An efficient computational method for the implementation of a semi-classical instanton approach using discretized path integrals

In the present paper, a numerical method for a semi-classical instanton method was examined. We implemented the instanton approach using discretized path integrals. The computational accuracy of the method is controlled by the following two parameters: the imaginary time duration (τ) and the time increment (Δτ), which represents the discretized path integral. To obtain accurate results, a long τ must be used in combination with a short Δτ; however, because the computational cost is virtually proportional to τ/Δτ, the instanton calculations were computationally expensive under these conditions. In the present study, we propose a method that reduces the computational cost and represents long τ instanton trajectories by employing an extended instanton trajectory from calculations based on a short τ. We applied the method to calculate tunnel splitting in a HO2 hydrogen transfer reaction using the double many-body extension IV potential as a validation.