A comparison of two methods for direct tunneling dynamics: Hydrogen exchange in the glycolate anion as a test case

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Abstract
Two methods for studying tunneling dynamics are compared, namely the instanton model and the approach of Truhlar and co-workers, which are based on the direct output of electronic structure calculations and thus are parameter free. They are employed to evaluate the zero-level tunneling splitting due to intramolecular hydrogen exchange in the glycolate anion. The first method was developed in a series of recent studies and presents a combination of the instanton theory with quantum-chemically computed potentials and force fields. For the compound at hand, which has 21 internal degrees of freedom, a complete potential-energy surface is generated in terms of the normal modes of the transition-state configuration. It is made up of the potential-energy curve along the tunneling coordinate and harmonic force fields at the stationary points. The level of theory used is HF/6–31++G**. All modes that are displaced between the equilibrium configuration and the transition state are linearly coupled to the tunneling mode, the couplings being proportional to the displacements in dimensionless units. These couplings affect the instanton trajectory profoundly and, depending on the symmetry of the skeletal modes, can enhance or suppress the tunneling. In the glycolate anion all modes have such displacements and thus are included in the calculation. Based on the similarity with malonaldehyde, it is argued that tunneling prevails in the studied process, and the zero-level tunneling splitting is predicted. The latter is found within the computational scheme developed earlier, which avoids explicit evaluation of the instanton path and thus greatly simpli-fies the tunneling dynamics. These results are tested by the method of large-curvature tunneling of Truhlar and co-workers implemented in a dual-level scheme. The potential energy surface needed for the dynamics calculations is generated at the semiempirical PM3 level of theory and then corrected by interpolation with high-level HF/6–31++G** results for the stationary points. The code corresponding to this approximation is in the package MORATE 6.5. The tunneling splittings found by the two approaches are in quantitative agreement. We have found that the computational scheme based on the instanton model is much less time consuming both in the static and dynamics part. This computational efficiency, also demonstrated in a number of earlier studies, merits future application of the method to fairly large systems of practical interest, such as clusters and organic compounds with excited-state proton transfer.

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