The Random Phase Approximation and beyond Random Phase Approximation methods based on Adiabatic Connection Fluctuation Dissipation Theorem (ACFD) are tested for structural phase transitions of different groups of materials, including metal to metal, metal to semiconductor, semiconductor to semiconductor transitions. Also the performance assessment of semilocal density functionals with or without empirical long range dispersion corrections has been explored for the same cases. We have investigated the structural phase transitions of three broad group of materials, semi- conductor to metal transitions involving two symmetric structures, semiconductor to metal and wide bandgap semiconductor to semiconductor transitions involving at least one lower symmetric structure and lastly special cases comprising metal to metal transitions and transitions between energetically very close structural phases. The first group contains Si (diamond → β-tin), Ge (diamond → β-tin) and SiC (zinc blende → rocksalt), second group contains GaAs (zinc blende → cmcm) and SiO 2 (quartz → stishovite) and third group contains Pb (fcc → hcp), C(graphite → diamond) and BN (cubic → hexagonal) respectively. We have found that the difference in behavior of exchange and correlation in semilocal functionals and ACFD methods is striking. For the former, the exchange potential and energy often comprise the majority of the binding described by density functional approximations, and the addition of the correlation energy and potential often induce only a (relatively) small shift from the exchange- only results. For the ACFD, however, non self-consistent EXX typically underbinds by a considerable degree resulting in wildly inaccurate results. Thus the addition of correlation leads to very large shifts in the exchange-only results, in direct contrast to semilocal correlation. This difference in behavior is directly linked to the non-local nature of the EXX, and even though the exchange-only starting point is often nowhere close to experiment, the non-local correlation from the ACFD corrects this deficiency and yields the missing binding needed to produce accurate results. Thus we find the ACFD approach to be vital in the validation of semilocal results and recommend its use in materials where experimental results cannot be straightforwardly compared to other approximate electronic structure calculations. Utilizing the second-order approximation to Random Phase Approximation renormalized (RPAr) many-body perturbation theory for the interacting density-density response function, we have used a so-called higher-order terms (HOT) approximation for the correlation energy. In combination with the first-order RPAr correction, the HOT method faithfully captures the infinite- order correlation for a given exchange-correlation kernel, yielding errors of the total correlation energy on the order of 1% or less for most systems. For exchange-like kernels, our new method has the further benefit that the coupling-strength integration can be completely eliminated resulting in a modest reduction in computational cost compared to the traditional approach. When the correlation energy is accurately reproduced by the HOT approximation, structural properties and energy differences are also accurately reproduced, as confirmed by finding interlayer binding energies of several periodic solids and compared that to some molecular systems along with some phase transition parameters of SiC. Energy differences involving fragmentation have proved to be challenging for the HOT method, however, due to errors that do not cancel between a composite system and its constituent pieces which has been verified in our work as well. / Physics