Abstract
This chapter introduces the Hubbard model and its applicability as a corrective tool for accurate modeling of the electronic properties of various classes of systems. The attainment of a correct description of electronic structure is critical for predicting further electronic-related properties, including intermolecular interactions and formation energies. The chapter begins with an introduction to the formulation of density functional theory (DFT) functionals, while addressing the origin of bandgap problem with correlated materials. Then, the corrective approaches proposed to solve the DFT bandgap problem are reviewed, while comparing them in terms of accuracy and computational cost. The Hubbard model will then offer a simple approach to correctly describe the behavior of highly correlated materials, known as the Mott insulators. Based on Hubbard model, DFT+U scheme is built, which is computationally convenient for accurate calculations of electronic structures. Later in this chapter, the computational and semiempirical methods of optimizing the value of the Coulomb interaction potential (U) are discussed, while evaluating the conditions under which it can be most predictive. The chapter focuses on highlighting the use of U to correct the description of the physical properties, by reviewing the results of case studies presented in literature for various classes of materials.
Highlights
Density functional theory (DFT) is one of the most convenient computational tools for the prediction of the properties of different classes of materials [1, 2]
DFT+U is applicable for all open shell orbitals, such as d and f orbitals for transition metal elements with localized orbitals existing in extended states, as in the case of many strongly correlated materials and perovskites, where localized 3d or 4f orbitals are embedded in elongated s-p states
Compared to other corrective approaches, the DFT+U formulation demonstrated to be simpler in terms of theoretical formulation and practical implementations with considerably lower computational cost, while having nearly the same predictive power; it can even capture properties of certain materials that cannot be captured by other higher level or exact calculations
Summary
Density functional theory (DFT) is one of the most convenient computational tools for the prediction of the properties of different classes of materials [1, 2]. We discuss the fundamental formulation of the LDA+U method and examine its applicability for practical implementations for different classes of materials, where DFT is usually found to be impractical. We present a review of the practical implementation of U, while assessing its corrective influence on improving the description of a variety of physical properties related to certain classes of materials. The effect of the calculation parameters on the chosen U value is discussed, including the choice of the localized basis set and the type of DFT functional employed.
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