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Representation of electron-nucleus cusps in Slater and Gaussian basis sets
Conrad C Moore1, Viktor N Staroverov1
1Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada.
The Journal of Chemical Physics
|December 24, 2025
Summary
This study shows that equations describing electron density cusps apply to approximate wavefunctions, justifying effective nuclear charge concepts for Slater-type and Gaussian-type orbitals.
Area of Science:
- Quantum Chemistry
- Computational Chemistry
Background:
- The Coulomb cusp of exact electron densities is described by a two-parameter equation involving nuclear charge (Z) and an anisotropy vector.
- Jump discontinuities in exact kinetic energy densities at nuclear positions are described by a similar three-parameter equation.
Purpose of the Study:
- To investigate if these equations describing exact electron and kinetic energy densities also apply to approximate wavefunctions.
- To determine the applicability of these concepts to Slater-type orbitals (STOs) and Gaussian-type orbitals (GTOs).
Main Methods:
- Analysis of electron and kinetic energy densities derived from STO and GTO basis sets.
- Comparison of cusp-shape parameters obtained from approximate wavefunctions with those of exact solutions.
Main Results:
- The same equations describing exact densities also describe approximate densities from STO and GTO wavefunctions, using basis-set-dependent parameters.
- Effective nuclear charge (Z) values are zero for GTOs, but cusp-shape parameters from STO and GTOs are comparable and converge to common limits.
- The findings provide a rigorous justification for extending effective nuclear charge and density anisotropy concepts to approximate wavefunctions.
Conclusions:
- The concepts of effective nuclear charge and density anisotropy can be rigorously extended to approximate wavefunctions in STO and GTO basis sets.
- These extensions are not inherent properties of exact solutions and may not apply universally to all basis sets.
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