The mechanism of a reaction is the collection of events that take place that lead to the products of a chemical transformation. Though there are some events in a chemical reaction that can be observed by experiment, such long-lived intermediates, many of the events are too short lived to be measured. Due to these restrictions and the advancements in the development of moderately scaling computational tools, it is becoming commonplace to use quantum mechanical software packages to model the mechanism of a reaction. Here, I used quantum mechanical calculations alongside experimental evidence provided by multiple collaborators to understand the reactivity of both heat- and light-mediated organic transformations. In chapter 2, I investigated the role of electron donor-acceptor complexes in the generation of alkyl and acyl radicals in the presence of visible light. In addition, the pathways to the experimentally observed products, alkyl and acyl thioethers, were modeled. The lowest energy pathway to product, post-radical generation, was radical addition to the radical electron donor-acceptor complex. For a photoredox-catalyzed method to cyclopropanes from a novel halomethyl radical precursor (Chapter 3), computations strongly supported a redox-neutral reductive radical/polar crossover mechanism over radical pathways, consistent with experimental trends. Investigation of the isomerization of cinnamyl chloride to cyclopropane via a commonly used photoredox catalyst (Chapter 4) revealed that the reaction was mediated via dexter energy transfer between photocatalyst and substrate over the more commonly proposed electron transfer, affording diastereoselective product formation. A dual nickel/photoredox-catalyzed coupling of sulfinate salts and aryl halides gave a mixture of aryl sulfide and aryl sulfone products (Chapter 5), suggesting that disproportionation of sulfone radical was leading to the formation of thiyl radical. Modeling the product determining steps indicated that the product distribution was controlled by radical addition of the thiyl radical to the nickel(II) species versus reductive elimination of the sulfone bound to the nickel(III) catalyst. A bicyclo[1.1.1]pentane diborylated with pinacolboryl groups, one at the arm and head position, was found to have reactivity only at the bridgehead position (Chapter 6). Calculations of a hydrozone coupling reaction performed by the Qin group found that the reactivity was due to the unique hybridization of the bridgehead position as well as increased steric interactions at the arm position. Finally, a sulfoxide synthesized from a sulfinate salt could be activated with Grignard reagent, affording coupling of the substituents originally bound to the sulfoxide. DFT calculations validated the role of the sulfurane intermediate acting as a mediator to the coupled product.