Perturbatively corrected ring-polymer instanton theory for accurate tunneling splittings

TL;DR

This paper presents a perturbative correction to ring-polymer instanton theory that incorporates higher-order potential derivatives, significantly improving the accuracy of tunneling splitting calculations in molecular systems.

Contribution

The authors develop RPI+PC, a method that adds perturbative corrections to instanton theory using third and fourth derivatives of the potential, enhancing accuracy for anharmonic systems.

Findings

Reduces error in tunneling splitting calculations from -11% to 2%.

Outperforms previous methods like diffusion Monte Carlo.

Applicable to full-dimensional molecular systems like malonaldehyde.

Abstract

We introduce an approach for calculating perturbative corrections to the ring-polymer instanton approximation to tunneling splittings (RPI+PC), by computing higher-order terms in the asymptotic expansion in $\hbar$. The resulting method goes beyond standard instanton theory by using information on the third and fourth derivatives of the potential along the tunneling path to include additional anharmonic effects. This leads to significant improvements both in systems with low barriers and in systems with anharmonic modes. We demonstrate the applicability of RPI+PC to molecular systems by computing the tunneling splitting in full-dimensional malonaldehyde and a deuterated derivative. Comparing to both experiment and recent quantum-mechanical benchmark results, we find that our perturbative correction reduces the error from -11% to 2% for hydrogen transfer and performs even better for the deuterated case. This makes our approach more accurate than previous calculations using diffusion Monte Carlo and path-integral molecular dynamics, while being more computationally efficient.