Exact Maps in Density Functional Theory for Lattice Models

In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and for the first time the exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in density functional theory. Having the explicit wavefunction-to- density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening. We show that for fully decoupled subsystems the intra-system steepening transforms into the well-known inter-system derivative discontinuity. An important conclusion is that for e.g. charge transfer processes between localized fragments within the same system it is not the usual inter-system derivative discontinuity that is missing in common ground-state functionals, but rather the differentiable intra-system steepening that we illustrate in the present work

Universal Dynamical Steps in the Exact Time-Dependent Exchange-Correlation Potential

We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially non-local and time non-local dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of non-equilibrium dynamical situations relevant for modeling of photo-chemical/physical processes: field-free evolution of a non-stationary state, resonant local excitation, resonant complete charge-transfer, and evolution under an arbitrary field. Lack of these steps in usual approximations yield inaccurate dynamics, for example predicting faster dynamics and incomplete charge transfer

Charge-transfer in time-dependent density-functional theory via spin-symmetry-breaking

Long-range charge-transfer excitations pose a major challenge for time-dependent density functional approximations. We show that spin-symmetry-breaking offers a simple solution for molecules composed of open-shell fragments, yielding accurate excitations at large separations when the acceptor effectively contains one active electron. Unrestricted exact-exchange and self-interaction-corrected functionals are performed on one-dimensional models and the real LiH molecule within the pseudopotential approximation to demonstrate our results.Comment: 5 pages, 4 figure

The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect

We address and quantify the role of non-adiabaticity ("memory effects") in the exchange-correlation (xc) functional of time-dependent density functional theory (TDDFT) for describing non-linear dynamics of many-body systems. Time-dependent resonant processes are particularly challenging for available TDDFT approximations, due to their strong non-linear and non-adiabatic character. None of the known approximate density functionals are able to cope with this class of problems in a satisfactory manner. In this work we look at the prototypical example of the resonant processes by considering Rabi oscillations within the exactly soluble 2-site Hubbard model. We construct the exact adiabatic xc functional and show that (i) it does not reproduce correctly resonant Rabi dynamics, (ii) there is a sizable non-adiabatic contribution to the exact xc potential, which turns out to be small only at the beginning and at the end of the Rabi cycle when the ground state population is dominant. We then propose a "two-level" approximation for the time-dependent xc potential which can capture Rabi dynamics in the 2-site problem. It works well both for resonant and for detuned Rabi oscillations and becomes essentially exact in the linear response regime. This new, fully non-adiabatic and explicit density functional constitutes one of the main results of the present work.Comment: 8 pages, 5 figure

Performance of the exact adiabatic density functional to describe Rabi physics

Trabajo presentado al American Physical Society Meeting, celebrado en Boston (US) del 27 de Febrero al 2 de Marzo de 2012.-- Título de la presentación: "Rabi oscillations within TDDFT: the example of the 2 site Hubbard model".Through the exact solution of few-electron systems interacting with a monochromatic laser we study the performance of adiabatic density functionals within time-dependent density-functional theory (TDDFT) to reproduce Rabi oscillations. The non-linear dynamics of the Kohn-Sham (KS) system shows the characteristic features of detuned Rabi oscillations even if the exact resonant frequency is used. We illustrate this effect by comparing the exact time-dependent many-body solution of a He-atom in one dimension and a few-site Hubbard model with the solution of TDDFT-KS equations for different adiabatic exchange-correlation functionals. Preventing the detuning introduces a new strong condition to be satisfied by approximate new xc-functionals.Peer reviewe

Static and time-dependent density functionals for non-linear processes

Doctoral thesis in Physics.[ES]: La presente tesis estudia y desarrolla diferentes aproximaciones a la teoría del funcional densidad estático (DFT) y dependiente del tiempo (TDDFT) para la descripción de procesos no lineales en sistemas electrónicos, abordando las virtudes y limitaciones de las aproximaciones (adiabaticas) que se usan normalmente en las simulaciones de respuesta dinámica a campos externos arbitrarios. En la primera parte de la tesis presentamos tres nuevos funcionales para describir el estado fundamental de un sistema fermionico. Los sistemas que se estudian son sistemas modelo de pocos electrones, mayormente en una dimensión, para los cuales se tiene acceso a la solución exacta.Mi primera contribución ha sido el desarrollo de un funcional adinámico local (LDAy LSDA) en una dimensión, construido usando resultados de simulaciones \Quantum Monte Carlo". Mi segunda contribución es un funcional con simetría de spin rota pero localización espacial correcta, que es capaz de reproducir satisfactoriamente las energías de transferencia de carga entre dos átomos de una molécula. El éxito de este último se puede entender en términos de un teorema de Koopmans generalizado. Mi tercera contribución al desarrollo de funcionales para el estado fundamental consiste en plantear el funcional exacto para el modelo de Hubbard de dos sitios, encontrado usando el método exacto propuesto por Levy y Lieb.En la segunda parte de la tesis se estudian los espectros ópticos lineales y no-lineales usando los funcionales del estado fundamental desarrollados en la primera parte de la tesis, bajo una perspectiva adiabática (esto es, que el funcional del estado fundamentales valido para situaciones fuera del equilibrio, por lo que solo depende de la densidad instantánea y no tiene memoria de la historia pasada de la densidad). Para estudiar la calidad de los diferentes funcionales y los efectos no-adiabaticos analizamos en detalle tanto excitaciones dobles como oscilaciones de Rabi (inclusive oscilaciones con transferencia espacial de carga). Las propagaciones temporales se hicieron usando el código octopus (http://tddft.org/progrms/octopus) y se desarrollaron códigos propios para los modelos de Hubbard y para la búsqueda del funcional adiabatico exacto. Dado el enorme cambio en la población de los dos niveles de energía implicados para una oscilación de Rabi (la población del estado fundamental pasa de 100 % a 0 % en medio ciclo de Rabi y viceversa para el estado excitado) estas constituyen un ejemplo de dinámica altamente no lineal y permiten estudiar la validez de las diferentes aproximaciones al funcional densidad dependiente del tiempo en este régimen.Hemos demostrado que los funcionales adiabaticos son incapaces de describir oscilaciones de Rabi resonantes ya que siempre dan lugar a la aparición de un desfase dinámico en la evolución temporal del momento de dipolo. En la última parte de la tesis se descubre y estudia la aparición de unas nuevas estructuras altamente no-locales (tanto en tiempo como en espacio) que presenta el funcional exacto de TDDFT para poder describir procesos dinámicos no-lineales arbitrarios. Estas estructuras (pico y escalón dinámico) deben tenerse en cuenta a la hora de desarrollar funcionales no-adiabaticos (esto es, con memoria) ya que son imprescindibles para poder abordar nuevos fenómenos de respuesta altamente no-lineal. Desde un punto de vista de las aplicaciones a sistemas complejos, los procesos dinámicos no-lineales que se han discutido en esta tesis y analizado en detalle en sistemas modelo de pocos electrones, juegan un papel primordial en la simulación de los procesos de transferencia de carga en células solares orgánicas o entre biomoleculas y para describir la dinámica conjunta de electrones y núcleos en respuesta a campos externos ultra intensos y ultra-rápidos (atosegundos) que son accesibles en la actualidad con las nuevas fuentes de luz de los "free-electron-lasers", entre otros.[EN]: The work presented in this thesis contributes to the developing of Time-DependentDensity Functional Theory, in particular to the development of new exchange-correlation density functionals capable of describing non-linear processes in which the changes of density in time are appreciable. Density Functional Theory is nowadays a standard tool to compute ground-state and dynamical properties of fermionic systems within condensed matter physics and quantum chemistry. Ground-state equilibrium geometries and total energies as well as excitation spectra in a wide variety of systems are accurately predicted. However, for processes like charge-transfer or dissociation of molecules, where non-locality in space and static-correlation play a key role, available local and semi-local functionals have shown to fail. In this thesis we develop a spin-broken density functional that overcomes the failure of the available functionals to predict long-range charge-transfer excitations energies between two open-shells fragments. Time-dependent phenomena of interest address the evolution of Coulomb systems under the action of time-dependent external potentials. The adiabatic approximation, which is obtained by plugging the time-dependent density into one of the existing ground-state density functionals, satisfactorily describes most linear processes. However, phenomena like double excitations or long-range charge-transfer excitations between open-shell fragments can not be captured if memory in the exchange-correlation functional is disregarded. Except for some current-density functionals and orbital-functionals which include some ’Kohn-Sham memory’ through the dependence on the Kohn-Sham orbitals, available exchange-correlation functionals don’t have memory (they are adiabatic). In addition to the above mentioned linear-response shortcomes, available functionals fail to reproduce strong-field non-sequential double ionization4 In this work we show that adiabatic functionals are unable to reproduce resonant dynamics involving the promotion of an electron to a target excited state. Resonant phenomena are a paradigmatic example of highly non-linear dynamics where the non-linearity is not due to the application of a strong external field but to the dramatic change of the electronic density in time. We show that non-adiabaticity is also relevant for resonant processes involving a long-range charge-transfer in space. Ultimately, we have identified dynamical structures that are present in the exact functional and are absent in adiabatic functionals. The missing dynamical step and peak condemn available adiabatic functionals to fail in the description of general (not only resonant) non-linear electron dynamics. Relevant examples of non-linear electron dynamics include coupled ion-electron dynamics involved in the new attosecond experiments and charge-transfer excitations within organic solar-cells and biomolecules, among many others. .En primer lugar debo y quiero agradecer, aunque este muy fuera de moda en estos dias que corren, al gobierno central de España. El Ministerio de Ciencia me concedio becas de ayuda para el estudio y becas de colaboracion con los servicios cientifico-tecnicos de la Universitat de Barcelona durante los años de carrera en Barcelona y posteriormente, una beca de doctorado FPI que me permitio ademas de vivir sin lujos pero dignamente durante estos años de doctorado en Donostia, hacer estancias en el extranjero.Peer reviewe