Hellmann-Feynman theorem and the definition of forces in quantum time-dependent and transport problems

Di Ventra, Massimiliano; Pantelides, Sokrates T

doi:10.1103/PhysRevB.61.16207

Title: Hellmann-Feynman theorem and the definition of forces in quantum time-dependent and transport problems

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Abstract

The conventional Hellmann-Feynman theorem for the definition of forces on nuclei is not directly applicable to quantum time-dependent and transport problems. We present a rigorous derivation of a general Hellmann-Feynman-like theorem that applies to all quantum mechanical systems and reduces to well-known results for ground-state problems. It provides a rigorous definition of forces in time-dependent and transport problems. Explicit forms of Pulay-like forces are derived and the conditions for them to be zero are identified. A practical scheme for ab initio calculations of current-induced forces is described and the study of the transfer of a Si atom between two electrodes is presented as an example. (c) 2000 The American Physical Society.

Authors:

Di Ventra, Massimiliano ^[1]; Pantelides, Sokrates T ^[1]

Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235 (United States)

Publication Date:: Thu Jun 15 00:00:00 EDT 2000

OSTI Identifier:: 20216791

Resource Type:: Journal Article

Journal Name:: Physical Review. B, Condensed Matter and Materials Physics

Additional Journal Information:: Journal Volume: 61; Journal Issue: 23; Other Information: PBD: 15 Jun 2000; Journal ID: ISSN 1098-0121

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM MECHANICS; TRANSPORT THEORY; TIME DEPENDENCE; GROUND STATES; SILICON; WAVE FUNCTIONS; ELECTRIC CURRENTS; THEORETICAL DATA

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                    Di Ventra, Massimiliano, Pantelides, Sokrates T, and Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831. Hellmann-Feynman theorem and the definition of forces in quantum time-dependent and transport problems.  United States: N. p., 2000. 
        Web.  doi:10.1103/PhysRevB.61.16207.

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                    Di Ventra, Massimiliano, Pantelides, Sokrates T, & Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831. Hellmann-Feynman theorem and the definition of forces in quantum time-dependent and transport problems.  United States.  https://doi.org/10.1103/PhysRevB.61.16207

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                    Di Ventra, Massimiliano, Pantelides, Sokrates T, and Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831. 2000.  
        "Hellmann-Feynman theorem and the definition of forces in quantum time-dependent and transport problems".  United States.  https://doi.org/10.1103/PhysRevB.61.16207.

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@article{osti_20216791,

  title        = {Hellmann-Feynman theorem and the definition of forces in quantum time-dependent and transport problems},

  author       = {Di Ventra, Massimiliano and Pantelides, Sokrates T and Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831},

  abstractNote = {The conventional Hellmann-Feynman theorem for the definition of forces on nuclei is not directly applicable to quantum time-dependent and transport problems. We present a rigorous derivation of a general Hellmann-Feynman-like theorem that applies to all quantum mechanical systems and reduces to well-known results for ground-state problems. It provides a rigorous definition of forces in time-dependent and transport problems. Explicit forms of Pulay-like forces are derived and the conditions for them to be zero are identified. A practical scheme for ab initio calculations of current-induced forces is described and the study of the transfer of a Si atom between two electrodes is presented as an example. (c) 2000 The American Physical Society.},

  doi          = {10.1103/PhysRevB.61.16207},

  url          = {https://www.osti.gov/biblio/20216791},
  journal      = {Physical Review. B, Condensed Matter and Materials Physics},

  issn         = {1098-0121},

  number       = 23,

  volume       = 61,

  place        = {United States},

  year         = {Thu Jun 15 00:00:00 EDT 2000},

  month        = {Thu Jun 15 00:00:00 EDT 2000}

}

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