Effect of the avoided crossing on the rovibrational energy levels, resonances, and predissociation lifetimes within the ground and first excited electronic states of lithium fluoride

TL;DR

This work develops a two-state, diabatized framework to describe LiF rovibrational spectra involving the X $^1\Sigma^{+}$ and B $^1\Sigma^{+}$ states near the avoided crossing. Ab initio MRDCI calculations supply adiabatic potentials, NACME, and DMFs over $r=1$–$17$ bohr, which are then analytically modeled and rotated to a smooth diabatic representation with a near-constant coupling, enabling stable two-channel calculations. The coupled equations are solved with the sinc-DVR method to obtain bound energies, resonances, and predissociation lifetimes, achieving transition frequency accuracies on the order of $10^{-3}$ cm$^{-1}$ and producing comprehensive X–X rovibrational line lists for $^{6}$LiF and $^{7}$LiF up to high $v$ and $J$. The study reveals two resonance types (tunneling below the barrier and crossing-induced above it), provides robust methods to extract $E_J$ and $\Gamma_J$, and demonstrates good agreement with experimental data and ExoMol benchmarks. Overall, it extends LiF spectroscopy to the first dissociation limit and offers a general diabatization-based framework applicable to other alkali halides with avoided crossings.

Abstract

We investigate the LiF spectrum up to $7800$ cm$^{-1}$ above the first dissociation limit. The ab initio calculations of the adiabatic potentials and other molecular functions are performed in a wide range of interatomic separations, $r=1$-17 bohr. We consider the model of two interacting electronic states including both the bound states and the resonances of two kinds, the tunneling resonances and the predissociative ones. The Born-Oppenheimer potentials are modeled with use of two functions imitating the diabatic terms whereas the coupling between them was set constant equal to the half of the minimum separation between the adiabatic terms, and then we define the final diabatic terms and the final diabatic coupling via the adiabatic potentials and the angle of the adiabatic-to-diabatic basis rotation obtained by integration of the nonadiabatic coupling matrix element. The energies of the bound states, as well as the positions and widths of the resonances are calculated. The observed transition frequencies are reproduced with the standard deviation of 0.0009 cm$^{-1}$ for $^7$LiF, 0.0006 cm$^{-1}$ for $^6$LiF, and within the experimental uncertainties for the most of the lines. The line lists for the bound-bound $X$-$X$ rovibrational transitions are calculated for quantum numbers $v\le50,Δv\le15,J\le170$ ($J\le200$ for the 0-0 and 1-0 bands).

Figures (10)

• Figure 1: The ab initio values of $\mathcal{N}$ (points) and the fit.
• Figure 2: The BO adiabatic ab initio (points) and fitted (full lines) potentials are shown along with the Rittner potential (dotted line) on the top panel; the BO diabatic potentials (dashed lines) and the diabatic coupling (dotted line) are shown on the bottom panel.
• Figure 3: The same as in Fig. \ref{['fig:Uadiadia']} in the region of the avoided crossing.
• Figure 4: The ab initio and fitted adiabatic dipole-moment functions.
• Figure 5: The mass-dependent nonadiabatic contribution to the ground-state potential. $\Tilde{N}_{11}=\mathcal{N}_{11}\cdot\mu/\hbar^2.$