Dissertations / Theses on the topic 'Quantum theory of atoms in molecules'

The many-electron Schrödinger equation for atoms and molecules still remains analytically insoluble after over 90 years of investigation. This has not deterred scientists from developing a large variety of elegant techniques and approximations to workaround this issue and make many-particle quantum calculations computationally tractable. This thesis presents an all-particle treatment of three-particle systems which represent the simplest, most complex, many-particle systems including electron correlation and nuclear motion effects; meaning they provide a close-up view of fundamental particle interaction. Fully-Correlated (FC) energies and wavefunctions are calculated to high accuracy (mJ mol−1 or better for energies); and the central theme of this work is to use the wavefunctions to study fundamental quantum chemical physics. Nuclear motion has not received the same attention as electronic structure theory and this complicated coupling of electron and nuclear motions is studied in this work with the use of intracule and centre of mass particle densities where it is found nuclear motion exhibits strong correlation. A highly accurate Hartree-Fock implementation is presented which uses a Laguerre polynomial basis set. This method is used to accurately calculate electron correlation energies using the Löwdin definition and Coulomb holes by comparing with our FC data. Additionally the critical nuclear charge to bind two electrons within the HF methodology is calculated. A modification to Pekeris' series solution method is implemented to accurately model excited states of three-particle systems, and adapted to include the effects of nuclear motion along with three Non-Linear variational Parameters (NLPs) to aid convergence. This implementation is shown to produce high accuracy results for singlet and triplet atomic excited S states and the critical nuclear charge to bind two electrons in both spin states is investigated. Geometrical properties of three-particle systems are studied using a variety of particle densities and by determining the bound state stability at the lowest continuum threshold as a function of mass. This enables us to better ascertain what is meant when we define a system as an atom or a molecule.

Due to the fast increasing capabilities of modern computers it is now feasible to calculate spectra of small atom and molecules with the greater level of accuracy than high-resolution measurements. The mathematical algorithms developed and implemented on high performance supercomputers for the quantum mechanical calculations are directly derived from the first principles of quantum mechanics. The codes developed are primarily used to verify, refine, and predict the energies associated within a given system and given angular momentum state of interest. The Hamiltonian operator used to determine the total energy in the approach presented is called the internal Hamiltonian and is obtained by rigorously separating out the center-of-mass motion (or the elimination of translational motion) from the laboratory-frame Hamiltonian. The methods utilized in the articles presented in this dissertation do not include relativistic corrections and quantum electrodynamic effects, nor do these articles assume the Born-Oppenheimer (BO) approximation with the exception of one publication. There is one major review article included herein which describes the major differences between the non-BO method and the BO approximation using explicitly correlated Gaussian (ECG) basis functions. The physical systems studied in this dissertation are the atomic elements with Z < 7 (although the discussion is not limited to these) and diatomic molecules such as H₂⁺ and H₂ including nuclear isotopic substitution studies with deuterium and tritium, as well as electronic substitutions with the muon particle. Preliminary testing for triatomic molecular functionals using a model potential is also included in this dissertation. It has been concluded that using all-particle ECGs with including the addition of nonzero angular momentum functions to describe nonzero angular momentum states is sufficient in determining the energies of these states for both the atomic and molecular case.

This Ph.D. thesis is focused on the application of quantum theory of atoms in molecules (QTAIM) based chemical descriptors to challenging chemical test-cases, as well as on the development of novel topological descriptors, like the Source Function for the spin density. The thesis is organized as follows: In chapter 1 the electron density (ED) of a very unusual structural feature in a synthetic beta–sultamic analogue (DTC), has been explored by both low-T single–crystal X–ray diffraction and quantum mechanical simulations to gain insights into the subtle interplay between structure, electron delocalization and crystal field polarization effects. The core chemical moiety in DTC is an uncommon 4–membered thiazete–1,1–dioxide heterocycle, where the formally single N–C bond is, on average, 0.018 Å shorter than the formally double N=C bond. Both local and non–local topological descriptors provided by QTAIM have been employed in the analysis of DTC in comparison with chemically related derivatives and possible implications from the viewpoint of the accurate in silico modelling of crystal structures are discussed. Particular attention is dedicated on such kind of issues in chemical and pharmaceutical industries, because the control of the crystal structure is really problematic in some cases; in fact different polymorphs of the same substance have different intensive physical properties, such as solubility, refraction index and conductivity and problems may arise in industrial processes related to the synthesis of chemicals and drugs on large scale. In chapter 2, we focused on the source function (SF) QTAIM based topological descriptor. The electron density (ED) at any point r within a system may be regarded as consisting of a sum of SF contributions S(r; X) representing a measure of how the various atomic basins (X) or groups of atomic basins defined through QTAIM contribute to determine the ρ(r) at r. Recently it was shown that the SF is able to reveal electron delocalization effects in planar electron conjugated systems, in terms of an increased capability of determining the ED along a given bond by the distant, though through-bonds connected, atomic basins and, at the same time, into a decreased ability to do so by the two atoms directly involved in the bond. Such an adjustment of sources then translates into a pictorial pattern of enhanced and reduced atomic SF contributions from, respectively, distant and nearby atoms, compared to the case of a partially or fully saturated network of bonds. Then we have extended such an analysis to the non planar conjugated systems, where the usual electron separation does no longer apply. Being based on the total ED, the SF analysis may be safely applied also in these less conventional electron delocalized systems. In the present Ph. D. thesis we have extended the SF reconstruction approach also to the electron density spin counterparts in vacuo. Such reconstruction was investigated both on simple (but chemically meaningful) spin-polarized molecular systems and on more complex single-molecule magnets. This investigation has showed that the difference between the two spin counterparts of electron density distribution can be reconstructed with a sufficient accuracy, analogously to the case of the total ED. Moreover, it was found that the SF for the electron spin density brings in precious chemical information, neatly distinguishing the quite different roles played by the unpaired electrons ED and the spin polarized ED due to the remaining electrons. Furthermore, quantitative answers to questions related to the transferability of the spin density in alkyl radicals or to the transmission of spin information in metal(s)-ligand systems were provided. Understanding, from a real space perspective, by which mechanisms spin information transmits, might be of relevance to interpret the fundamental magnetic interactions present in complex materials, such as for example coordination polymers or Heussler and half-Heussler alloys. As these interactions have a key role in spintronics, characterization of the chemical bond and interpretation of the electron spin density distributions in these systems through the SF analysis, could hopefully disclose structure-property relationships extremely useful for the design of materials with particular physical properties.

Abstract Charge density studies have been conducted on ten CB1 cannabinoid receptor antagonists via high resolution x-ray crystallography. Bond critical point values and various other properties derived from these studies including the electrostatic potential were analyzed in correlation to the affinity of each compound with the CB1 receptor. Correlation/anti-correlation was found between several properties and Ki. The data was also interpreted by principal component analysis with three principal components accounting for 85% of the data variation. Data mining was limit due to the low sample count and the requirements set for the inclusion of correlated/anti-correlated variables left fewer variables to analyze. The model presented is left for future interpretation.

Calcul des courbes de potentiel adiabatiques pour les géométries colinéaires et perpendiculaires, à l'aide d'un pseudopotentiel dépendant du moment orbital électronique et d'une approche à deux centres; bon accord avec les calculs ab initio existants. Examen des différentes symétries de ces systèmes dans le formalisme de la théorie des groupes, afin d'étudier les valeurs propres et facteurs propres de l'hamiltonien électronique. Calcul quantique des sections efficaces relatives des transitions de structure fine de Rb induites par collision avec H(2) ou D(2). En tenant compte des niveaux rotationnels moléculaires, obtention d'un très bon accord avec les résultats expérimentaux et interprétation de l'effet isotopique

This work deals with the role ab-initio calculations have in supporting and, when needed, helping to clarify the meaning of experimental findings. Furthermore, the extra information one gets from the wavefunction, that is the knowledge of the density matrix and of the pair density, both customarily unavailable from experiment, has revealed of uttermost importance in the study of the challenging chemical bond features investigated in this thesis. The charge densities of FeX2 marcasitic compounds, of crystalline K2SO4 and of a reference compound for magnetically active coordination polymers Zn(HCOO)2(H2O)2 have been analysed from both the experimental and crystallographic point of view.

Quantum mechanics became a foundation for incessant development of versatile computational methods for analysis of chemical and physical properties of molecules and crystals. A huge progress has been made in the fifield of density functional theory, since nowadays this theory offers the best compromise between precision of results and efficiency fiof computation. The chemical bonding analysis can be easily performed with real space methods based on chemical concepts introduced via partitioning of real space into chemically meaningful domains, since the orbital based approach is not well applicable due to the delocalized nature of plane waves. However the practical usage of those methods often requires a signifificant amount of computational resources. Some methods require the evaluation of so called domain overlap matrices, that is a formidable task for complex and low-symmetry systems. In the present research the author enables the investigation of complex solid compounds with real space chemical bonding indicators by introducing the derivation of the expression for the evaluation of the domain overlap matrix elements from the projected-augmented wave method. The corresponding program module was developed, which is capable to perform the real space chemical bonding analysis with a number of methods, like electron localizability indicators, electron localization function, localization/delocalization indices and domain averaged Fermi hole orbitals. The efficiency and the accuracy of the developed implementation is demonstrated by the comparison with the domain overlap matrix elements evaluation from the full-potential linearized augmented plane wave method on a set of simple compounds with three atoms per primitive cell at most. A set of complex periodic structures is analyzed and the capability of the present implementation to unravel intricate chemical bonding patterns is demonstrated.

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The intramolecular hydrogen bond occurs when the same molecules has both proton donor and proton acceptor groups in satisfactory configuration space for the formation of this interaction. It is important to note the changes in the structural, electronic and vibrational properties that occur due to the formation of this interaction. In the hydrogen bonding formation is an important phenomenon called charge transfer , where part of the electronic density of the proton acceptor species, Y, is transferred o the proton donor specie, HX. With respect to the vibrational spectrum are observed changes in the way of straightening of donor and acceptor proton species. Di-carbonyl compounds (C3H2O2R2) with their substituent groups (R=CH3, CN, H, NH2, OH and SH) were studied focusing on the energetic, structural, vibrational and electron density analysis. Initially the energy and structural analysis were carried out starting from the molecules optimized geometry. We also evaluated of the strength s hydrogen bonding and the length s intramolecular bond. The QTAIM study was performed to obtain the electron density s values and the electron density s Laplacian values and verify the existence of the bond critical point in the intramolecular hydrogen bond. From the harmonic vibrational spectra was possible to identify changes in the vibrational modes, related the intramolecular interaction s formation.
A ligação de hidrogênio intramolecular ocorre quando uma mesma molécula apresenta, simultaneamente, um grupo doador e outro receptor de próton, em configuração espacial favorável à formação dessa interação. É importante salientar as mudanças nas propriedades estruturais, eletrônicas e vibracionais que ocorrem devido à formação dessa interação. Na formação da ligação de hidrogênio ocorre um fenômeno importante denominado de transferência de carga , onde parte da densidade eletrônica da espécie receptora de próton, Y, é transferida para a espécie doadora de próton, HX. Com respeito aos espectros vibracionais, são observadas modificações nos modos de estiramento das espécies doadora e receptora de próton. Compostos di-carbonílicos (C3H2O2R2) com suas substituições (R=CH3, CN, H, NH2, OH e SH) foram estudados enfocando as análises energética, estrutural, vibracional e de densidade eletrônica. Inicialmente foram realizadas as análises energéticas e estruturais a partir da geometria otimizada das moléculas. Foram avaliados a força da ligação de hidrogênio e do comprimento da ligação intramolecular. O estudo usando a QTAIM foi realizado para adquirir os valores de densidade eletrônica e do Laplaciano da densidade eletrônica e verificar a existência do ponto crítico de ligação na ligação de hidrogênio intramolecular. A partir dos espectros vibracionais harmônicos foi possível identificar as variações no infravermelho, referentes à formação da interação intramolecular.

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The aim of this work was to study two kinds of intermolecular hydrogen bonding, the non-usual that is represented by the interaction between acetylene and the HX species (C2H2 --- HX) and the usual that is represented by the interaction between hydrogen cyanide and HX species, with X = F, Cl, CN, and HCCH. This interaction promotes changes in the structural, electronic and vibrational properties of the species involved. In this work, we employe d not onlycomputational-quantum methods MP2/6-311 + + G (d, p) and DFT/B3LYP/6-311 + + G (d, p) in order to study the structural, electronic and vibrational properties of those two types of intermolecular hydrogen bonding, but also we employed QTAIM and NBO methods to complement our research. The results have shown no significant differences between the two correlated methods employed for both types of hydrogen bonded complexes, leading us to suggest the use of the DFT/B3LYP method for studies of similar systems to those studied here, due to the lower computational demand. The increase in bond length of the HX species are enhanced due to formation of more linear complexes than T-complexes, in both calculation levels. The intermolecular bond length values in the complex HCN --- HX are smaller than in the complexes HCCH --- HX, and the values from MP2 and DFT/B3LYP are very close in each individual type of hydrogen complex, suggesting that the linear complexes are more stabilized by the formation of hydrogen bonding than the T-complexes, which can be proved by the values of the binding energy of hydrogen in HCN --- HX. Concerning the redshift effect in the harmonic vibrational mode of species HX, due to the formation of intermolecular bond, the values obtained for linear complexes hydrogen are higher than for the corresponding T-complexes, considering both calculation levels. Values were evaluated from the increase in the intensity values of the stretch mode HX bond formation due to intermolecular and, according to the model CCFOM, the term load flow is responsible for the effect on the increase of HX intensity. We also highlight the new vibrational modes, emphasizing the stretch mode of the intermolecular bond. From studies employing QTAIM, it was possible to obtain the values of electron density and the Laplacian electron density and evaluate these parameters in critical points in HX and intermolecular hydrogen bonding, thus confirming the formation of hydrogen bonded complexes. We evaluated the energy difference between π orbitals and lone pair of nitrogen (in HCN), for the species receiving proton and sigma antibonding for the hydrogen of HX, using the method of natural bond orbital variation.
O objeto de estudo deste trabalho foi a ligação de hidrogênio intermolecular de dois tipos, a não-usual representada pela interação entre o acetileno e espécies HX (C2H2---HX) e a usual representada pela interação entre o ácido cianídrico e espécies HX, com X=F, Cl, CN e HCCH. Esta interação provoca mudanças nas propriedades estruturais, eletrônicas e vibracionais das espécies envolvidas. Neste trabalho empregamos os métodos quântico-computacionais MP2/6-311++G(d,p) e DFT/B3LYP/6-311++G(d,p) para estudar as propriedades estruturais, eletrônicas e vibracionais dos dois tipos de ligação de hidrogênio intermolecular, além de complementar nossa investigação empregando os métodos QTAIM e NBO. Os resultados não mostraram diferenças significativas entre os dois métodos correlacionados empregados para ambos os tipos de complexos de hidrogênio, nos levando a sugerir o emprego do método DFT/B3LYP para estudos de sistemas semelhantes aos aqui estudados, devido a menor demanda computacional. Os valores de incremento no comprimento de ligação das espécies HX são mais acentuados devido à formação dos complexos lineares do que dos complexos-T, em ambos os níveis de cálculo. Os valores de comprimento de ligação intermolecular nos complexos HCN---HX são menores do que nos complexos HCCH---HX, sendo os valores MP2 e DFT/B3LYP bem próximos em cada tipo individual de complexo de hidrogênio, sugerindo que os complexos lineares são mais estabilizados pela formação da ligação de hidrogênio do que os complexos-T, fato que pode ser comprovado pelos valores da energia de ligação de hidrogênio em HCN---HX. Com respeito ao efeito redshift no modo vibracional harmônico das espécies HX, devido à formação da ligação intermolecular, os valores obtidos para os complexos de hidrogênio lineares são maiores do que para os correspondentes complexos-T, considerando ambos os níveis de cálculo. Foram avaliados os valores do incremento nos valores de intensidade do modo de estiramento de HX devido à formação da ligação intermolecular e, de acordo com o modelo CCFOM, o termo de fluxo de carga é o responsável pelo efeito no aumento da intensidade de HX. Foram ainda destacados os novos modos vibracionais, dando ênfase ao modo de estiramento da ligação intermolecular. Dos estudos empregando a QTAIM foi possível obter os valores da densidade eletrônica e do Laplaciano da densidade eletrônica e avaliar os valores desses parâmetros nos pontos críticos de ligação em HX e na ligação de hidrogênio intermolecular, comprovando dessa forma a formação dos complexos de hidrogênio. Com os estudos empregando o método dos orbitais naturais de ligação foi avaliada a diferença de energia entre os orbitais π (no acetileno) e o orbital do par de elétrons livres do nitrogênio (em HCN), para as espécies receptoras de próton, e o orbital sigma antiligante do hidrogênio em HX.

The study of ultracold atoms constitutes one of the hottest areas of atomic, molecular, and optical physics and quantum optics. The experimental and theoretical achievements in the last three decades in the control and manipulation of quantum matter at macroscopic scales lead to the so called third quantum revolution. Concretely, the recent advances in the studies of ultracold gases in optical lattices are particularly impressive. The very precise control of the diverse parameters of the ultracold gas samples in optical lattices provides a system that can be reshaped and adjusted to mimic the behaviour of other many-body systems: ultracold atomic gases in optical lattices act as genuine quantum simulators. The understanding of gauge theories is essential for the description of the fundamental interactions of our physical world. In particular, gauge theories describe one of the most important class of systems which can be addressed with quantum simulators. The main objective of the thesis is to study the implementation of quantum simulators for gauge theories with ultracold atomic gases in optical lattices. First, we analyse a system composed of a non-interacting ultracold gas in a 2D lattice under the action of an exotic and external gauge field related to the Heisenberg-Weyl gauge group. We describe a novel method to simulate the gauge degree of freedom, which consists of mapping the gauge coordinate to a real and perpendicular direction with respect to the 2D space of positions. Thus, the system turns out to be a 3D insulator with a non-trivial topology, specifically, a quantum Hall insulator. Next, we study an analog quantum simulation of dynamical gauge fields by considering spin-5/2 alkaline-earth atoms in a 2D honeycomb lattice. In the strongly repulsive regime with one particle per site, the ground state is a chiral spin liquid state with broken time reversal symmetry. The spin fluctuations around this configuration are given in terms of an emergent U(1) gauge theory with a Chern-Simons toplogical term. We also address the stability of the three lowest lying states, showing a common critical temperature. We consider experimentally measurable signatures of the mean field states, which can also be key insights for revealing the gauge structure . Then, we introduce the notion of constructive approach for the lattice gauge theories, which leads to a family of gauge theories, the gauge magnets. This family corresponds to quantum link models for the U(1) gauge theory, which consider a truncated dimensional representation of the gauge group. First of all, we (re)discover the phase diagram of the gauge magnet in 2+1 D. Then, we propose a realistic implementation of a digital quantum simulation of the U(1) gauge magnet by using Rydberg atoms, considering that the amount of resources needed for the simulation of link models is drastically reduced as the local Hilbert space shrinks from infinity to 2D (qubit). Finally, motivated by the advances in the simulation of open quantum systems, we turn to consider some aspects concerning the dynamics of correlated quantum many body systems. Specifically we study the time evolution of a quench protocol that conserves the entanglement spectrum of a bipartition. We consider the splitting of a critical Ising chain in two independent chains, and compare it with the case of joining two chains, which does not conserve the entanglement spectrum. We show that both quenches are both locally and globally distinguishable. Our results suggest that this conservation plays a fundamental role in both the out-of-equilibrium dynamics and the subsequent equilibration mechanism
L'estudi dels àtoms ultrafreds constitueix una de les àrees més actives de la física atòmica, molecular, òptica i de l'òptica quàntica. Els èxits teòrics i experimentals de les tres últimes dècades sobre el control i la manipulació de la matèria quàntica en escala macroscòpica condueix a l'anomenada tercera revolució quàntica. Concretament, els recents avenços en els estudis dels àtoms ultrafred en xarxes òptiques proporcionen un sistema que es pot reajustar i reorganitzat per imitar el comportament d'altres sistemes de molts cossos: els gasos d'àtoms ultrafreds en xarxes òptiques actuen com a genuïns simuladors quàntics. La comprensió de les teories de gauge és clau per a la descripció de les interaccions fonamentals del nostre món físic. Particularment, les teories de gauge descriuen una de les més importants classes de sistemes que poden ser tractats amb simuladors quàntics. L'objectiu principal de la tesi és estudiar la implementació de simuladors quàntics de teories de gauge amb gasos d'àtoms ultrafreds en xarxes òptiques. En primer lloc, analitzem un sistema format per un gas ultrafred no interaccionant en una xarxa 2D sota l'acció d'un camp de gauge exòtic i extern provinent del grup de gauge de Heisenberg-Weyl. Descrivim un nou mètode per simular el grau de llibertat gauge, que consisteix a associar la coordenada gauge a una coordenada real i perpendicular a l'espai 2D de les posicions. Així, el sistema resultar ser un aïllant 3D amb topologia no trivial, concretament un aïllant Hall quàntic. Seguidament, estudiem un simulador quàntic analògic de camps de gauge dinàmics amb àtoms alcalinoterris en una xarxa hexagonal. Al régim fortament repulsiu amb un àtom en cada lloc, l'estat fonamental és un líquid espinorial quiral amb la simetria d'inversió temporal trencada. Les fluctuacions d'espín al voltant d'aquesta configuració vénen descrites per una teoria gauge U(1) emergent amb un terme topològic de Chern-Simons. També tractem l'estabilitat dels tres estats amb mínima energia, tot observant una temperatura crítica comuna. Considerem indicis experimentals mesurables dels estats de camp mitjà, que poden ser claus per revelar l'estructura gauge. A continuació, introduïm un enfoc constructiu per a teories gauge en el reticle, la qual porta a una família de teories de gauge, els magnets de gauge. Aquesta família es correspon amb els models d'enllaços quàntics de la teoria gauge U(1). Primer, (re)descobrim el diagrama de fases del magnet de gauge en 2+1 D. Després, proposem una implementació realista d'un simulador quàntic digital del magnet de gauge U(1) amb àtoms de Rydberg, considerant que el nombre de recursos necessaris per a la simulació dels models d'enllaços es redueix dràsticament pel fet que l'espai d' Hilbert local disminueix de dimensió infinita a 2 (bit quàntic). Finalment, motivats pels avenços en la simulació de sistemes quàntics oberts, considerem alguns aspectes de la dinàmica de sistemes quàntics correlacionats de molts cossos. Específicament, estudiem l'evolució temporal en un protocol de canvi sobtat que conserva l'espectre d'entrellaçament d'una bipartició. Considerem la ruptura d'una cadena d'Ising en dues cadenes independents i ho comparem amb la unió de dues cadenes, la qual no conserva l'espectre d'entrellaçament
El estudio de los átomos ultrafríos constituye una de las áreas mas activas de la física atómica, molecular, óptica y de la óptica cuántica. Los logros teóricos y experimentales de las tres últimas décadas sobre el control y la manipulación de la materia cuántica a escala macroscópica conducen a la denominada tercera revolución cuántica. Concretamente, los avances recientes en los estudios de átomos ultrafríos en redes ópticas proporcionan un sistema que puede ser reajustado y reorganizado para imitar el comportamiento de otros sistemas de muchos cuerpos: los gases de átomos ultrafríos en redes ópticas actúan como genuinos simuladores cuánticos. La comprensión de las teorías de gauge es clave para la descripción de la interacciones fundamentales de nuestro mundo físico. En particular, las teorías de gauge describen una de las mas importante clase de sistemas que pueden ser abordados con simuladores cuánticos. El objetivo principal de la tesis es estudiar la implementación de simuladores cuánticos de teorías de gauge con gases de átomos ultrafríos en redes ópticas. En primer lugar, analizamos un sistema formado por un gas ultrafrío no interactuante en una red 2D, bajo la acción de un campo de gauge exótico y externo descrito por el grupo de gauge de Heisenberg-Weyl. Describimos un método novedoso para simular el grado de libertad gauge , que consiste en asociar la coordenada gauge a una coordenada real y perpendicular al espacio 2D de las posiciones. Así, el sistema resulta ser un aislante 3D con una topología no trivial, específicamente un aislante Hall cuántico. Seguidamente, estudiamos un simulador cuántico analógico de campos de gauge dinámicos, considerando átomos alcalinotérreos en una red hexagonal. En el régimen fuertemente repulsivo con una átomo en cada sitio, el estado fundamental es un liquido espinorial quiral con la simetría de inversión temporal rota. Las fluctuaciones de espín alrededor de dicha configuración vienen dadas en términos de una teoría de gauge U(1) emergente con un término topológico de Chern-Simons. También tratamos la estabilidad de los tres estados con mínima energía, observando una temperatura crítica común. Consideramos indicios experimentales medibles de los estados de campo medio, que pueden claves para revelar la estructura de gauge. A continuación, introducimos la noción del enfoque constructivo para teorías de gauge en el retículo, lo que conduce a una familia de teorías de gauge, los magnetos de gauge. Esta familia se corresponde con los modelos de enlaces cuánticos para la teoría de gauge U(1), los cuales consideran una representación dimensional truncada del grupo de gauge. Primeramente, (re)descubrimos el diagrama de fases del magneto de gauge en 2+1D. Seguidamente, proponemos un implementación realista de un simulador cuántico digital del magneto de gauge U(1) usando átomos de Rydberg, considerando que el número de recursos necesarios para la simulación de los modelos de enlace está drásticamente reducido debido a que el espacio de Hilbert local disminuye de infinitas dimensiones a 2 (bit cuántico). Finalmente, motivados por los avances en la simulación de sistemas cuánticos abiertos, consideramos algunos aspectos sobre la dinámica de sistemas cuánticos correlacionados de muchos cuerpos . Específicamente, estudiamos la evolución temporal en un protocolo de cambio súbito que conserva el espectro de entrelazamiento de una bipartición. Consideramos la ruptura de una cadena de Ising en dos cadenas independientes y lo comparamos con la unión de dos cadenas, la cual no conserva el espectro de entrelazamiento. Estos dos cambios abruptos son localmente y globalmente distinguibles. Nuestro resultado sugiere que la mencionada conservación juega un papel fundamental en la dinámica fuera de equilibrio y en el consiguiente equilibrio.

Through continual advancement in laser pulse technology. experimentalists now have al their disposal higher intensities (> 1015 W cm!) and shon.er pulse durations « 10 fs) than ever before. Using sllch technology it is possible to probe and manipulate the electronic and nuclear Illotions in even the smallest fastest-moving diatomic molecules. The first pan. of this thesis presents a simplified theoretical model that allows one to adequately treat the nuclear vibrational and photodissociation dynamics of the O2 ' molecular ion, when subjected to typical infrared wavelengths. Direct comparison between the predictions of this theoretical model and recent experimental observations is provided. The same model is then used as a basis for the proposal of a number of novel techniques that utilize ultrashort laser pulses to l;:ontrol both the dissociation pathway and the population ofthe bound vibrational levels. One of the main areas of theoretical and experimental advancement in recent decades has been the area of cold atom trapping and manipulation. The second part of this thesis considers the theoretical treatment of two interacting particles, confined in various one-dimensioDal potentials. These systems represent a fundamental building block that has been made accessible through recent developments in the field of ultracold atomic physics: The numerical scheme for the treatment of the two-particle system is described and results are presented for two-paJ1icles in a harmonic trap, a o-split harmonic trap. and a double-well potential. Propel1ies of the two-particle ground state and low-energy excited states are examined including the energy spectra, eigenfunctions, reduced single-particle density matrices, momentum distributions and entanglement. ]n particular, focussing upon how these quantities depend upon the two parameters, particle-particle interaction strength and barrier height. In this way, the present work relates to the scope of quantum state control, in such systems, through variation of 'experimentally accessible' control parameters.

Control is important for transferring theoretical scientific knowledge into practical technology for applications in numerous fields. This is why coherent control study is significant on every timescale to have a complete understanding of dynamic processes that occur on the electron, atomic and molecular levels. As a result, numerous schemes have been proposed to carry out effective quantum control of diverse systems and study the dynamics of these systems based on their natural timescales from the picoseconds (10-12 s), femtosecond (10-15 s) to attosecond (10-18 s) regimes. The goals of these various studies depend on the desired application, for instance in Photochemistry a long standing objective is achieving selective population transfer from an initial state to a desired target state with little or no diminution in the energy transferred. In quantum computation, a central issue is the excitation of unoccupied Rydberg states with numerous proposals for its use in the design and implementation of robust fast quantum gates. Also, since the advent of the generation of attosecond XUV pulses, doors have been opened for achieving control of atomic-scale electron dynamics and observing them in real-time. This thesis explores the modelling of dynamical light-matter interaction processes, like effective population inversion and generation of vibrational coherences in atoms and molecules, on their fundamental timescales using the density matrix (DM) theory under and beyond the rotating wave approximation (RWA). The thesis begins by introducing the concept of coherent control of simple quantum systems based on the DM formalism and expands the application to a more complex Oxazine system. Multiphoton p-pulse scheme is demonstrated for the control of population transfer in multilevel systems, for example with a trichromatic p-pulse having a set of areas v3 p, 2p and v3 p, complete population transfer in a four level system can be achieved. The aforementioned scheme is used to achieve effective control of low-lying Rydberg states in rubidium atoms, demonstrating how the effective control can be crucially affected by numerous physical processes. One main advantage of the density matrix approach over other theoretical approaches is that it allows the possibility of easily computing relaxation terms and other physical parameters critical to successful coherent control. The DM formalism is shown to be successful in properly describing the enhancement effects in atoms and complex molecular systems. It is robust in coherent control and quantum control spectroscopy (QCS) schemes and is extendable to numerous systems and geometric configurations. In the last part of the thesis, experiments on laser dressing processes in attosecond transient absorption spectroscopy are compared to numerical simulations using the DM analysis beyond the RWA. The research in this thesis opens a pathway to numerous studies using the DM formalism for applications in diverse fields of femtochemistry, attophysics, high precision spectroscopy and quantum information processing.
El control quàntic coherent és important per transferir coneixement científic teòric a la tecnologia, per a aplicacions en nombrosos camps. Per aquest motiu, l'estudi del control coherent és significatiu a totes les escales de temps, per comprendre de manera completa els processos dinàmics que es produeixen en els nivells electrònics, atòmics i moleculars. Com a resultat, s'han proposat nombrosos esquemes per dur a terme un control quàntic eficient de diversos sistemes i estudiar la dinàmica d'aquests sistemes basant-se en les seves escales de temps naturals, des dels picosegons (10-12 s), femtosegons (10-15 s) fins a règims d'attosegons (10-18 s). Els objectius d'aquests estudis depenen de l'aplicació desitjada, per exemple, en fotoquímica, un objectiu buscat extensivament és aconseguir una transferència selectiva de la població des d'un estat inicial fins a un estat final desitjat, amb poca o cap disminució de l'energia transferida. En computació quàntica, un tema central és l'excitació dels estats desocupats de Rydberg, amb nombroses propostes per al seu ús en el disseny i implementació de portes quàntiques robustes i ràpides. A més, des de l'arribada de la generació de polsos XUV d'attosegons, s'han obert camins per aconseguir el control de la dinàmica electrònica a escala atòmica i observar-la en temps real. Aquesta tesi explora la modelització de processos dinàmics d'interacció llum-matèria, com ara la inversió efectiva de població i la generació de coherències vibracionals en àtoms i molècules, en les seves escales de temps fonamentals, utilitzant la teoria de la matriu densitat (MD), en l'aproximació d'ona rotant (RWA) i més enllà. La tesi comença introduint el concepte de control coherent de sistemes quàntics simples basats en el formalisme de MD i amplia l'aplicació a un sistema més complexes, com ara oxazines. Es demostra l'esquema multifotó amb polsos p per al control de la transferència de població en sistemes multinivell, per exemple, amb un pols p-tricromàtic que té un conjunt d'àrees v3 p, 2p i v3 p, amb el qual la transferència completa de població en un sistema de quatre nivells pot ser aconseguit. L'esquema esmentat s'utilitza per aconseguir un control eficient d'estats de Rydberg en àtoms de rubidi, i es mostra com aquest control pot ser afectat crucialment per nombrosos processos físics. Un avantatge principal de l'estudi de la matriu densitat comparat amb altres enfocaments teòrics és que permet la possibilitat de computar fàcilment els termes de relaxació i altres paràmetres físics crítics per a un control coherent efectiu. Es demostra que el formalisme de la MD és exitós per descriure correctament l'amplificació d'efectes tant en àtoms com en sistemes moleculars més complexos. El formalisme de la MD és robust en esquemes de control coherent i d'espectroscòpia quàntica i és extensible a nombrosos sistemes i configuracions. En la darrera part de la tesi, es comparen experiments realitzats sobre processos de "vestiment" amb làsers intensos en espectroscòpia d'absorció transitòria d'attosegon amb simulacions numèriques utilitzant l'anàlisi de MD més enllà de la RWA. La recerca en aquesta tesi obre un camí a nombrosos estudis utilitzant el formalisme de MD per a aplicacions en diversos camps de femtoquímica, attofísica, espectroscòpia d'alta precisió i processament d'informació quàntica.

Nesta tese de doutorado apresentamos os resultados de quatro tópicos referentes a estudos de propriedades elétricas que são interpretados com o auxílio da Teoria Quântica de Átomos em Moléculas (QTAIM). No primeiro deles, foram calculados momentos de dipolo e suas derivadas através de um novo formalismo de divisão de átomos em moléculas, baseado em campos de forças de Ehrenfest (CFE), sendo que estes dados são comparados com aqueles advindos da QTAIM. Desta forma, um modelo alternativo de partição em carga - fluxo de carga - fluxo de dipolo (CFCFD) é discutido para derivadas do momento dipolar. Os resultados gerais obtidos pelo formalismo CFE foram satisfatórios em termos quantitativos, embora QTAIM ainda fornece uma descrição mais apropriada destes fenômenos das polarizações atômicas e de suas variações durante vibrações. Na sequência, investigamos os Atratores Não Nucleares (NNAs), que são identificados através de uma análise QTAIM da densidade eletrônica. O nosso intuito foi descobrir novas moléculas que apresentam essa peculiaridade, bem como encontrar padrões entre os casos encontrados que permitam contribuir para o entendimento dos fatores que levam ao seu aparecimento. Para isso trabalhamos com moléculas diatômicas homonucleares de elementos representativos com números atômicos que variavam de Z=1 até Z=38 e moléculas heteronucleares formadas pela combinação dos mesmos. Os nossos dados mostram que NNAs podem ser encontrados em alguns pontos dentro da faixa de distâncias internucleares investigada para quase todos os sistemas diatômicos homonucleares, exceto para as moléculas de Hidrogênio, Hélio e Estrôncio. Por sua vez, encontramos trinta casos de NNAs em sistemas heteronucleares, muitos dos quais ainda inéditos na literatura. Descobrimos também que a polarizabilidade atômica aparentemente tem um papel importante na explicação dos casos encontrados. Tratamos também de moléculas contendo interações fracas como as de Van der Waals (moléculas tri-atômicas contendo um gás nobre ligado a um composto diatômico iônico) de modo a investigar os valores de dipolos atômicos QTAIM de uma maneira mais direta, ou seja, via comparação com um modelo simples para estes compostos. Por fim, estudamos moléculas em estados excitados, sendo que nossa análise focou em dois casos peculiares (CO e de CF2N2) que apresentam momento de dipolo nulo no estado fundamental, enquanto valores significativos desta propriedade são observados em seus primeiros estados excitados. Desta forma, QTAIM foi fundamental para compreender como o processo de excitação pode levar à mudanças tão significativas em tais propriedades elétricas.
In this PhD thesis we present the results of four different topics that refer to a study of electric properties interpreted with The Quantum Theory of Atoms and Molecules (QTAIM). First, dipole moments and their derivatives were calculated from a new formalism based on Ehrenfest Force Fields (EFF) and a comparison with data from QTAIM is carried out. Therefore, the Charge-Charge Flux-Dipole Flux (CCFDF) model was discussed for the dipole moment derivatives. The results from EFF were satisfactory in quantitative terms although QTAIM still seems to be better for the description of atomic polarization and its variations during vibrations. In the sequence, we investigated the Non-Nuclear Attractors (NNAs) that could be identified with the QTAIM formalism. Our intention was to discover new molecules that present this peculiarity, as well as to find trends among these cases that allow contributing for the understanding of the factors that lead to their appearance. For this purpose, we selected homonuclear diatomic molecules of elements presenting atomic numbers ranging from Z=1 to Z=38 and heteronuclear diatomic molecules containing these same elements. Our data shows that NNAs could be found in almost every homonuclear molecule expect by the systems formed by Hydrogen, Helium, and Strontium. On other hand, we have found 30 cases of NNAs in heteronuclear molecules, many of them seen for the first time. We also have noticed that the atomic polarizabilities play a main role in the understanding of these cases. We also treated molecules containing weak Van der Waals interactions (triatomic complexes presenting a noble gas bonded to a diatomic ionic molecule) in order to investigate the atomic dipole values obtained with QTAIM in a direct way, that is, by means of a comparison using a simple model for this kind of bonding. Finally, we studied molecules in excited states. Our focus was in two peculiar cases (CO and CF2N2), which present null dipole moments in their ground states but exhibit significant dipole moment values in their first excited states. Therefore, QTAIM was fundamental to understand how the excitation process can lead to important changes in electric properties.

Les interférences quantiques apparaissant lors de la superposition cohérente d'états quantiques de la matière sont à l'origine de la compréhension et du contrôle de nombreux processus élémentaires. Dans cette thèse, deux problèmes distincts, qui ont pour origine de tels effets, sont discutés avec leurs applications potentielles : 1. Diffraction électronique induite par Laser (LIED) et imagerie des orbitales moléculaires ; 2. Effets collectifs dans des vapeurs denses et transparence électromagnétique induite par interaction dipôle-dipôle (DIET). La première partie de cette thèse traite du mécanisme de recollision dans des molécules linéaires simples lorsque le système est exposé à un champ laser infrarouge de forte intensité. Cette interaction provoque une ionisation tunnel du système moléculaire, conduisant à la création d'un paquet d'ondes électronique dans le continuum. Ce paquet d'ondes suit une trajectoire oscillante, dirigée par le champ laser. Cela provoque une collision avec l'ion parent qui lui a donné naissance. Ce processus de diffraction peut être de nature inélastique, engendrant la génération d'harmoniques d'ordre élevé (HHG) ou l'ionisation double non-séquentielle, ou de nature élastique, processus que l'on appelle généralement « diffraction électronique induite par laser ». La LIED porte des informations sur la molécule et sur l'état initial à partir duquel les électrons sont arrachés sous forme de motifs de diffraction formés en raison de l'interférence entre différentes voies de diffraction. Dans ce projet, une méthode est développée pour l'imagerie des orbitales moléculaires, reposant sur des spectres de photo-électrons obtenus par LIED. Cette méthode est basée sur le fait que la fonction d'ondes du continuum conserve la mémoire de l'objet à partir duquel elle a été diffractée. Un modèle analytique basé sur l'approximation de champ fort (SFA) est développé pour des molécules simples linéaires et appliqué aux orbitales moléculaires HOMO et HOMO-1 du dioxyde de carbone. L'interprétation et l'extraction des informations orbitalaires imprimées dans les spectres de photo-électrons sont présentées en détail. Par ailleurs, nous estimons que ce type d'approche pourrait être étendu à l'imagerie de la dynamique électro-nucléaire de tels systèmes. La deuxième partie de cette thèse traite des effets collectifs dans des vapeurs atomiques ou moléculaires denses. L'action de la lumière sur ces gaz crée des dipôles induits qui oscillent et produisent des ondes électromagnétiques secondaires. Lorsque les particules constitutives du gaz sont assez proches, ces ondes secondaires peuvent coupler les dipôles induits entre-eux, et lorsque cette corrélation devient prépondérante la réponse du gaz devient une réponse collective. Ceci conduit à des effets spécifiques pour de tels systèmes, comme l'effet Dicke, la superradiance, et les décalages spectraux de Lorentz-Lorenz ou de Lamb. A cette liste d'effets collectifs, nous avons ajouté un effet de transparence induite dans l'échantillon. Cet effet collectif a été appelé « transparence électromagnétique induite par interaction dipôle-dipôle ». La nature collective de l'excitation du gaz dense réduit la vitesse de groupe de la lumière transmise à quelques dizaines de mètre par seconde, créant ainsi une lumière dite « lente ». Ces effets sont démontrés pour les transitions D1 du 85Rb et d'autres applications potentielles sont également discutées
Quantum interference, coherent superposition of quantum states, are widely used for the understanding and engineering of the quantum world. In this thesis, two distinct problems that are rooted in quantum interference are discussed with their potential applications: 1. Laser induced electron diffraction (LIED) and molecular orbital imaging, 2. Collective effects in dense vapors and dipole induced electromagnetic transparency (DIET). The first part deals with the recollision mechanism in molecules when the system is exposed to high intensity infrared laser fields. The interaction with the intense field will tunnel ionize the system, creating an electron wave packet in the continuum. This wave packet follows an oscillatory trajectory driven by the laser field. This results in a collision with the parent ion from which the wave packet was formed. This scattering process can end up in different channels including either inelastic scattering resulting in high harmonic generation (HHG) and non-sequential double ionization, or elastic scattering often called laser induced electron diffraction. LIED carries information about the molecule and about the initial state from which the electron was born as diffraction patterns formed due to the interference between different diffraction pathways. In this project, a method is developed for imaging molecular orbitals relying on scattered photoelectron spectra obtained via LIED. It is based on the fact that the scattering wave function keeps the memory of the object from which it has been scattered. An analytical model based on the strong field approximation (SFA) is developed for linear molecules and applied to the HOMO and HOMO-1 molecular orbitals of carbon dioxide. Extraction of orbital information imprinted in the photoelectron spectra is presented in detail. It is anticipated that it could be extended to image the electro-nuclear dynamics of such systems. The second part of the thesis deals with collective effects in dense atomic or molecular vapors. The action of light on the vapor samples creates dipoles which oscillate and produce secondary electro-magnetic waves. When the constituent particles are close enough and exposed to a common exciting field, the induced dipoles can affect one another, setting up a correlation which forbids them from responding independently towards the external field. The result is a cooperative response leading to effects unique to such systems which include Dicke narrowing, superradiance, Lorentz-Lorenz and Lamb shifts. To this list of collective effects, one more candidate has been added, which is revealed during this study: an induced transparency in the sample. This transparency, induced by dipole-dipole interactions, is named “dipole-induced electromagnetic transparency”. The collective nature of the dense vapor excitation reduces the group velocity of the transmitted light to a few tens of meter per second resulting in 'slow' light. These effects are demonstrated for the D1 transitions of 85Rb and other potential applications are also discussed

Thesis (Ph. D.) -- University of Maryland, College Park, 2005.
Thesis research directed by: Chemical Physics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

The generalized local-spin-density functional (G-LSD) theory is proposed which avoids (a) the physical restriction used in the generalized exchange local-spin-density functional (GX-LSD) theory; (b) the homogeneous electron-density approximation in the Hartree-Fock-Slater (HFS) theory and in the Gaspar-Kohn-Sham (GKS) theory; and (c) the time-consuming step to search the optimal exchange parameter for each atom or ion in the X$ alpha$ and $ Xi$a theories. Theoretically, the G-LSD theory is more rigorous than the GX-LSD, HFS, GKS, and $ Xi$a theories. Numerically, the statistical total energies for atoms are better in the G-LSD theory than in the GKS theory.
Ionization potentials and electron affinities of atoms, the stability of singly and doubly charged negative ions, and the electronegativities, and hardnesses of the fractional charged atoms with Z $<$ 37 are calculated by the SIC-GX-LSD theory with the GWB Fermi-hole parameters and electron-correlation correction.
The self-interaction correction (SIC) is introduced into the multiple-Scattering X$ alpha$ (MS-X$ alpha$) method and used to calculate some molecules and molecular anions. The results show that the ionization potentials from the negative of the one-electron eigenvalues are as good as those obtained in the transition state calculation and in very good agreement with experiment.

Thesis (Ph.D)--Physics, Georgia Institute of Technology, 2009.
Committee Chair: Chapman, Michael; Committee Member: Citrin, David; Committee Member: Kennedy, T. A. Brian; Committee Member: Kuzmich, Alexander; Committee Member: Raman, Chandra. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Macroscopic and microscopic properties of molecular and solid-state systems are intimately related to the their electronic structure. The electron position and spin densities, which represent the probability distributions to find all or unpaired electrons in the space, contain information concerning several chemical-relevant properties, such as the chemical bonding and the magnetic behaviour. Understanding the fine atomic-level mechanism behind these properties is a key step to design chemical modifications to properly tune and develop materials or molecules with specific features. Topological descriptors can be used to extract information from these electron distributions. In this work, novel applications of the source function descriptor have been developed to gain further insights on the electron and spin density-related properties. These developments, together with other topological descriptors, were used to get further insights on relevant chemical systems. Firstly, the source function reconstruction was enlarged to a multi-dimensional grid of points with a particular focus on the two-dimensional maps. This analysis allows to see the ability of chosen subsets of atoms to reconstruct the density in the selected area within a cause-effect relationship and to rationalise the chemical or magnetic behaviours. The source function partial reconstructed maps depict if in a molecular region the atomic contributions are important, modest or negligible. Besides, they may also be useful for a proper selection of the reference points and for a full understanding of the source function percentages analysis. In fact, the choice of the reference point where to reconstruct the studied density is neither easy nor objective for non-standard situations, such as for the spin density. This novel application was applied to the study of the spin density on a couple of azido Cu complexes. The source function partial reconstructed maps allow to unravel the different role played by the paramagnetic centre Cu and the ligand atoms and to explain the spin transmission mechanism at a molecular level. Moreover, they enable to highlight the nature of the spin density differences between the two complexes and among adopted computational approaches. DFT functionals tend to over-delocalise the spin density towards the ligand atoms introducing a biased spin-polarization mechanism between the Cu and the ligand atoms. The same descriptor was then applied to the study of the hydrogen bonds in the DNA base pairs. The source function reveals the delocalised nature of these interactions, highlighting that distant groups and rings have non-negligible effects on the reconstruction of the electron density in the intermolecular region. Besides, the analysis demonstrates that the purine and pyrimidine bases equally contribute to the reconstruction of the electron density at the hydrogen bond critical points. The source function also reveals that subtle variations of the atomic source contributions occur when the pairs are ionized, revealing that sources and sinks effects redistribution plays an important role in the stabilization of the DNA base pairs. The source function was also used to develop a method to extract full population matrices purely based on the electron density distribution and then amenable to experimental determination. The peculiar features of this descriptor, in particular the cause-effect relationship, assign a profound chemical meaning to the matrix elements in contrast with other population analyses such as the Mulliken's one, where the matrix elements are associated to orbital overlaps. The latest breakthroughs on the development of this method are shown together with some numerical examples on very simple compounds. The full population matrices obtained using the source function descriptor are able to retrieve the major chemical features. A detailed analysis on the intermolecular interactions involved in the in vivo molecular recognition of the antimalarial drug chloroquine with the heme moiety has been carried out using a combined topological-energetic analysis. This work reveals that charged-assisted hydrogen bonds set up between the lateral chains of the chloroquine and the propionate group of the heme are the most important interactions in the drug:substrate recognition process.

Three-body systems provide the perfect framework for studying the quantum mechanics of both atoms and molecules. These studies can probe the fundamentals of particle interactions that underpin stability, reactivity and structure. This thesis contains a series of studies into the stability of ground state three-body systems. The focus of this thesis has been the high accuracy computation of three-body systems without recourse to either the Born-Oppenheimer (BO) approximationor approximation of the like-charged particle interaction, which for the case of atoms corresponds to the electron correlation. Principally the effects of mass and charge on the stability of systems is predicted. The complex nature of coupled electronic interaction is studied to the purpose of pursuing accurate electron correlation that underpins modern computational chemistry. The energies of three-body systems were calculated very accurately to typically mJ mol-1 accuracy or better whilst still producing reliable wavefunctions of which all other properties of the system could be calculated accurately. The energies of some of these systems are the lowest to date and all use the latest finite masses as published by CODATA. Computational codes were developed to achieve this accuracy using both numerical and computer algebra methods. These were designed to be efficient, extendable and, importantly, to calculate highly accurate energies, expectation values and wave functions. The masses of any three particles in which there exists at least one bound state below the lowest continuum threshold were identified. The importance of symmetry breaking in a asymmetric system was made clear as the difference in the masses become larger. A new method was developed to identify the lowest charge of a nucleus that can bind two electrons. This method is more effective then those previously available as it produces a variational upper bound to the true minimum charge in a single calculation. The method was employed to identify the minimum nuclear charge required for binding two electrons in atoms of various nuclear masses. Additionally the electronic structure of such systems was investigated by a judicious partitioning that separates the two electrons into an inner and outer component relative to the nucleus. The electron correlation was calculated using the Löwdin definition and a highly accurate Hartree-Fock (HF) implementation specifically designed for the task. The effects this electron correlation has on various properties was quantified including the coulomb hole. A second coulomb hole was found which was previously thought to be an artefact but remains even with this highly accurate implementation.

19 Dec 2004.
Published through the Information Bridge: DOE Scientific and Technical Information. "IS-T 2009" Ivana Adamovic. 12/19/2004. Report is also available in paper and microfiche from NTIS.

The past three decades have seen extraordinary progress in the manipulation of neutral atoms with laser light, to the point where it is now routine to trap and cool both individual atoms and entire atomic clouds to temperatures of only a few tens of nanoKelvin in a controlled and repeatable fashion. In this thesis we study several applications of Rydberg atoms - atoms with an electron in a highly excited state - within such ultracold atomic systems. Due to their highly-excited electron, Rydberg atoms have a number of exaggerated properties: in addition to being physically large, they have long radiative lifetimes, and interact strongly both with one another and with applied external fields. Rydberg atoms consequently find many interesting applications within ultracold atomic physics. We begin this thesis by analysing the way in which a rubidium atom prepared in an excited Rydberg state decays to the ground state. Using quantum defect theory to model the wavefunction of the excited electron, we compute branching ratios for the various decay channels that lead out of the Rydberg states of rubidium. By using these results to carry out detailed simulations of the radiative cascade process, we show that the dynamics of spontaneous emission from Rydberg states cannot be adequately described by a truncated atomic level structure. We then investigate the stability of ultra-large diatomic molecules formed by pairs of Rydberg atoms. Using quantum defect theory to model the electronic wavefunctions, we apply molecular integral techniques to calculate the equilibrium distance and binding energy of these molecular Rydberg states. Our results indicate that these Ryberg macro-dimers are predicted to show a potential minimum, with equilibrium distances of up to several hundred nanometres. In the second half of this thesis, we present a new method of symbolically evaluating functions of matrices. This method, which we term the method of path-sums, has applications to the simulation of strongly-correlated many-body Rydberg systems, and is based on the combination of a mapping between matrix multiplications and walks on weighted directed graphs with a universal result on the structure of such walks. After presenting and proving this universal graph theoretic result, we develop the path-sum approach to matrix functions. We discuss the application of path-sums to the simulation of strongly-correlated many-body quantum systems, and indicate future directions for the method.

We investigate chaotic ionization of highly excited hydrogen atom in crossed electric and magnetic fields (Rydberg atom) and intra-molecular relaxation in planar carbonyl sulfide (OCS) molecule. The underlying theoretical framework of our studies is dynamical systems theory and periodic orbit theory. These theories offer formulae to compute expectation values of observables in chaotic systems with best accuracy available in given circumstances, however they require to have a good control and reliable numerical tools to compute unstable periodic orbits. We have developed such methods of computation and partitioning of the phase space of hydrogen atom in crossed at right angles electric and magnetic fields, represented by a two degree of freedom (dof) Hamiltonian system. We discuss extensions to a 3-dof setting by developing the methodology to compute unstable invariant tori, and applying it to the planar OCS, represented by a 3-dof Hamiltonian. We find such tori important in explaining anomalous relaxation rates in chemical reactions. Their potential application in Transition State Theory is discussed.

In this thesis we study device-independent quantum key distribution based on energy-time entanglement. This is a method for cryptography that promises not only perfect secrecy, but also to be a practical method for quantum key distribution thanks to the reduced complexity when compared to other quantum key distribution protocols. However, there still exist a number of loopholes that must be understood and eliminated in order to rule out eavesdroppers. We study several relevant loopholes and show how they can be used to break the security of energy-time entangled systems. Attack strategies are reviewed as well as their countermeasures, and we show how full security can be re-established. Quantum key distribution is in part based on the profound no-cloning theorem, which prevents physical states to be copied at a microscopic level. This important property of quantum mechanics can be seen as Nature's own copy-protection, and can also be used to create a currency based on quantummechanics, i.e., quantum money. Here, the traditional copy-protection mechanisms of traditional coins and banknotes can be abandoned in favor of the laws of quantum physics. Previously, quantum money assumes a traditional hierarchy where a central, trusted bank controls the economy. We show how quantum money together with a blockchain allows for Quantum Bitcoin, a novel hybrid currency that promises fast transactions, extensive scalability, and full anonymity.
En viktig konsekvens av kvantmekaniken är att okända kvanttillstånd inte kan klonas. Denna insikt har gett upphov till kvantkryptering, en metod för två parter att med perfekt säkerhet kommunicera hemligheter. Ett komplett bevis för denna säkerhet har dock låtit vänta på sig eftersom en attackerare i hemlighet kan manipulera utrustningen så att den läcker information. Som ett svar på detta utvecklades apparatsoberoende kvantkryptering som i teorin är immun mot sådana attacker. Apparatsoberoende kvantkryptering har en mycket högre grad av säkerhet än vanlig kvantkryptering, men det finns fortfarande ett par luckor som en attackerare kan utnyttja. Dessa kryphål har tidigare inte tagits på allvar, men denna avhandling visar hur även små svagheter i säkerhetsmodellen läcker information till en attackerare. Vi demonstrerar en praktisk attack där attackeraren aldrig upptäcks trots att denne helt kontrollerar systemet. Vi visar också hur kryphålen kan förhindras med starkare säkerhetsbevis. En annan tillämpning av kvantmekanikens förbud mot kloning är pengar som använder detta naturens egna kopieringsskydd. Dessa kvantpengar har helt andra egenskaper än vanliga mynt, sedlar eller digitala banköverföringar. Vi visar hur man kan kombinera kvantpengar med en blockkedja, och man får då man en slags "kvant-Bitcoin". Detta nya betalningsmedel har fördelar över alla andra betalsystem, men nackdelen är att det krävs en kvantdator.

Atoms in optical lattices are promising candidates to implement quantum information processing. Their behaviour is well understood on a microscopic level, they exhibit excellent coherence properties, and they can be easily manipulated using external fields. In very deep optical lattices, each atom is restricted to a single lattice site and can be used as a qubit. If the lattice is shallow enough such that the atoms can move, their properties can be used to simulate certain condensed matter phenomena such as superconductivity. In this thesis, we show how technical problems of optical lattices such as restricted decoherence times, or fundamental shortcomings such as the lack of phonons or strong spin interactions, can be overcome by using current or near-future experimental techniques. We introduce a scheme that makes it possible to simulate model Hamiltonians known from high-temperature superconductivity. For this purpose, previous simulation schemes to realise the spin interaction terms are extended. We especially overcome the condition of a filling factor of exactly one, which otherwise would restrict the phase of the simulated system to a Mott-insulator. This scheme makes a large range of parameters accessible, which is difficult to cover with a condensed matter setup. We also investigate the properties of optical lattices submerged into a Bose-Einstein condensate (BEC). A weak-coupling expansion in the BEC-impurity interaction strength is used to derive a model that describes the lattice atoms in terms of polarons, i.e.~atoms dressed by Bogoliubov phonons. This is analogous to the description of electrons in solids, and we observe similar effects such as a crossover from coherent to incoherent transport for increasing temperatures. Moreover, the condensate mediates an attractive off-site interaction, which leads to macroscopic clusters at experimentally realistic parameters. Since the atoms in the lattice can also be used as a quantum register with the BEC mediating a two-qubit gate, we derive a quantum master equation to examine the coherence properties of the atomic qubits. We show that the system exhibits sub- and superdecoherence and that a fast implementation of the two-qubit gate competes with dephasing. Finally, we show how to realise the encoding of qubits in a decoherence-free subspace (DFS) using optical lattices. We develop methods for implementing robust gate operations on qubits encoded in a DFS exploiting collisional interactions between the atoms. We also give a detailed analysis of the performance and stability of the gate operations and show that a robust implementation of quantum repeaters can be achieved using our setup. We compare the robust repeater scheme to one that makes use of conventional qubits only, and show the conditions under which one outperforms the other.

Electron-electron correlation, excitation and quantum interference are generally important in attosecond physics, especially for imaging of atoms and molecules. These are the main topics addressed in this thesis, in the context of laser-induced nonsequential double ionization (NSDI). Excitation is the most extensive topic of this work and is addressed within a rigorous, semi-analytic study of the recollision-excitation with subsequent tunneling ionization (RESI) mechanism in laser-induced nonsequential double ionization (NSDI). This is the most comprehensive study of this mechanism performed in the context of the strong-field approximation to the preset date. Subsequently, we investigate potential imaging applications, by computing electron momentum distributions of atoms and molecules. For atoms, we show that the RESI electron momentum distributions depends very critically on the bound state wave function. For molecules, we address the influence of the molecular orbital geometry and of the molecular alignment with respect to the laser-field polarization, by computing the electron momentum distributions of N2 and Li2. We show that the electron-momentum distributions exhibit interference maxima and minima, either due to the electron emission at spatially separated centers, or to the orbital geometry, such as nodes of the atomic wavefunction. In this latter case, we do not restrict ourself only to RESI, and we also compute the electron momentum distributions of N2 for electron-impact ionization, in which we also observe two-center interference patterns when the molecule is aligned along the laserfield polarization direction. The above-mentioned momentum constraints, together with the strong dependence of the distributions on the bound states involved, the molecular orbital geometry and the molecular alignment angle may be important for singling out the RESI mechanism in actual physical situations and using NSDI in ultra-fast imaging. In the final chapter, we present the first step taken by us in order to address the above-stated issues using an approach beyond the strong field approximation.

Thesis (Ph.D.)--Michigan State University. Dept. of Physics and Astronomy, 2008.
Title from PDF t.p. (viewed on Apr. 3, 2009) Includes bibliographical references (p. 130-134). Also issued in print.

This thesis includes both experimental and theoretical investigations, presented in a series of eight papers. The experimental part ranges from the construction procedures of an apparatus for Bose-Einstein condensates, to full scale experiments using three different set-ups for ultracold atoms in optical lattices. As one of the main themes of the thesis, an experimental apparatus for production of Bose-Einstein Condensates is under construction. A magneto-optically trapped sample, hosting more than 200 million 87Rb atoms, have successfully been loaded into a magnetic trap with high transfer rate. The lifetime of the sample in the magnetic trap is in the range of 9 s, and the atoms have been shown to respond to evaporative cooling. The experiment is ready for optimization of the magnetic trap loading, and evaporative cooling parameters, which are the final steps for reaching Bose-Einstein condensation. The set-up is designed to host experiments including variable geometry optical lattices, and includes the possibility to align laser beams with high angular precision for this purpose. The breakdown of Bloch waves in a Bose-Einstein condensate is studied, attributed to the effect of energetic and dynamical instability. This experimental study is performed using a Bose-Einstein condensate in a moving one-dimensional optical lattice at LENS, Florence Italy. The optical lattice parameters, and the thermal distribution of the atomic sample required to trigger the instabilities, are detected, and compared with a theoretical model developed in parallel with the experiments. In close connection with these one-dimensional lattice studies, an experimental survey to characterize regimes of superradiant Rayleigh scattering and Bragg scattering is presented. Tunneling properties of repulsively bound atom pairs in double well potentials are characterized in an experiment at Johannes Gutenberg University, Mainz Germany. A three-dimensional optical lattice, producing an array of double wells with tunable properties is let to interact with a Bose-Einstein condensate. Pairs of ultracold atoms are produced on one side in the double wells, and their tunneling behavior, dependent on potential barrier and repulsion properties, is studied. A theoretical study of the crossover between one- and two-dimensional systems has been performed. The simulations were made for a two-dimensional array of atoms, where the behavior for different tunneling probabilities and atom-atom repulsion strengths was studied. Scaling relations for systems of variable sizes have been examined in detail, and numerical values for the involved variables have been found.

Chemistry
Ph.D.
The central objective of this dissertation is developing new methods for calculating higher-order nonlinear optical responses of atoms, molecules, and ions, and discussing the relevant physical mechanisms that give rise to harmonic generation, Kerr effect, and higher-order Kerr effect. The applications of nonlinear optical properties in development of predictive models for femtosecond laser filamentation dynamics, photoemission spectroscopy, imaging, and design of new molecular systems have motivated the theoretical investigations in advancing methods for calculating nonlinear optical properties and finding the optimum conditions for controlling the nonlinearities. The time-dependent nonlinear refractive index coefficient 4 n is investigated for argon and generalized for all noble gas atoms helium, neon, krypton, and xenon in the wavelengths ranging from 250 nm to 2000 nm, using ab initio methods. The secondorder polynomial fitting of DC-Kerr, electric-field-induced second-harmonic generation (ESHG), and static second-order hyperpolarizability have been performed, using an auxiliary electric field approach to obtain the corresponding fourth-order optical properties. An expression on the basis of static, DC-Kerr, DFWM fourth-order hyperpolarizability is derived, which allows the calculations of the DSWM coefficients with considerably reduced error. The results of the calculations suggest that filament stabilization is most likely to be induced by the generation of free electrons. Applications of these calculations resolve the HOKE controversy and are important for the development of predictive models for femtosecond laser filamentation dynamics. In a series of proof-of-concept studies, the approach was employed for calculating dynamic linear and nonlinear hyperpolarizability of the radical cations. In this regard, the polarizability and second-order hyperpolarizability of nitrogen radical cation were investigated, using density functional theory (DFT) and multi-configurational self-consistent field (MCSCF) methods. The open-shell electronic system of nitrogen radical cation provides negative second-order optical nonlinearity, suggesting that the hyperpolarizability coefficient for nitrogen radical cation, in the non-resonant regime is mainly composed of combinations of virtual one-photon transitions rather than two-photon transitions. The calculations of second-order optical properties for nitrogen radical cation as a function of bond length have been investigated to study the effect of internuclear bond distance on optical process. The variation of nonlinear responses versus bond length shows the potential application in finding optimum conditions for higher values of nonlinear coefficients. Furthermore, the computation of dynamic second-order hyperpolarizabilities for multiply ionized noble gases have been studied in the wavelength ranging from 100 nm to the red of the first multi-photon resonance all the way toward the static regime, using the MCSCF method. The results indicate that the second-order hyperpolarizability coefficients decrease when the electrons are removed from the systems. As the atoms reach higher ionization states, the second-order hyperpolarizability responses as a function of wavelength, become less dispersive. The second-order hyperpolarizability coefficients for each ionized species have also been investigated in terms of quantum state symmetries; the results suggest that the sign of the optical responses for each ionized atom depends on the spin of the quantum states defined for the ionized species. The calculations are of value for predictive models of high-harmonic generation in multiply ionized plasma at X-ray photon energies. This research also focuses on investigating possible mechanisms for photodissociation of polyatomic molecules (acetophenone and the substituted derivatives) ionized through strong field infrared laser pulses. In this regard, quantum mechanical methods are combined with pump-probe spectroscopy to understand and control the dissociation dynamics in strong field regime. The applications of quantum mechanical models in interpreting time-resolved wavepacket dynamics and achieving coherent control has stimulated the interest to explore the PESs and investigate the role of conical intersections in wavepacket dynamics in strong field regime. The electronic ground and excited states for acetophenone radical cation and the substituted derivatives have been investigated to probe the resonance features observed in measurements at 1370 nm with laser intensity of 1013 W cm-2. The ten lowest lying ionic potential energy surfaces (PESs) of the acetophenone radical cation were explored, and the three-state conical intersection was mapped onto the PES, using MCSCF model to propose a photo-dissociation mechanism for acetophenone undergoing tunnel ionization and elucidate the potential dissociation pathways for formation of benzoyl fragment ion, as well as phenyl, acylium, and butadienyl small fragment ions. Similar calculations are presented for propiophenone radical cation which support the existence of a one-photon transition from the ground ionic to a bright dissociative D2 state, where motion of the acetyl group from a planar to nonplanar structure within the pulse duration enables the otherwise forbidden transition. The wavepacket dynamics in acetophenone molecular ion is modeled using the classical wavepacket trajectory calculations, to propose the mechanism wherein the 790 nm probe pulse excites a wavepacket on the ground surface D0 to the excited D2 surface at a delay of 325 fs. The innovations of this research are used to design control strategies for selective bond-breaking in acetophenone radical cation, as well as design control schemes for other molecules.
Temple University--Theses

Force field methods are used to investigate the properties of a wide variety of chemical systems on a routine basis. The expression for the electrostatic energy typically does not take into account the anisotropic nature of the atomic electron distribution or the dependence of that distribution on the system geometry. This has been suggested as a cause of the failure of force field methods to reliably predict the behaviour of chemical systems. A method for incorporation of anisotropy and polarisation is described in this work. Anisotropy is modelled by the inclusion of multipole moments centred at atoms whose values are determined by application of the methods of Quantum Chemical Topology. Polarisation, the dependence of the electron distribution on system geometry, is modelled by training machine learning models to predict atomic multipole moments from knowledge of the nuclear positions of a system. The resulting electrostatic method can be implemented for any chemical system. An application to progressively more complex systems is reported, including small organic molecules and larger molecules of biological importance. The accuracy of the method is rigorously assessed by comparison of its predictions to exact interaction energy values. A procedure for generating transferable atomic multipole moment models is defined and tested. The electrostatic method can be combined with the empirical expressions used in force field calculations to describe total system energies by fitting parameters against ab initio conformational energies. Derivatives of the energy are given and the resulting multipolar polarisable force field can be used to perform geometry optimisation calculations. Future applications to conformational searching and problems requiring dynamic descriptions of a system are feasible.

A group theoretic approach to Layzer's 1/2 expansion method is explored. In part this builds on earlier work of Wulfman(2), of Moshinsky et al(l4), and of Sinanoglu, Herrick(lS), and Kellman (16) on second row atoms. I investigate atoms with electrons in the 3s-3p-3d shell and find: 1. Wulfman's constant of motion accurately predicts configuration mixing for systems with two to eight electrons in the 3s-3p subshell. 2. The same constant of motion accurately predicts configuration mixing for systems with two electrons in the 3s-3p-3d shell. 3. It accurately predicts configuration mixing in systems of high angular momentum L and of high spin angular momentum S containing three electrons in the 3s-3p-3d shell, but gives less accurate results when L and S are both small. I also show how effective nuclear charges may be calculated by a group theoretical approach. In addition I explore several new methods for expressing electron repulsion operators in terms of operators of the 80(4,2) dynamical group of one - electron atoms.

Cette thèse contribue aux développements de méthodes numériques utilisées pour reproduire la dynamique électronique induite par des processus à un et plusieurs photons dans les atomes et molécules. Dans le domaine perturbatif, la photoexcitation et la photoionisation ont été étudiées à l'aide de la théorie de la fonctionnelle de la densité à séparation de portée, dans le but de prendre en compte les effets d'interaction électron-électron. De plus, dans le domaine non-perturbatif, les spectres au-delà du seuil d'ionisation et les spectres de génération d'harmoniques d'ordres élevés ont été simulés en utilisant différentes représentations de la fonction d'onde dépendante du temps du système étudié. Cette étude ouvre la possibilité d'explorer des processus matière-rayonnement dans des systèmes plus complexes
The present PhD thesis contributes to the development of numerical methods used to reproduce the electron dynamics induced by single and multiphoton processes in atoms and molecules. In the perturbative regime, photoexcitation and photoionization have been studied in atoms with range-separated density-functional theory, in order to take into account the electron-electron interaction effects. Moreover, in the non-perturbative regime, above-threshold ionization and high-harmonic generation spectra have been simulated using different representations for the time-dependent wave function for the purpose of describing the continuum states of the irradiated system. Our studies open the possibility of exploring matter-radiation processes in more complex systems

A rigorous formalism for solving the Coulomb scattering problem is presented in this thesis. The approach is based on splitting the interaction potential into a finite-range part and a long-range tail part. In this representation the scattering problem can be reformulated to one which is suitable for applying exterior complex scaling. The scaled problem has zero boundary conditions at infinity and can be implemented numerically for finding scattering amplitudes. The systems under consideration may consist of two or three charged particles. The technique presented in this thesis is first developed for the case of a two body single channel Coulomb scattering problem. The method is mathematically validated for the partial wave formulation of the scattering problem. Integral and local representations for the partial wave scattering amplitudes have been derived. The partial wave results are summed up to obtain the scattering amplitude for the three dimensional scattering problem. The approach is generalized to allow the two body multichannel scattering problem to be solved. The theoretical results are illustrated with numerical calculations for a number of models. Finally, the potential splitting technique is further developed and validated for the three body Coulomb scattering problem. It is shown that only a part of the total interaction potential should be split to obtain the inhomogeneous equation required such that the method of exterior complex scaling can be applied. The final six-dimensional equation is reduced to a system of three dimensional equations using the full angular momentum representation. Such a system can be numerically implemented using the existing full angular momentum complex exterior scaling code (FAMCES). The code has been updated to solve the three body scattering problem.
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Submitted. Paper 5: Manuscript.