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\documentclass[11pt]{article}

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\title{QUANTUM TUNNELLING IN MOLECULES AND CLUSTERS}

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\author{\underline{\FirstName J.~O. \LastName RICHARDSON}%
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\address{Department of Chemistry and Applied Biosciences, ETH Zurich, Switzerland}

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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
\fancyfoot[C]{}
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\category {1}
\begin{document}

\maketitle  %% This will also build the list of author(s) and addresse(s).

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\index{Tunnelling}
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Quantum tunnelling leaves fingerprints in the high-resolution spectra of molecules and clusters.
This provides a serious challenge for theory to predict and interpret the spectrum.
I will discuss recent progress in methods based on path-integral formalism of quantum mechanics, which leads to practical methods for simulating tunnelling even in reasonably large molecules.
Instanton theory is based on a semiclassical approximation, from which one obtains a powerful approach requiring no more than a single classical trajectory.%
\footnote{\href{https://dx.doi.org/10.1063/1.5028352}{10.1063/1.5028352},
J. O. Richardson,
Perspective: Ring-polymer instanton theory,
J. Chem. Phys. 148, 200901 (2018).
}
The method has been used to elucidate the tunnelling splitting patterns in many molecules including water clusters.%
\footnote{\href{https://dx.doi.org/10.1126/science.aae0012}{10.1126/science.aae0012},
J. O. Richardson, C. P{\'e}rez, S. Lobsiger, A. A. Reid, B. Temelso, G. C. Shields, Z. Kisiel, D. J. Wales, B. H. Pate and S. C. Althorpe,
Concerted Hydrogen-Bond Breaking by Quantum Tunneling in the Water Hexamer Prism,
Science 351, 1310-1313 (2016).
}
More recently, we have developed perturbative corrections to instanton theory which can account for anharmonicity and correct the results in the case of low barriers.%
%For instance, this brings the predictions of the tunnelling splitting in malonaldehyde to within 2\% of the experimental measurement.%
\footnote{\href{https://arxiv.org/abs/2304.10963}{arXiv:2304.10963},
J. E. Lawrence, J. Du\v{s}ek and J. O. Richardson,
Perturbatively corrected ring-polymer instanton theory for accurate tunneling splittings,
accepted J. Chem. Phys. (2023).
}
For extremely anharmonic systems such as methyl rotations, a nonperturbative solution is required.
We have therefore developed a path-integral molecular dynamics approach, which in principle gives identical results to an exact solution of the Schr\"odinger equation and employs an ``Eckart spring'' to rigorously project out the ground rotational state.
However, our approach does not require wavefunctions and thus avoids the curse of dimensionality of traditional quantum-mechanical approaches, but instead scales linearly with system size.%  meaning that we can tackle larger molecules and clusters.%
\footnote{\href{https://arxiv.org/abs/2305.11002}{arXiv:2305.11002},
G. Trenins, L. Meuser, H. Bertschi, O. Vavourakis, R. Fl\"utsch and J. O. Richardson,
Exact tunnelling splittings from symmetrized path integrals,
accepted J. Chem. Phys. (2023).
}


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