Regensburg 2013 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 3: Quantum Dynamics, Decoherence and Quantum Information II
DY 3.2: Talk
Monday, March 11, 2013, 15:15–15:30, H39
The Hows and Whys of Multidimensional Instantons: Tunnelling effects in gas- and condensed-phase systems — •Jeremy O. Richardson1,2, Stuart C. Althorpe1, and Michael Thoss2 — 1Department of Chemistry, University of Cambridge, UK — 2Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7/B2, D-91058 Erlangen
We describe a simple method for locating semiclassical instantons in multidimensional systems [1]. Using steepest-descent integration of a discretized form of Feynman’s path integral, these instantons can be used to compute chemical reaction rates in the deep-tunnelling regime and the energy-level splitting pattern resulting from tunnelling between degenerate potential wells [2]. Applications are shown for systems in full dimensionality using ab initio potential-energy surfaces including proton-transfers and water cluster rearrangements [3].
The discretized instantons are closely related to the method of ring-polymer molecular dynamics [4], which explains why the latter is able to obtain reaction rates so reliably in the deep-tunnelling regime [1]. An extension to simulate nonadiabatic quantum dynamics using the mapping representation [5] in ring-polymer form is discussed.
[1] J. O. Richardson and S. C. Althorpe, J. Chem. Phys. 131, 214106 (2009). [2] ibid. 134, 054109 (2011). [3] J. O. Richardson, S. C. Althorpe and D. J. Wales 135, 124109 (2011). [4] I. R. Craig and D. E. Manolopoulos, J. Chem. Phys. 123, 034102 (2005). [5] G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997).