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 Title: Vibrational analysis of SICN X̃ 2Π system Author(s): Fukushima, Masaru Contributor(s): Ishiwata, Takashi Subject(s): Vibrational structure/frequencies Abstract: The laser induced fluorescence (~LIF~) spectrum of the $\tilde{A}$ $^2\Delta$ -- $\tilde{X}$ $^2\Pi$ transition was obtained for SiCN generated by laser ablation under supersonic free jet expansion. The vibrational structure of the dispersed fluorescence (~DF~) spectra from single vibronic levels (~SVL's~) was analyzed by numerical diagonalization procedure, in which Renner-Teller (~R-T~), anhamonicity, spin-orbit (~SO~), Herzberg-Teller (~H-T~), Fermi, and Sears interactions have been considered, where the Sears resonance is a second-order interaction combined from SO and H-T interactions with $\Delta K = \pm1$, $\Delta \Sigma = \mp1$, and $\Delta P = 0$. Four vibronic levels, $(01^10) \\mu \\Sigma_{\frac{1}{2}}^{(-)}$, $\kappa \\Sigma_{\frac{1}{2}}^{(+)}$, $(02^00) \\mu$ and $\kappa \\Pi_{\frac{1}{2}}$, are almost closed within the four basis functions by R-T and Sears interactions (~i.e.~the four-by-four transformation matrix below is close to ortho-normal~) \left( \begin{array}{l} |(01^10) \\mu \^2\Sigma^{(-)}\rangle \\ |(01^10) \\kappa \^2\Sigma^{(+)}\rangle \\ |(02^00) \\mu \^2\Pi_{\frac{1}{2}}\rangle \\ |(02^00) \\kappa \^2\Pi_{\frac{1}{2}}\rangle \end{array} \right) = \left( \begin{array}{rrrr} 0.9 & -0.4 & 0.0 & 0.0 \\ 0.4 & 0.8 & 0.3 & -0.2 \\ 0.2 & 0.4 & -0.8 & 0.4 \\ 0.0 & 0.0 & -0.5 & -0.8 \end{array} \right) \left( \begin{array}{l} | - \rangle | +\frac{1}{2} \rangle \| 01, +1 \rangle \\ | + \rangle | +\frac{1}{2} \rangle \| 01, -1 \rangle \\ | + \rangle | -\frac{1}{2} \rangle \| +12, 0 \rangle \\ | - \rangle | -\frac{1}{2} \rangle \| +12, +2 \rangle \end{array} \right) \notag \, where $| \Lambda \rangle | \Sigma \rangle | Kv_2, l \rangle = | - \rangle | +\frac{1}{2} \rangle | 01, +1 \rangle$ $etc.$ are basis functions of the vibronic Hamiltonian for the numerical diagonalization, and $| \Lambda \rangle$, $| \Sigma \rangle$, and $| Kv_2, l \rangle$ are basis functions of electronic, electron spin, and two dimensional harmonic oscillator, respectively. \if0 The two levels, $(01^10) \\kappa \\Sigma_{\frac{1}{2}}^{(+)}$ and $(02^00) \\mu \\Pi_{\frac{1}{2}}$, with $\Delta K = \pm1$ and $\Delta P = 0$, show typical example of Sears resonance with an almost one-to-one mixing \left( \begin{array}{l} |(01^10) \\kappa \^2\Sigma^{(+)}\rangle \\ |(02^00) \\mu \^2\Pi_{\frac{1}{2}}\rangle \end{array} \right) = \left( \begin{array}{rrrr} 0.8 & 0.3 \\ 0.4 & -0.8 \\ \end{array} \right) \left( \begin{array}{l} | + \rangle | +\frac{1}{2} \rangle \| 01, -1 \rangle \\ | + \rangle | -\frac{1}{2} \rangle \| +12, 0 \rangle \end{array} \right) \+ \\left( \begin{array}{rrrr} 0.4 & -0.2 \\ 0.2 & 0.4 \end{array} \right) \left( \begin{array}{l} | - \rangle | +\frac{1}{2} \rangle \| 01, +1 \rangle \\ | - \rangle | -\frac{1}{2} \rangle \| +12, +2 \rangle \end{array} \right) \notag \, where the off-diagonal terms are caused by Sears resonance, while the diagonals are came from R-T mostly. \fi The mixing coefficients of the two vibronic levels agree with those obtained from computational studies\footnote{V.~Brites, A.~O.~Mitrushchenkov, and C.~L\'{e}onard, J.~Chem.~Phys. 138, 104311 (2013)C.~L\'{e}onard, Private communication.}. The two levels among the four above, $(01^10) \\kappa \\Sigma_{\frac{1}{2}}^{(+)}$ and $(02^00) \\mu \\Pi_{\frac{1}{2}}$, with $\Delta K = \pm1$ and $\Delta P = 0$, show typical example of Sears resonance with an almost one-to-one mixing. Even for levels lying at $\sim$ 1,000 cm$^{-1}$, some of them are mixed heavily and widely with several levels, and their vibrational quantum numbers are thus meaningless. Issue Date: 2016-06-21 Publisher: International Symposium on Molecular Spectroscopy Genre: Conference Paper/Presentation Type: Text Language: En URI: http://hdl.handle.net/2142/91072 Rights Information: Copyright 2016 by the authors Date Available in IDEALS: 2017-01-26
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