Computer modeling of enzymes is a valuable complement to experiments. Quantum chemical studies of enzymatic reactions can provide a detailed description of the reaction mechanism and elucidate the roles of various residues in the active site. Different reaction pathways can be analyzed, and their feasibility be established based on calculated energy barriers. In the present thesis, density functional theory has been used to study the active sites and reaction mechanisms of three different enzymes, cytosine deaminase (CDA) from Escherichia coli, ω-transaminase from Chromobacterium violaceum (Cv-ωTA) and dinitrogenase reductase-activating glycohydrolase (DraG) from Rhodospirillum rubrum. The cluster approach has been employed to design models of the active sites based on available crystal structures. The geometries and energies of transition states and intermediates along various reaction pathways have been calculated, and used to construct the energy graphs of the reactions. In the study of CDA (Paper I), two different tautomers of a histidine residue were considered. The obtained reaction mechanism was found to support the main features of the previously proposed mechanism. The sequence of the events was established, and the residues needed for the proton transfer steps were elucidated. In the study of Cv-ωTA (Paper II and Paper III), two active site models were employed to study the conversion of two different substrates, a hydrophobic amine and an amino acid. Differences and similarities in the reaction mechanisms of the two substrates were established, and the role of an arginine residue in the dual substrate recognition was confirmed. In the study of DraG (Paper IV), two different substrate-binding modes and two different protonation states of an aspartate residue were considered. The coordination of the first-shell ligands and the substrate to the two manganese ions in the active site was characterized, and a possible proton donor in the first step of the proposed reaction mechanism was identified. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.</p>

The Quantum chemical cluster approach has been shown to be quite powerful and efficient in the modeling of enzyme active sites and reaction mechanisms. In this thesis, the reaction mechanisms of several enzymes have been investigated using the hybrid density functional B3LYP. The enzymes studied include four dinuclear zinc enzymes, namely dihydroorotase, N-acyl-homoserine lactone hydrolase, RNase Z, and human renal dipeptidase, two trinuclear zinc enzymes, namely phospholipase C and nuclease P1, two tungstoenzymes, namely formaldehyde ferredoxin oxidoreductase and acetylene hydratase, aspartate α-decarboxylase, and mycolic acid cyclopropane synthase. The potential energy profiles for various mechanistic scenarios have been calculated and analyzed. The role of the metal ions as well as important active site residues has been discussed.   In the cluster approach, the effects of the parts of the enzyme that are not explicitly included in the model are taken into account using implicit solvation methods.   For all six zinc-dependent enzymes studied, the di-zinc bridging hydroxide has been shown to be capable of performing nucleophilic attack on the substrate. In addition, one, two, or even all three zinc ions participate in the stabilization of the negative charge in the transition states and intermediates, thereby lowering the barriers.   For the two tungstoenzymes, several different mechanistic scenarios have been considered to identify the energetically most feasible one. For both enzymes, new mechanisms are proposed.   Finally, the mechanism of mycolic acid cyclopropane synthase has been shown to be a direct methyl transfer to the substrate double bond, followed by proton transfer to the bicarbonate.   From the studies of these enzymes, we demonstrate that density functional calculations are able to solve mechanistic problems related to enzymatic reactions, and a wealth of new insight can be obtained.

In this thesis, quantum cluster methods are used to calculate electronic properties of correlated-electron systems. A special focus lies in the determination of the ground state properties of a 3/4 filled triangular lattice within the one-band Hubbard model. At this filling, the electronic density of states exhibits a so-called van Hove singularity and the Fermi surface becomes perfectly nested, causing an instability towards a variety of spin-density-wave (SDW) and superconducting states. While chiral d+id-wave superconductivity has been proposed as the ground state in the weak coupling limit, the situation towards strong interactions is unclear. Additionally, quantum cluster methods are used here to investigate the interplay of Coulomb interactions and symmetry-breaking mechanisms within the nematic phase of iron-pnictide superconductors. The transition from a tetragonal to an orthorhombic phase is accompanied by a significant change in electronic properties, while long-range magnetic order is not established yet. The driving force of this transition may not only be phonons but also magnetic or orbital fluctuations. The signatures of these scenarios are studied with quantum cluster methods to identify the most important effects. Here, cluster perturbation theory (CPT) and its variational extention, the variational cluster approach (VCA) are used to treat the respective systems on a level beyond mean-field theory. Short-range correlations are incorporated numerically exactly by exact diagonalization (ED). In the VCA, long-range interactions are included by variational optimization of a fictitious symmetry-breaking field based on a self-energy functional approach. Due to limitations of ED, cluster sizes are limited to a small number of degrees of freedom. For the 3/4 filled triangular lattice, the VCA is performed for different cluster symmetries. A strong symmetry dependence and finite-size effects make a comparison of the results from different clusters difficult. The ground state in the weak-coupling limit is superconducting with chiral d+id-wave symmetry, in accordance to previous renormalization group approaches. In the regime of strong interactions SDW states are preferred over superconductivity and a collinaer SDW state with nonuniform spin moments on a quadrupled unit cell has the lowest grand potential. At strong coupling, inclusion of short-range quantum fluctuations turns out to favor this collinear state over the chiral phase predicted by mean-field theory. At intermediate interactions, no robust conclusion can be drawn from the results. Symmetry-breaking mechanisms within the nematic phase of the iron-pnictides are studied using a three-band model for the iron planes on a 4-site cluster. CPT allows a local breaking of the symmetry within the cluster without imposing long-range magnetic order. This is a crucial step beyond mean-field approaches to the magnetically ordered state, where such a nematic phase cannot easily be investigated. Three mechanisms are included to break the fourfold lattice symmetry down to a twofold symmetry. The effects of anisotropic magnetic couplings are compared to an orbital ordering field and anisotropic hoppings. All three mechanisms lead to similar features in the spectral density. Since the anisotropy of the hopping parameters has to be very large to obtain similar results as observed in ARPES, a phonon-driven transition is unlikely.

In this thesis, quantum cluster methods are used to calculate electronic properties of correlated-electron systems. A special focus lies in the determination of the ground state properties of a 3/4 filled triangular lattice within the one-band Hubbard model. At this filling, the electronic density of states exhibits a so-called van Hove singularity and the Fermi surface becomes perfectly nested, causing an instability towards a variety of spin-density-wave (SDW) and superconducting states. While chiral d+id-wave superconductivity has been proposed as the ground state in the weak coupling limit, the situation towards strong interactions is unclear. Additionally, quantum cluster methods are used here to investigate the interplay of Coulomb interactions and symmetry-breaking mechanisms within the nematic phase of iron-pnictide superconductors. The transition from a tetragonal to an orthorhombic phase is accompanied by a significant change in electronic properties, while long-range magnetic order is not established yet. The driving force of this transition may not only be phonons but also magnetic or orbital fluctuations. The signatures of these scenarios are studied with quantum cluster methods to identify the most important effects. Here, cluster perturbation theory (CPT) and its variational extention, the variational cluster approach (VCA) are used to treat the respective systems on a level beyond mean-field theory. Short-range correlations are incorporated numerically exactly by exact diagonalization (ED). In the VCA, long-range interactions are included by variational optimization of a fictitious symmetry-breaking field based on a self-energy functional approach. Due to limitations of ED, cluster sizes are limited to a small number of degrees of freedom. For the 3/4 filled triangular lattice, the VCA is performed for different cluster symmetries. A strong symmetry dependence and finite-size effects make a comparison of the results from different clusters difficult. The ground state in the weak-coupling limit is superconducting with chiral d+id-wave symmetry, in accordance to previous renormalization group approaches. In the regime of strong interactions SDW states are preferred over superconductivity and a collinaer SDW state with nonuniform spin moments on a quadrupled unit cell has the lowest grand potential. At strong coupling, inclusion of short-range quantum fluctuations turns out to favor this collinear state over the chiral phase predicted by mean-field theory. At intermediate interactions, no robust conclusion can be drawn from the results. Symmetry-breaking mechanisms within the nematic phase of the iron-pnictides are studied using a three-band model for the iron planes on a 4-site cluster. CPT allows a local breaking of the symmetry within the cluster without imposing long-range magnetic order. This is a crucial step beyond mean-field approaches to the magnetically ordered state, where such a nematic phase cannot easily be investigated. Three mechanisms are included to break the fourfold lattice symmetry down to a twofold symmetry. The effects of anisotropic magnetic couplings are compared to an orbital ordering field and anisotropic hoppings. All three mechanisms lead to similar features in the spectral density. Since the anisotropy of the hopping parameters has to be very large to obtain similar results as observed in ARPES, a phonon-driven transition is unlikely.