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 Title: Ro-vibrationally Averaged Molecular Structure Of Benzene     Ii. Computational Molecular Spectroscopy Study. Author(s): Hirano, Tsuneo Contributor(s): Baba, Masaaki; Nagashima, Umpei Subject(s): Structure determination Abstract: Since the 30 dimensional potential energy surface is beyond our reach, we tried to disclose why the C--H and C--D bond-lengths are observed as being almost identical\footnote{S. Kunishige, M. Baba, et al., J. Chem. Phys. {\bf 143}, 244302 (2015).} in terms of C--H stretching ($\mathbf{L}_{\rm str}$), out-of-plane ($\mathbf{L}_{\perp}$), and in-plane ($\mathbf{L}_{\parallel}$) local modes with respect to the C$_{\alpha}$--H(D)$_{\alpha}$ bond in the virtual triatomic molecules [C$_{5}$H(D)$_{5}$]--[C$_{\alpha}$]--H(D)$_{\alpha}$. The potential energy surface was determined at the valence-CCSD(T)/[aVQZ (H,C)] level of theory, and $r_{0}$-structure was determined from the DVR3D wavefuctions in Discrete Variable Representation. The virtual [C$_{5}$H(D)$_{5}$]--[C$_{\alpha}$]--H(D)$_{\alpha}$ molecule has its energy minimum at the linear configuration, so that our theory for linear triatomics\footnote{T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. \textbf{343}, 54 (2018); T. Hirano, U. Nagashima, M. Baba, J. Mol. Spectrosc. \textbf{369}, 111252 (2020); and references therein.} can be applied. The C$_{\alpha}$--H(D)$_{\alpha}$ stretching local mode ($\mathbf{L}_{\rm str}$) gives, as usual, longer C$_{\alpha}$--H$_{\alpha}$ than C$_{\alpha}$--D$_{\alpha}$ bond-lengths due to its anharmonicity. However, in both $\mathbf{L}_{\perp}$ and $\mathbf{L}_{\parallel}$ modes, the vibrationally averaged bond-length projected onto the principal axis is shorter for C$_{\alpha}$--H$_{\alpha}$ than for C$_{\alpha}$--D$_{\alpha}$ due to the larger averaged bending angle for the former bond. When we consider bond-lengths projected onto the $a$-$b$ principal axis plane, $r_{\rm 0,proj}$, these antithetical factors, i.e., one in the $\mathbf{L}_{\rm str}$ mode against the others in $\mathbf{L}_{\perp}$ and $\mathbf{L}_{\parallel}$ modes, nearly cancel ($\Delta =$ $r$(C--H) $-$ $r$(C--D) $=$ $-$0.0004 {\AA}), resulting in almost the same C--H and C--D bond lengths as is experimentally reported. The vibrationally averaged structure of benzene in the zero-point vibration state is predicted to be planar, but non-flat in the peripheral C--H bonds moiety, which is confirmed from the theoretical and experimental values of the inertial defect. Issue Date: 2021-06-25 Publisher: International Symposium on Molecular Spectroscopy Genre: Conference Paper / Presentation Type: Text Language: English URI: http://hdl.handle.net/2142/111224 Date Available in IDEALS: 2021-09-24
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