Instanton theory of tunnelling in molecules with asymmetric isotopic substitutions

TL;DR

This paper extends instanton theory to asymmetric double-well systems with different frequencies, providing a semiclassical method to compute tunnelling splittings, validated against models and applied to isotopic malonaldehyde.

Contribution

It generalizes instanton theory for asymmetric systems and applies the approach to complex molecules with isotopic substitutions.

Findings

The method accurately predicts energy level splittings in asymmetric models.

Benchmark results show good agreement with exact quantum calculations.

Application to malonaldehyde demonstrates the method's effectiveness in real molecular systems.

Abstract

We consider quantum tunnelling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. We derive a generalization of instanton theory for these asymmetric systems, leading to a semiclassical expression for the tunnelling matrix element and hence the energy level splitting. We benchmark the method using a set of one- and two-dimensional models, for which the results compare favourably with numerically exact quantum calculations. Using the ring-polymer instanton approach, we apply the method to compute the level splittings in various isotopic-substituted versions of malonaldehyde in full dimensionality and analyse the relative contributions from the zero-point energy difference and tunnelling effects.