Computation of derivatives for parameter optimization in least‐squares fitting of linear combinations of Slater‐type orbitals by Gaussians

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Abstract

The approximation of a linear combination of Slater‐type orbitals in terms of Gaussian functions is a many‐parameter optimization problem. Formulas for computation of the gradient of the overlap in parameter space are reported. An alternative method of computing the gradient is described, which is of general applicability. This technique permits the exact evaluation of a derivative, without derivation and programming of its analytic expression.

Original languageEnglish (US)
Pages (from-to)801-805
Number of pages5
JournalInternational Journal of Quantum Chemistry
Volume2
Issue number6
DOIs
StatePublished - Nov 1968

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Derivatives
orbitals
gradients
optimization
programming
derivation
evaluation
approximation

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

Cite this

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title = "Computation of derivatives for parameter optimization in least‐squares fitting of linear combinations of Slater‐type orbitals by Gaussians",
abstract = "The approximation of a linear combination of Slater‐type orbitals in terms of Gaussian functions is a many‐parameter optimization problem. Formulas for computation of the gradient of the overlap in parameter space are reported. An alternative method of computing the gradient is described, which is of general applicability. This technique permits the exact evaluation of a derivative, without derivation and programming of its analytic expression.",
author = "Lesk, {Arthur M.}",
year = "1968",
month = "11",
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pages = "801--805",
journal = "International Journal of Quantum Chemistry",
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publisher = "John Wiley and Sons Inc.",
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AB - The approximation of a linear combination of Slater‐type orbitals in terms of Gaussian functions is a many‐parameter optimization problem. Formulas for computation of the gradient of the overlap in parameter space are reported. An alternative method of computing the gradient is described, which is of general applicability. This technique permits the exact evaluation of a derivative, without derivation and programming of its analytic expression.

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