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Updated: Aug 23, 2026

All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics
Published on: January 19, 2018
Semiclassical tunneling splittings from short time dynamics: Herman-Kluk-propagation and harmonic inversion
1Institut fur Chemie, Physikalische und Theoretische Chemie, Freie Universitat Berlin, Takustr. 3, D-14195 Berlin, Germany.
Abstract:
We investigate a recently proposed method [J. Chem. Phys. 108, 9206 (1998)] to obtain tunneling splittings from short time cross-correlation matrices that were propagated according to the semiclassical propagator of Herman and Kluk. The energy levels were extracted by harmonic inversion of the cross-correlation matrix using the filter diagonalization technique. The aim of this study is twofold: First, the short time behavior of the Herman-Kluk-propagator and the meaning of using cross-correlation matrices rather than autocorrelation functions is addressed. Numerical examples are given for one- and two-dimensional model potentials. Second, the performance of the method is investigated for a system with considerable anharmonicity and coupling. Here the proton transfer in 3,7-dichlorotropolone is considered using an ab initio reaction surface Hamiltonian approach. For this example also the extension to more dimensions is critically discussed.
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