An energy-modified quantum defect method for the analysis of Rydberg spectra: Application to 2-butyne

Area of Science:

• Quantum Chemistry
• Molecular Spectroscopy
• Theoretical Chemistry

Background:

• High-resolution Rydberg absorption spectra provide crucial data for understanding molecular electronic structure.
• Interpreting complex spectra, especially for molecules like 2-butyne, often requires advanced theoretical methods.
• Traditional ab initio techniques can face challenges in accurately describing highly bound discrete states.

Purpose of the Study:

• To interpret the high-resolution Rydberg absorption spectrum of 2-butyne (C4H6).
• To apply multichannel quantum defect theory (MQDT) by extending continuum scattering calculations into the discrete spectral region.
• To demonstrate the utility of first-principles continuum calculations for analyzing challenging discrete electronic states.

Main Methods:

• Utilized multichannel quantum defect theory (MQDT).
• Adapted continuum scattering calculations and reaction matrices to the discrete Rydberg region using an energy-modified MQDT formulation.
• Incorporated energy dependences of quantum defects and dipole transition moments.

Main Results:

• Successfully interpreted over 40 Rydberg states (n ≈ 10 down to 3d and 4s levels) with an RMS error < 20 cm⁻¹.
• Identified five distinct Rydberg series belonging to three molecular symmetries.
• Observed that the Rydberg spectrum is dominated by the excitation of an e″ symmetry electron (fδ and gπ type).

Conclusions:

• The extended MQDT approach effectively interprets complex Rydberg spectra, outperforming standard ab initio methods for highly bound states.
• The study highlights the power of first-principles continuum calculations in molecular spectroscopy.
• Future work will quantitatively treat dipole absorption cross sections.