Calculation of molecular integrals over Slater-type orbitals using recurrence relations for overlap integrals and...

Area of Science:

• Computational Quantum Chemistry
• Theoretical Chemistry
• Atomic and Molecular Physics

Background:

• Accurate calculation of multicenter electron-repulsion integrals is essential for molecular electronic structure calculations.
• Traditional methods using Slater-type orbitals (STOs) can be computationally intensive.
• Developing efficient and accurate computational schemes is a persistent challenge in quantum chemistry.

Purpose of the Study:

• To establish recurrence relations for basic one-center Coulomb integrals over Slater-type orbitals (STOs).
• To utilize these relations and overlap integral recurrence relations for multicenter electron-repulsion integral calculations.
• To investigate the use of translation formulas for STOs derived from Lambda and Coulomb Sturmian exponential-type functions (ETFs).

Main Methods:

• Derivation of recurrence relations for one-center Coulomb integrals.
• Application of translation formulas for STOs based on Lambda and Coulomb Sturmian ETFs.
• Computation of multicenter electron-repulsion integrals using the developed formalism.

Main Results:

• The study successfully establishes recurrence relations for the required integrals.
• Calculations using Coulomb Sturmian ETFs demonstrate a faster convergence rate compared to standard STOs.
• High accuracy is achieved for STO quantum numbers, internuclear distances, and screening constants.

Conclusions:

• The developed recurrence relations provide an efficient method for calculating multicenter electron-repulsion integrals.
• Coulomb Sturmian ETFs offer a significant advantage in terms of convergence speed for these calculations.
• The high accuracy validates the approach for various atomic and molecular system parameters.