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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~)
\begin{equation} \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 \
| 0
1, +1 \rangle \\ | + \rangle | +\frac{1}{2} \rangle \
| 0
1, -1 \rangle \\ | + \rangle | -\frac{1}{2} \rangle \
| +1
2, 0 \rangle \\ | - \rangle | -\frac{1}{2} \rangle \
| +1
2, +2 \rangle \end{array} \right) \notag \
, \end{equation} where $| \Lambda \rangle | \Sigma \rangle | K
v_2, l \rangle = | - \rangle | +\frac{1}{2} \rangle | 0
1, +1 \rangle$ $etc.$ are basis functions of the vibronic Hamiltonian for the numerical diagonalization, and $| \Lambda \rangle$, $| \Sigma \rangle$, and $| K
v_2, l \rangle$ 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
\begin{equation} \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 \
| 0
1, -1 \rangle \\ | + \rangle | -\frac{1}{2} \rangle \
| +1
2, 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 \
| 0
1, +1 \rangle \\ | - \rangle | -\frac{1}{2} \rangle \
| +1
2, +2 \rangle \end{array} \right) \notag \
, \end{equation} 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:2016-08-22


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