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Density-Functional Methods for Excited States pp 219–271Cite as

Dynamical Processes in Open Quantum Systems from a TDDFT Perspective: Resonances and Electron Photoemission

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Part of the book series: Topics in Current Chemistry ((TOPCURRCHEM,volume 368))

Abstract

We present a review of different computational methods to describe time-dependent phenomena in open quantum systems and their extension to a density-functional framework. We focus the discussion on electron emission processes in atoms and molecules addressing excited-state lifetimes and dissipative processes. Initially we analyze the concept of an electronic resonance, a central concept in spectroscopy associated with a metastable state from which an electron eventually escapes (electronic lifetime). Resonances play a fundamental role in many time-dependent molecular phenomena but can be rationalized from a time-independent context in terms of scattering states. We introduce the method of complex scaling, which is used to capture resonant states as localized states in the spirit of usual bound-state methods, and work on its extension to static and time-dependent density-functional theory. In a time-dependent setting, complex scaling can be used to describe excitations in the continuum as well as wave packet dynamics leading to electron emission. This process can also be treated by using open boundary conditions which allow time-dependent simulations of emission processes without artificial reflections at the boundaries (i.e., borders of the simulation box). We compare in detail different schemes to implement open boundaries, namely transparent boundaries using Green functions, and absorbing boundaries in the form of complex absorbing potentials and mask functions. The last two are regularly used together with time-dependent density-functional theory to describe the electron emission dynamics of atoms and molecules. Finally, we discuss approaches to the calculation of energy and angle-resolved time-dependent pump–probe photoelectron spectroscopy of molecular systems.

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Notes

  1. 1.

    We mention for completeness that Siegert worked in a spherical system where the represented quantity is really r times the wavefunction; this however happens to yield the same equation as in the one-dimensional case.

  2. 2.

    The above discussion is, of course, very informal. Scrinzi and Piraux have presented a more complete argument on the link between outgoing wavefunctions and square integrability after complex scaling; see Scrinzi and Piraux [31], Appendix A.

  3. 3.

    This would be less of an advantage in Cartesian 3D calculations where a smooth scaling could be applied spherically, whereas the sharp scaling would need a cube to align its boundary with the grid.

  4. 4.

    An analogous approach was first presented by Hellums [64] in a single-particle picture.

  5. 5.

    To simplify notation we avoid explicitly writing out all the coordinates. We also use the same convention used in Kurth et al. [65] where operators are thought of as matrices with continuous indices along the spatial coordinates. We thus omit explicit reference to r and r′ and interpret operator products as integrals.

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Acknowledgments

We acknowledge financial support from the European Research Council Advanced Grant DYNamo (ERC-2010-AdG-267374), Ministerio de Economía y Competitividad or MINECO, Spanish Grant (FIS2013-46159-C3-1-P), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13), European Commission FP7 project CRONOS (Grant number 280879-2), COST Actions CM1204 (XLIC), and MP1306 (EUSpec).

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  1. Nano-bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Centro de Física de Materiales CSIC-UPV and DIPC, Universidad del País Vasco UPV/EHU, E-20018, Donostia–San Sebastián, Spain

    Ask Hjorth Larsen, Umberto De Giovannini & Angel Rubio

  2. Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany

    Angel Rubio

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  2. Umberto De Giovannini
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  3. Angel Rubio
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Corresponding authors

Correspondence to Ask Hjorth Larsen , Umberto De Giovannini or Angel Rubio .

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Editors and Affiliations

  1. Institut de Chimie Radicalaire, Université d'Aix-Marseille, Marseille, France

    Nicolas Ferré

  2. Inst. für Physikalische und Theoretische Chemie, Universität Bonn, Bonn, Germany

    Michael Filatov

  3. Institut für Physikalische und Theoretische Chemie, Goethe-Universität Frankfurt am Main, Frankfurt, Germany

    Miquel Huix-Rotllant

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© 2015 Springer International Publishing Switzerland

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Larsen, A.H., De Giovannini, U., Rubio, A. (2015). Dynamical Processes in Open Quantum Systems from a TDDFT Perspective: Resonances and Electron Photoemission. In: Ferré, N., Filatov, M., Huix-Rotllant, M. (eds) Density-Functional Methods for Excited States. Topics in Current Chemistry, vol 368. Springer, Cham. https://doi.org/10.1007/128_2014_616

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