementation of a Hubbard correction term (U).

Calculating spin crossover temperatures by a first-principles LDA+U scheme with parameter U evaluated from GW

The prediction of spin crossover (SCO) temperatures (T_1/2) depends sensitively on the description of local Coulomb correlation. Due to its balance between accuracy and computational cost, local density approximation combined with Hubbard U model (LDA+U) is an appealing tool for this purpose. Despite its accurate performance on energetic properties, such as spin adiabatic energy difference, it is well-known that the LDA+U approach would lose its predictive power if U is tuned to achieve close agreement with experiment for a certain property. On the other hand, a static U value cannot account for changes in the electronic structure. Here, we propose a framework to derive dynamical U (U_dyn) values for iron(ii) complexes from the many-body GW calculations. By performing model calculations on a series of compounds with varying ligand fields, we show that the U values determined in this way are local environment dependent, and the resulting LDA+U_dyn method could reproduce their experimental ground spin states. We present applications to selected SCO complexes illustrating that U_dyn considerably overcomes some of the drawbacks of employing a constant U in the calculation of thermochemical quantities. Using the described calculation procedure, the T_1/2 values are predicted with a small mean absolute error of 176 K with respect to experiment.

First-principles studies of spin-orbital physics in pyrochlore oxides

The pyrochlore oxides [Formula: see text]O₇ exhibit a complex interplay between geometrical frustration, electronic correlations, and spin-orbit coupling (SOC), due to the lattice structure and active charge, spin, and orbital degrees of freedom. Understanding the properties of these materials is a theoretical challenge, because their intricate nature depends on material-specific details and quantum many-body effects. Here we review our recent studies based on first-principles calculations and quantum many-body theories for 4d and 5d pyrochlore oxides with B  =  Mo, Os, and Ir. In these studies, the SOC and local electron correlations are treated within the local density approximation (LDA)  +  U and LDA  +  dynamical mean-field theory formalisms. We also discuss the technical aspects of these calculations.

A first-principles study on magnetic properties of the intrinsic defects in wurtzite ZnO

Since the origin of magnetism in ZnO-based diluted magnetic semiconductors (DMSs) is still controversial, in this work, we presented a detailed study on the magnetic, structural, and electronic properties of wurtzite ZnO-based DMS systems with point and complex intrinsic defects. Two outer electrons from neutral oxygen vacancy (V_O) occupy the a₁ orbital, making the inducted magnetic moment to be zero, while a cluster including three V_Os leads to a magnetic moment of ∼1 μ_B. The magnetic moment of the system with a Zn vacancy (V_Zn) is 1.65 μ_B. When two neutral V_Zns in different relative distances were created in respective supercells, the systems showed different magnetic moments induced by the unequal level between the highest electron occupied orbital of the defect state introduced by different V_Zn sites and the valence band maximum. The system of a neutral O occupying an octahedral site gives rise to a magnetic moment of 2 μ_B, while zinc interstitial and antisite defects do not cause spin polarization. The system with a complex defect of V_O and V_Zn is magnetic when those vacancies are adjacent but still do not cause the compensation effect. The oxygen interstitial defect is unstable, and V_Zn easily turns into the complex defect. We suggest that V_O clusters and V_Zn complex defects could likely be the origin of ferromagnetism in undoped ZnO.

Pressure Effects on the 4f Electronic Structure of Light Lanthanides

Using the satellite structure of the Lγ_{1} line in nonresonant x-ray emission spectra, we probe the high-pressure evolution of the bare 4f signature of the early light lanthanides at ambient temperature. For Ce and Pr the satellite peak experiences a sudden reduction concurrent with their respective volume collapse (VC) transitions. These new experimental results are supported by calculations using state-of-the-art extended atomic structure codes for Ce and Pr, and also for Nd, which does not exhibit a VC. Our work suggests that changes to the 4f occupation are more consistently associated with evolution of the satellite than is the reduction of the 4f moment. Indeed, we show that in the case of Ce, mixing of a higher atomic angular momentum state, driven by the increased hybridization, acts to obscure the expected satellite reduction. These measurements emphasize the importance of a unified study of a full set of microscopic observables to obtain the most discerning test of the underlying, fundamental f-electron phenomena at high pressures.

A new constraint DFT technique for self-consistent determination of U values

A new constraint density functional (DFT) technique workable in combination with the projector augmented wave (PAW) and pseudoptential (PP) methods was developed. This technique calculates the effective on-site-interaction parameter, U _eff, of correlated electrons of materials, self-consistently, by using the DFT  +  U method. The U _eff determined by this technique has a clear physical meaning in that it determines the electronic structures of strongly correlated electronic systems (SCESs) and vice versa. The technique was used to determine the U _eff of correlated electrons of neodymium sesquioxide (Nd₂O₃) and iron oxide (FeO), and it was shown to be effective for this purpose. It enables first principles DFT  +  U PAW and PP calculations of SCESs free from any empirical parameters.

Magnetization, resistivity, specific heat and ab initio calculations of Gd5Sb3

We report on the combined results of the structural, magnetic, transport and calorimetric properties of Mn₅Si₃-type hexagonal Gd₅Sb₃, together with ab initio calculations. It exhibits a ferromagnetic (FM)-like transition at 265 K, antiferromagnetic (AFM) Néel transition at 95.5 K followed by a spin-orientation transition at 62 K. The system is found to be in AFM state down to 2 K in a field of 70 kOe. The FM-AFM phase coexistence is not noticeable despite large positive Curie-Weiss temperature ([Formula: see text] K). Instead, low-temperature AFM and high-temperature FM-like phases are separated in large temperatures. Temperature-magnetic field (H-T) phase diagram reveals field-driven complex magnetic phases. Within the AFM phase, the system is observed to undergo field-driven spin-orientation transitions. Field-induced tricritical and quantum critical points appear to be absent due to the strong AFM nature and by the intervention of FM-like state between paramagnetic and AFM states, respectively. The metallic behavior of the compound is inferred from resistivity along with large Sommerfeld parameter. However, no sign of strong electron-correlations is reasoned from the Kadowaki-Wood's ratio [Formula: see text] [Formula: see text] cm · (mol · K)²(mJ)^-2, despite heavy γ. Essentially, ab initio calculations accounting for electronic correlations confirm AFM nature of low-temperature magnetic state in Gd₅Sb₃ and attainable FM ordering in agreement with experimental data.

The screened pseudo-charge repulsive potential in perturbed orbitals for band calculations by DFT+U

The conventional linear response overestimates the U in DFT+U calculations for solids with fully occupied orbitals. Here, we demonstrate that the challenge arises from the incomplete cancellation of the electron-electron Coulomb repulsion energy under external perturbation. We applied the second charge response, denoted as the "pseudo-charge" model, to offset such residue effects. Counteracting between these two charge response-induced Coulomb potentials, the U parameters are self-consistently obtained by fulfilling the conditions for minimizing the non-Koopmans energy. Moreover, the pseudo-charge-induced repulsive potential shows a screening behavior related to the orbital occupation and is potentially in compliance with the screened exact exchange-correlation of electrons. The resultant U parameters are self-consistent solutions for improved band structure calculations by the DFT+U method. This work extends the validity of the linear response method to both partially and fully occupied orbitals and gives a reference for estimating the Hubbard U parameter prior to other advanced methods. The U parameters were determined in a transferability test using both PBE and hybrid density functional methods, and the results showed that this method is independent of the functional. The electronic structures determined from the hybrid-DFT+U^hybrid approach are provided. Comparisons are also made with the recently developed self-consistent hybrid-DFT+U_w method.

Improved electronic structure and magnetic exchange interactions in transition metal oxides

We discuss the application of the Agapito Curtarolo and Buongiorno Nardelli (ACBN0) pseudo-hybrid Hubbard density functional to several transition metal oxides. For simple binary metal oxides, ACBN0 is found to be a fast, reasonably accurate and parameter-free alternative to traditional DFT  +  U and hybrid exact exchange methods. In ACBN0, the Hubbard energy of DFT  +  U is calculated via the direct evaluation of the local Coulomb and exchange integrals in which the screening of the bare Coulomb potential is accounted for by a renormalization of the density matrix. We demonstrate the success of the ACBN0 approach for the electronic properties of a series technologically relevant mono-oxides (MnO, CoO, NiO, FeO, both at equilibrium and under pressure). We also present results on two mixed valence compounds, Co₃O₄ and Mn₃O₄. Our results for these binary oxides and all the materials we have investigated, obtained at the computational cost of a standard LDA/PBE calculation, are in excellent agreement with hybrid functionals, the GW approximation and experimental measurements.

Probing Magnetism in the Vortex Phase of PuCoGa_{5} by X-Ray Magnetic Circular Dichroism

We measure x-ray magnetic circular dichroism (XMCD) spectra at the Pu M_{4,5} absorption edges from a newly prepared high-quality single crystal of the heavy-fermion superconductor ^{242}PuCoGa_{5}, exhibiting a critical temperature T_{c}=18.7  K. The experiment probes the vortex phase below T_{c} and shows that an external magnetic field induces a Pu 5f magnetic moment at 2 K equal to the temperature-independent moment measured in the normal phase up to 300 K by a superconducting quantum interference device. This observation is in agreement with theoretical models claiming that the Pu atoms in PuCoGa_{5} have a nonmagnetic singlet ground state resulting from the hybridization of the conduction electrons with the intermediate-valence 5f electronic shell. Unexpectedly, XMCD spectra show that the orbital component of the 5f magnetic moment increases significantly between 30 and 2 K; the antiparallel spin component increases as well, leaving the total moment practically constant. We suggest that this indicates a low-temperature breakdown of the complete Kondo-like screening of the local 5f moment.

Towards a First-Principles Determination of Effective Coulomb Interactions in Correlated Electron Materials: Role of Intershell Interactions

The determination of the effective Coulomb interactions to be used in low-energy Hamiltonians for materials with strong electronic correlations remains one of the bottlenecks for parameter-free electronic structure calculations. We propose and benchmark a scheme for determining the effective local Coulomb interactions for charge-transfer oxides and related compounds. Intershell interactions between electrons in the correlated shell and ligand orbitals are taken into account in an effective manner, leading to a reduction of the effective local interactions on the correlated shell. Our scheme resolves inconsistencies in the determination of effective interactions as obtained by standard methods for a wide range of materials, and allows for a conceptual understanding of the relation of cluster model and dynamical mean field-based electronic structure calculations.

The Bethe-Slater curve revisited; new insights from electronic structure theory

The Bethe-Slater (BS) curve describes the relation between the exchange coupling and interatomic distance. Based on a simple argument of orbital overlaps, it successfully predicts the transition from antiferromagnetism to ferromagnetism, when traversing the 3d series. In a previous article [Phys. Rev. Lett. 116, 217202 (2016)] we reported that the dominant nearestneighbour (NN) interaction for 3d metals in the bcc structure indeed follows the BS curve, but the trends through the series showed a richer underlying physics than was initially assumed. The orbital decomposition of the inter-site exchange couplings revealed that various orbitals contribute to the exchange interactions in a highly non-trivial and sometimes competitive way. In this communication we perform a deeper analysis by comparing 3d metals in the bcc and fcc structures. We find that there is no coupling between the E_g orbitals of one atom and T_2g orbitals of its NNs, for both cubic phases. We demonstrate that these couplings are forbidden by symmetry and formulate a general rule allowing to predict when a similar situation is going to happen. In γ-Fe, as in α-Fe, we find a strong competition in the symmetry-resolved orbital contributions and analyse the differences between the high-spin and low-spin solutions.

Racah materials: role of atomic multiplets in intermediate valence systems

We address the long-standing mystery of the nonmagnetic insulating state of the intermediate valence compound SmB₆. Within a combination of the local density approximation (LDA) and an exact diagonalization (ED) of an effective discrete Anderson impurity model, the intermediate valence ground state with the f-shell occupation 〈n_4f〉 = 5.6 is found for the Sm atom in SmB₆. This ground state is a singlet, and the first excited triplet state ~3 meV higher in the energy. SmB₆ is a narrow band insulator already in LDA, with the direct band gap of ~10 meV. The electron correlations increase the band gap which now becomes indirect. Thus, the many-body effects are relevant to form the indirect band gap, crucial for the idea of “topological Kondo insulator" in SmB₆. Also, an actinide analog PuB₆ is considered, and the intermediate valence singlet ground state is found for the Pu atom. We propose that [Sm, Pu]B₆ belong to a new class of the intermediate valence materials with the multi-orbital “Kondo-like" singlet ground-state. Crucial role of complex spin-orbital fⁿ–f ⁿ⁺¹ multiplet structure differently hybridized with ligand states in such Racah materials is discussed.

Molecular nanomagnets with switchable coupling for quantum simulation

Molecular nanomagnets are attractive candidate qubits because of their wide inter- and intra-molecular tunability. Uniform magnetic pulses could be exploited to implement one- and two-qubit gates in presence of a properly engineered pattern of interactions, but the synthesis of suitable and potentially scalable supramolecular complexes has proven a very hard task. Indeed, no quantum algorithms have ever been implemented, not even a proof-of-principle two-qubit gate. Here we show that the magnetic couplings in two supramolecular {Cr7Ni}-Ni-{Cr7Ni} assemblies can be chemically engineered to fit the above requisites for conditional gates with no need of local control. Microscopic parameters are determined by a recently developed many-body ab-initio approach and used to simulate quantum gates. We find that these systems are optimal for proof-of-principle two-qubit experiments and can be exploited as building blocks of scalable architectures for quantum simulation.

Rationalization of the Hubbard U parameter in CeO(x) from first principles: unveiling the role of local structure in screening

The density functional theory (DFT)+U method has been widely employed in theoretical studies on various ceria systems to correct the delocalization bias in local and semi-local DFT functionals with moderate computational cost. We present a systematic and quantitative study, aiming to gain better understanding of the dependence of Hubbard U on the local atomic arrangement. To rationalize the Hubbard U of Ce 4f, we employed the first principles linear response method to compute Hubbard U for Ce in ceria clusters, bulks, and surfaces. We found that the Hubbard U varies in a wide range from 4.3 eV to 6.7 eV, and exhibits a strong correlation with the Ce coordination number and Ce-O bond lengths, rather than the Ce 4f valence state. The variation of the Hubbard U can be explained by the changes in the strength of local screening due to O → Ce intersite transitions.

Coulomb interaction parameters in bcc iron: an LDA+DMFT study

We study the influence of Coulomb interaction parameters on electronic structure and magnetic properties of paramagnetic bcc Fe by means of the local density approximation plus dynamical mean-field theory approach. We consider the local Coulomb interaction in the density-density form as well as in the form with spin rotational invariance approximated by averaging over all directions of the quantization axis. Our results indicate that the magnetic properties of bcc Fe are mainly affected by the Hund's rule coupling J rather than by the Hubbard U. By employing the constrained density functional theory approach in the basis of Wannier functions of spd character, we obtain U = 4 eV and J = 0.9 eV. In spite of the widespread belief that U = 4 eV is too large for bcc Fe, our calculations with the obtained values of U and J result in a satisfactory agreement with the experiment. The correlation effects caused by U are found to be weak even for large U = 6 eV. The agreement between the calculated and experimental Curie temperatures is further improved if J is reduced to 0.8 eV. However, with the decrease of J, the effective local magnetic moment moves further away from the experimental value.

Advances in first-principles modelling of point defects in UO2: f electron correlations and the issue of local energy minima

Over the last decade, a significant amount of work has been devoted to point defect behaviour in UO2 using approximations beyond density functional theory (DFT), in particular DFT + U and hybrid functionals for correlated electrons. We review the results of these studies from calculations of bulk UO2 properties to the more recent determination of activation energies for self-diffusion in UO2, as well as a comparison with their experimental counterparts. We also discuss the efficiency of the three known methods developed to circumvent the presence of metastable states, namely occupation matrix control, U-ramping and quasi-annealing.

Many-body models for molecular nanomagnets

We present a flexible and effective ab initio scheme to build many-body models for molecular nanomagnets, and to calculate magnetic exchange couplings and zero-field splittings. It is based on using localized Foster-Boys orbitals as a one-electron basis. We apply this scheme to three paradigmatic systems, the antiferromagnetic rings Cr8 and Cr7Ni, and the single-molecule magnet Fe4. In all cases we identify the essential magnetic interactions and find excellent agreement with experiments.

What about U on surfaces? Extended Hubbard models for adatom systems from first principles

Electronic correlations together with dimensional constraints lead to some of the most fascinating properties known in condensed matter physics. As possible candidates where these conditions are realized, semiconductor (111) surfaces and adatom systems on surfaces have been under investigation for quite some time. However, state-of-the-art theoretical studies on these materials that include many-body effects beyond the band picture are rare. First principles estimates of inter-electronic Coulomb interactions for the correlated states are missing entirely, and usually these interactions are treated as adjustable parameters. In this work, we report on calculations of the interaction parameters for the group IV surface-adatom systems in the α-phase series of Si(111):C, Si, Sn, Pb. For all systems investigated, the inter-electronic Coulomb interactions are indeed large compared to the kinetic energies of the states in question. Moreover, our study reveals that intersite interactions cannot be disregarded. We explicitly construct an extended Hubbard model for the series of group IV surface-adatom systems on silicon, which can be used for further many-body calculations.

Low-energy models for correlated materials: bandwidth renormalization from Coulombic screening

We provide a prescription for constructing Hamiltonians representing the low-energy physics of correlated electron materials with dynamically screened Coulomb interactions. The key feature is a renormalization of the hopping and hybridization parameters by the processes that lead to the dynamical screening. The renormalization is shown to be non-negligible for various classes of correlated electron materials. The bandwidth reduction effect is necessary for connecting models to materials behavior and for making quantitative predictions for low-energy properties of solids.

Electronic structure and magnetic state of transuranium metals under pressure

The electronic structures of bcc Np, fcc Pu, Am, and Cm pure metals under pressure have been investigated employing the LDA + U method with spin-orbit coupling (LDA + U + SO). The magnetic state of the actinide ions was analyzed in both LS and jj coupling schemes to reveal the applicability of corresponding coupling bases. It was demonstrated that whereas Pu and Am are well described within the jj coupling scheme, Np and Cm can be described appropriately neither in a {mσ}, nor in a {jmj} basis, due to intermediate coupling scheme realization in these metals that requires some finer treatment. The LDA + U + SO results for the considered transuranium metals reveal band broadening and gradual 5f electron delocalization under pressure.

Band selection and disentanglement using maximally localized Wannier functions: the cases of Co impurities in bulk copper and the Cu(111) surface

We have adapted the maximally localized Wannier function approach of Souza et al (2002 Phys. Rev. B 65 035109) to the density functional theory based SIESTA code (Soler et al 2002 J. Phys.: Condens. Mater. 14 2745) and applied it to the study of Co substitutional impurities in bulk copper as well as to the Cu(111) surface. In the Co impurity case, we have reduced the problem to the Co d-electrons and the Cu sp-band, permitting us to obtain an Anderson-like Hamiltonian from well defined density functional parameters in a fully orthonormal basis set. In order to test the quality of the Wannier approach to surfaces, we have studied the electronic structure of the Cu(111) surface by again transforming the density functional problem into the Wannier representation. An excellent description of the Shockley surface state is attained, permitting us to be confident in the application of this method to future studies of magnetic adsorbates in the presence of an extended surface state.

Importance of conduction electron correlation in a Kondo lattice, Ce₂CoSi₃

Kondo systems are usually described by the interaction of the correlation induced local moments with the highly itinerant conduction electrons. Here, we study the role of electron correlations among conduction electrons in the electronic structure of a Kondo lattice compound, Ce₂CoSi₃, using high resolution photoemission spectroscopy and ab initio band structure calculations, where Co 3d electrons contribute in the conduction band. High energy resolution employed in the measurements helped to reveal the signatures of Ce 4f states derived Kondo resonance features at the Fermi level and the dominance of Co 3d contributions at higher binding energies in the conduction band. The lineshape of the experimental Co 3d band is found to be significantly different from that obtained from the band structure calculations within the local density approximations, LDA. Consideration of electron-electron Coulomb repulsion, U, among Co 3d electrons within the LDA + U method leads to a better representation of experimental results. The signature of an electron correlation induced satellite feature is also observed in the Co 2p core level spectrum. These results clearly demonstrate the importance of the electron correlation among conduction electrons in deriving the microscopic description of such Kondo systems.

Charge constrained density functional molecular dynamics for simulation of condensed phase electron transfer reactions

We present a plane-wave basis set implementation of charge constrained density functional molecular dynamics (CDFT-MD) for simulation of electron transfer reactions in condensed phase systems. Following the earlier work of Wu and Van Voorhis [Phys. Rev. A 72, 024502 (2005)], the density functional is minimized under the constraint that the charge difference between donor and acceptor is equal to a given value. The classical ion dynamics is propagated on the Born-Oppenheimer surface of the charge constrained state. We investigate the dependence of the constrained energy and of the energy gap on the definition of the charge and present expressions for the constraint forces. The method is applied to the Ru2+-Ru3+ electron self-exchange reaction in aqueous solution. Sampling the vertical energy gap along CDFT-MD trajectories and correcting for finite size effects, a reorganization free energy of 1.6 eV is obtained. This is 0.1-0.2 eV lower than a previous estimate based on a continuum model for solvation. The smaller value for the reorganization free energy can be explained by the fact that the Ru-O distances of the divalent and trivalent Ru hexahydrates are predicted to be more similar in the electron transfer complex than for the separated aqua ions.

Kondo conductance in an atomic nanocontact from first principles

The electrical conductance of atomic metal contacts represents a powerful tool for detecting nanomagnetism. Conductance reflects magnetism through anomalies at zero bias--generally with Fano line shapes--owing to the Kondo screening of the magnetic impurity bridging the contact. A full atomic-level understanding of this nutshell many-body system is of the greatest importance, especially in view of our increasing need to control nanocurrents by means of magnetism. Disappointingly, at present, zero-bias conductance anomalies are not calculable from atomistic scratch. Here, we demonstrate a working route connecting approximately but quantitatively density functional theory (DFT) and numerical renormalization group (NRG) approaches and leading to a first-principles conductance calculation for a nanocontact, exemplified by a Ni impurity in a Au nanowire. A Fano-like conductance line shape is obtained microscopically, and shown to be controlled by the impurity s-level position. We also find a relationship between conductance anomaly and geometry, and uncover the possibility of opposite antiferromagnetic and ferromagnetic Kondo screening--the latter exhibiting a totally different and unexplored zero-bias anomaly. The present matching method between DFT and NRG should permit the quantitative understanding and exploration of this larger variety of Kondo phenomena at more general magnetic nanocontacts.

Coulomb repulsion and correlation strength in LaFeAsO from density functional and dynamical mean-field theories

The LDA+DMFT (local density approximation combined with dynamical mean-field theory) computation scheme has been used to calculate spectral properties of LaFeAsO-the parent compound of the new high-T(c) iron oxypnictides. The average Coulomb repulsion [Formula: see text] and Hund's exchange J parameters for iron 3d electrons were calculated using the first-principles constrained density functional theory scheme in the Wannier functions formalism. Resulting values strongly depend on the number of states taken into account in the calculations: when the full set of O-2p, As-4p and Fe-3d orbitals and the corresponding bands are included, the interaction parameters [Formula: see text] eV and J = 0.8 eV are obtained. In contrast, when the basis set is restricted to the Fe-3d orbitals and bands only, the calculation gives much smaller values of [Formula: see text] eV, J = 0.5 eV. Nevertheless, DMFT calculations with both parameter sets and the corresponding basis sets result in a weakly correlated electronic structure that is in agreement with the experimental x-ray and photoemission spectra.

Bandstructure meets many-body theory: the LDA+DMFT method

Ab initio calculation of the electronic properties of materials is a major challenge for solid-state theory. Whereas 40 years' experience has proven density-functional theory (DFT) in a suitable form, e.g. local approximation (LDA), to give a satisfactory description when electronic correlations are weak, materials with strongly correlated electrons, say d- or f-electrons, remain a challenge. Such materials often exhibit 'colossal' responses to small changes of external parameters such as pressure, temperature, and magnetic field, and are therefore most interesting for technical applications. Encouraged by the success of dynamical mean-field theory (DMFT) in dealing with model Hamiltonians for strongly correlated electron systems, physicists from the bandstructure and many-body communities have joined forces and developed a combined LDA+DMFT method for treating materials with strongly correlated electrons ab initio. As a function of increasing Coulomb correlations, this new approach yields a weakly correlated metal, a strongly correlated metal, or a Mott insulator. In this paper, we introduce the LDA+DMFT method by means of an example, LaMnO(3). Results for this material, including the 'colossal' magnetoresistance of doped manganites, are presented. We also discuss the advantages and disadvantages of the LDA+DMFT approach.

A band structure analysis of the coexistence of superconductivity and magnetism in (Ho,Dy)Ni(2)B(2)C

The phenomenological theory of complex interplay of superconductivity and magnetism in Ho(1-x)Dy(x)Ni(2)B(2)C by Doh et al (1999 Phys. Rev. Lett. 83 5350) is based on the multi-band picture with at least one band which is strongly dominated by Ni 3d-electron orbitals. These orbitals are insensitive to the antiferromagnetic order of the (Ho, Dy) 4f-electrons, found in these alloys. In the present study we show by detailed analysis of the band structure that indeed such a band can be identified. This provides a microscopic justification of the basic idea underlying the phenomenological discussion.

Mutual experimental and theoretical validation of bulk photoemission spectra of Sr1-xCaxVO3

We report high-resolution high-energy photoemission spectra together with parameter-free LDA + DMFT (local density approximation + dynamical mean-field theory) results for Sr1-xCaxVO3, a prototype 3d(1) system. In contrast to earlier investigations the bulk spectra are found to be insensitive to x. The good agreement between experiment and theory confirms the bulk sensitivity of the high-energy photoemission spectra.