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25.As a preliminary calculation before the path integral simulation, we have checked that optimized structures and energies are reasonably accurate at this level of theory. For instance, the barrier heights calculated as the energy difference between TS and EQ structures in Li+(H3O2) and Na+(H3O2) are found to be 12.1 and 4.2 kJ/mol, respectively, with CCSD(T)/aug-cc-pVTZ single point calculation on the optimized geometry with CCSD(T)/cc-pVTZ. In our MP2(full)/aug-cc-pVDZ level, the barrier heights are calculated to be 11.9 and 4.8 kJ/mol, respectively, which are close to CCSD(T)/aug-cc-pVTZ result.
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27.The PIMD calculations are based on the massive Nosé–Hoover thermostat algorithm using normal mode transformation as in the previous works (see Ref. 21). All simulations were performed at 300 K with chain length parameter L = 4, Trotter number P = 16, number of steps 50000, and the step size dt = 0.1 and 0.15 fs for M+(H3O2) and M+(D3O2), respectively. The electronic structure is calculated by using on-the-fly ab initio MO with MP2(full)/aug-cc-pVDZ level.
28. Ab initio calculations with MP2(full)/aug-cc-pVDZ level have been performed along the one-dimensional proton-transfer coordinate, which is taken to be the intrinsic reaction coordinate connecting EQ–TS–EQ structures complemented by a set of partially optimized structures at larger OO separations than that of the EQ structure.

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Ab initio path integral molecular dynamics simulation of M+(H3O2 ) (M = Li, Na, and K) has been carried out to analyze how the structure and dynamics of a low-barrier hydrogen-bonded Zundel anion, H3O2 , can be affected by the counter alkali metal cation, M+. Our simulation predicts that the quantum proton transfer in Zundel anion can be strongly coupled to the motion of counter cation located nearby. A smaller cation can induce larger structural distortion of the Zundel anion fragment making the proton transfer barrier higher, and hence, lower the vibrational excitation energy. It is also argued that a large H/D isotope effect is present .


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