Rotational excitation of asymmetric-top molecular ions by electron impact: application to H$_2$O$^+$, HDO$^+$, and D$_2$O$^+$

Abstract

The rotational excitation of the three asymmetric-top molecular ion isotopologues H$_2$O$^+$, HDO$^+$, and D$_2$O$^+$ is studied theoretically using a combined framework of electron-molecule R-matrix scattering theory, multichannel quantum-defect theory, frame transformation theory, and the Coulomb-Born approximation. The latter two have been adapted here for asymmetric-top rotors. State-resolved cross sections and kinetic rate coefficients for transitions from the rotational ground state of the ions are presented. State-resolved rate coefficients for all calculated transitions $N=0\ldotstwo4$ are included as supplementary material and will be made available through the EMAA database.

Figures (4)

• Figure 1: The lowest few rotational states of the H2O+, HDO+, and D2O+ molecular ions within the ground vibronic state. The states are represented as small horizontal bars plotted at their rotational energy, their radiative transition lifetime $\tau$ is given to the nearest integer in seconds above the bar, and below the bar is the rotational state label $N_{K_aK_c}$. Lifetimes are determined from the Einstein $A$ coefficient for radiative decay, which is zero for dipole-forbidden transitions. States that have no dipole-allowed decay channels are assigned the lifetime $\infty$. Horizontal spacing is added for legibility, and colors are used to further distinguish between states with different $N$.
• Figure 2: The different cross sections for all dipole-allowed transitions in H2O+ (top left), D2O+ (top right), and HDO+ (bottom row) from the ground rotational state $0_{00}$, with each of the four cross sections in (\ref{['eqn:CB_combine']}) plotted. Note that HDO+ has two dipole-allowed transitions: $0_{00}\to1_{11}$ and $0_{00}\to1_{01}$. The rotational excitation threshold is denoted by a thin grey vertical line.
• Figure 3: Rate coefficients for all allowed transitions from $N=0\to1$ for H2O+, HDO+, and D2O+. Dashed lines represent transitions that are only allowed for HDO+ because of its lack of ortho/para symmetry.
• Figure 4: Rotational excitation (upper row) and de-excitation (lower row) rate coefficients as a function of kinetic temperature for H2O+ (left), HDO+, (middle), and D2O+ (right). Solid blue lines represent dipole-allowed transitions, dashed orange lines represent non-dipolar transitions.