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

Fengyi Li^{1, 2},
Xiaoxi Liu^{1, 2},
Xingyu Yang^{1, 2},
Jianwei Cao^{1
, ,},
Wensheng Bian^{1, 2
, ,}

1.
Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China

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Corresponding author: E-mail: caojw@iccas.ac.cn; bian@iccas.ac.cn

摘要

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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.
- Quantum dynamics /
- Isomerization /
- Isotope effect /
- Tunneling splitting /
- Double hydrogen transfer
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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).

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

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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.

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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 coordinates^a
$ \ \ Q_{i}\ \ $	Frequency	$Q_{i}^{\prime}$	Frequency	Motion^b
$ 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
FAD	1D	2D (Q₁，Q₆)	2D (Q₁, Q₃)	3D	4D	Expt.
DCOOH-HOOCH	0.4502	0.06595	0.03792	0.01372	0.01110	0.01106^a
DCOOH-HOOCD	0.43718	0.06480	0.03757	0.01388	0.01105	0.0123^b
HCOOD-HOOCH	0.09595	0.01143	0.00739	0.00196	0.00143	0.00113^c
HCOOD-DOOCH	0.018294	0.001738	0.001372	0.000424	0.000289	<0.00067^c
^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 $
FAD	$\Delta_3$	$\Delta_3/\Delta_0$	$\Delta_6$	$\Delta_6/\Delta_0$	$\Delta_8$	$\Delta_8/\Delta_0$
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

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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} $
Method	$ \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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