High elasticity is one of the most important characteristics of polymers. The entropy-driven elastic behavior dominates the low force regime. The entropic elasticity of single polymer chains can be described by one of the three classical models (i.e., the freely jointed chain, freely rotating chain, and wormlike chain models). At high forces, however, enthalpic elasticity which results from backbone deformations (variation of the bond length and angle) largely dominates single polymer elasticity. When the theoretical enthalpic elasticity of the polymer backbone from quantum mechanical (QM) calculations is considered, the backbone-determined polymer elasticity can be well described. These modified models are called QM models. Further force measurements reveal that in certain environments (e.g., in water or vacuum), the noncovalent interactions between side groups can significantly contribute to the single polymer elasticity. In this case, even the QM models failed to describe the elastic behavior of single polymers. In this study, the kinetics of noncovalent interactions with two states is incorporated into the QM models, where the effects of side groups are quantitatively taken into account. Experimentally, the single-chain elasticities of polymers with various backbone and side groups are obtained by means of single-molecule atomic force microscopy. It is found that for different types of polymers, theoretical predictions from the new models consist well with the experimental results. Accordingly, the noncovalent interactions in polymer systems can be precisely analyzed. By taking into account the effects of both polymer backbone and side groups, the new models, which are called TSQM models, are upgraded into structure-relevant quantitative ones. It is expected that the TSQM models can be used as general polymer models to reveal the structure and behavior of single polymer chains in various environments.