Single reference coupled cluster theory has been established as the method of choice for calculating electronic properties of small-to-medium size molecules. However, in typical multireference cases, such as bond breaking processes, biradicals, excited states, very high order excitations may be needed in the cluster operator to obtain reliable and accurate results, which is not practical due to the rapidly growing computational costs. Although there has been much e®ort to extend the applicability of single reference methods, there is little doubt that genuine multireference methods are indispensable. The method we are developing, the State Speci¯c Equation of Motion Coupled Cluster (SS-EOMCC) method, generalizes the state universal Equation of Motion Coupled Cluster (EOMCC)methods to a state specific version. SS-EOMCC works for both ground states and excited states. It is rigorously spin-adapted. The cluster operator amplitudes are solved, taking the complete- active-space self-consistent-¯eld function as the reference function. The differential relaxation effects are taken into account by diagonalizing the transformed Hamiltonian in the multireference configuration interaction singles (MRCIS) space. To implement the method, we developed an automatic program generator, the details of which are presented. The strategy used in approximating residual equations in SS-EOMCC is based on a novel normal order theory, which is a generalization of traditional particle-hole formalism based normal order theory. We discuss normal order theory in a general context, start with the version developed by Mukherjee and Kutzelnigg, and we furnish an algebraic proof for the corresponding contraction rules. Then we proceed to show how our normal order theory works. Finally we present the benchmark results to gauge the SS-EOMCC method. We calculate the triplet state state of F₂ to examine the behavior of the method for single reference systems, and study the singlet states of H₂O, CO and N₂ to test its performance for multireference systems. In addition, we illustrate the e®ect of a perturbative correction, which attempts to alleviate the redundancy issue. We also apply the method to study the energetics of end-on and side-on peroxide coordination in ligated Cu₂O₂ models, where SS-EOMCC[+2] employing a small active space achieves quite accurate results. The final diagonalization of the transformed Hamiltonian in the MRCIS space is expensive and limits the applicability of the method. We attempt to develop a cheaper internally contracted multireference coupled cluster method by introducing semi-internal excitation operators in the cluster operator such that the final diagonalization can be confined within the active space, but the results are not satisfactory yet. The Jeziorski-Monkhorst (JM) ansatz has been studied extensively, and different ways to resolve the redundancy issue have been explored. We analyze these JM-ansatz based methods, derive them in a simple way to disclose their connections transparently, and point out some problem in these methods. Another issue of general interest which is examined in the thesis is orbital invariance. For single reference methods the invariance property is usually clear, but this is not always the case for multireference methods. We analyze this problem from the tensor theory point of view, and propose a practical self-consistency-checking algorithm to determine whether a method is orbital invariant or not. We apply the algorithm to different methods, in particular, demonstrating the lack of the invariance property for JM-ansatz based methods.

Single reference coupled cluster theory has been established as the method of choice for calculating electronic properties of small-to-medium size molecules. However, in typical multireference cases, such as bond breaking processes, biradicals, excited states, very high order excitations may be needed in the cluster operator to obtain reliable and accurate results, which is not practical due to the rapidly growing computational costs. Although there has been much e®ort to extend the applicability of single reference methods, there is little doubt that genuine multireference methods are indispensable. The method we are developing, the State Speci¯c Equation of Motion Coupled Cluster (SS-EOMCC) method, generalizes the state universal Equation of Motion Coupled Cluster (EOMCC)methods to a state specific version. SS-EOMCC works for both ground states and excited states. It is rigorously spin-adapted. The cluster operator amplitudes are solved, taking the complete- active-space self-consistent-¯eld function as the reference function. The differential relaxation effects are taken into account by diagonalizing the transformed Hamiltonian in the multireference configuration interaction singles (MRCIS) space. To implement the method, we developed an automatic program generator, the details of which are presented. The strategy used in approximating residual equations in SS-EOMCC is based on a novel normal order theory, which is a generalization of traditional particle-hole formalism based normal order theory. We discuss normal order theory in a general context, start with the version developed by Mukherjee and Kutzelnigg, and we furnish an algebraic proof for the corresponding contraction rules. Then we proceed to show how our normal order theory works. Finally we present the benchmark results to gauge the SS-EOMCC method. We calculate the triplet state state of F₂ to examine the behavior of the method for single reference systems, and study the singlet states of H₂O, CO and N₂ to test its performance for multireference systems. In addition, we illustrate the e®ect of a perturbative correction, which attempts to alleviate the redundancy issue. We also apply the method to study the energetics of end-on and side-on peroxide coordination in ligated Cu₂O₂ models, where SS-EOMCC[+2] employing a small active space achieves quite accurate results. The final diagonalization of the transformed Hamiltonian in the MRCIS space is expensive and limits the applicability of the method. We attempt to develop a cheaper internally contracted multireference coupled cluster method by introducing semi-internal excitation operators in the cluster operator such that the final diagonalization can be confined within the active space, but the results are not satisfactory yet. The Jeziorski-Monkhorst (JM) ansatz has been studied extensively, and different ways to resolve the redundancy issue have been explored. We analyze these JM-ansatz based methods, derive them in a simple way to disclose their connections transparently, and point out some problem in these methods. Another issue of general interest which is examined in the thesis is orbital invariance. For single reference methods the invariance property is usually clear, but this is not always the case for multireference methods. We analyze this problem from the tensor theory point of view, and propose a practical self-consistency-checking algorithm to determine whether a method is orbital invariant or not. We apply the algorithm to different methods, in particular, demonstrating the lack of the invariance property for JM-ansatz based methods.

Made available in DSpace on 2016-04-25T20:21:42Z (GMT). No. of bitstreams: 1 TESE.pdf: 1275513 bytes, checksum: efe1a57c9a0faef939be17adff136be1 (MD5) Previous issue date: 2005-04-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The paradigm of the modernity has determined a new format in the social organization. The basic institutions began a long race to accompany the deep changes that influenced the humanity, and among them the Catholic Church, which was directly reached by the phenomenon of the secularism. The Catholic Church needed to review the posture of estrangement to the world to get enchant it again. The decline of the Brazilian Catholicism, verified from the census of 1940, became the Catholicism as an object of countless studies for the social sciences and kindred areas. Cândido Procópio Ferreira de Camargo made himself remarkable in that singular subject when presented a typology of Catholics from differentiated faces: traditional and internalized. Camargo's researches expresses the constitution of two individuals that live together, although in antagonistic positions, in the same Brazilian Catholic space. The present investigation has located in the Roman Apostolic Catholic Church in Brazil, in the attempt of answering to the reflexes of the modernity, above all in the combat to the secularism and the process characterized by Weber as disenchanting of the world ", which has oscillated between proximity practices and estrangement of the own " world ". The answers have generated ambiguous positions inside of the own hierarchy determining social and subjective directions that express two differentiated types of subjects. In this singular point, it was explored the concept of individual-in-constitution, considering that the people have been moved by the desire of life look for new forms of composing its self-image and, by means of identification with social practices that are capable of rescue them in its dignity. Hereby they project its lives in the continuous construction of a new social space in order to live well and happy. A citizenship in construction which is resulting of new collective individuals and, because of the identification of common social projects, has assumed the condition of temporary and in each new challenge may constituted as new social individuals moved by the desire which is "meaning of life ". To bring it up themes as the modernity, secularism, high modernity, subjectivity, individual-in-constitution and citizenship, it was prepared a structure of research that, while being focus on the Catholic Church in Brazil, define itself in the time and consider the ambiguities among the decades of 40 and 70. Starting from this historical period, we thought about us as high modernity in the process of self- reflection capable to notice the continuity of the paradoxical directions inside the Catholic Church, by means of the study in two ways of organization of the action of the Church: (CEBs) Base Ecclesiastic Community and the (MRCC) Movement of Catholic Charismatic Renewal . Both of them expresses the composition of two types of individuals characterized by a political participation returned to outside (social) and another for a mystic participation (subjective). The ideological discussion among the two social and subjective directions inside the Brazilian Catholic Church comparing, analyzing and discussing these two organization forms, and the intention of verify the individuals that emerge from them, and to what extent they go away or they are attracted as necessary and complementary, are the main objective of the present study. By means of the bibliographical and of the empiric researches , the investigation accomplished in CEBs and MRCC presents itself as necessary for the understanding of the Catholic Church in its current phase, becoming important for the social sciences. / O paradigma da modernidade determinou um novo formato na organização social. As instituições básicas iniciaram uma longa corrida para acompanhar as profundas mudanças que marcaram a humanidade, entre essas instituições, a Igreja Católica, diretamente atingida pelo fenômeno do secularismo, precisou rever a postura de distanciamento do mundo para conseguir novamente reencantá-lo. O declínio do catolicismo brasileiro, constatado desde o censo de 1940, fez com que ele fosse objeto de inúmeros estudos pelas ciências sociais e áreas afins. Notabilizou-se nesse singular Candido Procópio Ferreira de Camargo que apresentou uma tipologia de católicos de faces diferenciadas: tradicional e internalizada. As pesquisas de Camargo expressam a constituição de dois sujeitos que convivem, embora em posições antagônicas, no mesmo espaço católico brasileiro. A presente investigação situa-se nesta particularidade: a Igreja Católica Apostólica Romana no Brasil, na tentativa de responder aos reflexos da modernidade, sobretudo no combate ao secularismo e ao processo caracterizado por Weber como desencantamento do mundo , oscilou entre práticas de proximidade e distanciamento do próprio mundo . As respostas geraram posições ambíguas dentro da própria hierarquia determinando direções sociais e subjetivas que expressam dois tipos diferenciados de sujeitos. Neste singular, exploramos o conceito de sujeito-em-constituição, considerando que as pessoas, movidas pelo desejo de vida, buscam novas formas de compor a sua auto-imagem e, por meio da identificação com práticas sociais que são capazes de resgatá-las em sua dignidade, projetam as suas vidas na construção contínua de um novo espaço social para nele viver bem e ser feliz. Uma cidadania-em-construção é resultante de novos sujeitos coletivos os quais, pela identificação de projetos sociais comuns, assumem a condição de sujeitos provisórios para que em cada novo desafio, movidos pelo desejo elã da vida , se constituam como novos sujeitos sociais. Trazer a baila temas como modernidade, secularismo, alta modernidade, subjetividade, sujeito-em-constituição e cidadania, prepara o arcabouço da pesquisa que, ao ser focada sobre a Igreja Católica no Brasil, delimita-se no tempo, retomando as suas ambigüidades entre as décadas de 40 a 70. A partir deste recorte histórico, nos pensamos como alta modernidade no processo de auto reflexão capaz de perceber a continuidade das direções paradoxais no interior da Igreja católica, por meio do estudo de duas formas de organização da ação da Igreja: as Comunidades Eclesiais de Base (CEBs) e o Movimento de Renovação Carismática Católica (MRCC). Ambos expressam a composição de dois tipos de sujeitos caracterizados um por uma participação política voltada para fora (social) e o outro por uma participação mística (subjetiva). O embate ideológico entre duas direções sociais e subjetivas no interior da Igreja Católica brasileira comparando, analisando e discutindo estas duas formas de organização, procurando verificar os sujeitos que delas emergem e até que ponto distanciam-se ou se atraem como necessários e complementares, é o objeto do presente estudo. Por meio da pesquisa bibliográfica e da pesquisa empírica, a investigação realizada nas CEBs e MRCC descortina-se como necessária para a compreensão da Igreja Católica no Brasil em sua atual fase, sendo assim relevante para as ciências sociais.

Made available in DSpace on 2016-04-26T14:56:04Z (GMT). No. of bitstreams: 1 TESE.pdf: 1275513 bytes, checksum: efe1a57c9a0faef939be17adff136be1 (MD5) Previous issue date: 2005-04-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The paradigm of the modernity has determined a new format in the social organization. The basic institutions began a long race to accompany the deep changes that influenced the humanity, and among them the Catholic Church, which was directly reached by the phenomenon of the secularism. The Catholic Church needed to review the posture of estrangement to the world to get enchant it again. The decline of the Brazilian Catholicism, verified from the census of 1940, became the Catholicism as an object of countless studies for the social sciences and kindred areas. Cândido Procópio Ferreira de Camargo made himself remarkable in that singular subject when presented a typology of Catholics from differentiated faces: traditional and internalized. Camargo's researches expresses the constitution of two individuals that live together, although in antagonistic positions, in the same Brazilian Catholic space. The present investigation has located in the Roman Apostolic Catholic Church in Brazil, in the attempt of answering to the reflexes of the modernity, above all in the combat to the secularism and the process characterized by Weber as disenchanting of the world ", which has oscillated between proximity practices and estrangement of the own " world ". The answers have generated ambiguous positions inside of the own hierarchy determining social and subjective directions that express two differentiated types of subjects. In this singular point, it was explored the concept of individual-in-constitution, considering that the people have been moved by the desire of life look for new forms of composing its self-image and, by means of identification with social practices that are capable of rescue them in its dignity. Hereby they project its lives in the continuous construction of a new social space in order to live well and happy. A citizenship in construction which is resulting of new collective individuals and, because of the identification of common social projects, has assumed the condition of temporary and in each new challenge may constituted as new social individuals moved by the desire which is "meaning of life ". To bring it up themes as the modernity, secularism, high modernity, subjectivity, individual-in-constitution and citizenship, it was prepared a structure of research that, while being focus on the Catholic Church in Brazil, define itself in the time and consider the ambiguities among the decades of 40 and 70. Starting from this historical period, we thought about us as high modernity in the process of self- reflection capable to notice the continuity of the paradoxical directions inside the Catholic Church, by means of the study in two ways of organization of the action of the Church: (CEBs) Base Ecclesiastic Community and the (MRCC) Movement of Catholic Charismatic Renewal . Both of them expresses the composition of two types of individuals characterized by a political participation returned to outside (social) and another for a mystic participation (subjective). The ideological discussion among the two social and subjective directions inside the Brazilian Catholic Church comparing, analyzing and discussing these two organization forms, and the intention of verify the individuals that emerge from them, and to what extent they go away or they are attracted as necessary and complementary, are the main objective of the present study. By means of the bibliographical and of the empiric researches , the investigation accomplished in CEBs and MRCC presents itself as necessary for the understanding of the Catholic Church in its current phase, becoming important for the social sciences. / O paradigma da modernidade determinou um novo formato na organização social. As instituições básicas iniciaram uma longa corrida para acompanhar as profundas mudanças que marcaram a humanidade, entre essas instituições, a Igreja Católica, diretamente atingida pelo fenômeno do secularismo, precisou rever a postura de distanciamento do mundo para conseguir novamente reencantá-lo. O declínio do catolicismo brasileiro, constatado desde o censo de 1940, fez com que ele fosse objeto de inúmeros estudos pelas ciências sociais e áreas afins. Notabilizou-se nesse singular Candido Procópio Ferreira de Camargo que apresentou uma tipologia de católicos de faces diferenciadas: tradicional e internalizada. As pesquisas de Camargo expressam a constituição de dois sujeitos que convivem, embora em posições antagônicas, no mesmo espaço católico brasileiro. A presente investigação situa-se nesta particularidade: a Igreja Católica Apostólica Romana no Brasil, na tentativa de responder aos reflexos da modernidade, sobretudo no combate ao secularismo e ao processo caracterizado por Weber como desencantamento do mundo , oscilou entre práticas de proximidade e distanciamento do próprio mundo . As respostas geraram posições ambíguas dentro da própria hierarquia determinando direções sociais e subjetivas que expressam dois tipos diferenciados de sujeitos. Neste singular, exploramos o conceito de sujeito-em-constituição, considerando que as pessoas, movidas pelo desejo de vida, buscam novas formas de compor a sua auto-imagem e, por meio da identificação com práticas sociais que são capazes de resgatá-las em sua dignidade, projetam as suas vidas na construção contínua de um novo espaço social para nele viver bem e ser feliz. Uma cidadania-em-construção é resultante de novos sujeitos coletivos os quais, pela identificação de projetos sociais comuns, assumem a condição de sujeitos provisórios para que em cada novo desafio, movidos pelo desejo elã da vida , se constituam como novos sujeitos sociais. Trazer a baila temas como modernidade, secularismo, alta modernidade, subjetividade, sujeito-em-constituição e cidadania, prepara o arcabouço da pesquisa que, ao ser focada sobre a Igreja Católica no Brasil, delimita-se no tempo, retomando as suas ambigüidades entre as décadas de 40 a 70. A partir deste recorte histórico, nos pensamos como alta modernidade no processo de auto reflexão capaz de perceber a continuidade das direções paradoxais no interior da Igreja católica, por meio do estudo de duas formas de organização da ação da Igreja: as Comunidades Eclesiais de Base (CEBs) e o Movimento de Renovação Carismática Católica (MRCC). Ambos expressam a composição de dois tipos de sujeitos caracterizados um por uma participação política voltada para fora (social) e o outro por uma participação mística (subjetiva). O embate ideológico entre duas direções sociais e subjetivas no interior da Igreja Católica brasileira comparando, analisando e discutindo estas duas formas de organização, procurando verificar os sujeitos que delas emergem e até que ponto distanciam-se ou se atraem como necessários e complementares, é o objeto do presente estudo. Por meio da pesquisa bibliográfica e da pesquisa empírica, a investigação realizada nas CEBs e MRCC descortina-se como necessária para a compreensão da Igreja Católica no Brasil em sua atual fase, sendo assim relevante para as ciências sociais.

Multireference coupled cluster (MRCC) methods are a highly accurate approach for sys- tems with quasi-degeneracies, where the static correlation plays an important role. How- ever, while canonical MRCC is successful for many systems, it can be used only for small sized systems. Nonetheless, it was shown that large systems can be described by the domain-based local pair natural orbital approach (DLPNO). In our group, we developed DLPNO-MkCCSD, DLPNO-TCCSD and DLPNO-MkCCSD(T) methods, which were able to recover more than 99.7% of the canonical correlation energy, while the computation of systems with more than 2000 basis functions took only a few hours on a single CPU core. Moreover, we also implemented a tailored variant of MRCC which successfully described excited states of cyclobutadiene, while the traditional MRCC under-performed.