Estimating the binding energies of small molecules to RNA could help uncover their molecular recognition characteristics and be used to rationally design RNA-targeting chemical probes. Here, we leveraged the ability of the fragment molecular orbital (FMO) method to provide detailed pairwise energetic information to examine the interactions between the aptamer domain of the flavin mononucleotide (FMN)-responsive riboswitch and small-molecule ligands. After developing an efficient protocol for executing high-level FMO calculations on RNA-ligand complexes, we applied our protocol to nine FMN-aptamer-ligand complexes. We then used the results to identify "hot-spots" within the aptamer and decomposed pairwise interactions between the hot-spot residues and the ligands. Interestingly, we found that several of these hot-spot residues interact with the ligands via atypical CH···O hydrogen bonds and anion-π contacts, as well as (face-to-edge) T-shaped π-π interactions. We envision that our results should pave the way for the wider and more prominent use of FMO calculations to study structure-energy relationships in diverse RNA-ligand systems, which in turn may provide a basis for dissecting the molecular recognition characteristics of RNAs.