Accurate characterization of thermochemistry and kinetic properties requires high level ab initio approaches. In this dissertation, we present both ab initio quantum chemical applications and methodological development. We begin with a coupled cluster investigation on the lowest triplet state of ethylene. Properties like structures, energetics, and vibrational frequencies are reported to guide experimental observations. In the second study, three pathways of intramolecular rearrangements of cyclobutylidene are carefully characterized by using coupled cluster theory with up to perturbative quadruple excitations [CCSDT(Q)]. The predicted reaction rates show excellent agreement with experiments. Finally, we present an efficient implementation of density cumulant theory (DCT) with spin adaptation and the density fitting approximation. Its capability of tackling systems with challenging properties is proven by application to transition metal complexes.