Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment

Giesbertz, Klaas J. H.; Leeuwen, Robert van

doi:10.1063/1.4875338

Title: Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment

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Abstract

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r{sub 12}) depending on the interelectronic distance r{sub 12}. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long rangemore »« less

Authors:

Giesbertz, Klaas J. H. ^[1]; Leeuwen, Robert van ^[2]

Theoretical Chemistry, Faculty of Exact Sciences, VU University, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands)
Department of Physics, Nanoscience Center, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, Survontie 9, Jyväskylä (Finland)

Publication Date:: Wed May 14 00:00:00 EDT 2014

OSTI Identifier:: 22252855

Resource Type:: Journal Article

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 140; Journal Issue: 18; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CORRELATION FUNCTIONS; ELECTRON CORRELATION; ELECTRONS; INTERACTIONS; VAN DER WAALS FORCES; WAVE FUNCTIONS

Citation Formats


                    Giesbertz, Klaas J. H., and Leeuwen, Robert van. Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment.  United States: N. p., 2014. 
        Web.  doi:10.1063/1.4875338.

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                    Giesbertz, Klaas J. H., & Leeuwen, Robert van. Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment.  United States.  https://doi.org/10.1063/1.4875338

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                    Giesbertz, Klaas J. H., and Leeuwen, Robert van. 2014.  
        "Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment".  United States.  https://doi.org/10.1063/1.4875338.

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@article{osti_22252855,

  title        = {Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment},

  author       = {Giesbertz, Klaas J. H. and Leeuwen, Robert van},

  abstractNote = {Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r{sub 12}) depending on the interelectronic distance r{sub 12}. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r{sub 12}) needs to diverge for large r{sub 12} at large internuclear distances while for shorter bond distances it increases as a function of r{sub 12} to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.},

  doi          = {10.1063/1.4875338},

  url          = {https://www.osti.gov/biblio/22252855},
  journal      = {Journal of Chemical Physics},

  issn         = {0021-9606},

  number       = 18,

  volume       = 140,

  place        = {United States},

  year         = {Wed May 14 00:00:00 EDT 2014},

  month        = {Wed May 14 00:00:00 EDT 2014}

}

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