Bound and autoionizing potential energy curves in the CH molecule

TL;DR

This work develops a MQDT-based framework to extract bound-state and autoionizing potential-energy curves for CH from fixed-nuclei $R$-matrix data of CH$^+$, using two complementary routes: bound-state determination through closed-channel eigenphase analysis and autoionizing resonances from the energy dependence of the eigenphase sum. By transforming the short-range $R$-matrix to a physical $K$-matrix and selectively eliminating strongly closed channels, the authors obtain smooth, dense curves for five molecular symmetries and, where possible, their autoionizing widths. The study delivers extensive datasets of bound-state and autoionizing curves, with widths, organized by symmetry and supplemented by graphs and downloadable tables, enabling improved modeling of CH-related processes such as dissociative recombination. The approach demonstrates how fixed-nuclei scattering information can yield detailed bound-state and resonance structures, providing a valuable resource for benchmark calculations and future rovibrational or DR investigations in CH systems.

Abstract

This article presents a method of computing bound state potential curves and autoionizing curves using fixed-nuclei R-matrix data extracted from the Quantemol-N software suite. It is a method based on two related approaches of multichannel quantum-defect theory. One is applying bound-state boundary conditions to closed-channel asymptotic solution matrices and the other is searching for resonance positions via eigenphase shift analysis. We apply the method to the CH molecule to produce dense potential-curve data sets presented as graphs and supplied as tables in the publication supplement.

Figures (13)

• Figure 1: The energy derivative of the eigenphase sum at two inter-nuclear distances (for the $^2\Sigma^+$ symmetry, zoomed-in to a particular energy window). The widest peak visible at the $R=2.46$ bohr passes underneath the three narrow peaks at $R=2.47$ bohr.
• Figure 2: The full breadth of the $^2\Sigma^+$ symmetry curves of CH. The thick dashed curves are the CH$^+$ target states. The autoionizing curves are the continuous red curves between the ground target state and first excited target state. The bound-state curves are the continuous blue curves below the ground target state.
• Figure 3: The $^2\Sigma^+$ symmetry curves zoomed in. The dashed curves are CH$^+$ target states. The continuous curves above X$^1\Sigma^+$ are autoionizing curves and the ones below are bound-state curves.
• Figure 4: The $^2\Sigma^+$ symmetry curves relative to the ground target state energy (zoomed in to energies close to threshold). The autoionizing curves above threshold now also have a shaded area denoting curve widths.
• Figure 5: The $^2\Sigma^+$ symmetry bound-state curve effective quantum number (compared to ground target state).