This thesis is divided into two parts. In the first part we study thermodynamics of the two-dimensional Heisenberg ferromagnet with dipolar interaction. This interaction breaks the conditions of the Mermin-Wagner theorem, resulting in a finite transition temperature. Our calculations are done within the framework of the self-consistent spin-wave theory (SSWT), which is modified in order to include the dipolar interaction. Both quantum and classical versions of the Heisenberg model are considered. The second part of the thesis investigates the chemical bonding in solids from the first principles calculations. A new chemical bonding indicator called balanced crystal orbital overlap population (BCOOP) is developed. BCOOP is less basis set dependent than the earlier indicators and it can be used with full-potential density-functional theory (DFT) codes. We apply BCOOP formalism to the chemical bonding in the high-T_c superconductor MgB2 and the theoretically predicted MAX phase Nb3SiC2. We also study how the chemical bonding results in a repulsive hydrogen–hydrogen interaction in metal hydrides. The role of this interaction in the structural phase transition in Ti3SnHx is investigated.

Theoretical investigations of spectroscopic and magnetic properties of metallic systems in the bulk, as well as in nanostructured materials, have been performed within the density functional theory. The major part of the present work studies the differences between binding energies of electrons tightly bound to the atoms, the so-called core electrons (in contrast with the valence electrons), that is, core-level binding energy shift (CLS). By comparison between corresponding elemental core-levels for atoms situated in different chemical environments we obtain fundamental understanding of bonding properties of materials. The method of choice was the complete screening picture, which includes initial and final state effects on the same footing. The usefulness of CLS stems from that it is sensitive to differences in the chemical environment of an atom, which can be affected on one hand by the global composition of e.g. disordered materials, surfaces and interfaces, and on the other hand by the very local environment around an atom. Here CLSs have been obtained for both components in the fcc random alloys AgPd, CuPd, CuNi, CuPt, CuAu, PdAu, NiPd and NiPt. Moreover the model was extended to the Auger kinetic energy shift for the LMM Auger transition in AgPd alloys. Studies were also applied to the near surface and interface regions of PdMn nano structures on Pd(100), thin CuPd and AgPd films on inert Ru(0001), and at interfaces. The disorder broadening on CLS due to local environment effects was calculated in selected alloys. A part of the thesis concern investigations related to the magnetic ordering in Invar alloys, including the influence of local environment effects. A study was made for the dependence of effective exchange parameter on the electron concentration, volume and local chemical composition.

This thesis concerns quadratic response properties and their application to properties in Jablonski diagrams such as resonant two-photon absorption and excited state absorption. Our main interest lies in optical power limiting applications, and in this context, molecules containing heavy metal atoms prove superior. Therefore, we are interested in how relativity affects these properties, and in order to assess this, a four-component relativistic framework is adopted. To properly address the molecular properties of interest, both relativistic effects and electron correlation need to be accounted for. These two properties are not additive, and, therefore, correlation needs to be incorporated into the four-component framework. We present the implementation of quadratic response properties at the four-component density functional level of theory. For second-harmonic generation, we have, with numerical examples, demonstrated that correlation and relativity are indeed not additive and that the inclusion of noncollinear magnetization is of little importance. We report that both electron correlation as well as relativity strongly affect results for second-harmonic generation. For example, relativity alone reduces the µβ-response signal by 62% and 75% for meta- and ortho-bromobenzene, respectively, and enhances the same response by 17% and 21% for meta- and ortho-iodobenzene, respectively. In the four-component framework, we present the implementations of single and double residues of the quadratic response function, which allows for the evaluation of resonant two-photon absorption cross sections and excited state properties. Using these tools, we discuss different levels of approximation to the relativistic Hamiltonian and we demonstrate that for two-photon absorption, a proper treatment of relativistic effects qualitatively alters the spectrum. For example, already for an element as light as neon, significant differences are seen between the relativistic and nonrelativistic spectra as triplet transitions acquire substantial absorption cross sections in the former case. Finally, quantum mechanics in conjunction with electrodynamics is applied to determine clamping levels in macroscopic samples. The microscopic properties of the optically active chromophores are determined by response theory, and then, electrodynamics is used to describe the interactions between the chromophores and incident laser pulses. Using this approach a series of molecules have been investigated and their performances have been compared and ranked in order to find novel materials for optical power limiting applications.

A core level spectroscopy study of ice and water is presented in this thesis. Combining a number of experiments and spectrum calculations based on density functional theory, changes in the local valence electronic structure are shown to be sensitive to the local H-bonding configurations. Exploiting this sensitivity, we are able to approach important scientific problems for a number of aggregation states; liquid water, the water-metal interface, bulk and surface of hexagonal ice. For the H-bonded model system hexagonal ice, we have probed the occupied valence electronic structure by x-ray emission and x-ray photoelectron spectroscopy. Stepwise inclusion of different types of interactions within density functional theory, together with a local valence electron population analysis, show that it is essential to include intermolecular charge transfer together with internal s-p rehybridizations in order to describe the changes in electronic structure seen in the experiment. The attractive electrostatic interaction between water molecules is enhanced by a decrease in Pauli repulsion. A simple electrostatic model due to charge induction from the surrounding water is unable to explain the electronic structure changes. By varying the probing depth in x-ray absorption the structure of the bulk, subsurface and surface regions is probed in a thin ice film. A pronounced continuum for fully coordinated species in the bulk is in sharp contrast to the spectrum associated with a broken symmetry at the surface. In particular molecular arrangements of water with one uncoordinated OH group have unoccupied electronic states below the conduction band that are responsible for a strong anisotropic pre-edge intensity in the x-ray absorption spectrum. The topmost layer is dominated by an almost isotropic distribution of these species, which is inconsistent with an unrelaxed surface structure. For liquid water the x-ray absorption spectrum resembles that of the ice surface, indicating a domination of species with broken hydrogen bond configurations. The sensitivity to the local hydrogen bond configuration, in particular the sensitivity to broken bonds on the donor side, allows for a detailed analysis of the liquid water spectrum. Most molecules in liquid water are found in two-hydrogen-bonded configurations with one strong donor and one strong acceptor hydrogen bond. The results, consistent with diffraction data, imply that most molecules are arranged in strongly H-bonded chains or rings embedded in a disordered cluster network. Molecular dynamics simulations are unable to describe the experimental data. The water overlayer on the close-packed platinum surface is studied using a combination of core-level spectroscopy and density functional theory. A new structure for water adsorption on close-packed transition metal surfaces is found, where a weakly corrugated non-dissociated overlayer interacts via alternating oxygen-metal and hydrogen-metal bonds. The latter results from a balance between metal-hydrogen bond formation and OH bond weakening. The ultrashort core-hole lifetime of oxygen provides a powerful probe of excited state dynamics via studies of the non-radiative or radiative decay following x-ray absorption. Electrons excited into the pre-edge state for single donor species at the ice surface remain localized long enough for early time solvation dynamics to occur and these species are suggested as strong pre-existing traps to the hydrated electron. Fully coordinated molecules in the bulk contribute to a strong conduction band with electron transfer times below 0.5 femtoseconds. Upon core-ionization, both protons are found to migrate substantial distances on a femtosecond timescale. This unusually fast proton dynamics for non-resonant excitation is captured both by theory and experiment with a measurable isotope effect.

In this thesis, quantum-mechanical calculations within density-functional theory on metallic systems are presented. The overarching goal has been to investigate effects of disorder. In particular, one of the properties investigated is the bindingenergy shifts for core electrons in binary alloys using different theoretical methods. These methods are compared with each other and with experimental results. One such method, the so-called Slater-Janak transition state method relies on the assumption that the single-particle eigenvalues within density-functional theory are linear functions of their respective occupation number. This assumption is investigated and it is found that while the eigenvalues to a first approximation show linear behavior, there are also nonlinearities which can influence the core-level binding energy shifts. Another area of investigation has been iron based alloys at pressures corresponding to those in the Earth’s inner core. This has been done for the hexagonal close packed and face entered cubic structures. The effects of alloying iron with magnesium and nickel on the equation of state as well on the elastic properties have been investigated. The calculations have shown that the hexagonal close packed structure in FeNi is more isotropic than the face-centered cubic structure, and that adding Mg to Fe has a large impact on the elastic properties. Finally, the effects of disorder due to thermal motion of the atoms have been investigated through ab-initio molecular dynamics simulations. Within the limits of this method and the setup, it is found that the face-centered cubic structure of molybdenum can be dynamically stabilized at high temperature, leading to a metastable structure, on the average. The dynamical stabilization of face-centered cubic molybdenum also rendered it possible to accurately calculate the lattice stability relative to the body-centered cubic phase. Inclusion of temperature effects for the lattice stability using ab-initio molecular dynamics simulations resolves the disagreement between ab-initio calculations and thermochemical methods.

This thesis concerns methods of reduced complexity for electronic structure calculations.  When quantum chemistry methods are applied to large systems, it is important to optimally use computer resources and only store data and perform operations that contribute to the overall accuracy. At the same time, precarious approximations could jeopardize the reliability of the whole calculation.  In this thesis, the self-consistent field method is seen as a sequence of rotations of the occupied subspace. Errors coming from computational approximations are characterized as erroneous rotations of this subspace. This viewpoint is optimal in the sense that the occupied subspace uniquely defines the electron density. Errors should be measured by their impact on the overall accuracy instead of by their constituent parts. With this point of view, a mathematical framework for control of errors in Hartree-Fock/Kohn-Sham calculations is proposed.  A unifying framework is of particular importance when computational approximations are introduced to efficiently handle large systems. An important operation in Hartree-Fock/Kohn-Sham calculations is the calculation of the density matrix for a given Fock/Kohn-Sham matrix. In this thesis, density matrix purification is used to compute the density matrix with time and memory usage increasing only linearly with system size. The forward error of purification is analyzed and schemes to control the forward error are proposed. The presented purification methods are coupled with effective methods to compute interior eigenvalues of the Fock/Kohn-Sham matrix also proposed in this thesis.New methods for inverse factorizations of Hermitian positive definite matrices that can be used for congruence transformations of the Fock/Kohn-Sham and density matrices are suggested as well. Most of the methods above have been implemented in the Ergo quantum chemistry program. This program uses a hierarchic sparse matrix library, also presented in this thesis, which is parallelized for shared memory computer architectures. It is demonstrated that the Ergo program is able to perform linear scaling Hartree-Fock calculations. / QC 20100908

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This dissertation presents a study of the molecular mechanism underlying the highly efficient solar energy conversion processes that occur in the Photosystem I (PS I) reaction centers in plants and bacteria. The primary electron donor P700 is at the heart of solar energy conversion process in PS I and the aim is to obtain a better understanding of the electronic and structural organization of P700 in the ground and excited states. Static Fourier Transform Infra-Red (FTIR) difference spectroscopy (DS) in combination with site directed mutagenesis and Density Functional Theory (DFT) based vibrational frequency simulations were used to investigate how protein interactions such as histidine ligation and hydrogen bonding modulate this organization. (P700+-P700) FTIR DS at 77K were obtained from a series of mutants from the cyanobacterium Synechocystis sp. 6803 (S. 6803) where the amino acid residues near the C=O groups of the two chlorophylls of P700 where specifically changed. (P700+-P700) FTIR DS was also obtained for a set of mutants from C. reinhardtii where the axial ligand to A0-, the primary electron acceptor in PS I was modified. The FTIR DS obtained from these mutants provides information on the axial ligands, the hydrogen bonding status as well as the polarity of the environment of specific functional groups that are part of the chlorophyll molecules that constitute P700. Assignment of the FTIR bands to vibrational modes in specific types of environment is very difficult. In order to assist the assignment of the difference bands in experimental spectra DFT based vibrational mode frequency calculations were undertaken for Chl-a and Chl-a+ model molecular systems under different set of conditions; in the gas phase, in solvents using the Polarizable Continuum Model (PCM), in the presence of explicit solvent molecules using QM/MM methods, and in the presence of axial ligands and hydrogen bonds. DFT methods were also used to calculate the charge, spin and redox properties of Chl-a/Chl-a’ dimer models that are representative of P700, the primary electron donor in PS I.

In this thesis, theoretical and computer simulation studies of vibrational phase relaxation in various molecular liquids are presented. That includes liquid nitrogen, both along the coexistence line and the critical isochore, binary liquid mixture and liquid water. The focus of the thesis is to understand the dependence of the vibrational relaxation on the density, temperature, composition and the role of different interactions among the molecules. The density fluctuation of the solute particles in a solvent is studied systematically, where the computer simulation results are compared with the mode coupling theory (MCT). The classical density functional theory (DFT) is used to study the vibrational relaxation dynamics in molecular liquids with an aim to understand the heterogeneous nature of the dynamics commonly observed in experiments. Chapter 1 contains a brief overview of the earlier relevant theories, their successes and shortcomings in the light of the problems discussed in this thesis. This chapter discusses mainly the basic features of the vibrational dynamics of molecular liquids and portrays some of the theoretical frameworks and formalisms which are widely recognized to have contributed to our present understanding. Vibrational dephasing of nitrogen molecules is known to show highly interesting anomalies near its gas–liquid critical point. In Chapter 2, we present the results of extensive computer simulation studies and theoretical analysis of the vibrational phase relaxation of nitrogen molecules both along the critical isochore and the gas–liquid coexistence line. The simulation includes the different contributions (density (ρ), vibration–rotation (VR), and resonant transfer (Rs)) and their cross–correlations. Following Everitt and Skinner, we have included the vibrational coordinate (q) dependence of the inter–atomic potential, which is found to have an important contribution. The simulated results are in good agreement with the experiments. The linewidth (directly proportional to the rate of the vibrational phase relaxation) is found to have a lambda shaped temperature dependence near the critical point. As observed in the experimental studies, the calculated lineshape becomes Gaussian–like as the critical temperature (Tc) is approached while being Lorentzian–like at the temperatures away from Tc. Both the present simulation and a mode coupling theory (MCT) analysis show that the slow decay of the enhanced density fluctuations near the critical point (CP), probed at the sub–picosecond timescales by the vibrational frequency modulation, and an enhanced vibration–rotation coupling, are the main causes of the observed anomalies. Dephasing time (тv) and the root mean square frequency fluctuation (Δ) in the supercritical region are calculated. The principal results are: 1. a crossover from a Lorentzian–like to a Gaussian–like lineshape is observed as the critical point is approached along the critical isochore, 2. the root mean square frequency fluctuation shows a non–monotonic dependence on the temperature along the critical isochore, 3. the temperature dependent linewidth shows a divergence–like (λ–shaped) behavior along the coexistence line and the critical isochore. It is found that the linewidth calculated from the time integral of the normal coordinate time correlation function (CQ(t)) is in good agreement with the known experimental results. The origin of the anomalous temperature dependence of linewidth can be traced to simultaneous effects of several factors, (i) the enhancement of the negative cross–correlations of ρ with VR and Rs and (ii) the large density fluctuations as the critical point (CP) is approached. Due to the negative cross–correlations of ρ with VR and Rs the total decay becomes faster (correlation times are in the femtosecond scale). The reason for the negative cross–correlation between ρ and VR is explored in detail. A mode coupling theory (MCT) analysis shows a slow decay of the enhanced density fluctuations near the critical point. The MCT analysis demonstrates that the large enhancement of VR–coupling near CP may arise from a non–Gaussian behavior of the equilibrium density fluctuations. This enters through a non–zero value of the triplet direct correlation function. Many of the complex systems found in nature and used routinely in industry are multi–component systems. In particular, binary mixtures are highly non–ideal and play an important role in the industry. The dynamic properties are strongly influenced by composition fluctuations which are absent in the one component liquids. In Chapter 3, isothermal–isobaric (NPT) ensemble molecular dynamics simulation studies of vibrational phase relaxation (VPR) in a model system are presented. The model considers strong attractive interaction between the dissimilar species to prevent phase separation. The model reproduces the experimentally observed non–monotonic, nearly symmetric, composition dependence of the dephasing rate. In addition, several other experimentally observed features, such as the maximum of the frequency modulation correlation time (т c) at a mole fraction near 0.5 and the maximum rate enhancement by a factor of about 3 above the pure component value, are also reproduced. The product of the mean square frequency modulation ((Δω2(0))) with тc indicates that the present model is in the intermediate regime of the inhomogeneous broadening. The non–monotonic composition (χ) dependence of тv is found to be primarily due to the non–monotonic χ dependence of тc, rather than due to a similar dependence in the amplitude of (Δω2(0)). The probability distribution of Δω shows a markedly non–Gaussian behavior at intermediate composition (χ - 0.5). We have also calculated the composition dependence of the viscosity (η∗) in order to explore the correlation between the viscosity with that of тv and тc. It is found that both the correlation times essentially follow the nature of the composition dependence of the viscosity. A mode coupling theory (MCT) analysis is presented to include the effects of the composition fluctuations in binary mixture. Water is an interesting and attractive object for research, not only because of its great importance in life processes but also due to its unusual and intriguing properties. Most of the anomalous properties of water are related to the presence of a three–dimensional network of hydrogen bonds, which is constantly changing at ultrafast, sub–picosecond timescales. Vibrational spectroscopy provides the means to study the dynamics of processes involving only certain chemical bonds. The dynamics of hydrogen bonding can be probed via its reflection on molecular vibrations, e.g., the stretching vibrational mode of the O–H bond. Recently developed femtosecond infrared vibrational spectroscopy has proved to be valuable to study water dynamics because of its unique temporal resolution. Recent studies have shown that the vibrational relaxation of the O–H stretch of HDO occurs at an extremely fast timescale with time constant being less than 100 femtosecond. Here, in Chapter 4, we investigate the origin of this ultrafast vibrational dephasing using computer simulation and appropriate theoretical analysis. In addition to the usual fast vibrational dynamics due to the hydrogen bonding excitations, we find two additional reasons: (a) the large amplitude of angular jumps of the water molecules (with 30–40 fs time intervals) provide large contribution to the mean square vibrational frequency and (b) the projected force along the O–H bond due to the solvent molecules, on the oxygen (FO(t)) and hydrogen (FH (t)) atoms of the O–H bond exhibit a large negative cross–correlation (NCC) between FO(t) and FH (t). This NCC is shown to be partly responsible for a weak, non–Arrhenius temperature dependence of the relaxation rate. In the concluding note, Chapter 5 starts with a brief summary of the outcome of this thesis and ends up with suggestions of a few relevant problems that may prove worthwhile to be addressed in the future.

In the first two chapters we presented the basics of density functional theory and semiempirical LSD+U approximation, which was implemented in the full-potential local-orbital (FPLO) minimal-basis calculation scheme. In the third chapter we tested the implemented version of LSDA+U on 3d transitional metal monoxides. Essential improvement of the spectroscopic properties was obtained. A simple model describing the value and direction of the magnetic moment of a transition metal ion was presented. The model visualizes the interplay of the spin-orbit coupling and crystal field splitting. In the fourth chapter we calculated the electronic spectrum of the single Zn impurity in CuO2 plane considered as a vacancy in Cu 3d states. The analytic solution for the states of different symmetry was obtained. Depending on the strength of perturbation induced by the impurity on the neighboring Cu ions, the states are either resonant or localized. The critical values of the perturbation were computed. In the fifth chapter we presented the calculations for three novel vanadates: MgVO3, Sb2O2VO3 and VOMoO4. The tight-binding parameters and the exchange integrals were computed. The magnesium and antimony vanadates appeared to be spin-½ one-dimensional systems, the latter having much stronger one-dimensional character and being probably the best realization of inorganic spin-Peierls system. The molybdenum vanadate was found to be two-dimensional spin-½ system. The Mo 4d orbitals play an important role in the electronic transfer.