Topology-dependent refinement of molecular structures and vibrational properties

High-resolution rotational and vibrational spectroscopies now probe structural effects at a scale where the residual error of practical electronic-structure models is no longer a negligible background. For medium-sized molecules, this issue is especially evident in equilibrium structures, rotational constants, and vibrational frequencies derived from density-functional theory treatments. We introduce a topology-dependent local refinement scheme in which the residual error of a double-hybrid functional reference is corrected in the representation where it is most compact. A transferable core-valence layer, evaluated either empirically or using second-order Møller-Plesset perturbation theory, is kept separate from the valence hierarchy and can be applied from level 0 onward. At level 1, the bond field level 1 refinement contains the conjugation term, whereas pair-local level 1 generalizes the valence correction to additional selected atom-pair classes. Selected vibrational residuals are represented in normal-mode or fragment space. The correction layer is continuous along the potential-energy surface and anchors the residual term to a chemically defined local environment. The approach is assessed for polycyclic aromatic hydrocarbons, intramolecular OH⋯O systems, carbohydrates, and a nucleoside. In rigid covalent molecules, rotational-constant errors near 1% at the hybrid functional level are reduced by more than an order of magnitude. In hydrogen-bonded carbohydrates, the pair-local refinement lowers the discrepancies to below 0.3%. The OH⋯O(H) class provides an explicit case in which a transferable pair-local correction can be parameterized within an accessible high-level reference window. The results indicate that residual structural and vibrational errors are not best treated as uniform empirical remainders. They can be organized in low-dimensional representations selected by the molecular topology and by the observable being refined, providing an economical route to improved equilibrium structures and localized vibrational treatments within standard electronic-structure workflows.