The efficient computation of dynamic (time-dependent) molecular properties is a broad field with numerous applications in aiding molecular synthesis and design, with a particular preva- lence in spectroscopic predictions. Typical methods for computing the response of a molecu- lar system to an electromagnetic field (EMF) considers a quantum mechanical description of the molecule and a classical approximation for the EMF. Methods for describing light-matter interactions with high-accuracy electronic structure methods, such as coupled cluster (CC), are discussed, with a focus on improving the efficiency of such methods. The CC method suffers from high-degree polynomial scaling. In addition to the ground-state calculation, computing dynamic properties requires the description of sensitive excited-state effects. The cost of such methods often prohibits the accurate calculation of response prop- erties for systems of significant importance, such as large-molecule drug candidates or chiral species present in biological systems. While the literature is ripe with reduced-scaling meth- ods for CC ground-state calculations, considerably fewer approaches have been applied to excited-state properties, with even fewer still providing adequate results for realistic systems. This work presents three studies on the reduction of the cost of molecular property evalu- ations, in the hopes of closing this gap in the literature and widening the scope of current theoretical methods. There are two main ways of simulating time-dependent light-matter interactions: one may consider these effects in the frequency domain, where the response of the system to an EMF is computed directly; or, the response may be considered explicitly in the time domain, where wave function (or density) parameters can be propagated in time and examined in detail. Each methodology has unique advantages and computational bottlenecks. The first two studies focus on frequency-domain calculations, and employ fragmentation and machine- learning techniques to reduce the cost of single-molecule calculations or sets of calculations across a series of geometric conformations. The third study presents a novel application of the local correlation technique to real-time CC calculations, and highlights deficiencies and possible solutions to the approach. / Doctor of Philosophy / Theoretical chemistry plays a key role in connecting experimental results with physical inter- pretation. Paramount to the success of theoretical methods is the ability to predict molecular properties without the need for costly high-throughput synthesis, aiding in the determina- tion of molecular structure and the design of new materials. Light-matter interactions, which govern spectroscopic techniques, are particularly complicated, and sensitive to the theoreti- cal tools employed in their prediction. Compounding the issue of accuracy is one of efficiency — accurate theoretical methods typically incur steep scaling of computational cost (memory and processor time) with respect to the size of the system. An important aspect in improving the efficiency of these methods is understanding the nature of light-matter interactions at a quantum level. Many unanswered questions still remain, such as, "Can light-matter interactions be thought of as a sum of interactions be- tween smaller fragments of the system?" and "Can conventional methods of accelerating ground-state calculations be expected to perform well for spectroscopic properties?" The present work seeks to answer these questions through three studies, focusing on improving the efficiency of these techniques, while simultaneously addressing their fundamental flaws and providing reasonable alternatives.

Most research on solving the N-electron Schrödinger equation has focused on ground states; excited states are comparatively less studied, and represent a greater challenge for many ab initio methods. The challenge is exacerbated for systems with substantial multiconfigurational character (i.e., strongly-correlated systems) for which standard many-electron wavefunction methods relying on a single electronic configuration give qualitatively incorrect descriptions of electron correlation. This thesis explores approaches to molecular excited state properties that are computationally efficient, yet applicable to multiconfigurational systems. Specifically, we explore strategies that combine the Equation-of-Motion (EOM) approach with the types of correlated wavefunction ansätze that are suitable for strongly-correlated systems. While it is known that the EOM method provides a general strategy for computing electronic transition energies, the significant flexibility in how one formulates the EOM approach and how it can be applied as a post-processing tool for different wavefunctions is not always appreciated. We begin by reviewing the EOM approach, focussing on methods that can be formulated using the 1- and 2-electron reduced density matrices. We assess the accuracy of different EOM approaches for neutral and ionic excited states. We focus on EOM-based alternatives to the traditional extended Koopams’ Theorem for ionization energies and electron affinities as well as an EOM formulation for double ionization transitions that constitutes an extension of the hole-hole/particle-particle random phase approximation (RPA) to multideterminant wavefunction methods. Then we introduce FanEOM, an EOM extension of the Flexible Ansatz for N-electron Configuration Interaction (FANCI) [Comput. Theor. Chem. 1202, 113187 (2021)], and explore its application to spectroscopic properties. Using the EOM methods for electronic excitation and double ionization/double electron affinity transitions described in the initial part of this thesis (i.e., the extended random phase approximations, ERPA), we study adiabatic connection formulations (AC) for computing the residual dynamic correlation energy in correlated wavefunction methods. The key idea in these approaches is that the perturbation strength dependent 2-RDM that appears in the AC formula can be approximated through the solutions from the different variants of ERPA [Phys. Rev. Lett. 120, 013001 (2018)]. Finally, we present PyEOM, an open-source software package designed to help prototype and test EOM-based methods. / Thesis / Doctor of Philosophy (PhD)

京都大学 / 新制・課程博士 / 博士(人間・環境学) / 甲第23975号 / 人博第1027号 / 新制||人||242(附属図書館) / 2022||人博||1027(吉田南総合図書館) / 京都大学大学院人間・環境学研究科相関環境学専攻 / (主査)教授 田部 勢津久, 教授 吉田 寿雄, 教授 中村 敏浩, 教授 田中 勝久 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DFAM

Wave function based electronic structure methods have became a robust and reliable tool for the prediction and interpretation of the results of chemical experiments. However, they suffer from very steep scaling behavior with respect to an increase in the size of the system as well as very slow convergence of the correlation energy with respect to the basis set size. Thus these methods are limited to small systems of up to a dozen atoms. The first of these issues can be efficiently resolved by exploiting the local nature of electron correlation effects while the second problem is alleviated by the use of explicitly correlated R12/F12 methods. Since R12/F12 methods are central to this work, we start by reviewing their modern formulation. Next, we present the explicitly correlated second-order Mo ller-Plesset (MP2-F12) method in which all nontrivial post-mean-field steps are formulated with linear computational complexity in system size [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 144}, 144109 (2016)]. The two key ideas are the use of pair-natural orbitals for compact representation of wave function amplitudes and the use of domain approximation to impose the block sparsity. This development utilizes the concepts for sparse representation of tensors described in the context of the DLPNO-MP2 method by Neese, Valeev and co-workers [Pinski et al., {em J. Chem. Phys.} {bf 143}, 034108 (2015)]. Novel developments reported here include the use of domains not only for the projected atomic orbitals, but also for the complementary auxiliary basis set (CABS) used to approximate the three- and four-electron integrals of the F12 theory, and a simplification of the standard B intermediate of the F12 theory that avoids computation of four-index two-electron integrals that involve two CABS indices. For quasi-1-dimensional systems (n-alkanes) the bigO{N} DLPNO-MP2-F12 method becomes less expensive than the conventional bigO{N^{5}} MP2-F12 for $n$ between 10 and 15, for double- and triple-zeta basis sets; for the largest alkane, C$_{200}$H$_{402}$, in def2-TZVP basis the observed computational complexity is $N^{sim1.6}$, largely due to the cubic cost of computing the mean-field operators. The method reproduces the canonical MP2-F12 energy with high precision: 99.9% of the canonical correlation energy is recovered with the default truncation parameters. Although its cost is significantly higher than that of DLPNO-MP2 method, the cost increase is compensated by the great reduction of the basis set error due to explicit correlation. We extend this formalism to develop a linear-scaling coupled-cluster singles and doubles with perturbative inclusion of triples and explicitly correlated geminals [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 146}, 174108 (2017)]. Even for conservative truncation levels, the method rapidly reaches near-linear complexity in realistic basis sets; e.g., an effective scaling exponent of 1.49 was obtained for n-alkanes with up to 200 carbon atoms in a def2-TZVP basis set. The robustness of the method is benchmarked against the massively parallel implementation of the conventional explicitly correlated coupled-cluster for a 20-water cluster; the total dissociation energy of the cluster ($sim$186 kcal/mol) is affected by the reduced-scaling approximations by only $sim$0.4 kcal/mol. The reduced-scaling explicitly correlated CCSD(T) method is used to examine the binding energies of several systems in the L7 benchmark data set of noncovalent interactions. Additionally, we discuss a massively parallel implementation of the Laplace transform perturbative triple correction (T) to the DF-CCSD energy within density fitting framework. This work is closely related to the work by Scuseria and co-workers [Constans et al., {em J. Chem. Phys.} {bf 113}, 10451 (2000)]. The accuracy of quadrature with respect to the number of quadrature points has been investigated on systems of the 18-water cluster, uracil dimer and pentacene dimer. In the case of the 18-water cluster, the $mu text{E}_{text{h}}$ accuracy is achieved with only 3 quadrature points. For the uracil dimer and pentacene dimer, 6 or more quadrature points are required to achieve $mu text{E}_{text{h}}$ accuracy; however, binding energy of $<$1 kcal/mol is obtained with 4 quadrature points. We observe an excellent strong scaling behavior on distributed-memory commodity cluster for the 18-water cluster. Furthermore, the Laplace transform formulation of (T) performs faster than the canonical (T) in the case of studied systems. The efficiency of the method has been furthermore tested on a DNA base-pair, a system with more than one thousand basis functions. Lastly, we discuss an explicitly correlated formalism for the second-order single-particle Green's function method (GF2-F12) that does not assume the popular diagonal approximation, and describes the energy dependence of the explicitly correlated terms [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 147}, 121101 (2017)]. For small and medium organic molecules the basis set errors of ionization potentials of GF2-F12 are radically improved relative to GF2: the performance of GF2-F12/aug-cc-pVDZ is better than that of GF2/aug-cc-pVQZ, at a significantly lower cost. / Ph. D. / Chemistry has traditionally been considered an experimental science; however, since the dawn of quantum mechanics, scientists have investigated the possibility of predicting the outcomes of chemical experiments via the use of mathematical models. All molecular properties are encoded in the motion of the electrons, which can be quantitatively described by the many-body Schrödinger equation. However, the Schrödinger equation is too complicated to be solved exactly for realistic molecular systems, and so we must rely on approximations. The most popular way to solve the Schrödinger equation when high accuracy is required are the coupled-cluster (CC) family of methods. These methods can provide unsurpassed accuracy; one particularly accurate and popular method is the coupled-cluster singles and doubles with perturbative inclusion of triples (CCSD(T)) method. The CCSD(T) method is known as the “gold standard” of quantum chemistry, and, when combined with a high quality basis set, it gives highly accurate predictions (that is, close to the experimental results) for a variety of chemical properties. However, this method has a very steep scaling behavior with a computational cost of N⁷ , where N is the measure of the system size. This means that if we double the size of the system, the computation time will increase by roughly two orders of magnitude. Another problem is that this method shows very slow convergence to the complete basis set (CBS) limit. Thus, in order to reduce the basis set error caused by the incompleteness of the basis set, more than 100 basis functions per atom should be used, limiting this method to small systems of up to a dozen atoms. These two issues can be efficiently resolved by exploiting the local nature of electron correlation effects (reduced-scaling techniques) and by using explicitly correlated R12/F12 methods. The main focus of this thesis is to bridge the gap between reduced-scaling techniques and the explicit correlation formalism and to allow highly accurate calculations on large molecular systems with several hundred of atoms. As our first contribution to this field, we present a linear-scaling formulation of the explicitly correlated second-order Møller-Plesset method (MP2-F12) [Pavoŝević et al., J. Chem. Phys. 144, 144109 (2016)]. This is achieved by the use of pair-natural orbitals (PNOs) for the compact representation of the unoccupied space. The method shows near-linear scaling behavior on the linear alkane chains with a computational scaling of N^1.6 for the largest alkane, C₂₀₀H₄₀₂, recovering more than 99.9% of correlation energy. The MP2-F12 method is intrinsically inadequate if high accuracy is required, but our formulation of the linear-scaling MP2-F12 method lays a solid foundation for the accurate linear-scaling explicitly correlated coupled-cluster singles and doubles method with perturbative inclusion of triples (PNO-CCSD(T)-F12) [Pavoŝević et al., J. Chem. Phys. 146, 174108 (2017)]. We have demonstrated that the PNO-CCSD(T)-F12 method shows a near-linear scaling behavior of N^1.5 . The error introduced by reduce-scaling approximations is only 0.4 kcal/mol of the binding energy with respect to the canonical result in the case of a 20-water cluster which is much lower than the required chemical accuracy defined as 1 kcal/mol. Furthermore, the reduced-scaling explicitly correlated CCSD(T) method is used to examine the binding ener- gies of large molecular systems that are far beyond the reach of the conventional CCSD(T) method. Our prediction of the binding energy for of the coronene dimer is the most accurate theoretical estimate of binding energy of the coronene dimer to this date. Such a system is an example of an organic semiconductor used for light conversion. However, the modeling of light harvesting materials requires an accurate knowledge of ionization potentials (IP) and electron affinities (EA). We describe [Pavoŝević et al., J. Chem. Phys. 147, 121101 (2017)] how to incorporate an explicit correlation correction into the Green’s function formalism (GF2) that is used for the calculation of IPs. We show that the GF2-F12 method removes errors associated with the basis sets, allowing extremely accurate predictions of IPs to be made at a significantly lower cost than the parent GF2 method. The work presented in this thesis will set a stage for further developments in reduced-scaling explicitly correlated methods. Furthermore it will be a useful benchmarking method for parametrizing the popular DFT functionals making accurate predictions of the relative stability of different forms of pharmaceuticals. Due to the simplicity and generality of the GF2-F12 method, it has the potential to be used to augment more accurate Green’s function methods, such as NR2, allowing for the accurate prediction of IPs and EAs of large molecular and periodic systems.

Oxide dielectric breakdown is an old problem that has been studied over decades. It causes power dissipations and irreversible damage to the electronic devices. The aggressive downscaling of the device size exponentially increases the leakage current density, which also raises the risk of dielectric breakdown. It has been proposed that point defects, current leakages, impurity diffusions, etc. all contribute to the change of oxide chemical composition and ultimately lead to the dielectric breakdown. However, the conclusive cause and a clear understanding of the entire process of dielectric breakdown are still under debate. In this research, the electronic structure at metal/oxide interfaces is studied using first-principle calculations within the framework of Density Functional Theory (DFT) to investigate any possible key signature that would trigger the dielectric breakdown. A classical band alignment method, the Van de Walle method, is applied to the case study of the Al/crystal-SiO2 (Al/c-SiO2) interface. Point defects, such as oxygen vacancy (VO) and hydrogen impurity (IH), are introduced into the Al/c-SiO2 interface to study the effects on band offset and electronic structure caused by point defects at metal/oxide interfaces. It is shown that the bonding chemistry at metal/oxide interfaces, which is mainly ionic bond, polarizes the interface. It results in many interface effects such as the interface dipole, built-in voltage, band bending, etc. Charge density analysis also indicates that the interface can localize charge due to such ionic bonding. It is also found that VO at the interface traps metal electrons which closes the open -sp3 orbital. The analysis on local potential shows that the metal potential penetrates through a few layers of oxide starting from the interface, which metalizes the interfacial region and induces unoccupied states in the oxide band gap. In addition, it is shown that higher oxygen content at metal/oxide interfaces minimizes such metal potential invasion. In addition, an oxygen vacancy is created at multiple sites through the Al/c-SiO2 and Al/a-SiO2 interface systems, separately. The oxygen local pressure is also calculated before its removal using Quantum Stress Density theory. Correlations among electronic structure, stress density, and vacancy formation energy are found, which provide informative insights into the defect generation controlling and dielectric breakdown analysis. A new band alignment approach based on the projection of plane-waves (PWs) into the space-dependent atomic orbital (LCAO) basis is presented and tested against classical band offset methods -- the Van de Walle method. It is found that the new band alignment approach can provide a quantitative and reliable band alignment and can be applied to the heterojunctions consisting of amorphous materials. The new band alignment approach reveals the real-space dependency of the electronic structure at interfaces. In addition, it includes all interface effects, such as the interface dipole, built-in voltage, virtual oxide thinning, and band deformation, which cannot be derived using classical band offset methods. This new band alignment approach is applied to the case study of both the Al/amorphous-SiO2 (Al/a-SiO2) interface and the Al/c-SiO2. We have found that at extremely low dimensions, the reduction of the insulator character due to the virtual oxide thinning is a pure quantum effect. I highlight that the quantum tunneling current leakage is more critical than the decrease of the potential barrier height on the failure of the devices. / PHD / Metal/oxide interfaces have many applications in electronic devices such as Field Effect Transistors (FETs), resistive/dynamic Random-Access Memory (RAM) devices, Tunnel Junctions (TJs), Metal Oxide Semiconductor (MOS) devices, or Back-End-of-Line (BEOL) on integrate-circuits. The downscaling of devices dimension is still following the Moore’s Law. However, it brings several reliability challenges, such as the electric current leakage that is significant for ultrathin oxide films (< 5 nm). At low dimensionality, the stress induced leakage currents (SILC) caused by quantum effects exponentially increases. These electric conductions harm devices and constantly degrade insulating materials, until the degradation reaches a critical level called dielectric breakdown that ultimately leads to the electronic failure of the materials. The insulating/conducting transition is a complex and irreversible very well-known process. Experimentally, the observation of sudden electric current increase is a typical sign of the breakdown. Many experimental works in past decades suggest that point defects are very important to the initiation of dielectric breakdown, however they cannot be the only cause. Many other factors such as the electric voltage, material imperfection, mechanical stress, humidity, and temperature are also critical to the final breakdown. Therefore, a comprehensive and theoretical study is necessary to better understand the mechanisms behind the dielectric breakdown. It benefits the semiconductor industry for inventing new materials and exploring advanced techniques to prevent the occurrence of dielectric breakdown. In this dissertation, a set of theoretical case studies using the aluminum (Al) and silica (SiO₂) to explore correlations among different electronic, thermodynamic, and mechanical properties have been performed. This study reveals that all these material properties are intrinsically correlated and allow a clear understanding of the dielectric breakdown.

The field of theoretical chemistry has provided undeniably useful insights about molecular systems that otherwise, through experiment, would not be obtainable. We are constantly developing new and improved methods to fill in the gaps about how various factors including the electronic structure can affect the chemistry seen experimentally. The goal of most quantum chemistry methods is to develop a method that is widely applicable, has low computational costs, but with as much accuracy as possible. Some of the most challenging systems in our field include those that are considered strongly correlated. Strong correlation is usually referring to the need for a large number of configurations to properly model the chemistry. These systems can not be solved exactly, thus various approximations must be made. A set of methods that take advantage of truncating only the unimportant configurations to solve these challenging systems are selected configuration interaction methods. Even though these selected CI methods can often provide accurate results, their general application is limited by memory bottlenecks. In 2020, our group developed the Tensor Product Selected Configuration Interaction (TPSCI) method to overcome these memory bottlenecks. We take advantage of the local character of these strongly correlated systems by doing a change of basis into tensor products, then do a selected CI algorithm in that basis. In this dissertation, we discuss how we have extended TPSCI to compute excited states. We first test on a set of polycyclic aromatic hydrocarbons that were previously studied with TPSCI. We find very high accuracy and dimension reduction as compared to state of the art selected CI approaches. We then validate TPSCI's ability to study the electronic structure involved in the singlet fission process in tetracene tetramer with extending analysis using a Bloch effective Hamiltonian. This effective Hamiltonian allows for intuitive analysis of the singlet fission process. We also show how accurate and interpretable TPSCI can be on an open-shell biradical transition bimetallic complex, in addition to, hexabenzocoronene that is not straightforward clustering due to the conjugated benzene rings. To alleviate the previous system size limitations, we recently implemented a Restricted Active Space Configuration Interaction as a local solver for clusters. We present novel results of using this new solver on a tetracene dimer. We comment on specific coupling strengths and show the electronic dynamics of our TPSCI effective Hamiltonian which support a CT-mediated mechanism for the tetracene dimer singlet fission. / Doctor of Philosophy / The field of theoretical chemistry has used some of the fundamental principles in quantum mechanics to study the electronic structure of molecular systems for many years. The power of computational resources has increased over the years, facilitating the increased complexity and accuracy of quantum chemistry methods. This dissertation lies in the realm of pushing past previous molecular system computational limits with rewarding accuracy and increased interpretability. We achieve these goals by taking advantage of the localized nature in most of our chemistry vocabulary by using tensor product methods. Tensor product methods are able to separate a large problem into smaller units to overcome previous system size limitations while maintaining the desired accuracy. The main method focused on in this dissertation is a tensor product method called Tensor Product Selected Configuration Interaction (TPSCI) established by our research group in 2020. This dissertation covers the required background information including basic terminology and previously developed methods then presents very recent and novel research using TPSCI. We first focus on extending TPSCI to excited states since excited states are extremely important for many photochemical processes, spectral analysis, and chemical sensing. We then test TPSCI on a spectrum of systems that range from very local character (separated molecular units) to bimetallics to very delocalized (carbon-based conjugation) chemistry. We find TPSCI is able to handle this variety of systems with very high accuracy and allows for very in-depth qualitative analysis. Finally, we present novel results incorporating an additional approximation in the local solver to further extend TPSCI's applicability. To test this new local solver, we focus on a process called singlet fission which is promising to help overcome solar cell efficiency limits. We are able to match previously reported results for the tetracene dimer which supports the use of TPSCI to study larger singlet fission systems in future work. With the work presented in this dissertation, we have aimed to highlight the potential utility of TPSCI, motivating further developments and research in this direction.

Evaluating the permanent of a matrix is a fundamental computation that emerges in many domains, including traditional fields like computational complexity theory, graph theory, and many-body quantum theory and emerging disciplines like machine learning and quantum computing. While conceptually simple, evaluating the permanent is extremely challenging: no polynomial-time algorithm is available. This thesis presents a software package that we designed to evaluate the permanent of an arbitrary rectangular matrix, supporting three algorithms (the straightforward combinatoric algorithm, the Ryser algorithm, and the Glynn algorithm) and, optionally, automatically switching to the optimal algorithm based on the type and dimensionality of the matrix of interest. To do this, we developed an extension of the Glynn algorithm to rectangular matrices. Except for very small matrices (where the naive combinatoric algorithm is best) and very rectangular matrices (where the Ryser algorithm is the best), the Glynn algorithm is fastest. In addition to our computational tests, we applied the method by incorporating it into PyCI, allowing the antisymmetric product of interacting geminals wavefunction to be evaluated with unprecedented speed. We believe that the methods we developed, together with their efficient implementation, will be broadly useful to mathematicians, physicists, and chemists and, accordingly, our software package is distributed as free and open-source software on Github, at https://github.com/theochem/matrix-permanent. / Thesis / Master of Science (MSc)

The field of organic electronics, in which -conjugated, organic molecules and polymers are used as the active components (e.g., semiconductor, light emitter/harvester, etc.), has lead to a number a number of key technological developments that have been founded within fundamental research disciplines. In the Dissertation that follows, the research involves the use of quantum-chemical techniques to elucidate fundamental aspects of both intermolecular and intramolecular electron-transfer processes in organic, -conjugated molecules. The Dissertation begins with an introduction and brief review of organic molecular systems used as electron-transport semiconducting materials in device applications and/or in the fundamental studies of intramolecular mixed-valence processes. This introductory material is then followed by a brief review of the electronic-structure methods (e.g., Hartree-Fock theory and Density Functional Theory) and electron-transfer theory (i.e., semiclassical Marcus theory) employed throughout the investigations. The next three Chapters deal with investigations related to the characterization of non-rigid, -conjugated molecular systems that have amorphous solid-state properties used as the electron-transport layer in organic electronic and optoelectronic devices. Chapters 3 and 4 involve studies of silole- (silacyclopentadiene)-based materials that possess attractive electronic and optical properties in the solid state. Chapter 5 offers a preliminary study of dioxaborine-based molecular structures as electron-transport systems. In Chapters 6 8, the focus of the work shifts to investigations of organic mixed-valence systems. Chapter 6 centers on the examination of tetraanisylarylenediamine systems where the inter-redox site distances are approximately equal throughout the series. Chapter 7 examines the bridge-length dependence of the geometric structure, charge-(de)localization, and electronic coupling for a series of vinylene- and phenylene-vinylene-bridged bis-dianisylamines. In Chapter 8, the role of symmetric vibrations in the delocalization of the excess charge is studied in a dioxaborine radical-anion and a series of radical-cation bridged-bisdimethylamines. Finally, Chapter 9 provides a synopsis of the work and goals for future consideration.

Electronic structure calculations constitute a valuable tool to predict the properties of materials. In this study we propose an efficient scheme to study correlated electron systems with essentially only one free parameter, the screening length of the Coulomb potential. A general reformulation of the exchange energy of the correlated electron shell is combined with this method in order to analyze the calculations. The results are interpreted in terms of different polarization channels, due to different multipoles. The method is applied to various actinide compounds, in order to increase the understanding of the complicate behaviour of 5f electrons in these systems. We studied the non-magnetic phase of δ-Pu, where the spin polarization is taken over by a spin-orbit-like term that does not break the time reversal symmetry. We also find that a non-trivial high multipole of the magnetization density, the triakontadipole, constitutes the ordering parameter in the mysterious hidden order phase of the heavy-fermion superconductor URu2Si2. This type of multipolar ordering is also found to play an essential role in the hexagonal-based superconductors UPd2Al3,  UNi2Al3 and UPt3 and in the dioxide insulators UO2, NpO2 and PuO2. The triakontadipole moments are also present in all magnetic actinides we considered, except for Cm. These results led us to formulate a new set of rules for the ground state of a system, that are valid in presence of strong spin-orbit coupling interaction instead of those of Hund; the Katt's rules. Finally, we applied our method to a new class of high-Tc superconductors, the Fe-pnictides, where the Fe 3d electrons are moderately correlated. In these materials we obtain the stabilization of a low spin moment solution, in agreement with experiment, over a large moment solution, due to the gain in exchange energy in the formation of large multipoles of the spin magnetization density. / Felaktigt tryckt som Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 705

In disordered alloys, atoms belonging to the same chemical element will exhibit different environments. This leads to variations in the atoms’ local electronic structures, which in turn leads to variations in the binding energies of their core levels. These binding energies can be measured experimentally using core level X-ray photoelectron spectroscopy (XPS). Therefore, in theory at least, core level XPS can be used to resolve different environments in alloys. However, to make this a reality one must understand how an atom’s local electronic structure, and hence the binding energies of its core levels, are affected by local environment. In this thesis, two simple phenomenological models are explored which purport to correctly describe the local electronic structure of disordered alloys. The first model which we consider has its roots in chemical intuition; specifically, the notion that pairs of unlike atoms, i.e. atoms belonging to different chemical elements, transfer a certain quantity of charge, while like atoms do not. Using this model - known as the optimised linear charge model (OLCM) - the relationship between an atom’s local electronic structure, core level binding energies, and its environment is explored in detail, both in the bulk of disordered alloys and near their surfaces. As well as ‘homogeneous’ disordered alloys, in which the concentrations of the alloy’s constituent elements are the same throughout the entire alloy, various ‘inhomogeneous’ disordered alloy systems are considered. These include alloys exhibiting surface segregation - in which the concentrations at the surface differ from those in the bulk - as well as interfaces between two metals with various levels of intermixing. The results of our investigation of bulk inhomogeneous alloys are compared to analogous ab initio results, which confirms the model’s viability as a tool for rationalising the relationship between local electronic structure, core level binding energies, and environment. More generally, our results also reveal a number of interesting new phenomena. Firstly, the widths of spectra in inhomogeneous disordered alloys are significantly larger in some cases than is possible in any analogous homogeneous disordered alloy. Secondly, differences between the concentrations of each element at the surface and deep within the bulk cause a shift in the work function of the alloy under consideration. The latter results in qualitatively different trends than one would expect if this phenomenon was ignored, and prompts an alternative interpretation of the results of a recent experimental study. The second model which we consider is a particular case of the charge-excess functional model, in which the realised charges on all atoms are those which minimise a particular expression for the total energy of the system, and whose accuracy has been well established. The underlying assumptions and properties of this model are explored in detail, adding insight into the nature of the screening and inter-atomic interactions in disordered alloys. The model is shown to be equivalent to the OLCM for the case of binary alloys, and can therefore be considered to be the generalisation of the OLCM for alloys containing more than two chemical elements. The model is also used to derive analytical expressions for various physical quantities for any alloy, including the width of core level XPS spectra and the Madelung energy. These expressions are then used to investigate how the physical quantities to which they pertain vary with the concentrations of each element in a homogeneous disordered alloy consisting of three elements. Among other things, it was observed that the width of the core level XPS spectra is maximised when the concentrations of the two elements in the alloy with the largest electronegativity difference have equal concentrations, while the remaining element has a vanishing concentration.