Optimized coordinates for anharmonic vibrational structure theories.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Molecular Spectroscopy

Background:

• The vibrational self-consistent-field (VSCF) method is a key tool for calculating molecular vibrational energies.
• Normal coordinates, while useful, do not always provide the most efficient basis for VSCF calculations, especially for anharmonic systems.
• Previous work by Thompson and Truhlar laid groundwork for optimizing vibrational coordinates.

Purpose of the Study:

• To develop a procedure for determining optimal vibrational coordinates that minimize VSCF energy.
• To introduce new vibrational structure methods based on these optimized coordinates.
• To assess the performance and accuracy improvements offered by the new methods.

Main Methods:

• Developed a procedure to find optimal vibrational coordinates by minimizing VSCF ground-state energy.
• Implemented a robust optimization algorithm using Jacobi matrices.
• Introduced optimized-coordinate VSCF (oc-VSCF) and optimized-coordinate vibrational configuration interaction (oc-VCI) methods.
• Applied and tested methods on water, water dimer, and ethylene molecules.

Main Results:

• Optimized coordinates balance localization (high-frequency modes) and delocalization (low-frequency modes).
• oc-VSCF outperforms standard VSCF for localized modes.
• oc-VCI shows significantly faster convergence than VCI with respect to excitation rank.
• Reduced mean absolute errors in vibrational frequencies for water and water dimer using oc-VCI.
• Decreased mode coupling in ethylene's potential energy surface.

Conclusions:

• The developed optimal vibrational coordinates offer a more efficient basis for vibrational structure calculations.
• oc-VSCF and oc-VCI provide enhanced accuracy and faster convergence compared to traditional methods.
• The new methods are particularly beneficial for systems with mixed vibrational characteristics (e.g., stretching and skeletal modes).