An understanding of protein stability requires capturing dynamic rearrangements and coupled properties over long lengthscales. Nevertheless, the extent of coupling in these systems has typically only been studied for classical degrees of freedom. To understand the potential benefit of extending such analysis to the coupling of electronic structure properties, we have carried out extensive semi-empirical quantum mechanical molecular dynamics of two Trp-cage variants. Small differences in the sequence of the two peptides lead to differences in their thermal stability that are revealed through electronic structure coupling analysis. In comparison, we find limited evidence that geometric coupling can distinguish the behavior of the two peptides. We show that Asp1 in the more stable variant shows significantly enhanced coupling to both sequence-adjacent and more sequence-distant residues. Non-nearest-neighbor couplings are stronger in the more stable variant, indicating a network of residues that help stabilize the protein. Our study highlights the complementary benefit of charge coupling analysis to interpret protein structure-function relationships.