Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of His 80th Birthday

A collection of 18 scientific papers written in honor of Professor Karlheinz Schwarz's 80th birthday. The main topics include spectroscopy, excited states, DFT developments, results analysis, solid states, and surfaces

The density matrix renormalization group for ab initio quantum chemistry

During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. The MPS ansatz naturally captures exponentially decaying correlation functions. Therefore DMRG works extremely well for noncritical one-dimensional systems. The active orbital spaces in quantum chemistry are however often far from one-dimensional, and relatively large virtual dimensions are required to use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its computational cost, and its properties are discussed. Two important aspects to reduce the computational cost are given special attention: the orbital choice and ordering, and the exploitation of the symmetry group of the Hamiltonian. With these considerations, the QC-DMRG algorithm allows to find numerically exact solutions in active spaces of up to 40 electrons in 40 orbitals.Comment: 24 pages; 10 figures; based on arXiv:1405.1225; invited review for European Physical Journal

Algorithmes incrémentaux pour la théorie de la fonctionnelle de la densité

The ability to model molecular systems on a computer has become a crucial tool for chemists. Indeed molecular simulations have helped to understand and predict properties of nanoscopic world, and during the last decades have had large impact on domains like biology, electronic or materials development. Particle simulation is a classical method of molecular dynamic. In particle simulation, molecules are split into atoms, their inter-atomic interactions are computed, and their time trajectories are derived step by step. Unfortunately, inter-atomic interactions computation costs prevent large systems to be modeled in a reasonable time. In this context, our research team looks for new accurate and efficient molecular simulation models. One of our team's focus is the search and elimination of useless calculus in dynamical simulations. Hence has been proposed a new adaptively restrained dynamical model in which the slowest particles movement is frozen, computational time is saved if the interaction calculus method do not compute again interactions between static atoms. The team also developed several interaction models that benefit from a restrained dynamical model, they often updates interactions incrementally using the previous time step results and the knowledge of which particle have moved.In the wake of our team's work, we propose in this thesis an incremental First-principles interaction models. Precisely, we have developed an incremental Orbital-Free Density Functional Theory method that benefits from an adaptively restrained dynamical model. The new OF-DFT model keeps computation in Real-Space, so can adaptively focus computations where they are necessary. The method is first proof-tested, then we show its ability to speed up computations when a majority of particle are static and with a restrained particle dynamic model. This work is a first step toward a combination of incremental First-principle interaction models and adaptively restrained particle dynamic models.In the wake of our team's work, we propose in this thesis an incremental First-principles interaction models. Precisely, we have developed an incremental Orbital-Free Density Functional Theory method that benefits from an adaptively restrained dynamical model. The new OF-DFT model keeps computation in Real-Space, so can adaptively focus computations where they are necessary. The method is first proof-tested, then we show its ability to speed up computations when a majority of particle are static and with a restrained particle dynamic model. This work is a first step toward a combination of incremental First-principle interaction models and adaptively restrained particle dynamic models.L'informatique est devenue un outil incontournable de la chimie. En effet la capacité de simuler des molécules sur ordinateur a aidé à la compréhension du monde nanoscopic et à la prédiction de ses propriétés. La simulation moléculaire a eu ces dernières décennies un impact scientifique énorme en biologie, en électronique, en science des matériaux ... La simulation de particules est une des méthodes classiques de dynamique moléculaire, les molécules y sont divisées en atomes, leurs interactions relatives calculées et leurs trajectoires déduites pas à pas. Malheureusement un calcul précis des interactions entre atomes demande énormément d'opérations et donc de temps, ce qui limite la portée de la simulation moléculaire à des systèmes de taille raisonnable. C'est dans ce contexte que notre équipe recherche de nouveaux modèles de simulation moléculaire rapide et précis. Un des angles de recherche est l'élimination des calculs inutiles des simulations. L'équipe a ainsi proposé un modèle de dynamique moléculaire dite restreinte de manière adaptative dans lequel le mouvement des particules les plus lentes est bloqué. Si la simulation ne recalcule pas les interactions inchangées entre atomes bloqués, le calcul des interactions est plus rapide. L'équipe a aussi développé plusieurs modèles d'interactions plus efficaces pour des modèles de dynamique restreinte de particules, ils mettent à jour les interactions de façon incrémentale en utilisant les résultats du pas de temps précédent et la liste des particules mobiles. Dans le sillage des travaux de notre équipe de recherche, nous proposons dans cette thèse une méthode incrémentale pour calculer des interactions interatomique basées sur les modèles de Théorie de la Fonctionnelle de la Densité Sans Orbitale. La nouvelle méthode garde les calculs dans l'espace réel et peut ainsi concentrer les calculs où cela est nécessaire. Dans ce manuscrit nous vérifions cette méthode, puis nous évaluons les gains de vitesse lorsqu'une majorité de particule est bloquée, avec un modèle de dynamique restreinte. Ces travaux sont un pas vers la l'intégration de modèles d'interactions Premier-principes pour des modèles dynamiques restreint de manière adaptative

Electronic correlation and magnetic properties of one-dimensional systems

144 p.El objetivo principal de esta tesis es el análisis mediante teoría del funcional de la densidad de la relación entre las propiedades magnéticas y la estructura electrónica en sistemas unidimensionales. La realización experimental de este tipo de sistemas y su caracterización suele suponer un gran reto, por lo que un análisis teórico paralelo es imprescindible para prever sus propiedades. En el primer objetivo de nuestro trabajo analizamos las interacciones entre cadenas de óxidos de metales de transición de estequiometria XO2, X=Mn,Fe,Co,Ni, y el sustrato de platino sobre el que se crecen. El estudio previo de las cadenas aisladas permite identificar varios estados de espín en los átomos X, accesibles mediante variaciones en la interacción de Coulomb en el orbital d, lo que da lugar a variaciones en las propiedades magnéticas de canje de Heisenberg y anisotropía magnetocristalina. El apantallamiento de dicha interacción sucede mediante dos mecanismos de hibridación: con los ligandos O(p) y con el sustrato metálico. Un estudio mediante la técnica "constrained random phase approximation" nos permite su caracterización.En segundo lugar, aplicamos la experiencia obtenida en óxidos al estudio de las propiedades magnéticas de cadenas de Cr y Co unidos por el ligando orgánico "QDI" (2,5-diamino-1,4-benzoquinonediimine), lo que permite la interpretación de diversos experimentos de espectroscopia túnel y dicroísmo magnético

Generation of basis sets for accurate molecular calculations: Application to helium atom and dimer

A new approach for basis set generation is reported and tested in helium atom and dimer. The basis sets thus computed, named sigma, range from DZ to 5Z and consist of the same composition as Dunning basis sets but with a different treatment of contractions. The performance of the sigma sets is analyzed for energy and other properties of He atom and He dimer, and the results are compared with those obtained with Dunning and ANO basis sets. The sigma basis sets and their extended versions up to triple augmented provide better energy values than Dunning basis sets of the same composition, and similar values to those attained with the currently available ANO. Extrapolation to complete basis set of correlation energy is compared between the sigma basis sets and those of Dunning, showing the better performance of the former in this respec