Quantum mechanical (QM) and molecular docking methods are used to probe systems of biological and synthetic interest. Probing interactions of nucleobases within proteins, and properly modeling said interactions toward novel nucleobase development, is extremely difficult, and of great utility in RNA interference (RNAi) therapeutics. The issues in development of methods of modeling, as well as our approach at application of existing methods to prediction of 5'-nucleobase binding affinity of nucleobase analogs in short interfering RNA (siRNA) to the MID domain of the human Argonaut2 complex are discussed as are the experimental validation of our findings toward increasing or decreasing RNAi efficacy. Further, quantum mechanical methods were used to probe the pathways of interesting pericyclic organic reactions, theoretical as well as previously known, to better understand fundamental reaction patterns, and provide insight and predict trends in reactivity in support of synthetic collaborators. These include the investigation of [3,3] and [5,5] sigmatropic rearrangements of proposed linked cubane systems, and the propensity for 1,3,7-octatrienes to undergo [3,3] and [3,5] sigmatropic shifts. Also discussed is electrocyclizations under the influence of metal catalysts in the endo/exo selectivity of carbocation cyclizations and the proposed reaction cascade electrocyclizations thought to be involved in the production of Nitrogen analogs of the classic Nazarov product structure. Additionally, research and development in the field of chemical education is presented, specifically in the adaptation of computational chemistry research techniques to Blind and Visually Impaired (BVI) undergraduate and graduate students, as well as the development of curriculum for chemistry camps targeting young BVI students to encourage them to continue their education into chemistry and other Science, Technology, Engineering, and Mathematics (STEM) fields. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]