A quantum chemical investigation of the metal centres in cytochrome c oxidase

Quantum effects are often of key importance for the function of biological systems at molecular level. Cellular respiration, where energy is extracted from the reduction of molecular oxygen to water, is no exception. In this work, the end station of the electron transport chain in mitochondria, cytochrome c oxidase, is investigated using quantum chemical methodology. Cytochrome c oxidase contains two haems, haem a and haem a3. Haem a3, with its copper companion, CuB, is involved in the final reduction of oxygen into water. This binuclear centre receives the necessary electrons from haem a. Haem a, in turn, receives its electrons from a copper ion pair in the vicinity, called CuA. Density functional theory (DFT) has been used to clarify the charge and spin distributions of haem a, as well as changes in these during redox activity. Upon reduction, the added electron is shown to be evenly distributed over the entire haem structure, important for the accommodation of the prosthetic group within the protein. At the same time, the spin distribution of the open-shell oxidised state is more localised to the central iron. The exact spin density distribution has been disputed in the literature, however, different experiments indicating different distributions of the unpaired electron. The apparent contradiction is shown to be due to the false assumption of a unit amount of unpaired electron density; in fact, the oxidised state has about 1.3 unpaired electrons. The validity of the DFT results have been corroborated by wave function based coupled cluster calculations. Point charges, for use in classical force field based simulations, have been parameterised for the four metal centres, using a newly developed methodology. In the procedure, the subsystem for which point charges are to be obtained, is surrounded by an outer region, with the purpose of stabilising the inner region, both electronically and structurally. Finally, the possibility of vibrational promotion of the electron transfer step between haem a and a3 has been investigated. Calculating the full vibrational spectra, at DFT level, of a combined model of the two haems, revealed several normal modes that do shift electron density between the haems. The magnitude of the shift was found to be moderate, at most. The proposed mechanism could have an assisting role in the electron transfer, which still seems to be dominated by electron tunnelling.

Quantum Chemical Studies on Tropospheric Nucleation Mechanisms Involving Sulfuric Acid

Nucleation is the first step of the process by which gas molecules in the atmosphere condense to form liquid or solid particles. Despite the importance of atmospheric new-particle formation for both climate and health-related issues, little information exists on its precise molecular-level mechanisms. In this thesis, potential nucleation mechanisms involving sulfuric acid together with either water and ammonia or reactive biogenic molecules are studied using quantum chemical methods. Quantum chemistry calculations are based on the numerical solution of Schrödinger's equation for a system of atoms and electrons subject to various sets of approximations, the precise details of which give rise to a large number of model chemistries. A comparison of several different model chemistries indicates that the computational method must be chosen with care if accurate results for sulfuric acid - water - ammonia clusters are desired. Specifically, binding energies are incorrectly predicted by some popular density functionals, and vibrational anharmonicity must be accounted for if quantitatively reliable formation free energies are desired. The calculations reported in this thesis show that a combination of different high-level energy corrections and advanced thermochemical analysis can quantitatively replicate experimental results concerning the hydration of sulfuric acid. The role of ammonia in sulfuric acid - water nucleation was revealed by a series of calculations on molecular clusters of increasing size with respect to all three co-ordinates; sulfuric acid, water and ammonia. As indicated by experimental measurements, ammonia significantly assists the growth of clusters in the sulfuric acid - co-ordinate. The calculations presented in this thesis predict that in atmospheric conditions, this effect becomes important as the number of acid molecules increases from two to three. On the other hand, small molecular clusters are unlikely to contain more than one ammonia molecule per sulfuric acid. This implies that the average NH3:H2SO4 mole ratio of small molecular clusters in atmospheric conditions is likely to be between 1:3 and 1:1. Calculations on charged clusters confirm the experimental result that the HSO4- ion is much more strongly hydrated than neutral sulfuric acid. Preliminary calculations on HSO4- NH3 clusters indicate that ammonia is likely to play at most a minor role in ion-induced nucleation in the sulfuric acid - water system. Calculations of thermodynamic and kinetic parameters for the reaction of stabilized Criegee Intermediates with sulfuric acid demonstrate that quantum chemistry is a powerful tool for investigating chemically complicated nucleation mechanisms. The calculations indicate that if the biogenic Criegee Intermediates have sufficiently long lifetimes in atmospheric conditions, the studied reaction may be an important source of nucleation precursors.

Quantum Chemical Studies of Intermolecular Interactions

This thesis studies the intermolecular interactions in (i) boron-nitrogen based systems for hydrogen splitting and storage, (ii) endohedral complexes, A@C60, and (iii) aurophilic dimers. We first present an introduction of intermolecular interactions. The theoretical background is then described. The research results are summarized in the following sections. In the boron-nitrogen systems, the electrostatic interaction is found to be the leading contribution, as 'Coulomb Pays for Heitler and London' (CHL). For the endohedral complex, the intermolecular interaction is formulated by a one-center expansion of the Coulomb operator 1/rab. For the aurophilic attraction between two C2v monomers, a London-type formula was derived by fully accounting for the anisotropy and point-group symmetry of the monomers.

Studies of new inorganic species using relativistic quantum chemistry

In the present work the methods of relativistic quantum chemistry have been applied to a number of small systems containing heavy elements, for which relativistic effects are important. First, a thorough introduction of the methods used is presented. This includes some of the general methods of computational chemistry and a special section dealing with how to include the effects of relativity in quantum chemical calculations. Second, after this introduction the results obtained are presented. Investigations on high-valent mercury compounds are presented and new ways to synthesise such compounds are proposed. The methods described were applied to certain systems containing short Pt-Tl contacts. It was possible to explain the interesting bonding situation in these compounds. One of the most common actinide compounds, uranium hexafluoride was investigated and a new picture of the bonding was presented. Furthermore the rareness of uranium-cyanide compounds was discussed. In a foray into the chemistry of gold, well known for its strong relativistic effects, investigations on different gold systems were performed. Analogies between Au$^+$ and platinum on one hand and oxygen on the other were found. New systems with multiple bonds to gold were proposed to experimentalists. One of the proposed systems was spectroscopically observed shortly afterwards. A very interesting molecule, which was theoretically predicted a few years ago is WAu$_{12}$. Some of its properties were calculated and the bonding situation was discussed. In a further study on gold compounds it was possible to explain the substitution pattern in bis[phosphane-gold(I)] thiocyanate complexes. This is of some help to experimentalists as the systems could not be crystallised and the structure was therefore unknown. Finally, computations on one of the heaviest elements in the periodic table were performed. Calculation on compounds containing element 110, darmstadtium, showed that it behaves similarly as its lighter homologue platinum. The extreme importance of relativistic effects for these systems was also shown.

Computational Studies on Bimetallic Clusters

The chemical and physical properties of bimetallic clusters have attracted considerable attention due to the potential technological applications of mixed-metal systems. It is of fundamental interests to study clusters because they are the link between atomic surface and bulk properties. More information of metal-metal bond in small clusters can be hence released. The studies in my thesis mainly focus on the two different kinds of bimetallic clusters: the clusters consisting of extraordinary shaped all metal four-membered rings and a series of sodium auride clusters. As described in most general organic chemistry books nowadays, a group of compounds are classified as aromatic compounds because of their remarkable stabilities, particular geometrical and energetic properties and so on. The notation of aromaticity is essentially qualitative. More recently, the connection has been made between aromaticity and energetic and magnetic properties. Also, the discussions of the aromatic nature of molecular rings are no longer limited to organic compounds obeying the Hückel’s rule. In our research, we mainly applied the GIMIC method to several bimetallic clusters at the CCSD level, and compared the results with those obtained by using chemical shift based methods. The magnetically induced ring currents can be generated easily by employing GIMIC method, and the nature of aromaticity for each system can be therefore clarified. We performed intensive quantum chemical calculations to explore the characters of the anionic sodium auride clusters and the corresponding neutral clusters since it has been fascinating in investigating molecules with gold atom involved due to its distinctive physical and chemical properties. As small gold clusters, the sodium auride clusters seem to form planar structures. With the addition of a negative charge, the gold atom in anionic clusters prefers to carry the charge and orients itself away from other gold atoms. As a result, the energetically lowest isomer for an anionic cluster is distinguished from the one for the corresponding neutral cluster. Mostly importantly, we presented a comprehensive strategy of ab initio applications to computationally implement the experimental photoelectron spectra.

A New Rare-Gas Compound: HXeOXeH

Rare-gas chemistry is of growing interest, and the recent advances include the "insertion" of a Xe atom into OH and water in the rare-gas hydrides HXeO and HXeOH. The insertion of Xe atoms into the H-C bonds of hydrocarbons was also demonstrated for HXeCC, HXeCCH and HXeCCXeH, the last of which was the first rare-gas hydride containing two rare-gas atoms. We describe the preparation and characterization of a new rare-gas compound, HXeOXeH. HXeOXeH was prepared in solid xenon by photolysis of a suitable precursor, for example water, and subsequent mobilization of the photoproducts. The experimental identification was carried out by FTIR spectroscopy, isotopic substitution and by use of various precursors. The photolytical and thermal stability of the new rare-gas hydride was also studied. The experimental work was supported by extensive quantum chemical calculations provided by our co-workers. HXeOXeH forms in a cryogenic xenon matrix from neutral O and H atoms in a two-step diffusion-controlled process involving HXeO as an intermediate [reactions (1) and (2)]. This formation mechanism is unique in that a rare-gas hydride is formed from another rare-gas hydride. H + Xe + O → HXeO (1) HXeO + Xe + H → HXeOXeH (2) Similarly to other rare-gas hydrides, HXeOXeH has a strongly IR-active H-Xe stretching vibration, allowing its spectral detection at 1379.3 cm-1. HXeOXeH is a very high-energy metastable species, yet thermally more stable than many other rare-gas hydrides. The calculated bending barrier of 0.57 eV, is not enough to explain the observed stability, and HXeOXeH might be affected by additional stabilization from the solid xenon environment. Chemical bonding between xenon and environmentally abundant species like water is of particular importance due to the “missing-xenon” problem. The relatively high thermal stability of HXeOXeH compared to other oxygen containing rare-gas compounds is relevant in this respect. Our work also raises the possibility of polymeric (–Xe–O)n networks, similarly to the computationally studied (XeCC)n polymers.

Lewis Acid-Lewis Base Mediated Metal-Free Hydrogen Activation and Catalytic Hydrogenation

Organocatalysis, the use of organic molecules as catalysts, is attracting increasing attention as one of the most modern and rapidly growing areas of organic chemistry, with countless research groups in both academia and the pharmaceutical industry around the world working on this subject. The literature review of this thesis mainly focuses on metal-free systems for hydrogen activation and organocatalytic reduction. Since these research topics are relatively new, the literature review also highlights the basic principles of the use of Lewis acid-Lewis base pairs, which do not react irreversibly with each other, as a trap for small molecules. The experimental section progresses from the first observation of the facile heterolytical cleavage of hydrogen gas by amines and B(C6F5)3 to highly active non-metal catalysts for both enantioselective and racemic hydrogenation of unsaturated nitrogen-containing compounds. Moreover, detailed studies of structure-reactivity relationships of these systems by X-ray, neutron diffraction, NMR methods and quantum chemical calculations were performed to gain further insight into the mechanism of hydrogen activation and hydrogenation by boron-nitrogen compounds.

Magnetically induced currents and magnetic response properties of molecules

The magnetically induced currents in organic monoring and multiring molecules, in Möbius shaped molecules and in inorganic all-metal molecules have been investigated by means of the Gauge-including magnetically induced currents (GIMIC) method. With the GIMIC method, the ring-current strengths and the ring-current density distributions can be calculated. For open-shell molecules, also the spin current can be obtained. The ring-current pathways and ring-current strengths can be used to understand the magnetic resonance properties of the molecules, to indirectly identify the effect of non-bonded interactions on NMR chemical shifts, to design new molecules with tailored properties and to discuss molecular aromaticity. In the thesis, the magnetic criterion for aromaticity has been adopted. According to this, a molecule which has a net diatropic ring current might be aromatic. Similarly, a molecule which has a net paratropic current might be antiaromatic. If the net current is zero, the molecule is nonaromatic. The electronic structure of the investigated molecules has been resolved by quantum chemical methods. The magnetically induced currents have been calculated with the GIMIC method at the density-functional theory (DFT) level, as well as at the self-consistent field Hartree-Fock (SCF-HF), at the Møller-Plesset perturbation theory of the second order (MP2) and at the coupled-cluster singles and doubles (CCSD) levels of theory. For closed-shell molecules, accurate ring-current strengths can be obtained with a reasonable computational cost at the DFT level and with rather small basis sets. For open-shell molecules, it is shown that correlated methods such as MP2 and CCSD might be needed to obtain reliable charge and spin currents. The basis set convergence has to be checked for open-shell molecules by performing calculations with large enough basis sets. The results discussed in the thesis have been published in eight papers. In addition, some previously unpublished results on the ring currents in the endohedral fullerene Sc3C2@C80 and in coronene are presented. It is shown that dynamical effects should be taken into account when modelling magnetic resonance parameters of endohedral metallofullerenes such as Sc3C2@C80. The ring-current strengths in a series of nano-sized hydrocarbon rings are related to static polarizabilities and to H-1 nuclear magnetic resonance (NMR) shieldings. In a case study on the possible aromaticity of a Möbius-shaped [16]annulene we found that, according to the magnetic criterion, the molecule is nonaromatic. The applicability of the GIMIC method to assign the aromatic character of molecules was confirmed in a study on the ring currents in simple monocylic aromatic, homoaromatic, antiaromatic, and nonaromatic hydrocarbons. Case studies on nanorings, hexaphyrins and [n]cycloparaphenylenes show that explicit calculations are needed to unravel the ring-current delocalization pathways in complex multiring molecules. The open-shell implementation of GIMIC was applied in studies on the charge currents and the spin currents in single-ring and bi-ring molecules with open shells. The aromaticity predictions that are made based on the GIMIC results are compared to other aromaticity criteria such as H-1 NMR shieldings and shifts, electric polarizabilities, bond-length alternation, as well as to predictions provided by the traditional Hückel (4n+2) rule and its more recent extensions that account for Möbius twisted molecules and for molecules with open shells.

A computational study of Compton profiles of water - methanol solutions

The molecular level structure of mixtures of water and alcohols is very complicated and has been under intense research in the recent past. Both experimental and computational methods have been used in the studies. One method for studying the intra- and intermolecular bindings in the mixtures is the use of the so called difference Compton profiles, which are a way to obtain information about changes in the electron wave functions. In the process of Compton scattering a photon scatters inelastically from an electron. The Compton profile that is obtained from the electron wave functions is directly proportional to the probability of photon scattering at a given energy to a given solid angle. In this work we develop a method to compute Compton profiles numerically for mixtures of liquids. In order to obtain the electronic wave functions necessary to calculate the Compton profiles we need some statistical information about atomic coordinates. Acquiring this using ab-initio molecular dynamics is beyond our computational capabilities and therefore we use classical molecular dynamics to model the movement of atoms in the mixture. We discuss the validity of the chosen method in view of the results obtained from the simulations. There are some difficulties in using classical molecular dynamics for the quantum mechanical calculations, but these can possibly be overcome by parameter tuning. According to the calculations clear differences can be seen in the Compton profiles of different mixtures. This prediction needs to be tested in experiments in order to find out whether the approximations made are valid.

Parity violation in molecular magnetic resonance properties

The Standard Model of particle physics consists of the quantum electrodynamics (QED) and the weak and strong nuclear interactions. The QED is the basis for molecular properties, and thus it defines much of the world we see. The weak nuclear interaction is responsible for decays of nuclei, among other things, and in principle, it should also effects at the molecular scale. The strong nuclear interaction is hidden in interactions inside nuclei. From the high-energy and atomic experiments it is known that the weak interaction does not conserve parity. Consequently, the weak interaction and specifically the exchange of the Z^0 boson between a nucleon and an electron induces small energy shifts of different sign for mirror image molecules. This in turn will make the other enantiomer of a molecule energetically favorable than the other and also shifts the spectral lines of the mirror image pair of molecules into different directions creating a split. Parity violation (PV) in molecules, however, has not been observed. The topic of this thesis is how the weak interaction affects certain molecular magnetic properties, namely certain parameters of nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopies. The thesis consists of numerical estimates of NMR and ESR spectral parameters and investigations of the effects of different aspects of quantum chemical computations to them. PV contributions to the NMR shielding and spin-spin coupling constants are investigated from the computational point of view. All the aspects of quantum chemical electronic structure computations are found to be very important, which makes accurate computations challenging. Effects of molecular geometry are also investigated using a model system of polysilyene chains. PV contribution to the NMR shielding constant is found to saturate after the chain reaches a certain length, but the effects of local geometry can be large. Rigorous vibrational averaging is also performed for a relatively small and rigid molecule. Vibrational corrections to the PV contribution are found to be only a couple of per cents. PV contributions to the ESR g-tensor are also evaluated using a series of molecules. Unfortunately, all the estimates are below the experimental limits, but PV in some of the heavier molecules comes close to the present day experimental resolution.

Computational studies on new chemical species in the gas-phase and the solid-state.

There is intense activity in the area of theoretical chemistry of gold. It is now possible to predict new molecular species, and more recently, solids by combining relativistic methodology with isoelectronic thinking. In this thesis we predict a series of solid sheet-type crystals for Group-11 cyanides, MCN (M=Cu, Ag, Au), and Group-2 and 12 carbides MC2 (M=Be-Ba, Zn-Hg). The idea of sheets is then extended to nanostrips which can be bent to nanorings. The bending energies and deformation frequencies can be systematized by treating these molecules as an elastic bodies. In these species Au atoms act as an 'intermolecular glue'. Further suggested molecular species are the new uncongested aurocarbons, and the neutral Au_nHg_m clusters. Many of the suggested species are expected to be stabilized by aurophilic interactions. We also estimate the MP2 basis-set limit of the aurophilicity for the model compounds [ClAuPH_3]_2 and [P(AuPH_3)_4]^+. Beside investigating the size of the basis-set applied, our research confirms that the 19-VE TZVP+2f level, used a decade ago, already produced 74 % of the present aurophilic attraction energy for the [ClAuPH_3]_2 dimer. Likewise we verify the preferred C4v structure for the [P(AuPH_3)_4]^+ cation at the MP2 level. We also perform the first calculation on model aurophilic systems using the SCS-MP2 method and compare the results to high-accuracy CCSD(T) ones. The recently obtained high-resolution microwave spectra on MCN molecules (M=Cu, Ag, Au) provide an excellent testing ground for quantum chemistry. MP2 or CCSD(T) calculations, correlating all 19 valence electrons of Au and including BSSE and SO corrections, are able to give bond lengths to 0.6 pm, or better. Our calculated vibrational frequencies are expected to be better than the currently available experimental estimates. Qualitative evidence for multiple Au-C bonding in triatomic AuCN is also found.

Topological Quantum Computation - An Analysis of an Anyon Model Based on Quantum Double Symmetries

There exists various suggestions for building a functional and a fault-tolerant large-scale quantum computer. Topological quantum computation is a more exotic suggestion, which makes use of the properties of quasiparticles manifest only in certain two-dimensional systems. These so called anyons exhibit topological degrees of freedom, which, in principle, can be used to execute quantum computation with intrinsic fault-tolerance. This feature is the main incentive to study topological quantum computation. The objective of this thesis is to provide an accessible introduction to the theory. In this thesis one has considered the theory of anyons arising in two-dimensional quantum mechanical systems, which are described by gauge theories based on so called quantum double symmetries. The quasiparticles are shown to exhibit interactions and carry quantum numbers, which are both of topological nature. Particularly, it is found that the addition of the quantum numbers is not unique, but that the fusion of the quasiparticles is described by a non-trivial fusion algebra. It is discussed how this property can be used to encode quantum information in a manner which is intrinsically protected from decoherence and how one could, in principle, perform quantum computation by braiding the quasiparticles. As an example of the presented general discussion, the particle spectrum and the fusion algebra of an anyon model based on the gauge group S_3 are explicitly derived. The fusion algebra is found to branch into multiple proper subalgebras and the simplest one of them is chosen as a model for an illustrative demonstration. The different steps of a topological quantum computation are outlined and the computational power of the model is assessed. It turns out that the chosen model is not universal for quantum computation. However, because the objective was a demonstration of the theory with explicit calculations, none of the other more complicated fusion subalgebras were considered. Studying their applicability for quantum computation could be a topic of further research.

Simulations of dimensionally reduced effective theories of high temperature QCD

Quantum chromodynamics (QCD) is the theory describing interaction between quarks and gluons. At low temperatures, quarks are confined forming hadrons, e.g. protons and neutrons. However, at extremely high temperatures the hadrons break apart and the matter transforms into plasma of individual quarks and gluons. In this theses the quark gluon plasma (QGP) phase of QCD is studied using lattice techniques in the framework of dimensionally reduced effective theories EQCD and MQCD. Two quantities are in particular interest: the pressure (or grand potential) and the quark number susceptibility. At high temperatures the pressure admits a generalised coupling constant expansion, where some coefficients are non-perturbative. We determine the first such contribution of order g^6 by performing lattice simulations in MQCD. This requires high precision lattice calculations, which we perform with different number of colors N_c to obtain N_c-dependence on the coefficient. The quark number susceptibility is studied by performing lattice simulations in EQCD. We measure both flavor singlet (diagonal) and non-singlet (off-diagonal) quark number susceptibilities. The finite chemical potential results are optained using analytic continuation. The diagonal susceptibility approaches the perturbative result above 20T_c$, but below that temperature we observe significant deviations. The results agree well with 4d lattice data down to temperatures 2T_c.