Generalized vibrational perturbation theory in curvilinear internal coordinates: Theory and applications

Second-order vibrational perturbation theory (VPT2) is widely employed for the calculation of anharmonic vibrational properties thanks to its favorable balance between accuracy and computational cost. However, the presence of strong vibrational resonances requires dedicated treatments beyond standard perturbative approaches. In this work, a generalized VPT2 framework based on curvilinear internal coordinates is developed. Closed-form expressions are derived for the interaction terms associated with Fermi and Darling–Dennison resonances, including 1–1, 2–2, and 1–3 couplings. In contrast to conventional Cartesian-coordinate formulations, the present treatment accounts for additional kinetic-energy contributions arising from the non-diagonal form of the vibrational kinetic-energy operator. The resulting methodology has been implemented in a general computational engine and has been validated through applications to representative molecular systems. The importance of the variational treatment of resonances is highlighted through the investigation of selected case studies, while the flexibility of the proposed framework is demonstrated through its combination with dual-level schemes employing different electronic-structure methods for harmonic and anharmonic contributions. The present work extends the applicability of perturb-then-diagonalize approaches in curvilinear coordinates and provides an efficient route toward accurate anharmonic calculations for medium- and large-sized molecular systems.