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Concept# Density functional theory

Summary

Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry.
DFT has been very popular for calculations in solid-state physics since the 1970s. However, DFT was not considered accurate enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactions. Computationa

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We present a first-principles investigation of the structural, electronic, and magnetic properties of the pristine and Fe-doped alpha-MnO2 using density-functional theory with extended Hubbard functionals. The onsite U and intersite V Hubbard parameters are determined from first-principles and self-consistently using density-functional perturbation theory in the basis of Lowdin-orthogonalized atomic orbitals. For the pristine alpha-MnO2 we find that the so-called C2-AFM spin configuration is the most energetically favorable, in agreement with the experimentally observed antiferromagnetic ground state. For the Fe-doped alpha-MnO2 two types of doping are considered: Fe insertion in the 2 x 2 tunnels and partial substitution of Fe for Mn. We find that the interstitial doping preserves the C2 AFM spin configuration of the host lattice only when both onsite U and intersite V Hubbard corrections are included, while for the substitutional doping the onsite Hubbard U correction alone is able to preserve the C2-AFM spin configuration of the host lattice. The oxidation state of Fe is found to be +2 and +4 in the case of the interstitial and substitutional doping, respectively, while the oxidation state of Mn is +4 in both cases. This work paves the way for accurate studies of other MnO2 polymorphs and complex transition-metal compounds when the localization of 3d electrons occurs in the presence of strong covalent interactions with ligands.

The Kohn-Sham formulation of density functional theory (DFT) has posed itself as one of the most popular and versatile methods for condensed phase studies owing to its reasonable accuracy and affordable computational cost. DFT, in principle, yields exact ground state energy, including dispersion forces that are of primordial importance in chemical and biological systems. Yet with many exchange-correlation functionals in practical use such as the local density approximation or generalized gradient approximations, DFT either provides sporadic results or fails completely to account for these forces. In consequence, various methods offering remedy for this shortcoming have been proposed in this active field of research. In particular, dispersion-corrected atom-centered potentials (DCACPs) serve as a robust and efficient way to include these weak forces in a fully self-consistent manner within current DFT frameworks. The aim of this thesis is twofold: first, to improve the predictive power and the understanding of the DCACP concept; second, applying DCACPs to systems of increasing complexity starting with dimers, continuing through larger clusters and ending with the condensed phase. The success of the second aim not only justifies the use of DCACPs but more importantly, provides insights to the role dispersion forces play in the systems investigated. We first draw on the atoms-in-molecules theory and a multi-center density expansion to justify the form and universality of DCACPs. A library of DCACPs calibrated with an improved penalty functional against high-level ab initio references is presented. With the library in hand, we extend our studies to systems of biological significance, mainly constituents of proteins and DNA; polycyclic aromatic molecules intercalated in between segments of DNA are the center of focus. The application of DCACPs is then furthered to the condensed phase and the importance of van der Waals interactions in liquid water is investigated.

Electronic-structure simulations have been impacting the study of materials properties thanks to the simplicity of density-functional theory, a method that gives access to the ground state of the system. Although very important, ground-state properties represent just part of the information, and often technological applications rely more on excited-state properties. In the context of density-functional theory, the latter are difficult to extract and one usually has to resort to more sophisticated approaches. In the last years, Koopmans spectral functionals have emerged as an effective method which combines the feasibility of density-functional theory with the accuracy of more complex methods, such as many-body perturbation theory. While retaining its simplicity, Koopmans functionals extend the domain of density-functional theory providing direct access to charged excitations, and ultimately to the photoemission spectra of materials. This approach has been extensively employed in finite systems, displaying an accuracy which is comparable to that of state-of-the-art many-body perturbation theory methods. In extended systems, calculations were bound to the supercell (Gamma-only) method, preventing the access to the full band structure of the system. In this work we overcome this limitation, proving that a band structure description of the energy spectrum is possible, and providing a scheme to carry out calculations in crystalline materials. The first result of this work consists in proving the compliance of Koopmans functionals with the translation symmetry of the system. The validity of Bloch's theorem, thus the possibility of describing the spectrum via a band structure picture, depends on this condition. Because of the orbital-density-dependent nature of the functional, the invariance of the total energy with respect to unitary transformations of the one-electron orbitals is broken. The energy is then minimized by a particular set of orbitals, called ``variational'', which are strongly localized in space. In extended periodic systems, the localized, thus non-periodic, character of the variational orbitals is inherited by the effective orbital-density-dependent Hamiltonians, which apparently break the translation symmetry of the system. Here we show that, by requiring the variational orbitals to be Wannier functions, the translation symmetry is preserved and Bloch's theorem holds. In the second part, we devise a scheme to unfold the band structure from supercell (Gamma-only) calculations, and reconstruct the k-dependence of the quasiparticle energies. This method is then used to compute the band structures of a set of benchmark semiconductors and insulators. Finally, we describe a novel formulation of Koopmans functionals for extended periodic systems, which exploits from the beginning the translation properties of Wannier functions to realize a primitive cell-based implementation of Koopmans functionals. Results obtained from this second approach are also discussed. In the last part, we present the preliminary study of impurity states arising in crystalline materials in the presence of point defects.