^{1}, Masanori Tachikawa

^{1,a)}and Motoyuki Shiga

^{1,2}

### Abstract

Temperature dependence on the structural fluctuations of Zundel cation, , and its isotopomers, and , have been studied using path integral molecular dynamics simulations in which nuclear quantum effect is fully taken into account. It has been found that the fluctuations of hydrogen-oxygen and oxygen-oxygen distances, which are relevant to the hydrogen bonded structure, grow drastically as the temperature increases within the range of investigation between 100 K and 900 K. The fluctuation with respect to the position of non-bonded hydrogen also increases substantially as the temperature increases. The temperature dependence on the fluctuation is greater for or than that of , since the zero-point effect of the former is less than the latter.

The authors thank Professor Braams, Dr. Huang, and Professor Bowman for providing the program code of the HBB potential energy surface. The present study was supported by the Grant-in-Aid for Scientific Research by Ministry of Education, Culture, Sports, Science and Technology, Japan (Kakenhi), Grant Nos. 22018024 and 23350010 for both M.T. and M.S., Grant Nos. 23655019 and 23104513 for M.T., and Grant No. 22750023 for M.S.

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

III. RESULTS AND DISCUSSION

A. Energy

B. Hydrogen-bonded structure

C. Non hydrogen-bonded hydrogen atoms

IV. CONCLUSION

### Key Topics

- Quantum effects
- 13.0
- Reaction mechanisms
- 9.0
- Hydrogen bonding
- 5.0
- Potential energy surfaces
- 5.0
- Zero point energy
- 5.0

## Figures

(a) Schematic illustration of in the optimized geometry. (b) The definition of X A, X B, , and .

(a) Schematic illustration of in the optimized geometry. (b) The definition of X A, X B, , and .

One-dimensional probability densities of with respect to (a) δOH* at 100 K, (b) δOH* at 900 K, (c) R OO at 100 K, and (d) R OO at 900 K, respectively, for quantum (QM) simulations of (red), (purple), (blue), and classical (CL) (black) simulation. Units of distribution are in arbitrary units.

One-dimensional probability densities of with respect to (a) δOH* at 100 K, (b) δOH* at 900 K, (c) R OO at 100 K, and (d) R OO at 900 K, respectively, for quantum (QM) simulations of (red), (purple), (blue), and classical (CL) (black) simulation. Units of distribution are in arbitrary units.

Potential energy surface as a function of R OO and δOH*. Units in cm−1.

Potential energy surface as a function of R OO and δOH*. Units in cm−1.

Two-dimensional probability density as a function of R OO and δOH*. The results are shown for quantum simulations of (a) , (b) (c) , and (d) classical simulation of at 100 K, and quantum simulations of (e) , (f) , (g) , and (h) classical simulation of at 900 K.

Two-dimensional probability density as a function of R OO and δOH*. The results are shown for quantum simulations of (a) , (b) (c) , and (d) classical simulation of at 100 K, and quantum simulations of (e) , (f) , (g) , and (h) classical simulation of at 900 K.

One-dimensional probability densities as a function of d at (a) 100 K and (b) 900 K, and as a function of ϕ at (c) 100 K and (d) 900 K, respectively, for quantum (QM) simulations of (red), δOH* (purple), (blue), and classical (CL) (black) simulation. Units of distribution are in arbitrary units.

One-dimensional probability densities as a function of d at (a) 100 K and (b) 900 K, and as a function of ϕ at (c) 100 K and (d) 900 K, respectively, for quantum (QM) simulations of (red), δOH* (purple), (blue), and classical (CL) (black) simulation. Units of distribution are in arbitrary units.

Two-dimensional probability densities in quantum with respect to δOH* and d at (a) 100 K and (b) 900 K, and with respect to δOH* and ϕ at (c) 100 K and (d) 900 K, respectively.

Two-dimensional probability densities in quantum with respect to δOH* and d at (a) 100 K and (b) 900 K, and with respect to δOH* and ϕ at (c) 100 K and (d) 900 K, respectively.

## Tables

The average energies (⟨E⟩) (kcal/mol) on and its isotopomers at each temperature.

The average energies (⟨E⟩) (kcal/mol) on and its isotopomers at each temperature.

Average value of OO bond lengths (R OO) and the statistical errors in the quantum simulation (PIMD) and classical simulations (MD) at various temperatures. Unit in Å. The equilibrium distance is 2.386 (Å).

Average value of OO bond lengths (R OO) and the statistical errors in the quantum simulation (PIMD) and classical simulations (MD) at various temperatures. Unit in Å. The equilibrium distance is 2.386 (Å).

Average value of |δOH*| and the statistical errors in the quantum simulation (PIMD) and classical simulations (MD) at various temperatures. Unit in Å. The equilibrium distance is 0 (Å).

Average value of |δOH*| and the statistical errors in the quantum simulation (PIMD) and classical simulations (MD) at various temperatures. Unit in Å. The equilibrium distance is 0 (Å).

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