The Waddington mechanism, or the Waddington-type reaction pathway, is crucial for low-temperature oxidation of both alkenes and alcohols. In this study, the Waddington mechanism in the oxidation chemistry of butene and butanol isomers was systematically investigated. Fundamental quantum chemical calculations were conducted for the rate constants and thermodynamic properties of the reactions and species in this mechanism. Calculations were performed using two different ab initio solvers: Gaussian 09 and Orca 4.0.0, and two different kinetic solvers: PAPR and MultiWell, comprehensively. Temperature- and pressure-dependent rate constants were performed based on the transition state theory, associated with the Rice Ramsperger Kassel Marcus and master equation theories. Temperature-dependent thermochemistry (enthalpies of formation, entropy, and heat capacity) of all major species was also conducted, based on the statistical thermodynamics. Of the two types of reaction, dissociation reactions were significantly faster than isomerization reactions, while the rate constants of both reactions converged toward higher temperatures. In comparison, between two ab initio solvers, the barrier height difference among all isomerization and dissociation reactions was about 2 and 0.5 kcal/mol, respectively, resulting in less than 50%, and a factor of 2-10 differences for the predicted rate coefficients of the two reaction types, respectively. Comparing the two kinetic solvers, the rate constants of the isomerization reactions showed less than a 32% difference, while the rate of one dissociation reaction (P1 <-> WDT12) exhibited 1-2 orders of magnitude discrepancy. Compared with results from the literature, both reaction rate coefficients (R4 and R5 reaction systems) and species' thermochemistry (all closed shell molecules and open shell radicals R4 and R5) showed good agreement with the corresponding values obtained from the literature. All calculated results can be directly used for the chemical kinetic model development of butene and butanol isomer oxidation.