This thesis will focus on the computational chemistry of radical intermediates as well as the thermodynamics and kinetics that characterize their reactions. The acroylyl (C₃H₃O) and butadienyl (C₄H₅) radicals each exhibit a 1,2 and 1,3 configurational isomer, separated by low activation barriers. Parallel addition reactions of these radical isomers with π-bond containing reactants are investigated using ab initio quantum chemistry calculations in order to explore the balance between kinetic and thermodynamic control. We expect the computed energies to be chemically accurate, with errors ≤ 4 kJ/mol, and the RRKM rate coefficients to be accurate within approximately 10%. Effective first-order rate coefficients and branching ratios of the 1,2 to 1,3 product were calculated from 500 K to 2,000 K and from 10⁻⁵ bar to 10 bar. The trifluoromethyl (CF₃) radical has shown promise as a key intermediate in the functionalization of methane. The thermodynamics of this functionalization mechanism have been calculated using the B3LYP/cc-pVDZ level and basis. The free energy of reaction for each step in the mechanism also includes solvent corrections using the COSMO model, and the overall process is shown to be exergonic at 333 K and 27.0 atm. Finally, highly accurate calculations using multireference methods are carried out on selected low-molecular weight hydrocarbon radicals. The energy differences between different spin states of these molecules are relatively small. These energy landscapes are investigated using coupled-cluster methods and MCSCF conical intersections.