First-principles calculation of effective onsite Coulomb interactions of3dtransition metals: Constrained local density functional approach with maximally localized Wannier functions

Abstract

We present a new ab initio method for calculating effective onsite Coulomb interactions of itinerant and strongly correlated electron systems. The method is based on constrained local density functional theory formulated in terms of maximally localized Wannier functions. This scheme can be implemented with any basis, and thus allows us to perform the constrained calculation with plane-wave-based electronic-structure codes. We apply the developed method to the evaluation of the onsite interaction of 3d transition-metal series. The results are discussed using a heuristic formula for screened Coulomb interactions.Properties of itinerant and strongly correlated electron systems are widely discussed with phenomenological Hamiltonians such as Anderson-impurity [1] and Hubbard models [2]. These models embody essential aspects of correlated electrons, and can be solved numerically or sometimes analytically for special cases. However, parameters in the models are often determined empirically so that the employed model should reproduce experimental results of interest.Recently, there has been growing interest in constructing model Hamiltonians from first principles [3]. The principal motivation for such a study is a so-called long-standing "beyond LDA" problem. One of recent major approaches toward correlated electrons from first principles is combining densityfunctional theory within local density approximation (LDA) with dynamical mean-field theory (DMFT) [4]. The main idea of this method is to map a first-principles Hamiltonian onto a lattice-fermion model to which the DMFT method is applicable, so developments of tractable but rational mapping techniques are highly needed.An important notice in constructing ab initio model Hamiltonians lies in an evaluation of an onsite interaction parameter known as the Hubbard U . Transfer parameters can be easily obtained by representing a one-body ab initio Hamiltonian with a spatially localized (or atomic) orbital, while the U parameter evaluated with a one-center Coulomb integral of the atomic orbital gives a rather large value relative to that deduced from experiments [5,6]. This is because a screening effect of surrounding valence electrons is completely neglected in the evaluation of the value. A representative treatment for calculating U including the screening effect is a constrained approach [7,8]. It gives an optimally screened U , because, in that calculation, the U value is obtained from a response of the system to a change in a local charge density, thus incorporating the valence-electron-screening effect statically into the U calculation.An important point in performing the constrained calculation is a choice of basis functions to define the charge density of localized electrons. The use of an atom-centered localized basis set like a linear muffin-tin orbital (LMTO) [9] facilitates this definition, so constrained calculations to date have been performed with LMTO-based electronic-structure codes. The method has been widely applied to investigations of effective Hubbar...

Theory of proximity-induced exchange coupling in graphene on hBN/(Co, Ni)

“…From recent studies of graphene on copper [49] we know that the copper bands have to be shifted down in energy by U = 1.0 eV to match the measured band structure from angle-resolved photoemission spectroscopy experiments. From other DFT studies [72][73][74][75][76], mainly on metal oxides, it is not possible to get a unique value for U . Thus we apply U = 1.0 eV as a generic representative.…”

Exchange coupling transformations in Cu (II) heterospin complexes of “breathing crystals” under structural phase transitions

“…Y. Zhang and H. Jiang took U(Cu) = 6.5 eV 27 to calculate magnetic coupling in binuclear copper complexes Cu 2 (bpy) 2 (H 2 O) 2 (µ-C 2 O 4 ). Constrained calculation of effective on-site Coulomb interactions of 3d transition metals including Cu was performed by Nakamura et al 28 and it was found that U(Cu) = 9.0 eV is a relevant value. Generally speaking, a more accurate determination of the U parameters should involve a self-consistent procedure, where a linear response computation is repeatedly performed for the DFT+U ground state, until a convergence is reached.…”

Construction and solution of a Wannier-functions based Hamiltonian in the pseudopotential plane-wave framework for strongly correlated materials

“…(7)(8)(9)(10)(11) and for the matrix elements by Eqs. (13) and (14). It can be convenient also to back transform from WFs to the plane-waves basis.…”

“…Another way to determine the Coulomb interaction parameter U is to use constrained DFT calculations, 11,12,13,14 where the screening and relaxation effects are taken into account explicitly in a self-consistent procedure. If one uses the assumption that the contribution to the DFT total energy from the interaction between d-electrons is given by Eq.…”

“…DFT can provide not only good data for the kinetic energy terms in the model Hamiltonians, but also gives a practical alternative way to calculate the Coulomb parameter U using constrained DFT calculations 11,12,13,14 . In the constrained calculations, the DFT equations are solved with a fixed occupancy of the localized orbitals, and U is defined as a derivative of the orbital energy with respect to its occupancy.…”