Vibrational Tunneling Spectra of Molecules with Asymmetric Wells: A Combined Vibrational Configuration Interaction and Instanton Approach

Abstract

A combined approach that uses the vibrational configuration interaction (VCI) and semiclassical instanton theory was developed to study vibrational tunneling spectra of molecules with multiple wells in full dimensionality. The method can be applied to calculate low-lying vibrational states in the systems with an arbitrary number of minima, which are not necessarily equal in energy or shape. It was tested on a two-dimensional double-well model system and on malonaldehyde, and the calculations reproduced the exact quantum mechanical (QM) results with high accuracy. The method was subsequently applied to calculate the vibrational spectrum of the asymmetrically deuterated malonaldehyde with nondegenerate vibrational frequencies in the two wells. The spectrum is obtained at a cost of single-well VCI calculations used to calculate the local energies. The interactions between states of different wells are computed semiclassically using the instanton theory at a comparatively negligible computational cost. The method is particularly suited to systems in which the wells are separated by large potential barriers and tunneling splittings are small, for example, in some water clusters, when the exact QM methods come at a prohibitive computational cost.

Tunneling splittings in the vibrationally excited states of water trimer

“…The approach we used to calculate the TS patterns here gives a quantitative agreement with the exact quantum results for malonaldhyde. 59 There are, however, several reasons why the accuracy of the present results is substantially lower. A shallow well for the flip motion is one source of error already discussed above.…”

“…58 Our approach works for asymmetric paths, encountered in the water trimer, and treats longitudinal and transverse excitations on an equal footing. 58 The application on malonaldehyde 59 showed that the method gives a quantitative agreement with the exact quantum results for TSs in the low-lying vibrational states.…”

Ring-Polymer Instanton Tunneling Splittings of Tropolone and Isotopomers using a Δ-Machine Learned CCSD(T) Potential: Theory and Experiment Shake Hands

“…First, d = 1 2 ( E l − E r ) is the contribution due to the asymmetry of the double well, which can easily be evaluated by simply measuring the zero-point energies of the left and right wells, E normall and E r . In this work, these energies are calculated within the harmonic approximation, although in principle anharmonic contributions can also be included in cases where the harmonic approximation is not sufficient . Second, ℏΩ is the contribution due to quantum tunneling effects.…”

“…In this work, these energies are calculated within the harmonic approximation, although in principle anharmonic contributions can also be included in cases where the harmonic approximation is not sufficient. 62 Second, ℏΩ is the contribution due to quantum tunneling effects. The experimental observable is the level splitting, which can be predicted…”