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Evaluation of overlap integrals with integer and noninteger n Slater-type orbitals using auxiliary functions
Israfil Guseinov1, Bahtiyar Mamedov
1Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Canakkale, Turkey. iguseinov@altavista.net
Journal of Molecular Modeling
|November 5, 2002
Summary
New formulas simplify overlap integral calculations for Slater-type orbitals. These series expansions are accurate for large quantum numbers, aiding computational chemistry and quantum mechanics research.
Area of Science:
- Quantum Chemistry
- Computational Physics
Background:
- Calculating overlap integrals is crucial for molecular electronic structure.
- Existing methods can be computationally intensive for large quantum numbers.
Purpose of the Study:
- To derive series expansion formulas for overlap integrals.
- To accommodate both integer and noninteger Slater-type orbitals (ISTOs and NISTOs).
- To provide accurate calculations for large quantum numbers.
Main Methods:
- Derivation of series expansion formulae.
- Utilizing auxiliary functions A(sigma) and B(k).
- Expressing overlap integrals as a product of these functions.
Main Results:
- Formulas are applicable to arbitrary integer and noninteger Slater-type orbitals.
- The series simplifies to a closed expression for integer quantum numbers.
- Accurate results obtained for quantum numbers up to n=n'=60 and n*=n'*<33.
Conclusions:
- The derived formulae offer an efficient method for calculating overlap integrals.
- These formulas are particularly valuable for systems with large quantum numbers.
- The method ensures satisfactory accuracy across various screening constants and internuclear distances.