Single-walled carbon nanotubes (SWCNTs) are unique materials that exhibit chirality-specific properties due to their one-dimensional confinement. As a result, they are explored for a wide range of applications including single-photon sources in communications devices. Despite progress in this area, SWCNTs still suffer from a relatively narrow range of energies of emission features that fall short of the ~1500 nm desired for long-distance lossless data transfer. One approach that is frequently used to resolve this involves chemical functionalization with aryl groups. However, this approach is met with a number of fundamental issues. First, chirality-specific SWCNTs must be acquired for subsequent functionalization. Synthesis of such samples has thus far eluded experimental efforts. As such, post-synthetic non-covalent functionalization is required to break bundles and create disperse SWCNTs that can undergo further separation, processing, and functionalization. Second, a number of low-energy emission features are introduced upon functionalization across a 200 nm range. The origin of such diverse emission features remains unknown. The research presented here focuses on computationally addressing these issues. A series of polyfluorene polymers possessing sidechains of varying length are explored using molecular mechanics to determine the impact of alkyl sidechains on SWCNT-conjugated polymer interaction strength and morphology. Additionally, density functional theory (DFT) and linear-response time-dependent DFT (TDDFT) are used to explore the effect of functionalization on emission features. A prerequisite to these calculations involves constructing finite-length SWCNT systems with similar electronic structure to their infinite counterparts: a methodological approach for the formation of such systems is presented. The optical features for aryl-functionalized SWCNTs are then explored. It is shown that the predominant effect on the energies of emission features involves the configuration of functionalization, with the identity of the functional group only playing a minor role. While the qualitative effect of such functionalization is determined, a quantitative comparison to experiment requires correction for several sources of computational error. A model to correct for such effects is also developed. This research not only explains the origin of the multiple emission features in functionalized SWCNTs for the first time but also lays the groundwork for their further computational exploration.