Quantum Dynamics Calculations on Isotope Effects of Hydrogen Transfer Isomerization in the Formic Acid Dimer
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Abstract: We present a quantum dynamics study on the isotope effects of hydrogen transfer isomerization in the formic acid dimer, and this is achieved by multidimensional dynamics calculations with an efficient quantum mechanical theoretical scheme developed by our group, on a full-dimensional neural network ab initio potential energy surface. The ground-state and fundamental tunneling splittings for four deuterium isotopologues of formic acid dimer are considered, and the calculated results are in very good general agreement with the available experimental measurements. Strong isotope effects are revealed, the mode-specific fundamental excitation effects on the tunneling rate are evidently influenced by the deuterium substitution of H atom with the substitution on the OH bond being more effective than on the CH bond. Our studies are helpful for acquiring a better understanding of isotope effects in the double-hydrogen transfer processes.
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Key words:
- Quantum dynamics /
- Isomerization /
- Isotope effect /
- Tunneling splitting /
- Double hydrogen transfer
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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. 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 (Q1,Q6) 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.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 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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