Neglected Importance of Anharmonicity in Quantifying the Renner-Teller Effect

Area of Science:

• Quantum chemistry
• Molecular spectroscopy
• Theoretical chemistry

Background:

• Linear molecules in degenerate electronic states exhibit the Renner-Teller (RT) effect.
• Existing formulas for quantifying the RT effect primarily use harmonic terms.
• Harmonic approximations are insufficient for molecules with double-well potentials along bending coordinates.

Purpose of the Study:

• To develop a novel formula for quantifying the Renner-Teller effect.
• To incorporate anharmonic terms into the RT effect quantification.
• To improve the description of vibronic interactions in molecules with double-well potentials.

Main Methods:

• Development of a new mathematical formula for the RT effect.
• Inclusion of anharmonic terms, sign functions, and delta functions.
• Mathematical proof of the formula's capability to differentiate RT splitting degrees.

Main Results:

• The proposed formula explicitly includes anharmonic terms for improved accuracy.
• A parameter derived from the new formula categorizes RT effect strength: weak (<1, positive), medium (negative), and large (>1).
• The formula successfully differentiates various degrees of Renner-Teller splitting.

Conclusions:

• The new formula provides a more accurate quantification of the Renner-Teller effect, especially for systems with anharmonic potentials.
• It offers a robust method for classifying the magnitude of the RT effect in different molecular systems.
• This work advances the understanding of vibronic interactions in linear molecules with degenerate electronic states.