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.

Spin and relativistic motion of bound states

The wave functions of moving bound states may be expected to contract in the direction of motion, in analogy to a rigid rod in classical special relativity, when the constituents are at equal (ordinary) time. Indeed, the Lorentz contraction of wave functions is often appealed to in qualitative discussions. However, only few field theory studies exist of equal-time wave functions in motion. In this thesis I use the Bethe-Salpeter formalism to study the wave function of a weakly bound state such as a hydrogen atom or positronium in a general frame. The wave function of the e^-e^+ component of positronium indeed turns out to Lorentz contract both in 1+1 and in 3+1 dimensional quantum electrodynamics, whereas the next-to-leading e^-e^+\gamma Fock component of the 3+1 dimensional theory deviates from classical contraction. The second topic of this thesis concerns single spin asymmetries measured in scattering on polarized bound states. Such spin asymmetries have so far mainly been analyzed using the twist expansion of perturbative QCD. I note that QCD vacuum effects may give rise to a helicity flip in the soft rescattering of the struck quark, and that this would cause a nonvanishing spin asymmetry in \ell p^\uparrow -> \ell' + \pi + X in the Bjorken limit. An analogous asymmetry may arise in p p^\uparrow -> \pi + X from Pomeron-Odderon interference, if the Odderon has a helicity-flip coupling. Finally, I study the possibility that the large single spin asymmetry observed in p p^\uparrow -> \pi(x_F,k_\perp) + X when the pion carries a high momentum fraction x_F of the polarized proton momentum arises from coherent effects involving the entire polarized bound state.

Structure of Relativistic States

QCD factorization in the Bjorken limit allows to separate the long-distance physics from the hard subprocess. At leading twist, only one parton in each hadron is coherent with the hard subprocess. Higher twist effects increase as one of the active partons carries most of the longitudinal momentum of the hadron, x -> 1. In the Drell-Yan process \pi N -> \mu^- mu^+ + X, the polarization of the virtual photon is observed to change to longitudinal when the photon carries x_F > 0.6 of the pion. I define and study the Berger-Brodsky limit of Q^2 -> \infty with Q^2(1-x) fixed. A new kind of factorization holds in the Drell-Yan process in this limit, in which both pion valence quarks are coherent with the hard subprocess, the virtual photon is longitudinal rather than transverse, and the cross section is proportional to a multiparton distribution. Generalized parton distributions contain information on the longitudinal momentum and transverse position densities of partons in a hadron. Transverse charge densities are Fourier transforms of the electromagnetic form factors. I discuss the application of these methods to the QED electron, studying the form factors, charge densities and spin distributions of the leading order |e\gamma> Fock state in impact parameter and longitudinal momentum space. I show how the transverse shape of any virtual photon induced process, \gamma^*(q)+i -> f, may be measured. Qualitative arguments concerning the size of such transitions have been previously made in the literature, but without a precise analysis. Properly defined, the amplitudes and the cross section in impact parameter space provide information on the transverse shape of the transition process.

Elliptic flow of thermal photons in heavy-ion collisions at Relativistic Heavy Ion Collider and Large Hadron Collider

We calculate the thermal photon transverse momentum spectra and elliptic flow in $\sqrt{s_{NN}} = 200$ GeV Au+Au collisions at RHIC and in $\sqrt{s_{NN}} = 2.76$ TeV Pb+Pb collisions at the LHC, using an ideal-hydrodynamical framework which is constrained by the measured hadron spectra at RHIC and LHC. The sensitivity of the results to the QCD-matter equation of state and to the photon emission rates is studied, and the photon $v_2$ is discussed in the light of the photonic $p_T$ spectrum measured by the PHENIX Collaboration. In particular, we make a prediction for the thermal photon $p_T$ spectra and elliptic flow for the current LHC Pb+Pb collisions.

Reconsidering Relativism and Intentionalism in Interpretation : Donald Davidson, Hermeneutics, and Pragmatism

This study focuses on two philosophical issues related to the interpretation of art. Firstly, it considers the role of authorial intentions in interpretation. Secondly, the study raises the issue of relativism in interpretation through a discussion of the relativistic tendencies apparent in the views of three major figures of contemporary philosophy: Joseph Margolis, Hans-Georg Gadamer, and Richard Rorty. The major goal of the thesis is to develop a theory of interpretation supporting the role of authorial intentions in interpretation on the basis of Donald Davidson s late philosophy of language and the holistic account of interpretation that underlies different parts of his philosophy. It is my belief that an intentionalist view of interpretation built on Davidsonian elements manages to form the most convincing defense of that interpretive position against the skepticism present in the views of Margolis, Gadamer, and Rorty. The theoretical issues addressed in the thesis are illuminated by discussions of case-examples, most importantly Richard Wagner s The Valkyrie, Thomas Adés America: A Prophecy, and some symphonies by Dimitri Shostakovich. In chapter one, I present a critical discussion of Margolis robust relativism. While finding Margolis criticism of the self-refutive argument plausible, I, nevertheless, argue that the relativistic logic Margolis offers should not be favored in interpretation. The first parts of chapter two outline Davidsonian intentionalism by presenting a reading of Davidson s later work in philosophy of language and mind, and by indicating its relationship to Davidson s views of literature. Then, I shall compare Davidson s ideas with some recent modest forms of intentionalism found in analytic aesthetics, and argue that Davidsonian intentionalism is in many respects more satisfactory compared to them. Chapter three engages Gadamer s hermeneutics by defending E.D. Hirsch s criticism of Gadamer. Uncovering the shortcomings in the replies of Gadamer s followers to Hirsch s criticism serves as a basis for the defense of intentionalism in interpretation carried out in the chapter. That defense is then extended with a discussion of some recent hermeneutic readings of Davidson s views. Chapter four deals with the standing of intentionalism through Rorty s pragmatist approach to literature. By indicating the position of pragmatist notions of aesthetic experience and imagination in Davidsonian intentionalism, it is shown that an intentionalist approach need not be as impoverished with regard to the value Rorty attributes to literature as he assumes. The concluding chapter outlines some ways in which one can be a pluralist with regard to art and interpretation without falling into relativism.

Uskonto ilman uskontoa : Radikaalin postmodernin uskonnonfilosofian haaste

Religion without religion. The challenge of radical postmodern philosophy of religion. The aim of this study is to examine the central ideas of Mark C. Taylor, Don Cupitt, and Grace Jantzen on the subject of the philosophy of religion. The method is a qualitative, systematic analysis of the works of the aforementioned philosophers. The purpose is to present, analyze, identify, find connections, and to gain an understanding of the original texts. This thesis shows that radical postmodern religion is “religion without religion”. God is “dead” and the concept of God is seen as “writing”, an ideal, a relationship of meanings or a language. In ethics, there are no objective values or principles. People must create their own morality. Reality is each person´s concept of reality. Language is universal in that language and reality cannot be considered separately. The human subject is contingent and formed in the linguistic and social context. According to postmodern feminism, the ideas that men present as facts are often degrading to women, distort reality and support the power of men. For this reason, we should create a new kind of philosophy of religion and a new language that takes women into consideration. Finally, we will study some philosophers, who have used postmodern ideas in a more moderate manner. In this way, we will look for a balanced solution between modernism and postmodernism. This study shows that the postmodern idea of religion is very different from classical Christianity. Ethics becomes subjective, anarchistic and nihilistic. Epistemology is relativistic and the human being becomes the measure of all things. Objective reality becomes blurry. Language is seen to be game-like, and it has no relation to reality. The moral responsibility of a subject becomes problematic. Science and rationality come into question without the permanent core provided by our consciousness. Women are not in an epistemologically privileged position. The truth claims by either men or women must each be evaluated one at a time. Many postmodern ideas can successfully be made of use if used in moderate manner.

Tieteellinen ajattelu yliopisto-opinnoissa : haastattelututkimus psykologian, teologian ja farmasian opiskelijoista

The aim of this dissertation is to explore the academic thinking and personal epistemology of university students. More specifically, the aim is to understand and promote students’ research and academic skills as a central goal of academic studies in the research-intensive university of Helsinki. Two of the four studies examine the personal epistemology of psychology students in different study phases, and the variation in personal epistemology among final-year psychology, theology and pharmacy students. Furthermore, personal epistemology was explored as a phenomenon among the student groups. In the fourth study the individual answers of the students interviewed are investigated in more detail. The main focus is on examining students’ beliefs about the nature of knowledge and knowledge acquisition as a representation of their personal epistemology. Study I presents a model which describes the main elements and aspects of teaching and learning in pharmacy education. Firstly, the meaning of quality of teaching and learning is explored. On the basis of this information, the study concentrates on the pedagogical implications of changing pharmacy teaching to improve the quality of learning. Study II describes the results of a cross-sectional study of psychology students participating in undergraduate and master’s level psychology programmes. The students (N = 53) were interviewed concerning their beliefs about knowledge and knowing, the aim being to explore students’ responses about thinking and reasoning. The results are analysed using content analysis to create categories of personal epistemology and comparisons among the students according to the phase of their studies. Study III examines interdisciplinary differences in final-year psychology, pharmacy and theology students’ (N = 52) academic thinking and personal epistemology. The aims of study IV are to examine and compare the consistency of personal epistemology profiles among university students (N = 87) representing three academic disciplines. The individual answers are examined and rated on a scale from absolutist to evaluativist thinking. On the basis of this data, three personal epistemology profiles are identified: a) absolutist profiles; b) relativistic profiles; and c) evaluativist profiles consisting of the subgroups entitled “limited” and “sophisticated”. The results of the studies clearly demonstrate that personal epistemology varies between students in different age groups, study phases, and disciplines. Three categories, including several subcategories, emerge to describe the personal epistemology of students. Furthermore, three personal epistemology profiles can be identified from the data. The comparison between students reveals interesting differences and similarities among student groups, and developmental trends of personal epistemology.

Noncommutative Gravitation as a Gauge Theory of Twisted Poincaré Symmetry

Gravitaation kvanttiteorian muotoilu on ollut teoreettisten fyysikkojen tavoitteena kvanttimekaniikan synnystä lähtien. Kvanttimekaniikan soveltaminen korkean energian ilmiöihin yleisen suhteellisuusteorian viitekehyksessä johtaa aika-avaruuden koordinaattien operatiiviseen ei-kommutoivuuteen. Ei-kommutoivia aika-avaruuden geometrioita tavataan myös avointen säikeiden säieteorioiden tietyillä matalan energian rajoilla. Ei-kommutoivan aika-avaruuden gravitaatioteoria voisi olla yhteensopiva kvanttimekaniikan kanssa ja se voisi mahdollistaa erittäin lyhyiden etäisyyksien ja korkeiden energioiden prosessien ei-lokaaliksi uskotun fysiikan kuvauksen, sekä tuottaa yleisen suhteellisuusteorian kanssa yhtenevän teorian pitkillä etäisyyksillä. Tässä työssä tarkastelen gravitaatiota Poincarén symmetrian mittakenttäteoriana ja pyrin yleistämään tämän näkemyksen ei-kommutoiviin aika-avaruuksiin. Ensin esittelen Poincarén symmetrian keskeisen roolin relativistisessa fysiikassa ja sen kuinka klassinen gravitaatioteoria johdetaan Poincarén symmetrian mittakenttäteoriana kommutoivassa aika-avaruudessa. Jatkan esittelemällä ei-kommutoivan aika-avaruuden ja kvanttikenttäteorian muotoilun ei-kommutoivassa aika-avaruudessa. Mittasymmetrioiden lokaalin luonteen vuoksi tarkastelen huolellisesti mittakenttäteorioiden muotoilua ei-kommutoivassa aika-avaruudessa. Erityistä huomiota kiinnitetään näiden teorioiden vääristyneeseen Poincarén symmetriaan, joka on ei-kommutoivan aika-avaruuden omaama uudentyyppinen kvanttisymmetria. Seuraavaksi tarkastelen ei-kommutoivan gravitaatioteorian muotoilun ongelmia ja niihin kirjallisuudessa esitettyjä ratkaisuehdotuksia. Selitän kuinka kaikissa tähänastisissa lähestymistavoissa epäonnistutaan muotoilla kovarianssi yleisten koordinaattimunnosten suhteen, joka on yleisen suhteellisuusteorian kulmakivi. Lopuksi tutkin mahdollisuutta yleistää vääristynyt Poincarén symmetria lokaaliksi mittasymmetriaksi --- gravitaation ei-kommutoivan mittakenttäteorian saavuttamisen toivossa. Osoitan, että tällaista yleistystä ei voida saavuttaa vääristämällä Poincarén symmetriaa kovariantilla twist-elementillä. Näin ollen ei-kommutoivan gravitaation ja vääristyneen Poincarén symmetrian tutkimuksessa tulee jatkossa keskittyä muihin lähestymistapoihin.

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.

Pappi ja Raamattu : Suomen evankelis-luterilaisen kirkon pappien suhde Raamattuun

The Pastor and the Bible: Finnish Evangelical Lutheran Pastors Relationship with the Bible Since 1970s there has been extensive discussion in Finland about questions relating to the interpretation of the Bible. The themes of this discussion have focused on the trustworthiness and authority of the Bible, and the discussion has attracted participation not only from representatives of the Evangelical Lutheran Church of Finland but also from representatives of the academic community. The discussion has resulted in extensive publication on the relation of postmodern theology to the Bible. Despite this debate and the texts that have been produced, there is little empirical data on how Evangelical Lutheran pastors with theological education view the Bible. In the present study, 22 pastors of the Evangelical Lutheran Church of Finland were interviewed about how they defined their relationship with the Bible. The interview material was analyzed by means of data-based content analysis. The analysis showed, first, that the pastors viewed the Bible as a mirror of the spiritual growth that they had experienced in the past. Second, the Bible was viewed as a source in the interpretation of matters of faith. The third theme concerned the pastors key experiences in their relationship with the authority of the Bible. The time periods that were significant in defining pastors spiritual growth and past perspective on the Bible included childhood, youth, the period of theological education, and the time spent as a pastor. In childhood, the Bible was part of the spiritual atmosphere of the home, and parents and grandparents made a crucial contribution to the child s emerging view of the Bible. In childhood, the Bible was essentially the Old Testament and its exciting stories. In youth, reading the Bible became more personal, and the teachings of Jesus began to take on a more central role. In youth, most of the interviewees had strong experiences of faith and began to view the Bible as an absolute and divine source of dogma. The period of theological studies meant a change in their relationship with the Bible and particularly, revelation of the human aspects of the Bible. These changes were associated with a deepening of belief in the Bible and also a painful crisis in questions related to the trustworthiness of the Bible. For many of the interviewees, their relationship with the Bible changed also when they started their work as pastors. When faced with a call to work as a pastor, the interviewees created a synthesis of the secure faith that they had experienced in their childhood and the more critical views with which they had become acquainted during their theological education. Pastorhood meant the beginning of public teaching of the Bible. The interviewees felt that, in this new role, they discovered again - but now in a deeper sense - the trustworthiness in the bible that they had experienced during their childhood. Based on the interviewees experiences during the periods mentioned above, five different interpretations were formed regarding how the interviewed pastors viewed their past relationship with the Bible. These interpretations were detachment from literal interpretation of the Bible (1), changes in their relationship with the Bible arising from experiences of faith (2), a slow process during which their relationship with the Bible became more human (3), overcoming hardships (4), and no change in their relationship with the Bible (5). In interpretations 1-3, the past was described as a linear development and journey towards a more coherent relationship with the Bible. Interpretations 4-5, in turn, reflected a desire to detach oneself from the perspectives of linear development and change and, instead, emphasize the immutable and process-like nature of one s relationship with the Bible. Concerning the Bible as a source in matters of faith, a conspicuous aspect of the interviews was that all pastors wanted to disconnect themselves from a fundamentalistic view of the Bible, regarding this as an intellectually dishonest relationship with the Bible. On the other hand, none of the interviewees supported a totally relativist view of the Bible. Instead, all interviewees regarded the Bible as a vital source for both them and the Evangelical Lutheran Church. Between the two poles of extremely fundamental and extremely relativistic views, four different categories of viewing the Bible emerged from the interviews: absolute truth (a), a book about the message of salvation (b), a book about holiness and generous love (c), and a source of inspiration (d). The views in categories (a) and (b) emphasized the divine nature of the Bible. According to the pastors who expressed these views, the Bible contains a clear and trustworthy message of God. The views in categories (c) and (d), in turn, emphasized the human aspects of the Bible. The pastors who expressed these views regarded the Bible as a collection of books that was born in a specific historical and cultural context and includes material characteristic to this time. Due to the time-bound nature of the Bible, each generation has to update its view of the Bible. The views in categories (c) and (d) arose from human reality. Comparisons of the views in the different categories indicated that despite their obvious differences, they also shared some common features. The views in categories (a) and (d) shared the common feature of absoluteness, which was seen in category (a) as an emphasis on dogmatism and in category (d) as an emphasis on rationalism. The views in categories (b) and (c), in turn, shared the common feature of a flexible and dynamic relationship with the Bible. The key experiences that appeared to characterize pastors relationship with the authority of the Bible were a joy that arises from self-evidence, awakening to confusion, fear of openness, falling back upon paradoxes, and new confidence. These experiences reveal the circular nature of the process that was common to all interviewees interpretation of their relationship with the Bible. That is, the interviewees experiences of their relationship with the Bible seem to go through a circular process that is activated again and again in new life events. It is like a journey from self-evidence towards critical questions and again back to new confidence. The interview material showed, hence, that relationship with the Bible are characterized by a process that involves experiences of trust, questioning and new trust. The present study brings out the multifaceted reality of pastors relationship with the Bible. The study breaks down contradictions between conservative and liberal views of the Bible by showing how representatives of these opposing poles share commonalities in their attitudes. The study points to a close association between an individual s life history and his or her relationship with the Bible, and lays the groundwork for future studies to investigate the relation between personality and view of the Bible.

Measuring the Cosmic Microwave Background : Topics along the analysis pipeline

The first quarter of the 20th century witnessed a rebirth of cosmology, study of our Universe, as a field of scientific research with testable theoretical predictions. The amount of available cosmological data grew slowly from a few galaxy redshift measurements, rotation curves and local light element abundances into the first detection of the cos- mic microwave background (CMB) in 1965. By the turn of the century the amount of data exploded incorporating fields of new, exciting cosmological observables such as lensing, Lyman alpha forests, type Ia supernovae, baryon acoustic oscillations and Sunyaev-Zeldovich regions to name a few. -- CMB, the ubiquitous afterglow of the Big Bang, carries with it a wealth of cosmological information. Unfortunately, that information, delicate intensity variations, turned out hard to extract from the overall temperature. Since the first detection, it took nearly 30 years before first evidence of fluctuations on the microwave background were presented. At present, high precision cosmology is solidly based on precise measurements of the CMB anisotropy making it possible to pinpoint cosmological parameters to one-in-a-hundred level precision. The progress has made it possible to build and test models of the Universe that differ in the way the cosmos evolved some fraction of the first second since the Big Bang. -- This thesis is concerned with the high precision CMB observations. It presents three selected topics along a CMB experiment analysis pipeline. Map-making and residual noise estimation are studied using an approach called destriping. The studied approximate methods are invaluable for the large datasets of any modern CMB experiment and will undoubtedly become even more so when the next generation of experiments reach the operational stage. -- We begin with a brief overview of cosmological observations and describe the general relativistic perturbation theory. Next we discuss the map-making problem of a CMB experiment and the characterization of residual noise present in the maps. In the end, the use of modern cosmological data is presented in the study of an extended cosmological model, the correlated isocurvature fluctuations. Current available data is shown to indicate that future experiments are certainly needed to provide more information on these extra degrees of freedom. Any solid evidence of the isocurvature modes would have a considerable impact due to their power in model selection.

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.

Dark solitons in holographic superfluids

We construct dark soliton solutions in a holographic model of a relativistic superfluid. We study the length scales associated with the condensate and the charge density depletion, and find that the two scales differ by a non-trivial function of the chemical potential. By adjusting the chemical potential, we study the variation of the depletion of charge density at the interface.

Hyperfine effects in the nuclear magnetic resonance of paramagnetic molecules

Paramagnetic, or open-shell, systems are often encountered in the context of metalloproteins, and they are also an essential part of molecular magnets. Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for chemical structure elucidation, but for paramagnetic molecules it is substantially more complicated than in the diamagnetic case. Before the present work, the theory of NMR of paramagnetic molecules was limited to spin-1/2 systems and it did not include relativistic corrections to the hyperfine effects. It also was not systematically expandable. --- The theory was first expanded by including hyperfine contributions up to the fourth power in the fine structure constant α. It was then reformulated and its scope widened to allow any spin state in any spatial symmetry. This involved including zero-field splitting effects. In both stages the theory was implemented into a separate analysis program. The different levels of theory were tested by demonstrative density functional calculations on molecules selected to showcase the relative strength of new NMR shielding terms. The theory was also tested in a joint experimental and computational effort to confirm assignment of 11 B signals. The new terms were found to be significant and comparable with the terms in the earlier levels of theory. The leading-order magnetic-field dependence of shielding in paramagnetic systems was formulated. The theory is now systematically expandable, allowing for higher-order field dependence and relativistic contributions. The prevailing experimental view of pseudocontact shift was found to be significantly incomplete, as it only includes specific geometric dependence, which is not present in most of the new terms introduced here. The computational uncertainty in density functional calculations of the Fermi contact hyperfine constant and zero-field splitting tensor sets a limit for quantitative prediction of paramagnetic shielding for now.