# Exact quantum dynamics background of dispersion interactions: case study for CH$_4\cdot$Ar in full (12) dimensions

## TL;DR

This study develops a full-dimensional quantum model for the methane-argon complex, enabling detailed analysis of dispersion interactions and vibrational states with high accuracy, surpassing simplified models.

## Contribution

It provides the first full 12-dimensional ab initio potential energy surface and variational vibrational calculations for CH₄·Ar, improving accuracy over reduced-dimensionality models.

## Key findings

- 12D vibrational energies have less than 0.07 cm⁻¹ rms error.
- Full-dimensional model accurately describes dissociation behavior.
- Reduced models show significant deviations from full-dimensional results.

## Abstract

A full-dimensional \emph{ab initio} potential energy surface of spectroscopic quality is developed for the van-der-Waals complex of a methane molecule and an argon atom. Variational vibrational states are computed on this surface including all twelve (12) vibrational degrees of freedom of the methane-argon complex using the GENIUSH computer program and the Smolyak sparse grid method. The full-dimensional computations make it possible to study fine details of the interaction and distortion effects and to make a direct assessment of the reduced-dimensionality models often used in the quantum dynamics study of weakly-bound complexes. A 12-dimensional (12D) vibrational computation including only a single harmonic oscillator basis function (9D) to describe the methane fragment (for which we use the ground-state effective structure as the reference structure) has a 0.40 cm$^{-1}$ root-mean-square error (rms) with respect to the converged 12D bound-state excitation energies, which is less than half of the rms of the 3D model set up with the $\langle r \rangle_0$ methane structure. Allowing 10 basis functions for the methane fragment, the rms of the bound state vibrational energies is reduced to 0.07 cm$^{-1}$, which is much better than the 3D models. The full-dimensional potential energy surface correctly describes the dissociation of the system, which together with further development of the variational (ro)vibrational methodology opens the route for the study of the role of dispersion forces on the excited methane vibrations and the energy transfer from the intra- to the intermolecular vibrational modes.

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Source: https://tomesphere.com/paper/1908.05432