A Fortran 90 Hartree-Fock program for one-dimensional periodic π\pi-conjugated systems using Pariser-Parr-Pople model

Pariser-Parr-Pople (P-P-P) model Hamiltonian is employed frequently to study the electronic structure and optical properties of $\pi$-conjugated systems. In this paper we describe a Fortran 90 computer program which uses the P-P-P model Hamiltonian to solve the Hartree-Fock (HF) equation for infinitely long, one-dimensional, periodic, $\pi$-electron systems. The code is capable of computing the band structure, as also the linear optical absorption spectrum, by using the tight-binding (TB) and the HF methods. Furthermore, using our program the user can solve the HF equation in the presence of a finite external electric field, thereby, allowing the simulation of gated systems. We apply our code to compute various properties of polymers such as $trans$-polyacetylene ($t$-PA), poly-\emph{para}-phenylene (PPP), and armchair and zigzag graphene nanoribbons, in the infinite length limit.Comment: 33 pages, 11 figures (included), submitted for publicatio

Modelización del proceso de interacción de los analgésicos nicotínicos frente al subtipo α4β 2 del receptor nAChR

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Química. Fecha de lectura: 20-02-200

Nonequilibrium Green Functions Simulations on the Next Level: Theoretical Advances and Applications to Finite Lattice Systems

This thesis is devoted to the description of correlated finite lattice systems under nonequilibrium conditions. In this context, the lack of small parameters in the corresponding standard many-body equations makes it difficult to construct suitable approximations for theoretical tools, which renders the computation of relevant observables numerically costly and impractical. At the same time, rigorous predictions for the ultrafast dynamics in correlated lattices are highly valuable for the understanding of many state-of-the-art experiments. The nonequilibrium Green functions (NEGF) technique is particularly well-suited to meet the challenging demands that come with the description of the nontrivial interplay between quantum correlations and nonequilibrium effects in excited lattice systems. However, in order to apply the approach on a practically relevant scale, several methodological improvements come to be indispensable. The present thesis contains these theoretical advances of the NEGF method, alongside with—thus accessible—applications to ultracold atoms in optical lattices and excited finite graphene nanostructures

Developments in multiscale ONIOM and fragment methods for complex chemical systems

Multiskalenprobleme werden in der Computerchemie immer allgegenwärtiger und bestimmte Klassen solcher Probleme entziehen sich einer effizienten Beschreibung mit den verfügbaren Berechnungsansätzen. In dieser Arbeit wurden effiziente Erweiterungen der Multilayer-Methode ONIOM und von Fragmentmethoden als Lösungsansätze für derartige Probleme entwickelt. Dabei wurde die Kombination von ONIOM und Fragmentmethoden im Rahmen der Multi-Centre Generalised ONIOM entwickelt sowie die eine Multilayer-Variante der Fragment Combinatio Ranges. Außerdem wurden Schemata für elektronische Einbettung derartiger Multilayer-Systeme entwickelt. Der zweite Teil der Arbeit beschreibt die Implementierung im Haskell-Programm "Spicy" und demonstriert Anwendungen derartiger Multiskalen-Methoden

Computational and Theoretical Developements for (Time Dependent) Density Functional Theory

En esta tesis se presentan avances computacionales y teoricos en la teoria de funcionales de la densidad (DFT) y en la teoria de funcionales de la densidad dependientes del tiempo (TDDFT). Hemos explorado una posible nueva ruta para la mejora de los funcionales de intercambio y correlacion (XCF) en DFT, comprobado y desarrollado propagadores numericos para TDDFT, y aplicado una combinacion de la teoria de control optimo con TDDFT.En los ultimos anos, DFT se ha convertido en el metodo mas utilizado en el area de estructura electronica gracias a su inigualable relacion entre coste y precision. Podemos usar DFT para calcular multitud de propiedades fisicas y quimicas de atomos, moleculas, nanoestructuras, y materia macroscopica. El factor principal que determina la precision que podemos alcanzar usando DFT es el XCF, un objeto desconocido para el cual se han propuesto cientos de aproximaciones distintas. Algunas de estas aproximaciones funcionan correctamente en ciertas situaciones, pero a dia de hoy no existe un XCF que pueda aplicarse con certeza sobre su validez a un sistema arbitrario. Mas aun, no hay una forma sistematica de refinar estos funcionales. Proponemos y exploramos, para sistemas unidimensionales, una nueva manera de estudiarlos y optimizarlos basada en establecer una relacion con la interaccion entre electrones.TDDFT es la extension de DFT a problemas dependientes del tiempo y problemas conestados excitados, y es tambien uno de los metodos mas populares (a veces el unico metodo que se puede poner en practica) en la comunidad de estructura electronica para tratar conellos. De nuevo, la razon detras de su popularidad reside en su relacion precision/coste computacional, que nos permite tratar sistemas mayores y mas complejos. Puede usarse en combinacion con la dinamica de Ehrenfest, un tipo de dinamica molecular no adiabatica.Hemos ido mas alla y hemos combinado TDDFT y la dinamica de Ehrenfest con la teoria de control optimo, creando un instrumento que nos permite, por ejemplo, predecir la forma de los pulsos laser que inducen una explosion de Coulomb en clusters de sodio. A pesar del buen rendimiento computacional de TDDFT en comparacion con otros metodos, hallamos que el coste de estos calculos era bastante elevado.Motivados por este hecho, tambien dedicamos una parte del trabajo de la tesis a la investigacion computacional. En particular, hemos estudiado e implementado familias de propagadores numericos que no se habian examinado en el contexto de TDDFT. Mas concretamente, metodos con varios pasos previos, formulas Runge-Kutta exponenciales, y las expansiones de Magnus sin conmutadores. Finalmente, hemos implementado modificaciones de estas expansiones de Magnus sin conmutadores para la propagacion de las ecuaciones clasico-cuanticas que resultan de la combinacion de la dinamica de Ehrenfest con TDDFT.In this thesis we present computational and theoretical developments for density functional theory (DFT) and time dependent density functional theory (TDDFT). We have explored a new possible route to improve exchange and correlation functionals (XCF) in DFT, tested and developed numerical propagators for TDDFT, and applied a combination of optimal control theory with TDDFT. In recent years, DFT has become the most used method in the electronic structure field thanks to its unparalleled precision/computational cost relationship. We can use DFT to accurately calculate many physical and chemical properties of atoms, molecules, nanostructures, and bulk materials. The main factor that determines the precision that we can obtain using DFT is the XCF, an unknown object for which hundreds of different approximations have been proposed. Some of these approximations work well enough for certain situations, but to this day there is no XCF that can be reliably applied to any arbitrary system. Moreover, there is no clear way for a systematic refinement of these functionals. We propose and explore, for one-dimensional systems, a new way to optimize them, based on establishing a relationship with the electron-electron interaction. TDDFT is the extension of DFT to time-dependent and excited-states problems, and it is also one of the most popular methods (sometimes the only practical one) in the electronic structure community to deal with them. Once again, the reason behind its popularity is its accuracy/computational cost ratio, which allows us to tackle bigger, more complex systems. It can be used in combination with Ehrenfest dynamics, a non-adiabatic type of molecular dynamics. We have furthermore combined both TDDFT and Ehrenfest dynamics with optimal control theory, a scheme that has allowed us, for example, to predict the shapes of the laser pulses that induce a Coulomb explosion in different sodium clusters. Despite the good numerical performance of TDDFT compared to other methods, we found that these computations were still quite expensive. Motivated by this fact, we have also dedicated a part of the thesis work to computational research. In particular, we have studied and implemented families of numerical propagators that had not been tested in the context of TDDFT. More concretely, linear multistep schemes, exponential Runge-Kutta formulas, and commutator-free Magnus expansions. Moreover, we have implemented modifications of these commutator-free Magnus methods for the propagation of the classical-quantum equations that result of combining Ehrenfest dynamics with TDDFT.<br /