The article information
 Masaaki Baba, Ayumi Kanaoka, Akiko Nishiyama, Masatoshi Misono, Takayoshi Ishimoto, Taro Udagawa
 Baba Masaaki, Kanaoka Ayumi, Nishiyama Akiko, Misono Masatoshi, Ishimoto Takayoshi, Udagawa Taro
 Large Amplitude Motion in 9Methylanthracene: HighResolution Spectroscopy and Ab Initio Theoretical Calculation
 利用高分辨率光谱和从头算理论研究9甲基蒽的大振幅运动
 Chinese Journal of Chemical Physics, 2020, 33(1): 812
 化学物理学报, 2020, 33(1): 812
 http://dx.doi.org/10.1063/16740068/cjcp1910188

Article history
 Received on: October 27, 2019
 Accepted on: December 13, 2019
b. Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Toruń 87100, Poland;
c. Department of Applied Physics, Faculty of Science, Fukuoka University, Jonanku, Fukuoka 8140180, Japan;
d. Association of International Arts and Science Institute of Natural Science, Yokohama City University, Kanazawaku, Yokohama 2360027, Japan;
e. Department of Chemistry and Biomolecular Science, Faculty of Engineering, Gifu University, Yanagido, Gifu 5011193, Japan
Large amplitude motion plays an important role in the excitedstate dynamics of a polyatomic molecule. CH
For 9MA, the potential energy curve shows a sixfold barrier because of CH
It is of note that the barrier height is considerably different between 9MA
The detail of our experimental setup is described here briefly. The light source for highresolution spectroscopy was a singlemode Ti:Sapphire laser (Microlase, MBR110) pumped by a CW Nd:YVO
In order to accurately stabilize and to control the laser light wavelength, we employed a homemade system of an optical frequency comb locked to the GPS signal. The uncertainties in determining the transition frequencies of observed spectral lines were approximately 10 kHz in our measurement system.
The laser light beam was crossed with a pulsed supersonic jet collimated by a conical skimmer (orifice diameter 2 mm) at right angles to get rid of Doppler broadening. Fluorescence from the excited molecules was collected to the cathode's surface of a photomultiplier (Hamamatsu R595) and the output was processed by a gated photon counter (Stanford Research SR400). The change in fluorescence intensity with the laser light wavelength was recorded as a Dopperfree fluorescence excitation spectrum using the Labview system.
Ⅲ. LEVEL STRUCTURE OF CHIn CH
$ \begin{eqnarray} \left[ F \frac{\partial^2}{\partial \phi^2} + \frac{V_3}{2} (1\cos 3\phi) \right]\Psi = E_m \Psi \label{eq:01 HamiltonianCH3} \end{eqnarray} $  (1) 
where
$ \begin{eqnarray} E_{m} = F{m}^2 \;, \; \:\:\:\: m = 0, \pm1, \pm2, \cdots \label{eq:02 V=0Eigenvalue} \end{eqnarray} $  (2) 
The eigenvalues for
$ \begin{eqnarray} \langle m  H  m \rangle \hspace{0.15cm}&=&\hspace{0.15cm} F m^2 + \frac{V_3}{2}\end{eqnarray} $  (3) 
$ \begin{eqnarray} \langle m  H  m \pm 3 \rangle \hspace{0.15cm}&=&\hspace{0.15cm}  \frac{V_3}{4}\end{eqnarray} $  (4) 
The
In the case of 9MA, the potential energy curve is sixfold symmetric with respect to the CH
$ \begin{eqnarray} \left[ F \frac{\partial^2}{\partial \phi^2} + \frac{V_6}{2} (1\cos 6\phi) \right] \Psi = E_m \Psi \end{eqnarray} $  (5) 
The eigenvalues are obtained by diagonalizing the energy matrix, in which nonvanishing matrix elements are
$ \begin{eqnarray} \langle m  H  m \rangle &=& F m^2 + \frac{V_6}{2} \end{eqnarray} $  (6) 
$ \begin{eqnarray} \langle m  H  m \pm 6 \rangle &=&  \frac{V_6}{4} \end{eqnarray} $  (7) 
The
Two conformers, staggered (FIG. 2(a)) and eclipsed (FIG. 2(b)), are considered to be the stable structures at the potential minima. The rotational constants are, however, identical because the CH
FIG. 3 shows the Dopplerfree fluorescence excitation spectrum of 9MA
First, we performed theoretical calculations at the standard level with geometry optimization, MP2/631G(d, p) for the S
We found that the observed highresolution spectrum was not simply reproduced only with the rigidrotor rotational constants,
$ \begin{eqnarray} \hat{H} & = &  \frac{1}{2m_e} \sum\limits_i \nabla_i{^2}  \sum\limits_i \sum\limits_A \frac{Z_A}{r_{iA}} + \sum\limits_{i>j} \frac{1}{r_{ij}} \nonumber \\ & & \frac{1}{2 M_p} \sum\limits_p \nabla_p{^2} + \sum\limits_{p} \sum\limits_{A} \frac{Z_p Z_A}{r_{pA}} +\sum\limits_{p>q} \frac{Z_p Z_q}{r_{pq}} \nonumber \\ && \sum\limits_i \sum\limits_p \frac{Z_p}{r_{ip}} + \sum\limits_{A>B}^M \frac{Z_A Z_B}{R_{AB}} \; \label{eq:07 HamiltonianMCMO} \end{eqnarray} $  (8) 
The indices of
We calculated the barrier height to CH
Although the MC_MOMP2 calculations reproduced the barrierheight reduction in 9MA
It should be noted that the main cause of barrier to CH
In summary, the vibrational and rotational level structure of 9methylanthracene has been investigated by observing and analyzing the highresolution and highprecision spectrum, and it is well understood with the basic theoretical considerations originally established by LiHong Xu and Jon Hougen for small molecules such as methanol and acetaldehyde. The final goal is to perform a global fit of all vibrational and rotational levels relatied to the CH
Masaaki Baba is deeply grateful to the late Dr. LiHong Xu and Dr. Jon T. Hougen for their kind help and encouragement for this work.
We all thank LiHong and Jon for their great contributions to establishing the Asian Workshop on Molecular Spectroscopy.
[1] 
L.H. Xu, and J. T. Hougen, J. Mol. Spectrosc.
173, 540(1995).
DOI:10.1006/jmsp.1995.1255 
[2] 
L.H. Xu, R. M. Lees, and J. T. Hougen, J. Chem. Phys.
110, 3835(1999).
DOI:10.1063/1.478272 
[3] 
L.H. Xu, J. T. Hougen, R. M. Lees, and M. A. Mekhtiev, J. Mol. Spectrosc.
214, 175(2002).
DOI:10.1006/jmsp.2002.8573 
[4] 
Y.P. Lee, Y.J. Wu, R. M. Lees, L.H. Xu, and J. T. Hougen, Science
311, 365(2006).
DOI:10.1126/science.1121300 
[5] 
L.H. Xu, J. T. Hougen, J. M. Fisher, and R. M. Lees, J. Mol. Spectrosc.
260, 88(2010).
DOI:10.1016/j.jms.2010.01.001 
[6] 
L.H. Xu, J. T. Hougen, and R. M. Lees, J. Mol. Spectrosc.
293, 38(2013).

[7] 
L.H. Xu, R. M. Lees, J. T. Hougen, J. M. Bowman, X. Huang, and S. Carter, J. Mol. Spectrosc.
299, 11(2014).
DOI:10.1016/j.jms.2014.02.007 
[8] 
S. P. Belov, G. Yu. Golubiatnikov, A. V. Lapinov, V. V. Ilyushin, E. A. Alekseev, A. A. Mescheryakov, J. T. Hougen, and L.H. Xu, J. Chem. Phys.
145, 024307(2016).
DOI:10.1063/1.4954941 
[9] 
L.H. Xu, E. M. Reid, B. Guislain, J. T. Hougen, E. A. Alekseev, and I. Krapivin, J. Mol. Spectrosc.
342, 116(2017).
DOI:10.1016/j.jms.2017.06.008 
[10] 
L.H. Xu, J. T. Hougen, G. Yu. Golubiatnikov, S. P. Belov, A. V. Lapinov, E. A. Alekseev, I. Krapivin, L. Margulés, R. A. Motiyenko, and S. Bailleux, J. Mol. Spectrosc.
357, 11(2019).
DOI:10.1016/j.jms.2018.12.003 
[11] 
D. R. Borst, and D. W. Pratt, J. Chem. Phys.
113, 3658(2000).
DOI:10.1063/1.1287392 
[12] 
M. Baba, K. Mori, M. Saito, Y. Kowaka, Y. Noma, S. Kasahara, T. Yamanaka, K. Okuyama, T. Ishimoto, and U. Nagashima, J. Phys. Chem. A
113, 2366(2009).
DOI:10.1021/jp808550r 
[13] 
M. Baba, I. Hanazaki, and U. Nagashima, J. Chem. Phys.
82, 3938(1985).
DOI:10.1063/1.448886 
[14] 
M. Baba, U. Nagashima, and I. Hanazaki, J. Chem. Phys.
83, 3514(1985).
DOI:10.1063/1.449156 
[15] 
J. D. Lewis, T. B. Malloy Jr., T. H. Chao, and J. Laane, J. Mol. Spectrosc.
12, 427(1972).

[16] 
J. D. Lewis, and J. Laane, J. Mol. Spectrosc.
65, 147(1977).
DOI:10.1016/00222852(77)903678 
[17] 
J. T. Hougen, J. Mol. Spectrosc.
256, 170(2009).
DOI:10.1016/j.jms.2009.04.011 
[18] 
A Program for Simulating Rotational Structure, C. M. Western, University of Bristol, http://pgopher.chm.bris.ac.uk

[19] 
M. Baba, M. Saitoh, K. Taguma, K. Shinohara, K. Yoshida, Y. Semba, S. Kasahara, N. Nakayama, H. Goto, T. Ishimoto, and U. Nagashima, J. Chem. Phys.
130, 134315(2009).
DOI:10.1063/1.3104811 
[20] 
T. Ishimoto, Y. Ishihara, H. Teramae, M. Baba, and U. Nagashima, J. Chem. Phys.
128, 184309(2008).
DOI:10.1063/1.2917149 
[21] 
T. Ishimoto, Y. Ishihara, H. Teramae, M. Baba, and U. Nagashima, J. Chem. Phys.
129, 214116(2008).
DOI:10.1063/1.3028540 
[22] 
T. Ishimoto, M. Baba, U. Nagashima, N. Nakayama, and M. Koyama, J. Comput. Chem. Jpn.
15, 199(2016).
DOI:10.2477/jccj.20160024 
[23] 
M. Tachikawa, K. Mori, H. Nakai, and K. Iguchi, Chem. Phys. Lett.
290, 437(1998).
DOI:10.1016/S00092614(98)005193 
[24] 
T. Udagawa, T. Tsuneda, and M. Tachikawa, Phys. Rev.
89, 052519(2014).
DOI:10.1103/PhysRevA.89.052519 
[25] 
T. Udagawa, and M. Tachikawa, J. Chem. Phys.
125, 244105(2006).
DOI:10.1063/1.2403857 
[26] 
M. Nakagaki, E. Nishi, K. Sakota, H. Nakano, and H. Sekiya, Chem. Phys.
328, 190(2006).
DOI:10.1016/j.chemphys.2006.06.043 
b. 波兰哥白尼大学物理、天文和信息学院物理研究所，托伦 87100;
c. 日本福冈大学理学院应用物理系，福冈市城南区 8140180;
d. 日本横滨市立大学国际艺术与自然科学研究所协会, 横滨金泽区 2360027;
e. 日本岐阜大学工程学院化学与生物分子科学系, 岐阜柳堂 5011193