Optimized curvilinear coordinates in vibration correlation methods: Quasi-degenerate perturbation theory

We employ curvilinear molecular vibrational coordinates constructed using recently developed normalizing flow techniques and optimize them within the vibrational self-consistent field framework. This is done by minimizing either the ground-state vibrational energy or a configuration-averaged energy over a selected set of vibrational states. The quality of the optimized coordinates for correlated calculations is assessed using second-order quasi-degenerate vibrational perturbation theory. Applications to H2CO, trans-HCOOH, and CH3F demonstrate significant improvements in vibrational energies compared to standard valence coordinates, across fundamental, combination, and overtone bands, including states exhibiting strong Fermi resonances. The improvements arise from a reduction in vibration correlation, produced by redistributing dominant low-order couplings in the Hamiltonian into weaker and more uniformly distributed higher-order contributions.