Energies and Lifetimes with Complex-Scaling

By Daniel Lee Whitenack1, Adam Wasserman1

1. Purdue University

Calculate the resonance energies and lifetimes of a user-defined potential with a uniform complex-scaling transformation.

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Published on 25 Oct 2012 All versions

doi:10.4231/D34T6F282 cite this



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Uniform complex-scaling is a widely used technique to calculate the energies and lifetimes of resonances (or metastable states). In this method the coordinates in a system's Hamiltonian are rotated into the complex plane. This leaves the bound states untouched but reveals new stationary points in the spectrum corresponding to the resonances. With this NanoHUB tool, one-electron resonance energies and lifetimes can by calculated via a complex-scaled Schr"dinger equation solved with the Fourier Grid Hamiltonian method. The parameters of the potential can be modified to explore how the energetic position and width (inverse lifetime) of the lowest energy resonance (LER) are influenced by the potential's shape. In addition, the complex density associated with the LER is caclculated. From this complex density one can learn about geometrical preferences of decay (a sort of 1D reactivity of the metastable state).

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This work was supported by the Purdue Research Foundation, the Donors of the American Chemical Society Petroleum Research Fund Grant No. PRF# 49599-DNI6, and the National Science Foundation CAREER program Grant No. CHE-1149968.


N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, London, 2011).


D. L. Whitenack and A. Wasserman, "Density Functional Resonance Theory: complex density functions, convergence, orbital energies, and functionals," accepted by J. Phys. Chem., http://arxiv.org/abs/1202.5214

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Researchers should cite this work as follows:

  • Daniel Lee Whitenack; Adam Wasserman (2015), "Energies and Lifetimes with Complex-Scaling," http://nanohub.org/resources/cscale. (DOI: 10.4231/D34T6F282).

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