The exact exchange-correlation kernel is a functional derivative of the exact time-dependent exchange-correlation (XC) potential with respect to the time-dependent density, evaluated at the ground-state density. As the XC potential is not known, the exact kernel is also unavailable. Therefore, it must be modeled either using many-body perturbation theory or by satisfying the exact constraints for various prototype systems such as the paradigm uniform electron gas (UEG). The random phase approximation (RPA) neglects the kernel, therefore, fails to provide the accurate ground- and excited-state properties for various systems from a simple uniform electron gas to more complex periodic ones. There are numerous corrections to RPA available, including kernel-corrected RPA, often called the beyond-RPA (bRPA) methods. In this work, we employed various bRPA methods for a diverse set of systems together with RPA. At first, we applied RPA based methods to study the phase stability of the cesium halides. Cesium halides phase stability is one of the stringent tests for a density functional approximation to assess its accuracy for dispersion interaction. Experimentally, CsF prefers the rocksalt (B1) phase, while the other halides CsCl, CsBr, and CsI prefer the cesium chloride (B2) phase. Without dispersion interaction, PBE and PBE0 predict all halides to prefer the B1 phase. However, all RPA based methods predict the experimental observations. The bRPA methods usually improve the quantitative prediction over RPA for the ground-state equilibrium properties of cesium halides. Next, we explored binary intermetallic alloys, where we showed that RPA successfully predicts the accurate formation energies of weakly bonded alloys. However, a kernel corrected RPA is needed when dealing with strongly bonded alloys with partially filled d-band metals. We utilized the renormalized ALDA (rALDA) and rAPBE kernel as bRPA methods. Exact constraints and appropriate norms such as the uniform electron gas are very useful to construct various approximations for the exchange-correlation potentials in the ground-state, and the exchange-correlation kernel in the linear-response theory within the TDDFT. These mathematical formulations not only guide us to formulate more robust nonempirical methods, but they also have more predictive power. We showed the importance of these constraints by calculating plasmon dispersion of the uniform electron gas using the non-local, energy-optimized (NEO) kernel using only a few constraints. More predictive power comes with more constraint satisfaction. As a result, we developed a new wavevector- and frequency-dependent exchange-correlation kernel that satisfies all the constraints that it should satisfy with a real frequency. It gives accurate ground-state correlation energy and describes the charge density wave in low-density UEG. It also predicts an accurate plasmon dispersion with a finite lifetime at wavevectors less than the critical one, where the plasmon dispersion meets the electron-hole continuum. / Physics

In this thesis, I study the electronic and structural phase diagrams of the superconducting 122 iron pnictides systems Ba1-xKx(Fe1-yCoy)2As2 and EuFe2(As1-xPx)2 by means of the local probe techniques 57Fe Mössbauer spectroscopy (MS) and muon spin relaxation (muSR). For both isovalent substitution strategies - Co/K for Fe/Ba and P for As, respectively - the antiferromagnetic Fe ordering and orthorhombic distortion of the parent compounds BaFe2As2 and EuFe2As2 are subsequently suppressed with increasing chemical substitution and superconductivity arises, once long-range and coherent Fe magnetic order is sufficiently but not entirely suppressed. For Ba1-xKx(Fe1-yCoy)2As2 in the charge compensated state (x/2=y), a remarkably similar suppression of both, the orthorhombic distortion and Fe magnetic ordering, as a function of increasing substitution is observed and a linear relationship between the structural and the magnetic order parameter is found. Superconductivity is evidenced at intermediate substitution with a maximum Tsc of 15 K coexisting with static magnetic order on a microscopic length scale. The appearance of superconductivity within the antiferromagnetic state can by explained by the introduction of disorder due to nonmagnetic impurities to a system with a constant charge carrier density. Within this model, the experimental findings are compatible with the predicted s± pairing symmetry. For EuFe2(As1-xPx)2, the results from 57Fe MS and ZF-muSR reveal an intriguing interplay of the local Eu 2+ magnetic moments and the itinerant magnetic Fe moments due to the competing structures of the iron and europium magnetic subsystems. For the investigated single crystals with x=0.19 and 0.28, 57Fe MS evidences the interplay of Fe and Eu magnetism by the observation of a transferred hyperfine field below Tafm at which the Eu subsystem orders into a canted A-type AFM magnetic structure. Furthermore, an additional temperature dependent out-of-plane tilting of the static Fe hyperfine field is observed below the onset of static Eu ordering. ZF-muSR shows a strong increase of the local field at the muon site below Tafm=20 K and a crossover from isotropic to anisotropic Eu spin-dynamics between 30 and 10 K. The temperature dependence of the spin dynamics, as derived from the muSR dynamic relaxation rates, are related to a critical slowing down of Eu-spin fluctuations which extends to even much higher temperatures (~100 K). They also effect the experimental linewidth observed in the 57Fe MS experiments. The strong influence of the Eu magnetic order onto the primary observables in both methods prevents conclusive interpretation of the experimental data with respect to a putative interplay of Fe magnetism and superconductivity.