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Related Experiment Videos

Gaussian-type function set without prolapse for the Dirac-Fock-Roothaan equation.

Hiroshi Tatewaki1, Yoshihiro Watanabe

  • 1Institute of Natural Sciences, Nagoya City University, Nagoya, Aichi 467-8501, Japan. htatewak@ncs.cc.nagoya-cu.ac.jp

Journal of Computational Chemistry
|September 30, 2003
PubMed
Summary

A new Gaussian-type function set for the Dirac-Fock-Roothaan equation was developed. This universal set accurately calculates atomic energies for various elements, showing minimal error for mercury and inert gases.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Atomic Physics

Background:

  • Accurate atomic energy calculations are crucial in quantum chemistry.
  • The Dirac-Fock-Roothaan equation requires efficient basis sets for relativistic calculations.
  • Existing Gaussian-type function (GTF) sets can suffer from variation collapse.

Purpose of the Study:

  • To develop a novel Gaussian-type function (GTF) set for the Dirac-Fock-Roothaan (DFR) equation.
  • To ensure the GTF set is free from variation collapse.
  • To evaluate the universality and accuracy of the developed GTF set for various atoms.

Main Methods:

  • Generation of a GTF set without variation collapse for the DFR equation.
  • Determination of exponent parameters using an even-tempered approach for s, p, d, and f symmetries.

Related Experiment Videos

  • Application of the GTF set to mercury, inert gas atoms (Ne, Ar, Kr, Xe, Rn, No), and an open-shell atom (Es).

    • Main Results:

    • A GTF set with 7-62 primitive functions was generated for mercury.
    • The total energy calculated using the new GTF set for mercury closely matched the numerical Dirac-Fock (NDF) result (-19648.849251 vs -19648.849250 hartree).
    • The absolute error (deltaTE) for all tested atoms was very small, with a maximum of 2.8 x 10(-6) hartree, demonstrating the set's potential as a universal basis set.

    Conclusions:

    • The developed GTF set is robust and avoids variation collapse.
    • The GTF set provides highly accurate total energies for a wide range of atoms, including heavy and open-shell elements.
    • This set shows significant potential for use as a universal basis set in relativistic atomic structure calculations.