Double-counting Term Research Articles

Magnetic anisotropy of a Dy atom on a graphene/Cu(111) surface

The electronic structure and magnetism of individual Dy atoms adsorbed on the graphene/Cu(111) surface is investigated using the combination of the density functional theory with the Hubbard-I approximation to the Anderson impurity model ($\mathrm{DFT}+\mathrm{U}+\mathrm{HIA}$). We find that the results of the $\mathrm{DFT}+\mathrm{U}+\mathrm{HIA}$ depend on the choice of the double-counting term. For fully localized limit, the divalent ${\mathrm{Dy}}^{2+}$ adatom is found, with the total magnetic moment of $9.71\phantom{\rule{4pt}{0ex}}{\ensuremath{\mu}}_{B}$. The spin and orbital magnetic moments are evaluated, and compared with the x-ray magnetic circular dichroism data. The calculated positive magnetic anisotropy energy determines the out-of-plane orientation of the Dy adatom magnetic moment, in agreement with available experimental data.

Decomposing value added in gross exports

Several papers using intercountry IO tables have developed frameworks to decompose value added in gross exports and to remove potential double-counting in intermediate inputs. But these papers rely on different definitions for the domestic value added, foreign value added and double-counting terms, depending in particular on the perspective from which gross exports are decomposed (world level, country level or bilateral level). At this stage, it is very difficult for any user of value-added trade statistics to know what is calculated and which type of decomposition should be used. In this paper, we provide a general framework that relies on extraction matrices to unambiguously and consistently define domestic and foreign value-added terms in the world, country and bilateral perspective. This framework allows us to classify existing decompositions based on the perspective taken and their definition of double-counting. We also indicate the most relevant decompositions for different types of trade analysis.

Comparing particle-particle and particle-hole channels of the random phase approximation

We present a comparative study of particle-hole and particle-particle channels of random-phase approximation (RPA) for molecular dissociations of different bonding types. We introduced a direct particle-particle RPA scheme, in analogy to the direct particle-hole RPA formalism, whereby the exchange-type contributions are excluded. This allows us to compare the behavior of the particle-hole and particle-particle RPA channels on the same footing. Our study unravels the critical role of exchange contributions in determining behaviors of the two RPA channels for describing stretched molecules. We also made an attempt to merge particle-hole RPA and particle-particle RPA into a unified scheme, with the double-counting terms removed. However, benchmark calculations indicate that a straightforward combination of the two RPA channels does not lead to a successful computational scheme for describing molecular dissociations.

Effect of the double-counting functional on the electronic and magnetic properties of half-metallic magnets using the GGA+U method

Methods based on the combination of the usual density functional theory (DFT) codes with the Hubbard models are widely used to investigate the properties of strongly correlated materials. Using first-principle calculations we study the electronic and magnetic properties of 20 half-metallic magnets performing self-consistent GGA+U calculations using both the atomic-limit (AL) and around-mean-field (AMF) functionals for the double counting term, used to subtract the correlation part from the DFT total energy, and compare these results to the usual generalized-gradient-approximation (GGA) calculations. Overall the use of AMF produces results similar to the GGA calculations. On the other hand the effect of AL is diversified depending on the studied material. In general the AL functional produces a stronger tendency towards magnetism leading in some cases to unphysical electronic and magnetic properties. Thus the choice of the adequate double-counting functional is crucial for the results obtained using the GGA+U method.

Computing total energies in complex materials using charge self-consistent DFT + DMFT

We have formulated and implemented a fully charge self-consistent density functional theory plus dynamical mean-field theory methodology which enables an efficient calculation of the total energy of realistic correlated electron systems. The density functional portion of the calculation uses a planewave basis set within the projector augmented wave method enabling study of systems with large, complex unit cells. The dynamical mean-field portion of the calculation is formulated using maximally localized Wannier functions, enabling a convenient implementation which is independent of the basis set used in the density functional portion of the calculation. The importance of using a correct double-counting term is demonstrated. A generalized form of the standard double-counting correction, which we refer to as the ${U}^{\ensuremath{'}}$ form, is described in detail and used. For comparison, the density functional plus $U$ method is implemented within the same framework including the generalized double counting. The formalism is validated via a calculation of the metal-insulator and structural phase diagrams of the rare-earth nickelate perovskites as functions of applied pressure and A-site rare-earth ions. The calculated density functional plus dynamical mean-field results are found to be consistent with experiment. The density functional plus $U$ method is shown to grossly overestimate the tendency for bond disproportionation and insulating behavior.

Density functional tight binding

This paper reviews the basic principles of the density-functional tight-binding (DFTB) method, which is based on density-functional theory as formulated by Hohenberg, Kohn and Sham (KS-DFT). DFTB consists of a series of models that are derived from a Taylor series expansion of the KS-DFT total energy. In the lowest order (DFTB1), densities and potentials are written as superpositions of atomic densities and potentials. The Kohn-Sham orbitals are then expanded to a set of localized atom-centred functions, which are obtained for spherical symmetric spin-unpolarized neutral atoms self-consistently. The whole Hamilton and overlap matrices contain one- and two-centre contributions only. Therefore, they can be calculated and tabulated in advance as functions of the distance between atomic pairs. The second contributions to DFTB1, the DFT double counting terms, are summarized together with nuclear repulsion energy terms and can be rewritten as the sum of pairwise repulsive terms. The second-order (DFTB2) and third-order (DFTB3) terms in the energy expansion correspond to a self-consistent representation, where the deviation of the ground-state density from the reference density is represented by charge monopoles only. This leads to a computationally efficient representation in terms of atomic charges (Mulliken), chemical hardness (Hubbard) parameters and scaled Coulomb laws. Therefore, no additional adjustable parameters enter the DFTB2 and DFTB3 formalism. The handling of parameters, the efficiency, the performance and extensions of DFTB are briefly discussed.

Consistent LDA’ + DMFT approach to the electronic structure of transition metal oxides: Charge transfer insulators and correlated metals

We discuss the recently proposed LDA’ + DMFT approach providing a consistent parameter-free treatment of the so-called double counting problem arising within the LDA + DMFT hybrid computational method for realistic strongly correlated materials. In this approach, the local exchange-correlation portion of the electron-electron interaction is excluded from self-consistent LDA calculations for strongly correlated electronic shells, e.g., d-states of transition metal compounds. Then, the corresponding double-counting term in the LDA’ + DMFT Hamiltonian is consistently set in the local Hartree (fully localized limit, FLL) form of the Hubbard model interaction term. We present the results of extensive LDA’ + DMFT calculations of densities of states, spectral densities, and optical conductivity for most typical representatives of two wide classes of strongly correlated systems in the paramagnetic phase: charge transfer insulators (MnO, CoO, and NiO) and strongly correlated metals (SrVO3 and Sr2RuO4). It is shown that for NiO and CoO systems, the LDA’ + DMFT approach qualitatively improves the conventional LDA + DMFT results with the FLL type of double counting, where CoO and NiO were obtained to be metals. Our calculations also include transition-metal 4s-states located near the Fermi level, missed in previous LDA + DMFT studies of these monoxides. General agreement with optical and the X-ray experiments is obtained. For strongly correlated metals, the LDA’ + DMFT results agree well with the earlier LDA + DMFT calculations and existing experiments. However, in general, LDA’ + DMFT results give better quantitative agreement with experimental data for band gap sizes and oxygen-state positions compared to the conventional LDA + DMFT method.

Method to include explicit correlations into density-functional calculations based on density-matrix functional theory

A variational formulation for the calculation of interacting fermion systems based on the density-matrix functional theory is presented. Our formalism provides for a natural integration of explicit many-particle effects into standard density-functional-theory-based calculations and it avoids the ambiguities of double-counting terms inherent in other approaches. Like the dynamical mean-field theory, we employ a local approximation for explicit correlations. Aiming at the ground state only, we trade some of the complexity of Green's-function-based many-particle methods against efficiency. Using short Hubbard chains as test systems, we demonstrate that the method captures ground-state properties, such as left-right correlation, beyond those accessible by mean-field theories.

Ensemble interpretation ofL(S)DA+U

We propose an ensemble interpretation of the $\text{L}(\text{S})\text{DA}+U$ functional aiming at the construction of a well-defined rigorous scheme as a reference point for further investigations of the functional. An explicit ensemble state, which realizes the conventional $\text{L}(\text{S})\text{DA}+U$ interaction term proportional to the product of the orbital-occupation numbers, is presented. It cannot, however, represent the correct interaction in the general case as it produces spurious self-interaction. We propose to consider the interaction term as resulting from a variational problem and present a method for its solution. As a functional of orbital occupations the interaction term results in piecewise constant corrections to the orbital potentials. The double-counting term is treated as the value of the interaction term for a spherically symmetric atomic configuration. The resulting expression is related to the so-called atomic limit for the double-counting term. It completely cancels the isotropic part (corresponding to the parameter $U$ of the Hubbard model) of the interaction term, so that only the anisotropic part responsible for the so-called orbital polarization correction remains.

First-principles calculation of atomic force in theLSDA+Uformalism

We derive a formula for the atomic force within the $\text{LSDA}+U$ formalism by differentiating analytically the $\text{LSDA}+U$ total-energy functional with respect to atomic positions. The rotationally invariant form of the $\text{LSDA}+U$ functional and the fully localized limit for the double-counting term are considered. The electronic wave functions are expanded with either plane waves or pseudoatomic orbitals (PAOs). In the PAO-basis case, the Pulay correction is also considered and included. Our formula for the atomic force is numerically tested with antiferromagnetic bulk NiO and reproduces successfully the forces obtained from numerical derivative of the total-energy values with respect to atomic displacements. As an application, we study atomic vibrations in NiO and MnO, and obtain transverse-optic phonon frequencies which are consistent with previous theoretical results. Our force formula will make it very efficient to perform large-scale calculations of atomic and phononic structures of strongly correlated materials using the $\text{LSDA}+U$ method.

Anisotropy and magnetism in theLSDA+Umethod

Consequences of anisotropy (variation in orbital occupation) and magnetism, and their coupling, are analyzed for local-spin-density approximation (LSDA) plus interaction term U $(\text{LSDA}+\text{U})$ functionals, with both the commonly used ones as well as less commonly applied functionals. After reviewing and extending some earlier observations for an isotropic interaction, the anisotropies are examined more fully and related to use with the local-density approximation or with the LSDA. The total energies of all possible integer configurations of an open $f$ shell are presented for three functionals, where some differences are found to be dramatic. Differences between how the commonly used ``around mean-field'' (AMF) and ``fully localized limit'' (FLL) functionals perform are traced to such differences. The $\text{LSDA}+\text{U}$ interaction term, when applied self-consistently, usually enhances spin magnetic moments and orbital polarization, and the double-counting terms of both functionals provide an opposing moderating tendency (``suppressing the magnetic moment''). The AMF double-counting term gives magnetic states a significantly larger energy penalty than does the FLL counterpart.

Tight-Binding Density Functional Theory: An Approximate Kohn−Sham DFT Scheme

The DFTB method is an approximate KS-DFT scheme with an LCAO representation of the KS orbitals, which can be derived within a variational treatment of an approximate KS energy functional. But it may also be related to cellular Wigner-Seitz methods and to the Harris functional. It is an approximate method, but it avoids any empirical parametrization by calculating the Hamiltonian and overlap matrices out of DFT-derived local orbitals (atomic orbitals, AO's). The method includes ab initio concepts in relating the Kohn-Sham orbitals of the atomic configuration to a minimal basis of the localized atomic valence orbitals of the atoms. Consistent with this approximation, the Hamiltonian matrix elements can strictly be restricted to a two-center representation. Taking advantage of the compensation of the so-called "double counting terms" and the nuclear repulsion energy in the DFT total energy expression, the energy may be approximated as a sum of the occupied KS single-particle energies and a repulsive energy, which can be obtained from DFT calculations in properly chosen reference systems. This relates the method to common standard "tight-binding" (TB) schemes, as they are well-known in solid-state physics. This approach defines the density-functional tight-binding (DFTB) method in its original (non-self-consistent) version.

Improved description of charged Higgs boson production at hadron colliders

We present a new method for matching the two twin-processes gb->H+/-t and gg->H+/-tb in Monte Carlo event generators. The matching is done by defining a double-counting term, which is used to generate events that are subtracted from the sum of these two twin-processes. In this way we get a smooth transition between the collinear region of phase space, which is best described by gb->H+/-t, and the hard region, which requires the use of the gg->H+/-tb process. The resulting differential distributions show large differences compared to both the gb-> H+/-t and gg->H+/-tb processes illustrating the necessity to use matching when tagging the accompanying b-jet.

First-principles approach to the electronic structure of strongly correlated systems: combining the GW approximation and dynamical mean-field theory.

We propose a dynamical mean-field approach for calculating the electronic structure of strongly correlated materials from first principles. The scheme combines the GW method with dynamical mean-field theory, which enables one to treat strong interaction effects. It avoids the conceptual problems inherent to conventional "LDA+DMFT," such as Hubbard interaction parameters and double-counting terms. We apply a simplified version of the approach to the electronic structure of nickel and find encouraging results.

A new tight binding total energy method for ferroelectric oxides

We have developed a tight-binding electronic structure framework, which includes explicit treatment of Coulombic interactions (with ion-size effects), charge transfer effects and an overlap matrix, and has total energy capabilities. This method is applied to the study of structural phase transitions in ferroelectric oxides, with emphasis on KNbO3, and, to a lesser degree, on KTaO3. In this framework the energy is composed of four parts; 1) a sum over the band energies, 2) ion-ion interaction, 3) an electron-electron double counting term, and 4) Coulombic interactions with ion size effects for near neighbors and point ion interactions for the rest. The self-energies are assumed to be different from the atomic term values due to charge transfer effects. The off site Hamiltonian matrix elements include interactions up to 3rd near-neighbors. The overlap matrix was taken to be proportional to the Hamiltonian matrix. The electrostatic interactions were calculated using the Ewald method, where for near-neighbors...

Tight-binding total energy study of phase transitions in KNBO3

Abstract We have developed a tight-binding electronic structure framework with total-energy capabilities which includes an explicit treatment of charge transfer effects and non-point-ion interactions. In this framework, the total energy is composed of four parts: i) A sum over the band energies, which includes charge transfer effects in the self energies and an overlap matrix proportional to the Hamiltonian matrix, ii) an electron-electron double counting term, iii) a core-core interaction term, and iv) a term that produces Coulombic interactions, where, for first near neighbors, we include a penetration factor that serves to appropriately decrease screening effects. Electronic self consistency is established by updating the self-energy contributions to the Hamiltonian according to the results of a population analysis. Based upon these calculations, we present a potential-energy surface of potassium niobate with respect to symmetry lowering displacements. These results are consistent with a system that sp...

First-principles calculation of impurity-solution energies in Cu and Ni.

We present ab initio calculations for the solution energies of 3d impurities in Cu and Ni hosts. The calculations are based on density-functional theory and the KKR Green's-function method. We apply a grand-canonical energy functional which is extremal against non-particle-conserving charge variations and give an extension of Lloyd's formula for complex energies. The full nonsphericity of the charge density is used in the double counting terms. Test calculations show that it is sufficient to take the perturbation of one shell of host atoms around the impurity into account. The calculated solution energies of 3d impurities in Cu and Ni are in good agreement with the experimental data and with the values predicted by Miedema's model.