Quantum Dynamics Calculations on Isotope Effects of Hydrogen Transfer Isomerization in the Formic Acid Dimer

Fengyi Li Xiaoxi Liu Xingyu Yang Jianwei Cao Wensheng Bian

Fengyi Li, Xiaoxi Liu, Xingyu Yang, Jianwei Cao, Wensheng Bian. Quantum Dynamics Calculations on Isotope Effects of Hydrogen Transfer Isomerization in the Formic Acid Dimer[J]. Chinese Journal of Chemical Physics . doi: 10.1063/1674-0068/cjcp2301009
Citation: Fengyi Li, Xiaoxi Liu, Xingyu Yang, Jianwei Cao, Wensheng Bian. Quantum Dynamics Calculations on Isotope Effects of Hydrogen Transfer Isomerization in the Formic Acid Dimer[J]. Chinese Journal of Chemical Physics . doi: 10.1063/1674-0068/cjcp2301009

doi: 10.1063/1674-0068/cjcp2301009

Quantum Dynamics Calculations on Isotope Effects of Hydrogen Transfer Isomerization in the Formic Acid Dimer

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  • Figure  1.  Selected contour plots of the surface cuts along the relevant saddle-point normal coordinates ($ Q_i $), with the other normal coordinates fixed at zero ($ Q_i $ in a.u. and energies in kcal/mol).

    Figure  2.  The typical vibrational modes of the formic acid dimer.

    Figure  3.  Ratio of tunneling rates for H-transfer isomerization between four deuterium isotopologues and the formic acid dimer calculated by the present quantum dynamics scheme with 4D model.

    Table  I.   Formic acid dimer (FAD) normal coordinates, as well as the normal frequencies (in cm−1) on the present surface.

    Saddle-point normal coordinates FAD normal coordinatesa
    $ \ \ Q_{i}\ \ $ Frequency $Q_{i}^{\prime}$ Frequency Motionb
    $ Q_{1 } $ 1370i $Q_{1 }^{\prime}$ 71 $\tau_{\rm{R} }$
    $ Q_{2 } $ 81 $Q_{2 }^{\prime}$ 169 $\beta_{\rm{R}}$
    $ Q_{3 } $ 227 $Q_{3 }^{\prime}$ 176 $\delta_{\rm{R}}$
    $ Q_{4 } $ 229 $Q_{4 }^{\prime}$ 210 $\nu_{\rm{R}}$
    $ Q_{5 } $ 308 $Q_{5 }^{\prime}$ 252 $\delta_{\rm{R}}$
    $ Q_{6 } $ 516 $Q_{6 }^{\prime}$ 276 $\beta_{\rm{R}}$
    $ Q_{7 } $ 590 $Q_{7 }^{\prime}$ 688 $\beta_{\rm{OCO}}$
    $ Q_{8 } $ 751 $Q_{8 }^{\prime}$ 715 $\beta_{\rm{OCO}}$
    $ Q_{9 } $ 801 $Q_{9 }^{\prime}$ 960 $\delta_{\rm{OH}}$
    $ Q_{10 } $ 1087 $Q_{10 }^{\prime}$ 983 $\delta_{\rm{OH}}$
    $ Q_{11 } $ 1088 $Q_{11 }^{\prime}$ 1082 $\delta_{\rm{CH}}$
    $ Q_{12 } $ 1258 $Q_{12 }^{\prime}$ 1098 $\delta_{\rm{CH}}$
    $ Q_{13 } $ 1338 $Q_{13 }^{\prime}$ 1254 $\nu_{\rm{OCO}}(+)$
    $ Q_{14 } $ 1373 $Q_{14 }^{\prime}$ 1260 $\nu_{\rm{OCO}}(+)$
    $ Q_{15 } $ 1403 $Q_{15 }^{\prime}$ 1404 $\beta_{\rm{OCH}}$
    $ Q_{16 } $ 1404 $Q_{16 }^{\prime}$ 1412 $\beta_{\rm{OCH}}$
    $ Q_{17 } $ 1405 $Q_{17 }^{\prime}$ 1462 $\beta_{\rm{OHO}}$
    $ Q_{18 } $ 1405 $Q_{18 }^{\prime}$ 1488 $\beta_{\rm{OHO}}$
    $ Q_{19 } $ 1603 $Q_{19 }^{\prime}$ 1714 $\nu_{\rm{OCO}}(-)$
    $ Q_{20 } $ 1703 $Q_{20 }^{\prime}$ 1775 $\nu_{\rm{OCO}}(-)$
    $ Q_{21 } $ 1739 $Q_{21 }^{\prime}$ 3079 $\nu_{\rm{CH}}$
    $ Q_{22 } $ 1751 $Q_{22 }^{\prime}$ 3093 $\nu_{\rm{CH}}$
    $ Q_{23 } $ 3101 $Q_{23 }^{\prime}$ 3204 $\nu_{\rm{OH}}$
    $ Q_{24 } $ 3106 $Q_{24 }^{\prime}$ 3313 $\nu_{\rm{OH}}$
    a Obtained at the equilibrium geometry.b $ \nu$ is stretch, $\beta$ is in-plane bend, $\delta$ is out-of-plane bend, $\tau$ is torsion, $\rm{R}$ in subscript is intermolecular, + represents symmetric and – represents antisymmetric.
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    Table  II.   Ground-state tunneling splitting for the deuterium isotopologues calculated with different models, energies in cm−1. Calculations are performed with the 1D $(Q_1)$, 2D $(Q_1, Q_6)$, 2D $(Q_1, Q_3)$, 3D $(Q_1, Q_6, Q_3)$ and 4D $(Q_1, Q_6, Q_3, Q_8)$ models, respectively.

    FAD $\Delta_0 $/cm−1
    1D 2D (Q1Q6) 2D (Q1, Q3) 3D 4D Expt.
    DCOOH-HOOCH 0.4502 0.06595 0.03792 0.01372 0.01110 0.01106a
    DCOOH-HOOCD 0.43718 0.06480 0.03757 0.01388 0.01105 0.0123b
    HCOOD-HOOCH 0.09595 0.01143 0.00739 0.00196 0.00143 0.00113c
    HCOOD-DOOCH 0.018294 0.001738 0.001372 0.000424 0.000289 <0.00067c
    a The value is reported in Ref.[26] by microwave spectroscopic experiment.
    b The experimental value measured in Ref.[24].
    c The value is obtained in Ref.[25] by measuring the vibration-rotation-tunneling absorption spectra.
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    Table  III.   Fundamental tunneling splittings for the deuterium isotopologues calculated with the 4D model .

    FAD $ Q_3 $ $ Q_6 $ $ Q_8 $
    $\Delta_3$ $\Delta_3/\Delta_0$ $\Delta_6$ $\Delta_6/\Delta_0$ $\Delta_8$ $\Delta_8/\Delta_0$
    DCOOH-HOOCH 0.10944 9.86 0.00550 0.50 0.01050 0.95
    DCOOH-HOOCD 0.10651 9.84 0.00759 0.69 0.00972 0.88
    HCOOD-HOOCH 0.01726 12.07 0.00012 0.09 0.00103 0.72
    HCOOD-DOOCH 0.00410 14.18 0.00010 0.34 0.00016 0.56
    下载: 导出CSV

    Table  IV.   The frequencies ($ \omega $in cm−1) and fundamental tunneling splittings for the formic acid dimer calculated with the 4D model.

    Method$ Q_3 $$ Q_6 $$ Q_8 $$ Q_{17} $
    $ \omega $$ \Delta_i $$ \Delta_i/\Delta_0 $$ \omega $$ \Delta_i $$ \Delta_i/\Delta_0 $$ \omega $$ \Delta_i $$ \Delta_i/\Delta_0 $$ \omega $$ \Delta_i $$ \Delta_i/\Delta_0 $
    This work 172.87 0.1176 9.67 207.84 0.0081 0.67 688.12 0.0106 0.87 1360.39 0.0072 0.61
    Expt. [51] $161\; $ $677 \; $
    Expt. [52] $165\; $ $194\; $
    Expt. [53] $682\; $
    Expt.a [25] $1371.8$ $0.0004$
    a The value is obtained by measuring the vibration-rotation-tunneling absorption spectra.
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  • 收稿日期:  2023-01-18
  • 录用日期:  2023-03-29
  • 网络出版日期:  2023-04-04

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