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.

The variational quantum eigensolver (VQE) approach is currently one of the most promising strategies for simulating chemical systems on quantum hardware. In this work, I will describe a new quantum algorithm and a new set of classical algorithms based on VQE. The quantum algorithm, ADAPT-VQE, shows promise in mitigating many of the known limitations of VQEs: Ansatz ambiguity, local minima, and barren plateaus are all addressed to varying degrees by ADAPT-VQE. The classical algorithm family, O2DX-UCCSD, draws inspiration from VQEs, but is classically solvable in polynomial time. This group of algorithms yields equations similar to those of the linearized coupled cluster theory (LCCSD) but is more systematically improvable and, for X = 3 or X = ∞, can break single bonds, which LCCSD cannot do. The overall aim of this work is to showcase the richness of the VQE algorithm and the breadth of its derivative applications. / Doctor of Philosophy / A core goal of quantum chemistry is to compute accurate ground-state energies for molecules. Quantum computers promise to simulate quantum systems in ways that classical computers cannot. It is believed that quantum computers may be able to characterize molecules that are too large for classical computers to treat accurately. One approach to this is the variational quantum eigensolver, or VQE. The idea of a VQE is to use a quantum computer to measure the molecular energy associated with a quantum state which is parametrized by some classical set of parameters. A classical computer will use a classical optimization scheme to update those parameters before the quantum computer measures the energy again. This loop is expected to minimize the quantum resources needed for a quantum computer to be useful, since much of the work is outsourced to classical computers. In this work, I describe two novel algorithms based on the VQE which solve some of its problems.

The efficient computation of dynamic (time-dependent) molecular properties is a broad field with numerous applications in aiding molecular synthesis and design, with a particular preva- lence in spectroscopic predictions. Typical methods for computing the response of a molecu- lar system to an electromagnetic field (EMF) considers a quantum mechanical description of the molecule and a classical approximation for the EMF. Methods for describing light-matter interactions with high-accuracy electronic structure methods, such as coupled cluster (CC), are discussed, with a focus on improving the efficiency of such methods. The CC method suffers from high-degree polynomial scaling. In addition to the ground-state calculation, computing dynamic properties requires the description of sensitive excited-state effects. The cost of such methods often prohibits the accurate calculation of response prop- erties for systems of significant importance, such as large-molecule drug candidates or chiral species present in biological systems. While the literature is ripe with reduced-scaling meth- ods for CC ground-state calculations, considerably fewer approaches have been applied to excited-state properties, with even fewer still providing adequate results for realistic systems. This work presents three studies on the reduction of the cost of molecular property evalu- ations, in the hopes of closing this gap in the literature and widening the scope of current theoretical methods. There are two main ways of simulating time-dependent light-matter interactions: one may consider these effects in the frequency domain, where the response of the system to an EMF is computed directly; or, the response may be considered explicitly in the time domain, where wave function (or density) parameters can be propagated in time and examined in detail. Each methodology has unique advantages and computational bottlenecks. The first two studies focus on frequency-domain calculations, and employ fragmentation and machine- learning techniques to reduce the cost of single-molecule calculations or sets of calculations across a series of geometric conformations. The third study presents a novel application of the local correlation technique to real-time CC calculations, and highlights deficiencies and possible solutions to the approach. / Doctor of Philosophy / Theoretical chemistry plays a key role in connecting experimental results with physical inter- pretation. Paramount to the success of theoretical methods is the ability to predict molecular properties without the need for costly high-throughput synthesis, aiding in the determina- tion of molecular structure and the design of new materials. Light-matter interactions, which govern spectroscopic techniques, are particularly complicated, and sensitive to the theoreti- cal tools employed in their prediction. Compounding the issue of accuracy is one of efficiency — accurate theoretical methods typically incur steep scaling of computational cost (memory and processor time) with respect to the size of the system. An important aspect in improving the efficiency of these methods is understanding the nature of light-matter interactions at a quantum level. Many unanswered questions still remain, such as, "Can light-matter interactions be thought of as a sum of interactions be- tween smaller fragments of the system?" and "Can conventional methods of accelerating ground-state calculations be expected to perform well for spectroscopic properties?" The present work seeks to answer these questions through three studies, focusing on improving the efficiency of these techniques, while simultaneously addressing their fundamental flaws and providing reasonable alternatives.

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.