The instanton theory is reformulated with use of the path integral approach and the Wentzel–Kramers–Brillouin approximation to the Schrödinger equation. Both approaches are shown to provide the same results. A new practically useful semiclassical formula is derived for the tunneling splitting of the ground state, which can be implemented for high-dimensional systems. The theory is applicable to systems of arbitrary Riemannian metric and is also supplemented by a practical numerical recipe to evaluate the instanton trajectory, i.e., periodic orbit, in multidimensional space. Numerical examples are presented for three-dimensional (3D) and 21D systems of HO2 and malonaldehyde, respectively.
A practical and accurate semiclassical method for calculating the tunneling splitting of the ground state in polyatomic molecules is presented based on a recent version of the instanton theory [J. Chem. Phys. 115, 6881 (2001)]. The method uses ab initio quantum chemical data for the potential energy surface without any concomitant extrapolation and requires only a small number of ab initio data points to get convergence even for large molecules. This enables one to use an advanced level of electronic structure theory and achieve a high accuracy of the result. The method is applied to the 9-atomic malonaldehyde molecule by making use of the potential energy surface at the level of CCSD(T) with the hybrid basis set of aug-cc-pVTZ (for oxygen atoms and the transferred hydrogen atom) and cc-pVTZ (for other atoms).
We report an accurate and efficient full dimensional semiclassical ab initio method for calculation of energy level splitting due to tunneling in polyatomic system. The method is applied to 21-dimensional 9-atomic malonaldehyde molecule. The tunneling splittings obtained are ΔE(H)=21.2 cm−1 for hydrogen atom transfer and ΔE(D)=3.0 cm−1 for deuterium atom transfer, which are in excellent agreement with the experimental values of 21.6 cm−1 and, 2.9 cm−1 respectively. We believe that the present analysis gives the final solution to the longstanding problem.
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