Nowdays, coupled cluster method belongs to one of the most used quantum chemical methods. However, the single-reference coupled cluster methods are not able to describe systems where the static correlation have an important role. Multireference coupled cluster methods developed in our group can describe both static and dy- namic correlation and can be used for problematic systems. Together with explicitly correlated wavefunction, which can properly describe the electronic cusp and speed up the convergence to the complete ba- sis set limit, they are able to calculate computationally demanding diradicals. Multireference CC calculations of tetramethylenethane have been perforemd and the performance of explicitly correlated version is discussed. Calculations of the isomerization of bicyclobu- tane using the multireference approach are presented as well. 1

The theoretical work presented in this thesis is concerned with the highest possible oxidation states of the 5d transition metal row. Based on a validation study of several DFT functionals against accurate coupled-cluster CCSD(T) methods we will present calculations on a series of new high oxidation state HgIV species. Quantum-chemical calculations have also been applied to various fluoro complexes of gold in oxidation states +V through +VII to evaluate the previously claimed existence of AuF7. The calculations indicate clearly that the oxidation state (+V), e.g., in [AuF5]2, remains the highest well-established gold oxidation state. Further calculations on iridium in oxidation state (+VII) show that IrF7 and IrOF5 are viable synthetic targets, whereas higher oxidation states of iridium appear to be unlikely. Structures and stabilities of several osmium fluorides and oxyfluorides were also studied in this thesis. It is shown that homoleptic fluorides all the way up to OsF8 may exist. Combining the results of the most accurate quantum-chemical predictions of this thesis and of the most reliable experimental studies, we observe a revised trend of the highest oxidation states of the 5d transition metal row. From lanthanum (+III) to osmium (+VIII), there is a linear increase of the highest oxidation states with increasing atomic number. Thereafter, we observe a linear descent from osmium (+VIII) to mercury (+IV). We will also present a short outlook to the transition metals of the 3d and 4d row and their highest reachable oxidation states. / In der vorliegenden theoretischen Arbeit wurden mittels quantenchemischer Methoden die höchsten Oxidationsstufen der späten Übergangselemente untersucht. Um eine adäquate Beschreibung dieser Systeme zu gewährleisten, wurde zuerst eine Validierungsstudie verschiedener Dichtefunktionale, die mit hochgenauen coupled-cluster CCSD(T) Berechnungen verglichen wurden, durchgeführt. Das zugrundeliegende Referenzsystem war Quecksilber in der Oxidationsstufe +IV (HgF4, HgCl4, HgH4). Es wurden Strukturoptimierungen von Minima und Übergangszuständen, Atomisierungsenergien sowie die entsprechenden Zerfallsreaktionen für die Systeme betrachtet. Basierend auf diesen Ergebnissen konnten weitere HgIV Systeme mit sogenannten „Weakly Coordinating Anions“ wie z.B. [OTeF5]-, [AsF6]-, [Sb2F11]- usw. unter Verwendung von Dichtefunktionalmethoden untersucht werden. Die beiden Verbindungen Hg[OTeF5]4 und Hg[AsF6]4 scheinen dabei die Oxidationsstufe +IV am besten zu stabilisieren. Quantenchemische Methoden wurden ebenfalls zur Berechnung von Fluorkomplexen des Goldes in den Oxidationsstufen von +V bis +VII verwendet. Dabei wurde insbesondere überprüft, ob das angeblich experimentell gefundene AuF7 tatsächlich existiert. Es konnte gezeigt werden, dass eine Existenz von AuF7 unter den in der Literatur angegebenen Bedingungen sehr wahrscheinlich ausgeschlossen werden kann. Diese Instabilität wird ebenfalls für das quantenchemisch untersuchte AuF6 beobachtet. Somit bleibt die Oxidationsstufe +V in [AuF5]2 die höchste erreichbare Oxidationsstufe für Gold. Basierend auf coupled-cluster CCSD(T) Berechnungen konnten die Verbindungen des Iridiums in der Oxidationsstufe +VII (IrF7, IrOF5) als thermochemisch stabil vorhergesagt werden, wohingegen die höheren Iridiumverbindungen des IrVIII und IrIX sehr unwahrscheinlich sind. Außerdem wurden Strukturen und Stabilitäten verschiedener Osmiumfluoride und Oxyfluoride in dieser Arbeit diskutiert. Es konnte gezeigt werden, dass ausgehend von OsF6 auch die höheren Verbindungen OsF7 und OsF8 experimentell zugänglich sein sollten. Kombiniert man die in dieser Arbeit vorhergesagten Verbindungen in ihren höchsten Oxidationsstufen mit den verlässlichsten experimentellen Untersuchungen, so beobachtet man einen revidierten Trend der höchsten Oxidationsstufen der 5d-Übergangsmetallreihe: Direkt proportional zur Ordnungszahl steigen die höchsten Oxidationszahlen zunächst linear an, von Os (+VIII) bis hin zu Hg (+IV) kann ein linearer Abfall beobachtet werden. Abschließend werden in dieser Arbeit die höchsten Oxidationsstufen der 3d und 4d Übergangsmetalle in einer kurzen Übersicht vorgestellt.

In non-relativistic quantum mechanics, stationary states of molecules and atoms are described by eigenvectors of the Hamiltonian operator. For one-electron systems, such as the hydrogen atom, the solution of the eigenvalue problem (Schro ̈dinger’s equation) is straightforward, and the results show excellent agreement with experiment. Despite this success, the multi electron problem corresponding to virtually every system of interest in chemistry has resisted attempts at exact solution. Perhaps the most popular method for obtaining approximate, yet very accurate results for the ground states of molecules is the coupled cluster approximation. Coupled cluster methods move beyond the simple, average field Hartree-Fock approximation by including the effects of excited configurations generated in a size consistent manner. In this paper, the coupled cluster approximation is developed from first principles. Diagrammatic methods are introduced which permit the rapid calculation of matrix elements appearing in the coupled cluster equations, along with a systematic approach for unambiguously determining all necessary diagrams. A simple error bound is obtained for the ground state energy by considering the coupled cluster equations as entries in the first column of a matrix whose eigenvalues are the exact eigenvalues of the Hamiltonian. In addition, a strategy is considered for treating the error in the ground state energy perturbatively.

Stuttgart, Univ., Diss., 2008.

Submitted by João Arthur Martins (joao.arthur@ufpe.br) on 2015-03-03T18:31:59Z No. of bitstreams: 2 MVPS_tese_versao_final_completa_sem_assinatura.pdf: 9794248 bytes, checksum: e8b0b56cd04ef0be4abb905d4891a1cb (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) / Made available in DSpace on 2015-03-03T18:31:59Z (GMT). No. of bitstreams: 2 MVPS_tese_versao_final_completa_sem_assinatura.pdf: 9794248 bytes, checksum: e8b0b56cd04ef0be4abb905d4891a1cb (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Previous issue date: 2012-08-17 / CNPq e FACEPE / Este documento apresenta a Tese de doutorado do estudante Marcus Vinicius Pereira dos Santos ao Programa de P´os-Gradua¸c˜ao em Ciˆencia de Materiais da Universidade Federal de Pernambuco. Neste trabalho procurou-se avaliar propriedades eletrˆonicas, espectrosc ´opicas e catal´ıticas de trˆes tipos de materiais moleculares: fenestranos, alcaplanos e o 1,4-benzenodimetanol. Os fenestranos possuem uma subunidade espiroalcano e apresentam como caracter´ısticas energ´eticas principais: energias de ioniza¸c˜ao da mesma ordem de metais alcalinos terrosos tais como c´alcio (6,11 eV), magn´esio (7,64 eV) e ber´ılio (9,32 eV), cujos valores est˜ao intimamente relacionados com o menor valor do ˆangulo torsional envolvendo o carbono central e seus carbonos vizinhos ( ). Por sua vez, o valor deste ˆangulo torsional est´a associado aos tipos de an´eis, `a presen¸ca ou n˜ao das liga¸c˜oes duplas e a quantidade de liga¸c˜oes duplas por anel. Isto permite um controle muito sens´ıvel n˜ao s´o da energia de ioniza¸c˜ao, mas tamb´em da energia de tens˜ao do anel, o que ´e essencial para se propor, simultaneamente, compostos com car´ater doador de el´etrons e sinteticamente vi´aveis para aplica¸c˜ao em sistemas aceitador-ponte-doador (A-B-D) utilizados em ´optica n˜ao-linear (NLO). Contudo, os alcaplanos s˜ao os materiais moleculares mais indicados como doadores de el´etrons em sistemas A-B-D, uma vez que possuem energias de ioniza¸c˜ao menores que 5 eV, mesmo em compostos que n˜ao possuem o ´atomo de carbono central tetracoordenado completamente plano (ptC), e assim como os fenestranos, possuem um controle sens´ıvel das propriedades energ´eticas com rela¸c˜ao ao valor de . A presen¸ca de liga¸c˜oes duplas nos an´eis e de grupos laterais do tipo -CH2- permite um controle diferenciado dessas propriedades, inclusive a supress˜ao da dependˆencia da energia de ioniza¸c˜ao com a planaridade (valor de ), o que permite o relaxamento da estrutura sem perder o baixo valor da energia de ioniza¸c˜ao do material. Por´em, os alcaplanos normalmente possuem tens˜oes de anel e entalpias de forma¸c˜ao maiores que os fenestranos, o que explica a dificuldade de s´ıntese desses compostos. A aproxima¸c˜ao PICVib, procedimento in´edito para an´alise da frequˆencia de modos normais espec´ıficos, mostra-se como uma alternativa simples, geral, robusta e com excelente desempenho na previs˜ao de frequˆencias vibracionais, mesmo com baixas energias (100 cm−1). Com seu aux´ılio, ´e poss´ıvel transpor facilmente a barreira de utiliza¸c˜ao de m´etodos p´os-Hartree-Fock mais sofisticados, com fun¸c˜oes de base triplo zeta que incluem fun¸c˜oes difusas e de polariza¸c˜ao, em sistemas moleculares com cerca de 50 ´atomos. J´a sua vers˜ao de baixo custo, a PICVib-v, requer bastante cautela para uso, uma vez que depende fortemente do qu˜ao diferente ´e a geometria obtida como m´etodo low comparada vi RESUMO vii `aquela fornecida pelo m´etodo high. Existe algum alcaplano ptC est´avel? Ao contr´ario do que foi comentado e proposto na literatura, acreditamos que uma resposta definitiva n˜ao pode ser dada por metodologias baseadas no funcional da densidade ou at´e mesmo com a teoria de perturba¸c˜ao de segunda ordem, pois em v´arios casos estudados nesta tese esses m´etodos forneceram resultados discordantes e contradit´orios. Com teorias mais sofisticadas, como ´e o caso de “coupled-cluster”(CC) aliado ao PICVib (ou PICVib-v), constata-se que dentre os quatro compostos analisados contendo ptC, o dimetilespiroalcaplano proposto por Radom apresenta uma frequˆencia imagin´aria no valor de 371i cm−1 calculada com o m´etodo CCSD, contradizendo um dos principais resultados obtidos na literatura, al´em dos pr´oprios resultados obtidos neste trabalho com o m´etodo MP2 (com diferentes fun¸c˜oes de base). Os resultados CCSD mostram ainda que dois compostos com ptC apresentam frequˆencias reais, mas ambos apresentam instabilidade da fun¸c˜ao de onda. Assim, acreditamos que o tratamento empregado ´e inadequado. A nossa proposta de alcaplano com ptC ´e inst´avel, pois apresenta constante de for¸ca negativa. Assim, n˜ao resta nenhum composto proposto com ptC que seja est´avel. Acreditamos que por causa da estrutura eletrˆonica ex´otica e pouco usual destes compostos, o uso de m´etodos quˆanticos tradicionais podem levar `a conclus˜oes equivocadas acerca da estabilidade de alcaplanos com ptC. Entretanto, a problem´atica da estabilidade n˜ao afeta a proposta desta tese, pois excelentes grupos doadores de el´etrons podem ser obtidos com alcaplanos contendo carbono central tetracoordenado quase-plano (quase-ptC). Desse modo, utilizando esses grupos doadores em sistemas A-B-D, obtivemos valores de polarizabilidades (), primeira () e segunda () hiperpolarizabilidades compar´aveis aos maiores valores j´a relatados na literatura. Infelizmente, problemas na instabilidade da fun¸c˜ao de onda n˜ao permitem que esses c´alculos sejam realizados com fun¸c˜oes de base mais sofisticadas. Com rela¸c˜ao ao processo de cat´alise com o 1,4-benzenodimetanol (BDM), os mecanismos de rea¸c˜oes SN2 e E2 envolvendo o ´ıon acetato e o cloroetano s˜ao espontˆaneos, mas somente s˜ao catalisados pela intera¸c˜ao com o BDM no solvente dimetilsulf´oxido (DMSO), mostrando que os efeitos do solvente s˜ao essenciais para se observar a cat´alise dessa rea ¸c˜ao. Mesmo com a proposi¸c˜ao de novos caminhos reacionais SN2 e E2, essa tendˆencia se mant´em. A modifica¸c˜ao do BDM com a inclus˜ao de mais um grupo -CH2-OH n˜ao favorece a cat´alise desses mecanismos. Contudo, do ponto de vista termodinˆamico, os mecanismos de rea¸c˜oes SN2 s˜ao espontˆaneos n˜ao apenas em DMSO, mas tamb´em em fase g´as. O mesmo n˜ao ocorre para os diferentes mecanismos E2, em que a espontaneidade ocorre apenas em DMSO.

There is a need for reliable rules of thumb for various applications in the area of biochemistry, supramolecular chemistry and material sciences. Simultaneously, the amount of information, which we can gather from X-ray crystal geometries about the nature of recognition processes, is limited. Deeper insight into the noncovalent interactions playing the most important role is needed in order to revise these universal rules governing any recognition process. In this thesis, systematic development and study of the accuracy of the computational chemistry methods followed by their applications in protein DNA and host guest systems, are presented. The non-empirical quantum mechanical tools (DFT-D, MP2.5, CCSD(T) etc. methods) were utilized in several projects. We found and confirmed unique low lying interaction energies distinct from the rest of the distributions in several amino acid−base pairs opening a way toward universal rules governing the selective binding of any DNA sequence. Further, the predictions and examination of changes of Gibbs energies (ΔG) and its subcomponents have been made in several cases and carefully compared with experiments. We determined that the choline (Ch+) guest is bound 2.8 kcal/mol stronger (calculated ΔG) than acetylcholine (ACh+) to self-assembled triple helicate rigid...

Optical and spectroscopic molecular properties are key to characterizing the behavior of molecules interacting with an applied electromagnetic field of light. Response theory has been used for a long time to calculate such properties in the frequency domain. Real-time (RT) methods solve for the frequency-dependent properties in the time domain by explicitly propagating the time-dependent wave function. Various quantum chemical methods can be incorporated with the RT formalism, including Hartree-Fock, density functional theory, configurational interaction, coupled cluster, etc. Among these, coupled cluster (CC) methods provide high accuracy for systems with strong electron correlation, making RT-CC implementations intriguing. All applications of CC methods face a substantial challenge due to their high-order polynomial scaling. For RT-CC methods, two aspects may be explored to improve the efficiency, the numerical techniques regarding the RT propagation and the reduced-scaling methods regarding CC itself. In this work, we start with the exploration of the hardware used for the calculations and the numerical integration methods for propagating the wave function parameters. Firstly, a GPU-enabled Python implementation has been developed by conducting the tensor contractions on GPUs utilizing PyTorch, a machine learning package, that has similar syntax as NumPy for tensor operations. A speedup of a factor of 14 is obtained for the RT-CCSD/cc-pVDZ absorption spectrum calculation of the water tetramer. Furthermore, to optimize the performance on GPUs, single-precision arithmetic is added to the implementation to achieve an additional speedup of a factor of two. Lastly, a group of integrators for solving differential equations are introduced to the RT framework, including regular explicit integrators, adaptive integrators, and a mixed-step-size approach customized for strong-field simulations. The optimal choice of the integrator depends on the requiring accuracy, stability and efficiency. In addition to being highly accurate, CC methods are also systematically improvable and provide a hierarchy of accuracy. Based upon the RT-CCSD implementation, the coupled cluster singles, doubles and approximate triples (CC3) method, favorable for calculating frequency-dependent properties, is tailored to the RT framework for high excitation and approximate orbital relaxation. The calculation is tested on both CPUs and GPUs, with a significant speedup gained from GPUs for the water cluster test cases. To further expand the range of applications of our RT-CC implementation, dynamic polarizabilities, first hyperpolarizabilities, and the G' tensor are calculated from induced electric and magnetic dipole moments using finite-difference methods. A discussion has also been conducted to compare RT-CC3 with RT-CCSD, and time-dependent nonorthogonal orbital-optimized coupled cluster doubles (TDNOCCD) method. Additionally, electron dynamics, including the Rabi oscillation and exited state to excited state transitions, have also been explored utilizing the well-developed RT-CC framework. / Doctor of Philosophy / Theoretical studies aim to match experiments, but more importantly, provide insights to interpret and predict experimental data. Calculating optical properties related to light-matter interactions is one of the most crucial tasks for characterizing molecular properties. In experiments, electromagnetic radiation in the form of light is applied to the system. The absorption or emission of light can be measured to identify, for example, the electronic structure of the molecule. In theoretical simulations, this applied radiation is represented by a perturbation operator that is added to the Hamiltonian in the Schrödinger equation. Quantum chemists are dedicated to developing methods that provide a better description of the spectroscopy. In the current work, the frequency, shape and the intensity of the radiation can all be finely-tuned, similar to experimental setups. The framework for extracting optical properties from time-dependent trajectories of induced dipole moments is established for accurate and efficient simulations. To improve efficiency and make the method feasible for real-world applications, a strong understanding of light-matter interactions on a quantum level and proper utilization of computational resources are both necessary. Improvements achieved and presented in this dissertation demonstrate a powerful tool for a better understanding of the nature of the interaction between the system and the electromagnetic radiation.

We give an overview of quantum chemical methods with a particular emphasis on the development of high-accuracy quantum chemical models. The reliability of these methods often hinges on whether enough electron correlation is included in the truncated wave function. As an example, we investigate the structures of m-benzyne and its fluorinated derivative, tetrafluoro-m-benzyne where the inclusion of triple excitations is paramount to correctly describe through-bond delocalization of the monocyclic form. At the CCSDT/6-31G** level of theory, the C1–C3 distance of the minimum energy form of m-benzyne is 2.0°A and the profile of the PES along the C1–C3 distance is that of an asymmetric, single-well, in agreement with previous density-functional theory and coupled cluster studies. In addition, the calculated CCSD(T) fundamental frequencies are in excellent agreement with the measured infrared frequencies, thus confirming the monocyclic form of m-benzyne. For tetrafluoro-m-benzyne, however, the increased eclipsing strain between the ring-external Câ X bonds stabilizes the bicyclo[3.1.0]hexatriene form: the C1–C3 distance is calculated at the CCSD(T)/cc-pVTZ level to be approximately 1.75 °A, which is in the range of elongated CC bonds. Computed harmonic vibrational frequencies compare reasonably well with the experimental neon-matrix difference spectrum and provide further evidence for the existence of a bicyclic form. We also report an extension of the coupled cluster iterative-triples model, CC3, to excited states of open-shell molecules, including radicals. We define the method for both spin-unrestricted Hartree-Fock (UHF) and spin-restricted open-shell Hartree-Fock (ROHF) reference determinants and discuss its efficient implementation in the PSI3 program package. The program is streamlined to use at most O(N7) computational steps and avoids storage of the triple-excitation amplitudes for both the ground-and excited-state calculations. The excitation-energy program makes use of a Lowdin projection formalism (comparable to that of earlier implementations) that allows computational reduction of the Davidson algorithm to only the single- and double-excitation space, but limits the calculation to only one excited state at a time. However, a root-following algorithm may be used to compute energies for multiple states of the same symmetry. Benchmark applications of the new methods to the lowest valence 2B1 state of the allyl radical, low-lying states of the CH and CO+ diatomics, and the nitromethyl radical show substantial improvement over ROHF- and UHF-based CCSD excitation energies for states with strong double-excitation character or cases suffering from significant spin contamination. For the allyl radical, CC3 adiabatic excitation energies differ from experiment by less than 0.02 eV, while for the 2§+ state of CH, significant errors of more than 0.4 eV remain. Finally, ground- and excited-state dipole moments are derived diagramatically and were recently developed within the PSI3 quantum chemistry package. However, convergence problems with computing the left-hand excited-state has prevented us from reporting any meaningful results. Thus, future work includes solving this convergence problem before the effects of triple excitations on one-electron properties can be reported with certainty. / Ph. D.

One of the most promising methods for surmounting the high-degree polynomial scaling wall associated with electron correlating wave function methods is the local correlation technique of Pulay and Saebø. They have proposed using a set of localized occupied and virtual orbitals free of the canonical constraint commonly employed in quantum chemistry, resulting in a method that scales linearly (in the asymptotic limit) with molecular size. Pulay and Saeb$oslash; first applied their methods to configuration interaction and later to M$oslash;ller-Plesset perturbation theory. Werner et al. have have extended the local correlation scheme of Pulay and Saeb$oslash; to coupled-cluster theory. One of the pitfalls of the local correlation methods developed by Pulay and Saeb$oslash; is the dependence of domain selection on the molecular geometry. In other words, as the geometry changes the domain structure of the local correlation calculation can change also, leading to discontinuities in the potential energy surface. We have examined the size of these discontinuities for the homolytic bond cleavage of fluoromethane and the heterolytic bond dissociation of singlet ketene and propadienone. Properties such as polarizabilities and optical rotation are realized through linear response theory, where the Hamiltonian is subject to an external perturbation and the wave function is allowed to respond to the applied perturbation. Within the context of local correlation it is necessary to understand how the domain structure alters in response to an applied perturbation. We have proposed using solutions to the CPHF equations (coupled-perturbed Hartree-Fock) in order to predict the correlation response to an applied perturbation. We have applied this technique to the calculation of polarizabilities, with very favorable results, and also to optical rotation, with mixed results. / Ph. D.

Coupled cluster (CC) and density functional theory (DFT) are highly regarded as robust quantum chemical methods for accurately predicting a wide variety of properties, such as molecular structures, thermochemical data, vibrational spectra, etc., but there has been little focus on the theoretical prediction of optical rotation. This property, also referred to as circular birefringence, is inherent to all chiral molecules and occurs because such samples exhibit different refractive indices for left- and right- circularly polarized light. This thesis focuses on the theoretical prediction of this chiroptic property using CC and DFT quantum chemical models. Several small chiral systems have been studied, including (S)-methyloxirane, (R)-epichlorohydrin, (R)-methylthiirane, and the conformationally flexible molecules, (R)-3-chloro-1-butene and (R)-2-chlorobutane. All predicted results have been compared to recently published gas-phase cavity ringdown polarimetry data. When applicable, well-converged Gibbs free energy differences among confomers were determined using complete-basis-set extrapolations of CC energies in order to obtain Boltzmann-averaged specific rotations. The overall results indicate that the theoretical rotation is highly dependent on the choice of optimized geometry and basis set (diffuse functions are shown to be extremely important), and that there is a large difference between the CC and DFT predicted values, with DFT usually predicting magnitudes that are larger than those of coupled cluster theory. / Ph. D.