Tunneling And Ring Opening In The Cyclopropyl Radical And Cation

We report spectroscopic studies of the cyclopropyl radical and cation (c-C$_{3}$H$_{5}$). The cation especially is unstable towards ring-opening to allylic geometries, and the radical exhibits tunneling splitting due to inversion tunneling by the $\alpha$-H atom that lies out of the C-C-C ring plane$^{1}$. These large amplitude motion phenomena complicate the photoionization (and other) spectra and the determination of properties that are of interest due to ring strain in this fundamental cyclic radical. Through a multiscale reduced-dimension $\textit{ab initio}$ description of the potential energy surfaces of both the radical and the cation, the rotational and ionization spectra of the radical are simulated using advanced perturbative and variational rovibrational treatments. The results are compared with experimental photoionization data from the literature and new measurements$^{2}$. \noindent{[1] Dong $\textit{et al.}$; J. Phys. Chem. A; 2006; 110; 3059-3070.} \noindent{[2] Dyke $\textit{et al.}$; J. Chem. Soc., Faraday Trans. 2; 1985; 81; 1573-1586.

Franck-Condon spectra of unbound and imaginary-frequency vibrations via correlation functions: a branch-cut free, numerically stable derivation

Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both real and imaginary harmonic frequencies. The derivation rests on Lie algebra techniques that map otherwise complicated exponential operator arithmetic to simpler matrix formulae. The expressions for the zero- and finite-temperature harmonic auto-correlation functions have been carefully structured both to be free of branch-cut discontinuities and to remain numerically stable with finite-precision arithmetic. Simple extensions correct the harmonic Franck-Condon approximation for the lowest-order anharmonic and Herzberg-Teller effects. Quantitative simulations are shown for several examples, including the electronic absorption spectra of F$_2$, HOCl, CH$_2$NH, and NO$_2$.Comment: 34 pages, 4 figure