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.

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.

Digital elevation model error in terrain analysis

Digital elevation models (DEMs) have been an important topic in geography and surveying sciences for decades due to their geomorphological importance as the reference surface for gravita-tion-driven material flow, as well as the wide range of uses and applications. When DEM is used in terrain analysis, for example in automatic drainage basin delineation, errors of the model collect in the analysis results. Investigation of this phenomenon is known as error propagation analysis, which has a direct influence on the decision-making process based on interpretations and applications of terrain analysis. Additionally, it may have an indirect influence on data acquisition and the DEM generation. The focus of the thesis was on the fine toposcale DEMs, which are typically represented in a 5-50m grid and used in the application scale 1:10 000-1:50 000. The thesis presents a three-step framework for investigating error propagation in DEM-based terrain analysis. The framework includes methods for visualising the morphological gross errors of DEMs, exploring the statistical and spatial characteristics of the DEM error, making analytical and simulation-based error propagation analysis and interpreting the error propagation analysis results. The DEM error model was built using geostatistical methods. The results show that appropriate and exhaustive reporting of various aspects of fine toposcale DEM error is a complex task. This is due to the high number of outliers in the error distribution and morphological gross errors, which are detectable with presented visualisation methods. In ad-dition, the use of global characterisation of DEM error is a gross generalisation of reality due to the small extent of the areas in which the decision of stationarity is not violated. This was shown using exhaustive high-quality reference DEM based on airborne laser scanning and local semivariogram analysis. The error propagation analysis revealed that, as expected, an increase in the DEM vertical error will increase the error in surface derivatives. However, contrary to expectations, the spatial au-tocorrelation of the model appears to have varying effects on the error propagation analysis depend-ing on the application. The use of a spatially uncorrelated DEM error model has been considered as a 'worst-case scenario', but this opinion is now challenged because none of the DEM derivatives investigated in the study had maximum variation with spatially uncorrelated random error. Sig-nificant performance improvement was achieved in simulation-based error propagation analysis by applying process convolution in generating realisations of the DEM error model. In addition, typology of uncertainty in drainage basin delineations is presented.

Modeling Asymmetries in Financial Data with Multiplicative Error Models

This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

Preoperative visual acuity of cataract patients. Repeatability of visual acuity and refractive error measurements in clinical settings

Visual acuities at the time of referral and on the day before surgery were compared in 124 patients operated on for cataract in Vaasa Central Hospital, Finland. Preoperative visual acuity and the occurrence of ocular and general disease were compared in samples of consecutive cataract extractions performed in 1982, 1985, 1990, 1995 and 2000 in two hospitals in the Vaasa region in Finland. The repeatability and standard deviation of random measurement error in visual acuity and refractive error determination in a clinical environment in cataractous, pseudophakic and healthy eyes were estimated by re-examining visual acuity and refractive error of patients referred to cataract surgery or consultation by ophthalmic professionals. Altogether 99 eyes of 99 persons (41 cataractous, 36 pseudophakic and 22 healthy eyes) with a visual acuity range of Snellen 0.3 to 1.3 (0.52 to -0.11 logMAR) were examined. During an average waiting time of 13 months, visual acuity in the study eye decreased from 0.68 logMAR to 0.96 logMAR (from 0.2 to 0.1 in Snellen decimal values). The average decrease in vision was 0.27 logMAR per year. In the fastest quartile, visual acuity change per year was 0.75 logMAR, and in the second fastest 0.29 logMAR, the third and fourth quartiles were virtually unaffected. From 1982 to 2000, the incidence of cataract surgery increased from 1.0 to 7.2 operations per 1000 inhabitants per year in the Vaasa region. The average preoperative visual acuity in the operated eye increased by 0.85 logMAR (in decimal values from 0.03to 0.2) and in the better eye 0.27 logMAR (in decimal values from 0.23 to 0.43) over this period. The proportion of patients profoundly visually handicapped (VA in the better eye <0.1) before the operation fell from 15% to 4%, and that of patients less profoundly visually handicapped (VA in the better eye 0.1 to <0.3) from 47% to 15%. The repeatability visual acuity measurement estimated as a coefficient of repeatability for all 99 eyes was ±0.18 logMAR, and the standard deviation of measurement error was 0.06 logMAR. Eyes with the lowest visual acuity (0.3-0.45) had the largest variability, the coefficient of repeatability values being ±0.24 logMAR and eyes with a visual acuity of 0.7 or better had the smallest, ±0.12 logMAR. The repeatability of refractive error measurement was studied in the same patient material as the repeatability of visual acuity. Differences between measurements 1 and 2 were calculated as three-dimensional vector values and spherical equivalents and expressed by coefficients of repeatability. Coefficients of repeatability for all eyes for vertical, torsional and horisontal vectors were ±0.74D, ±0.34D and ±0.93D, respectively, and for spherical equivalent for all eyes ±0.74D. Eyes with lower visual acuity (0.3-0.45) had larger variability in vector and spherical equivalent values (±1.14), but the difference between visual acuity groups was not statistically significant. The difference in the mean defocus equivalent between measurements 1 and 2 was, however, significantly greater in the lower visual acuity group. If a change of ±0.5D (measured in defocus equivalents) is accepted as a basis for change of spectacles for eyes with good vision, the basis for eyes in the visual acuity range of 0.3 - 0.65 would be ±1D. Differences in repeated visual acuity measurements are partly explained by errors in refractive error measurements.

Improving GPS time series for geodynamic studies

Accurate and stable time series of geodetic parameters can be used to help in understanding the dynamic Earth and its response to global change. The Global Positioning System, GPS, has proven to be invaluable in modern geodynamic studies. In Fennoscandia the first GPS networks were set up in 1993. These networks form the basis of the national reference frames in the area, but they also provide long and important time series for crustal deformation studies. These time series can be used, for example, to better constrain the ice history of the last ice age and the Earth s structure, via existing glacial isostatic adjustment models. To improve the accuracy and stability of the GPS time series, the possible nuisance parameters and error sources need to be minimized. We have analysed GPS time series to study two phenomena. First, we study the refraction in the neutral atmosphere of the GPS signal, and, second, we study the surface loading of the crust by environmental factors, namely the non-tidal Baltic Sea, atmospheric load and varying continental water reservoirs. We studied the atmospheric effects on the GPS time series by comparing the standard method to slant delays derived from a regional numerical weather model. We have presented a method for correcting the atmospheric delays at the observational level. The results show that both standard atmosphere modelling and the atmospheric delays derived from a numerical weather model by ray-tracing provide a stable solution. The advantage of the latter is that the number of unknowns used in the computation decreases and thus, the computation may become faster and more robust. The computation can also be done with any processing software that allows the atmospheric correction to be turned off. The crustal deformation due to loading was computed by convolving Green s functions with surface load data, that is to say, global hydrology models, global numerical weather models and a local model for the Baltic Sea. The result was that the loading factors can be seen in the GPS coordinate time series. Reducing the computed deformation from the vertical time series of GPS coordinates reduces the scatter of the time series; however, the long term trends are not influenced. We show that global hydrology models and the local sea surface can explain up to 30% of the GPS time series variation. On the other hand atmospheric loading admittance in the GPS time series is low, and different hydrological surface load models could not be validated in the present study. In order to be used for GPS corrections in the future, both atmospheric loading and hydrological models need further analysis and improvements.

Monte Carlo Simulations of Molecular Clusters in Nucleation

A better understanding of the limiting step in a first order phase transition, the nucleation process, is of major importance to a variety of scientific fields ranging from atmospheric sciences to nanotechnology and even to cosmology. This is due to the fact that in most phase transitions the new phase is separated from the mother phase by a free energy barrier. This barrier is crossed in a process called nucleation. Nowadays it is considered that a significant fraction of all atmospheric particles is produced by vapor-to liquid nucleation. In atmospheric sciences, as well as in other scientific fields, the theoretical treatment of nucleation is mostly based on a theory known as the Classical Nucleation Theory. However, the Classical Nucleation Theory is known to have only a limited success in predicting the rate at which vapor-to-liquid nucleation takes place at given conditions. This thesis studies the unary homogeneous vapor-to-liquid nucleation from a statistical mechanics viewpoint. We apply Monte Carlo simulations of molecular clusters to calculate the free energy barrier separating the vapor and liquid phases and compare our results against the laboratory measurements and Classical Nucleation Theory predictions. According to our results, the work of adding a monomer to a cluster in equilibrium vapour is accurately described by the liquid drop model applied by the Classical Nucleation Theory, once the clusters are larger than some threshold size. The threshold cluster sizes contain only a few or some tens of molecules depending on the interaction potential and temperature. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range, as predicted by the McGraw-Laaksonen scaling law. By calculating correction factors to Classical Nucleation Theory predictions for the nucleation barriers of argon and water, we show that the corrected predictions produce nucleation rates that are in good comparison with experiments. For the smallest clusters, the deviation between the simulation results and the liquid drop values are accurately modelled by the low order virial coefficients at modest temperatures and vapour densities, or in other words, in the validity range of the non-interacting cluster theory by Frenkel, Band and Bilj. Our results do not indicate a need for a size dependent replacement free energy correction. The results also indicate that Classical Nucleation Theory predicts the size of the critical cluster correctly. We also presents a new method for the calculation of the equilibrium vapour density, surface tension size dependence and planar surface tension directly from cluster simulations. We also show how the size dependence of the cluster surface tension in equimolar surface is a function of virial coefficients, a result confirmed by our cluster simulations.

Quantum Space-Time and Noncommutative Gauge Field Theories

Arguments arising from quantum mechanics and gravitation theory as well as from string theory, indicate that the description of space-time as a continuous manifold is not adequate at very short distances. An important candidate for the description of space-time at such scales is provided by noncommutative space-time where the coordinates are promoted to noncommuting operators. Thus, the study of quantum field theory in noncommutative space-time provides an interesting interface where ordinary field theoretic tools can be used to study the properties of quantum spacetime. The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.

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.

Applications of dimensional reduction to electroweak and QCD matter

When heated to high temperatures, the behavior of matter changes dramatically. The standard model fields go through phase transitions, where the strongly interacting quarks and gluons are liberated from their confinement to hadrons, and the Higgs field condensate melts, restoring the electroweak symmetry. The theoretical framework for describing matter at these extreme conditions is thermal field theory, combining relativistic field theory and quantum statistical mechanics. For static observables the physics is simplified at very high temperatures, and an effective three-dimensional theory can be used instead of the full four-dimensional one via a method called dimensional reduction. In this thesis dimensional reduction is applied to two distinct problems, the pressure of electroweak theory and the screening masses of mesonic operators in quantum chromodynamics (QCD). The introductory part contains a brief review of finite-temperature field theory, dimensional reduction and the central results, while the details of the computations are contained in the original research papers. The electroweak pressure is shown to converge well to a value slightly below the ideal gas result, whereas the pressure of the full standard model is dominated by the QCD pressure with worse convergence properties. For the mesonic screening masses a small positive perturbative correction is found, and the interpretation of dimensional reduction on the fermionic sector is discussed.