Development and application of ab initio methods for the study of electronic excitations in molecules and extended solids: GW approximation and constrained DFT

Abstract

El objetivo principal de esta tesis fue la implementación dentro del código SIESTA de dos métodos de primeros principios para el estudio de excitaciones electrónicas en moléculas y sólidos extendidos. Los métodos son la aproximación GW y el ’constrained’ DFT. Los métodos fueron implementados usando bases de orbitales extrictamente localizados generadas por SIESTA. El uso de este tipo de orbitales abre la posibilidad de estudiar sistemas que contienen miles de átomos. La aproximación GW es un método derivado de la teoría de perturbaciones de muchos cuerpos para la funcin de Green de una partícula, que se usa para el cálculo de las energías de excitación de quasipart ículas. En este trabajo, se implementó el método propuesto por F. Giustino et al. [3], que solo requiere el uso de los estados electrónicos ocupados para calcular los ingredientes de esta aproximación: la función de Green y el potencial de Coulomb apantallado. En método de ’constrained’ DFT se impone una ligadura sobre la densidad electrnica del sistema a través de un potencial apropiado. En esta tesis se implementó una versión modificada de la aproximación propuesta por Q. Wu and T. Van Voorhis [4] para encontrar el potencial de ’constraining’ de manera eficiente. El método se extendió para el caso de sistemas periódicos. Como una aplicación del método, se estudiaron procesos de transferencia de carga en el conductor oránico TTF-TCNQ. Una aplicación interesante de los métodos implementados es el estudio de los procesos electrónicos que tienen lugar en las celdas solares y dispositivos fotovoltaicos. El material ms ampliamente usado en la fabriacin de estos dispositivos es el TiO2 en fase anatase dopada con impurezas de nitrógeno o sensibilizada con colorantes orgánicos. Como un paso previo al estudio de las excitaciones electrnicas de este material, se caracterizaron sus propiedades electrónicas, estructurales, t y vibracionales usando la teoría DFT. Además, se estudiaroon las energías ’binding’ de los niveles de core de las diferentes especies químicas.

The main aim of this thesis is the implementation in the SIESTA code (a widely used academic computational program based on the density functional theory DFT for the simulation of materials) [1, 2] of two powerful methods for the study of electronic excitations in molecules and extended solids. The methods are the so-called constrained density functional theory (CDFT) and the GW approximation and they are implemented within the strictly localized orbital formalism as defined in SIESTA. The use of local bases opens the possibility of calculating electronic excitations in systems containing thousands of atoms. The GW approximation is a powerful method derived from manybody perturbation theory for the one-particle Green function to calculate quasiparticle excitation energies. We implement the approach proposed by F. Giustino et al. [3] that only requires the use of the occupied electronic states to compute the Green function and screened Coulomb interaction, and from which one constructs the self-energy operator, . In this approach, the Green function is approximated to that of a non-interacting electron system and calculated using a inhomogeneous linear system, while the dynamically screened potential is calculated through the self-consistent linear-response Sternheimer equation. Since the original equations were stated within the plane waves formalism, here we rewrite these equations for basis sets of strictly localized orbitals. As an application of our approach for the dynamically screened potential, we calculate the dielectric function of several insulating and semiconducting materials: LiCl, diamond, silicon and germanium, comparing our results with plane-waves calculations. In the constrained density functional theory, we impose a constraint upon the electronic density of a system through an appropriate potential (called constraining potential) to obtain a neutral excitation. We implement a modified version of the approach proposed by Q.Wu and T. Van Voorhis [4, 5, 6] to find the constraining potential efficiently. Moreover, we extend the method for the case of periodic solids. As an application of our CDFT method, we study the charge transfer between the TTF and TCNQ molecules in the TTF-TCNQ conducting organic salt, where it has been suggested from XPS experiments that the charge transfer process is dynamic, leading to the coexistence of TTF0-TCNQ0 and TTF1+-TCNQ1− charge states [7, 8]. An interesting potential application of our implemented methods is the study of electronic excitations in semiconductor-based solar cells and photovoltaic devices to the efficient design and fabrication of such devices [9, 10, 11]. One of the most extensively used materials for the fabrication of these devices is the anatase TiO2 whether doped with nitrogen impurities or sensitized with dye molecules. Using the DFT machinery we characterize this material as the first step before the calculation of their electronic excitations. We study native defects: oxygen vacancies and interstitial titanium, and nitrogen impurities at interstitial or substitutional position in the anatase matrix. The electronic, structural and thermodynamic properties of all these point defects with different charge states were calculated. Moreover, we study the lattice dynamic of defective anatase in order to determine how defects affect the vibrational modes of pristine anatase and what are the new features arising from defects. We calculate the binding energy shifts of the N 1s, O 1s and Ti 3p core levels to contribute to the full characterization of the defects. Our results of lattice dynamic and core level binding energy shifts are compared with experimental data from Raman and XPS spectroscopy, respectively.