Accurate and Affordable Vibrational Spectra of Large Molecules: Primary, Auxiliary, and Spectator Modes in a Perturb-then-Diagonalize Framework

Vibrational spectra convey a wealth of structural and dynamical information; however, their reliable assignment and interpretation often benefit from the integration of complementary spectroscopic techniques and require the support of accurate quantum chemical calculations. The harmonic approximation is frequently insufficient for quantitative spectroscopy, while fully anharmonic treatments rapidly become computationally prohibitive for large and flexible molecular systems, in particular, for biomolecules. In this framework, we introduce a general perturb-then-diagonalize approach that relies on a three-class partitioning of normal modes into primary, auxiliary, and spectator subsets and combines numerical strategies based on analytical Hessians and analytical gradients. Accurate anharmonic contributions are explicitly included for the modes of primary interest, while the influence of external modes is accounted for through finite differences of analytical gradients, avoiding the much more expensive evaluation of Hessians. Several case studies demonstrate the robustness, ease of use, and accuracy of the proposed approach across a broad range of molecular systems, including situations in which vibrational and rotational spectroscopic data provide complementary information. When combined with a dual-level strategy in which accurate methods are employed for harmonic terms and less expensive methods for anharmonic contributions, the present framework enables vibrational spectra of near-spectroscopic accuracy for biomolecules and other chemically rich systems. More complex environments can be addressed by coupling the method with multilayer approaches.