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

Area of Science:

• Quantum Chemistry
• Molecular Spectroscopy
• Computational Chemistry

Background:

• Standard valence coordinates can limit accuracy in molecular vibrational energy calculations.
• Vibrational self-consistent field (VSCF) methods are widely used but can be sensitive to coordinate choices.
• Correlated calculations often require sophisticated coordinate systems for high precision.

Purpose of the Study:

• To introduce and validate a novel set of curvilinear molecular vibrational coordinates.
• To improve the accuracy of vibrational energy calculations within the VSCF framework.
• To assess the performance of these coordinates for correlated calculations using perturbation theory.

Main Methods:

• Utilized normalizing flow techniques to construct curvilinear molecular vibrational coordinates.
• Optimized these coordinates using the vibrational self-consistent field (VSCF) framework.
• Assessed coordinate quality with second-order quasi-degenerate vibrational perturbation theory (QD-VPT2).

Main Results:

• Optimized curvilinear coordinates significantly improved vibrational energies for H2CO, trans-HCOOH, and CH3F.
• Enhancements were observed across fundamental, combination, and overtone vibrational bands.
• The new coordinates effectively handled states with strong Fermi resonances.

Conclusions:

• The developed curvilinear coordinates offer substantial improvements over standard valence coordinates.
• These coordinates reduce vibrational correlation by redistributing Hamiltonian couplings.
• This approach provides a more accurate foundation for computational molecular spectroscopy.