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.

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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).

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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.