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A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the Schrödinger equation with a general potential energy surface.

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Název: A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the Schrödinger equation with a general potential energy surface.
Autoři: Wodraszka, Robert, Carrington, Tucker
Zdroj: Journal of Chemical Physics; 4/21/2019, Vol. 150 Issue 15, pN.PAG-N.PAG, 12p, 2 Graphs
Témata: POTENTIAL energy surfaces, SCHRODINGER equation, POINT set theory, COLLOCATION methods, PHYSICAL & theoretical chemistry
Abstrakt: Standard multiconfiguration time-dependent Hartree (MCTDH) calculations use a direct product basis and rely on the potential being a sum of products (SOPs). The size of the direct product MCTDH basis scales exponentially with the number of atoms. Accurate potentials may not be SOPs. We introduce an MCTDH approach that uses a pruned basis and a collocation grid. Pruning the basis significantly reduces its size. Collocation makes it possible to do calculations using a potential that is not a SOP. The collocation point set is a Smolyak grid. Strategies using pruned MCTDH bases already exist, but they work only if the potential is a SOP. Strategies for using MCTDH with collocation also exist, but they work only if the MCTDH basis is a direct product. In this paper, we combine a pruned basis with collocation. This makes it possible to mitigate the direct-product basis size problem and do calculations when the potential is not a SOP. Because collocation is used, there are no integrals and no need for quadrature. All required matrix-vector products can be evaluated sequentially. We use nested sets of collocation points and hierarchical basis functions. They permit efficient inversion of the (large) matrix whose elements are basis functions evaluated at points, which is necessary to transform values of functions at points to basis coefficients. The inversion technique could be used outside of chemical physics. We confirm the validity of this new pruned, collocation-based (PC-)MCTDH approach by calculating the first 50 vibrational eigenenergies of CH2NH. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Chemical Physics is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the Schrödinger equation with a general potential energy surface.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Wodraszka%2C+Robert%22">Wodraszka, Robert</searchLink><br /><searchLink fieldCode="AR" term="%22Carrington%2C+Tucker%22">Carrington, Tucker</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: Journal of Chemical Physics; 4/21/2019, Vol. 150 Issue 15, pN.PAG-N.PAG, 12p, 2 Graphs
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22POTENTIAL+energy+surfaces%22">POTENTIAL energy surfaces</searchLink><br /><searchLink fieldCode="DE" term="%22SCHRODINGER+equation%22">SCHRODINGER equation</searchLink><br /><searchLink fieldCode="DE" term="%22POINT+set+theory%22">POINT set theory</searchLink><br /><searchLink fieldCode="DE" term="%22COLLOCATION+methods%22">COLLOCATION methods</searchLink><br /><searchLink fieldCode="DE" term="%22PHYSICAL+%26+theoretical+chemistry%22">PHYSICAL & theoretical chemistry</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Standard multiconfiguration time-dependent Hartree (MCTDH) calculations use a direct product basis and rely on the potential being a sum of products (SOPs). The size of the direct product MCTDH basis scales exponentially with the number of atoms. Accurate potentials may not be SOPs. We introduce an MCTDH approach that uses a pruned basis and a collocation grid. Pruning the basis significantly reduces its size. Collocation makes it possible to do calculations using a potential that is not a SOP. The collocation point set is a Smolyak grid. Strategies using pruned MCTDH bases already exist, but they work only if the potential is a SOP. Strategies for using MCTDH with collocation also exist, but they work only if the MCTDH basis is a direct product. In this paper, we combine a pruned basis with collocation. This makes it possible to mitigate the direct-product basis size problem and do calculations when the potential is not a SOP. Because collocation is used, there are no integrals and no need for quadrature. All required matrix-vector products can be evaluated sequentially. We use nested sets of collocation points and hierarchical basis functions. They permit efficient inversion of the (large) matrix whose elements are basis functions evaluated at points, which is necessary to transform values of functions at points to basis coefficients. The inversion technique could be used outside of chemical physics. We confirm the validity of this new pruned, collocation-based (PC-)MCTDH approach by calculating the first 50 vibrational eigenenergies of CH<subscript>2</subscript>NH. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Chemical Physics is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1063/1.5093317
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      – Code: eng
        Text: English
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        PageCount: 12
        StartPage: N.PAG
    Subjects:
      – SubjectFull: POTENTIAL energy surfaces
        Type: general
      – SubjectFull: SCHRODINGER equation
        Type: general
      – SubjectFull: POINT set theory
        Type: general
      – SubjectFull: COLLOCATION methods
        Type: general
      – SubjectFull: PHYSICAL & theoretical chemistry
        Type: general
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      – TitleFull: A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the Schrödinger equation with a general potential energy surface.
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            NameFull: Wodraszka, Robert
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            – D: 21
              M: 04
              Text: 4/21/2019
              Type: published
              Y: 2019
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