This thesis describes the application of wave function-based and perturbative methods to extended systems, primarily semiconductors. In Chapter 1, I introduce the quantum chemistry problem along with current progress in the field. I then provide some requisite fundamental theory associated with the wave function-based methods and periodic boundary conditions. In Chapter 2, I describe the relationship between the traditional extended system GW method and the traditionally molecular coupled-cluster formalism through diagrammatic analysis. We find that the popular coupled cluster singles and doubles (CCSD) method contains most of the diagrams in GW theory and more, and the more accurate coupled cluster singles and doubles with perturbative triples (CCSD(T)) method contains all GW diagrams and more. Benchmarking on the GW100 test set indicates that CCSD and a number of its approximations are more accurate than GW theory. In Chapter 3, I evaluate the potential for using composite schemes to reduce the computational cost of the CCSD method. We use focal point and downfolding techniques for excited state results for the GW100 along with some sample solids. Using composite methods reduces the cost of CCSD by reducing the number of orbitals treated at a higher level of theory, which is very similar to the active space methods used in single- and multi-reference calculations. In Chapters 4 and 5, I describe how to best treat finite size effects for wave function-based methods, including the impact of including terms like the Madelung constant and which extrapolation form to use. After establishing this, we use the prescribed procedure to compare the equation-of-motion second-order M{\o}ller-Plesset (EOM-MP2) method to the MP2 method of Gr\"{u}neis and the GW method for a standard test set of 11 solid-state systems. We find that the MP2 method performs qualitatively and quantitatively poorly for extended systems, but EOM-MP2 and GW perform qualitatively well, with quantitative MAEs of 0.40 and 0.68eV, respectively relative to a zero-point corrected electronic band gap.

No description available.

This licentiate thesis deals with quantum chemistry methods for large systems. In particular, the thesis focuses on the efficient construction of the Coulomb and exchange matrices which are important parts of the Fock matrix in Hartree--Fock calculations.The methods described are also applicable in Kohn--Sham Density FunctionalTheory calculations, where the Coulomb and exchange matrices areparts of the Kohn--Sham matrix. Screening techniques for reducing the computational complexity of bot Coulomb and exchange computations are discussed, as well as the fast multipole method, used for efficient computation of the Coulomb matrix. The thesis also discusses how sparsity in the matrices occurring in Hartree--Fock and Kohn--Sham Density Functional Theory calculations can be used to achieve more efficient storage of matrices as well as more efficient operations on them. As an example of a possible type of application, the thesis includes a theoretical study of Heisenberg exchange constants, using unrestricted Kohn--Sham Density Functional Theory calculations. / QC 20101123

DNA provides the genetic code which is almost universal in all living organisms. When DNA is exposed to ultra-violet light it can cause cell degradation and mutation which are two of the major causes which lead to cancer. The nature of decay in DNA oligomers is a widely studied topic. Fluorescence and Transient Absorption (TA) experiments on polynucleotides which compare the behavior of the decay to the monomer bases have revealed the presence of longer-lived components in the multimeric systems. There has been heated debate over the character of the excited states responsible for the long-lived signals. Theoretical methods are well suited to compliment experiment by providing a description of processes and physical properties on the molecular level. We have studied π-stacked adenines in the gas-phase with Quantum Mechanical (QM) methods, but also in the helical environment using high-level ab initio methods, classical simulations and the combination of the two (QM/MM). Inclusion of the environmental interactions dramatically alters the shape of the potential energy surfaces due to steric interactions from the backbone and interactions with the surrounding bases and environment. This work examines the complete picture of photophysical processes occurring in adenine oligonucleotides within the helical environment after the absorption of a photon: the nature of initial absorption and the subsequent radiative and non-radiative decay pathways. It contributes key discoveries inherent to the mechanisms which govern photo-initiated processes in DNA, and also contributes to our fundamental knowledge of the photophysical behavior of π-stacked chromophores. The work reveals the effects of π-stacking interactions and the environment on photo-initiated processes in oligonucleotides. It reveals that excitonic coupling is responsible for the key differences in features in the absorption spectrum of adenine oligomers compared to the isolated bases, illustrates the role of charge transfer (CT) mixing in both absorption and decay processes, and the importance of bonded excimers in deactivation. The work also illustrates that CT excimers are responsible for the long-lived signals evidenced in Transient Absorption and Fluorescence experiments and that neutral excimers can exist within the DNA helical environment. It also adds to the discussion in the field on the nature of photodecay mechanisms occurring within the DNA helix. / Chemistry

In the Kane silicon-based electron-mediated nuclear spin quantum computer architecture, phosphorus is doped at precise positions in a silicon lattice, and the P donor nuclear spins act as qubits. Logical operations on the nuclear spins are performed using externally applied magnetic and electric fields. There are two important interactions: the hyperfine and exchange interactions, crucial for logical qubit operations. Single qubit operations are performed by applying radio frequency magnetic fields resonant with targeted nuclear spin transition frequencies, tuned by the gate-controlled hyperfine interaction. Two qubit operations are mediated through the exchange interaction between adjacent donor electrons. It is important to examine how these two interactions vary as functions of experimental parameters. Here we provide such an investigation. First, we examine the effects of varying several experimental parameters: gate voltage, magnetic field strength, inter donor separation, donor depth below the silicon oxide interface and back gate depth, to explore how these variables affect the donor electron density. Second, we calculate the hyperfine interaction and the exchange coupling as a function of these parameters. These calculations were performed using various levels of effective mass theory. In the first part of this thesis we use a multi-valley effective mass approach where we incorporate the full Si crystal Bloch structure in calculating the donor electron energy in the bulk silicon. Including the detailed Bloch structure is very computationally intensive, thus when we considered the effect of the externally applied fields in the second and third part, we employ an approach where we focus on the smooth donor-modulated envelope function to determine the response of the donor electron to the applied electric and magnetic fields and qubit position in the lattice. The electric field potential was obtained using Technology Computer Aided Design software, and the interfaces were modelled as a barrier using a step function. One of the critical results of this theoretical study was finding that there exist two regimes for the behaviour of the donor electron in response to the applied gate voltage, dependent on donor distance from the gate. When the qubit is in close proximity to the gate the electron transfer to the gate is gradual. However if the qubit is located far enough from the gate, we found that the donor electron is ionised toward the gate for gate voltages above a certain threshold. Another significant development we have made is in our calculations of the exchange coupling between two adjacent donor electrons. We extended our original Heitler-London basis to describe the two-electron system, and adopted a molecular orbital method where we included a a basis of 78 singlet and 66 triplet two-electron states. In addition to calculating a more accurate exchange coupling, we also evaluated the energy spectrum of the two electron double donor system. We aim to provide relevant information for the experimental design of these devices and highlight the significance of environmental factors other than gate potential that affect the donor electron.

Applications of computational quantum chemistry are presented, including an analysis of the photophysics of cyclic trinuclear coinage metal pyrazolates, an investigation into a potential catalytic cycle utilizing transition metal scorpionates to activate arene C-H bonds, and a presentation of the benchmarking of a new composite model chemistry (the correlation consistent composite approach, ccCA) for the prediction of classical barrier heights. Modeling the pyrazolate photophysics indicates a significant geometric distortion upon excitation and the impact of both metal identity and substituents on the pyrazolates, pointing to ways in which these systems may be used to produce rationally-tuned phosphors. Similarly, thermodynamic and structural investigations into the catalyst system points to promising candidates for clean catalytic activation of arenes. The ccCA was found to reproduce classical reaction barriers with chemical accuracy, outperforming all DFT, ab initio, and composite methods benchmarked.

The presence of charge transfer (CT) interactions is clear in a variety of systems. In CT, some electron density is shifted from one molecule to another (non-bonded) molecule. The importance of this CT interaction is unclear. Previous attempts to look at the conse- quences of CT required the use of ab initio molecular dynamics (AIMD), a computationally intensive method. Herein, a method for including CT in force field (FF) simulations is described. It is efficient, produces charges in agreement with AIMD, and prevents long- ranged CT. This CT MD method has been applied to monatomic ions in water. When solvated, ions do not have an integer charge. Anions give up some electron density to their ligands, and cations receive some electron density from their ligands. In bulk, the first solvation shell does not compensate for all CT, i.e. the charge is not smeared out over the first solvation shell. Rather, some charge is also found in the second solvation shell and further into the bulk. The charge of the first solvation shell depends on the balance between ion-water and water-water CT. When an interface is present, the charge outside of the second solvation shell will reside at the interface. This occurs even when the ion is over 15 Å away from the surface. The effect of long-ranged CT is mediated by changes in the hydrogen bonding patterns in water induced by the ions (not direct CT from the ions to distant waters). The model has also been applied to water’s ‘‘self-ions’’ hydronium and hydroxide. Trajectories from the multi-state empirical valence bond model (MS-EVB3) are analyzed. The differences between monatomic and molecular ions are explored. The direction of CT and the effect of hydrogen bonding with the ion are considered. The damping of CT as ligands are added is discussed and a method to improve the MD model, in order to account for damping, is proposed.

Neste trabalho, são utilizados diversos métodos de química teórica para estudar as propriedades eletrônicas e o espectro de absorção de seis corantes catiônicos: laranja de acridina (LA), proflavina (PF), safranina (SF), vermelho neutro (VN), azul de metileno (AM) e tionina (TN). Inicialmente é realizado um estudo para verificar a influência do solvente na geometria e no espectro desses corantes utilizando diversos métodos de química quântica, o método de solvatação contínuo IEFPCM e a simulação de Monte Carlo (MC). A seguir são estudados a diprotonação, a dimerização e alguns modelos para a argila do tipo montmorilonita e para a interação desta com os corantes, fenômenos esses que explicam a metacromasia observada experimentalmente. / This work presents a theoretical study on the electronic properties and the absorption spectra of six cationic dyes: acridine orange, proflavine, safranine, neutral red, methylene blue and thionine. First of all, we have carried out calculations to verify the solvent effects on geometries and spectra employing methods of Quantum Chemistry and including solvent effects with the polarizable continnum model and Monte Carlo (MC) simulation. Also, we have studied diprotonation, dimerization and some models of the montmorillonite clay and its interaction with the cationic dyes under study here, phenomena that explain the experimental methacromatic behavior of these dyes.

Neste trabalho, uma combinação de cálculos de mecânica quântica, simualções computacionais e teoria de perturbação termodinâmica, foi usada para estudar a solvatação do carbono de etileno (EC) e do carbonato de propileno (PC) em água. As estruturas do líquido foram geradas usando simulações com o método Monte Carlo e amostragem de Metropólis. A função de autocorrelação em energia foi usada para analisar a correlação estatística entre estas configurações. Após uma analise detalhada das ligações de hidrogênio, configurações supermoleculares descorrelacionadas ( carbonato + ligações de hidrogênio cercadas por 350 moléculas de água tratadas como cargas pontuais) foram amostradas das simulações e cálculos do momento de dipolo, no nível de cálculo MP2/ aug-cc-pvDZ, foram realizados. Em média foram formadas 1,4 ligações de hidrogênio entre a água e os solutos (EC ou PC). Foi obtido um momento de dipolo médio 9,9 ± 0,2 D para o EC-água e de 10,6 ± 0,2 D para o PC-água. Finalmente, simulações com o método de Monte Carlo no ensemble NPT e a técnica de perturbação de energia livre foram usados para determinar as energias livres de solvação, e os resultados foram Gsolv = -15,1 ± 0,8 Kcal/ mol para o EC em água e Gsolv = -15,3 ± 1,2 Kcal/mol para o PC em água. A análise destes resultados leva a conclusão de que o EC e o PC são igualmente estáveis em solução aquosa, ou seja, a metilação não tem efeito significativo na solvatação do PC e nem influência a formação das ligações de hidrogênio. / In this work, a combination of quantum mechanics, Monte Carlo simulations and thermodynamic perturbation theory was used to study the solvation of ethylene carbonate (EC) and propylene carbonate (PC) in water. The liquid structures was generated by NVT Monte Carlo simulation using standard procedures for the Metropolis sampling technique. The auto-correlation function of the energy was used to analyse the statistical correlation between the configurations (carbonates + hydrogen bonds sorrounded by 350 water molcules treated as point charges) were smpled from the simulations and dipole moment calculations, at the MP2/ aug-cc-pvDZ, were performed. On average, 1,4 hydrogen bonds were formed between water and the solutes (EC or PC). An average dipole momento of 9,9 ± 0,2 D was obtained for EC-water and 10,6 ± 0,2 D for PC-water. Finally, Monte Carlo simulations in the NPT ensemble combined with free energy pertubation technique were used to determine solvation free energies, and the results were Gsolv = -15,1 ± 0,8 kcal/mol for EC in water and Gsolv = -15,3 ± 1,2 kcal/mol for PC in water. The analysis of these results leads to the conclusion that EC and PC are equally stable in aqueous solution, i.e, the methylation hás no effect on the solvation of PC and no influence on the hydrogen bond formation.

O objetivo deste trabalho é estudar as reações de isomerização e cisão dos isômeros C2F2Cl2, e determinar entalpias de formação e potenciais de ionização para derivados halogenados do eteno, através de cálculos ab initio, e ainda, para algumas reações determinar a constante de velocidade microcanônica k(E*), segundo o formalismo da teoria RRKM. Foram obtidas a barreira energética e a estrutura do estado de transição para a reação de isomerização do (Z)-CFCl=CFCl ao isômero (E)-CFCl=CFCl, que ocorre através de um estado de transição com uma barreira de energia calculada de 54,223 kcal/mol com o método CASSCF. Foi analisada a possibilidade de a isomerização ocorrer via intermediários etilidenos halosubstituídos, porém as barreiras de energia para estas reações e resultados obtidos para a constante de velocidade k(E*) indicam que a reação direta predomina sobre as vias de formação de etilideno halosubstituído em baixas energias, até cerca de 154 kcal/mol pelo menos. A não observação, experimentalmente, de formação do isômero CF2=CCl2 a partir desses intermediários também corrobora com os resultados obtidos através dos cálculos. Para as reações de cisão de ligação C=C dos compostos CF2=CCl2, (Z) e (E)-CFCl=CFCl e CF2=CCl, as curvas de energia em função do comprimento desta ligação mostram que a cisão do CF2=CCl ocorre a uma energia menor do que para as demais substâncias. Porém, a cisão da ligação C-Cl na substância CF2=CCl2 é a que possui a menor barreira energética. Utilizando a teoria variacional do estado de transição, determinamos a estrutura do estado de transição para esta reação e a constante de velocidade microcanônica, k(E*), sendo esta maior que as determinadas para a formação dos etilidenos halosubstituídos. Potenciais de ionização adiabáticos (PIA) e verticais (PIV) de haloetenos foram obtidos utilizando as teorias G2 e G3. Os resultados obtidos com a teoria G3 são mais próximos dos valores experimentais, ou tão exatos quanto, comparados aos valores calculados encontrados na literatura. As mudanças na energia de correlação eletrônica e energia de relaxação dos orbitais são importantes para a obtenção de resultados de PIV quantitativamente melhores em comparação com os resultados obtidos a partir da energia do HOMO. Também foram feitos cálculos de entalpias de formação para etilenos halogenados utilizando as teorias G2 e G3 utilizando reações isodésmicas. A comparação entre os valores calculados por nós e outros valores calculados encontrados na literatura mostram que apesar das reações isodésmicas serem um método capaz de gerar bons resultados, devido ao cancelamento dos erros nos valores calculados, o resultado final é dependente dos valores experimentais escolhidos. / We report ab initio calculations on the isomerization and fission reactions of C2F2Cl2 isomers and also the enthalpies of formation and the ionization potentials of halogenated ethylenes. We have also evaluated the microcanonical rate constant k(E*) using the RRKM formalism to gain more insight into mechanistics details of some reactions. The energy barrier and the structure of the transition state for the isomerization reaction of (Z)-CFCl=CFCl to (E)-CFCl=CFCl, occurs by a transition state with a calculated barrier of 54,223 kcal/mol using the CASSCF method. The isomerization reactions through ethilidene halosubstituted intermediates was also tested, however the energy barriers to these reactions showed be greater and the results obtained for the rate constant k(E*) stated that the direct reaction predominates over the formation of the halosubstituted ethilidene at low energies, until 154 kcal/mol at least. The experimentaly unobserved formation of CF2=CCl2 from intermiaries confirms the calculated results. For the fission reaction of the C=C bond on CF2=CCl2, (Z) and (E)-CFCl=CFCl and CF2=CCl , the plots of energy as a function of the bond length show that the fission of CF2=CCl occurs with the lowest energy of all these reactions. However, the fission of C-Cl on the CF2=CCl2 shows to have the lowest energy barrier. By the variational transition state theory, we have determined the structure of the transition state for that reaction and the rate constant k(E*), beeing this higher than that determined to the halosubstituted ethylenes. Adiabatic ionization potentials (AIPs) and vertical ionization potentials (VIPs) for haloethylenes were obtained applying G2 and G3 theories. The results obtained with G3 theory are the nearest within the experimental values or, at least, with the same exactness, compared with other earlier calculated methods. The changes in eletronic correlation energy and orbital relax energy are important to achieve quantitatively better results comparativily with results obtained from HOMO energy. Moreover, we have done calculations of enthalpies of formation of haloethylenes using G2 and G3 theories using isodesmic reactions. The comparison among the values calculated by us and other values found in the literature shows that, however the use of isodesmic reactions may be a method able to achieve good results, because the calculated errors in the energy values are being cancelled , the final result is very dependent on the choosen experimental values.