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Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions.

Frank E Harris1

  • 1Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA and Quantum Theory Project, University of Florida, P.O. Box 118435, Gainesville, Florida 32611, USA.

The Journal of Chemical Physics
|June 3, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces new formulas for calculating atomic kinetic energy using the Hylleraas-CI method. These formulas simplify complex calculations by reducing them to overlap and potential-energy integrals, improving accuracy for quantum chemistry computations.

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Area of Science:

  • Quantum Chemistry
  • Atomic Physics
  • Computational Chemistry

Background:

  • Hylleraas-CI method uses Slater-type orbital products with interelectron distance terms.
  • Calculating atomic kinetic energy matrix elements for Hylleraas-CI with general angular momentum is computationally challenging.
  • Existing methods lack formulas to express these matrix elements in terms of overlap and potential-energy integrals.

Purpose of the Study:

  • To develop new formulas for atomic kinetic energy matrix elements within the Hylleraas-CI framework.
  • To simplify the computation of these matrix elements for general angular momentum.
  • To enable more efficient and accurate quantum mechanical calculations for atoms.

Main Methods:

  • Application of angular-momentum theory.
  • Utilized vector spherical harmonics for integral reduction.
  • Derived formulas connecting kinetic energy integrals to overlap and potential-energy integrals.

Main Results:

  • Successfully derived formulas for atomic kinetic energy integrals in the Hylleraas-CI method.
  • Demonstrated the reduction of kinetic energy integrals to overlap and potential-energy matrix elements.
  • Validated the new formulas against published atomic integrals, confirming their accuracy.

Conclusions:

  • The developed formulas provide a significant advancement for Hylleraas-CI calculations.
  • This work overcomes a major computational hurdle in applying Hylleraas-CI to atomic systems.
  • The findings facilitate more accurate and efficient quantum chemical computations for atomic structures.