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Over the past few decades, single-molecule magnets (SMMs) have been an area of significant interest due to their plethora of potential uses, including possible applications to quantum computing and compact data storage devices. Although theoretical chemistry calculations could aid our understanding of the magnetic couplings present in these types of systems, they are often multiconfigurational in nature, making them difficult to model with tradi- tional single-reference approaches. Methods to handle these types of strongly correlated systems have been developed but often have significant drawbacks, and so these molecules remain difficult to model computationally. In this work, we discuss the application of Fock-space CI approaches to large transition metal complexes. First, we introduce a novel formalism which combines the spin-flip (SF), ioniza- tion potential (IP), and electron affinity (EA) approaches. This redox spin-flip approach, the restricted active space spin-flip and ionization potential/electron affinity (RAS-SF-IP/EA) method, is applied to several molecules exhibiting double exchange behavior. Model Hamil- tonian parameters are extracted from energy gaps and found to be in qualitative agreement with experiment. Having shown the efficacy of this approach, we move on to optimization, using a diagrammatic approach to derive equations for several RAS-1SF-IP/EA schemes. These equations allow direct construction of the most expensive intermediates in the David- son algorithm and should provide significant speedup, allowing application of Fock-space CI approaches to larger systems than ever before. The derived equations are implemented in the LibRASSF package in Q-Chem, as well as in an open-source PyFockCI code, avail- able on GitHub. A Bloch effective Hamiltonian formalism is also utilized to extract model Hamiltonian parameters from RAS-1SF calculations, allowing more nuanced studies of the Heisenberg J couplings present in many molecules with magnetically coupled sites. Over- all, our work with Fock-space CI provides a way to study magnetic couplings in very large strongly correlated systems at relatively low computational cost. This work was supported by a grant from the U.S. Department of Energy: DE-SC0018326. / Doctor of Philosophy / Humans have been familiar with magnets for thousands of years, and we have found a variety of useful applications for them. Magnets are used in everything from navigational devices to credit cards to data storage. Most people are familiar with large, solid magnets, but in the 1990s, it was discovered that individual molecules, called single-molecule magnets (SMMs), could also exhibit magnetic behavior. This means that in the presence of some external magnetic field, like the field caused by the presence of another magnet, the electrons in a SMM will align themselves with the field, and the electrons will maintain that alignment for some period of time after the field is removed. These SMMs have been a significant area of interest to scientists because they have a variety of interesting applications, including applications to quantum computing. In cases such as these, theoretical chemistry can offer useful insight. Broadly, the purpose of theoretical chemistry is to describe chemical problems using mathematical equations. We can use computational models to obtain information about the behavior of electrons in a particular system (the so-called electronic structure) and consequently, we can model the magnetic couplings in a given molecule. However, SMMs are difficult to model using tra- ditional theoretical methods because they often contain multiple orbitals which have nearly the same energy. In these cases, it often becomes ambiguous which orbitals ought to be oc- cupied by electrons; the effect this has on the energy is called "strong correlation". Ideally, one ought to consider all possible fillings of the orbitals, but most methods do not account for this and assume only one configuration is important when solving for the shapes of the orbitals. In this work, we combine two previously-introduced approaches, the spin-flip (SF) and ioniza- tion potential/electron affinity (IP/EA) approaches, to handle strongly correlated systems. In the SF-IP/EA approach, one adds or removes electrons and flips their spins in order to remove all of the ambiguity in orbital occupations. Once we determine the shapes of the or- bitals for this unambiguous state, the electrons are added, removed, or spin-flipped in order to obtain the desired strongly correlated state. We then solve for the energy of the system while considering all possible configurations within the set of ambiguously-occupied orbitals, allowing us to treat them on equal footing. We also study the effect of adding additional configurations to account for contributions from other orbitals, which provides more accu- rate results, albeit at a higher computational cost. Our method is less expensive than many other wavefunction-based methods used for these systems, and it yields qualitatively correct results, allowing theoreticians to study magnetic couplings in SMMs in a straightforward and inexpensive way. We also discuss optimization of our code, as well as an extension of our code that allows us to obtain coupling information for systems containing multiple magnetic sites. It is our hope that these developments will provide useful insights into the electronic structure of these SMM systems.

Made available in DSpace on 2016-06-02T20:16:43Z (GMT). No. of bitstreams: 1 2389.pdf: 676894 bytes, checksum: 7c529b06a0e41de3d113cccbae2281c9 (MD5) Previous issue date: 2009-02-18 / Universidade Federal de Sao Carlos / In the Quantum Optics area, the construction of effective hamiltonian is a matter of great importance, since from them we can generate and manipulate quantum states and logical operations. In this work we discuss 3 approximate methods for obtaining such effective hamiltonians: i) adiabatic elimination, ii) method of effective dynamics for oscillating hamiltonians and iii) nonlinear small rotations. Here we analyze the regime of validity of these techniques, their disadvantages and advantages. We note that, although adiabatic elimination is the most used and known, it has inconsistencies and can provide incorrect effective hamiltonians. The method of effective dynamics, although a very simple technique, also has inconsistencies and is not applicable to dissipative systems. Moreover, the method of nonlinear small rotations, which appears as the most accurate, is rarely used in the literature. / Em Óptica Quântica a construção de hamiltonianos efetivos é um assunto de suma importância, visto que a partir deles podemos manipular e gerar estados quânticos e operações lógicas. Nesta dissertação discutimos 3 métodos aproximativos para a obtenção de hamiltonianos efetivos: i) a eliminação adiabática, ii) o métodos de dinâmicas efetivas para hamiltonianos oscilantes e iii) o método de pequenas rotações não-lineares, de forma a analisar o regime de validade destas técnicas, desvantagens e vantagens. Notamos que, embora a eliminação adiabática seja a mais utilizada e divulgada, apresenta inconsistências e prevê hamiltonianos efetivos incorretos. O método de dinâmicas efetivas, embora seja uma técnica simples e muito operacional, também apresenta inconsistência e não se aplica a sistemas dissipativos. Por outro lado, o método de pequenas rotações não-lineares, que aparece como o mais preciso, é muito pouco utilizado na literatura.