Numerical treatment of two-center overlap integrals

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Two-center overlap integrals are crucial but computationally challenging in molecular quantum mechanics.
• Existing methods for evaluating these integrals often face accuracy and efficiency limitations.
• The presence of spherical Bessel integrals complicates analytical and numerical evaluations.

Purpose of the Study:

• To develop a highly accurate and efficient algorithm for evaluating two-center overlap integrals.
• To apply Sidi's nonlinear D transformation to address convergence issues in oscillatory integrals.
• To demonstrate the superiority of the D transformation over existing methods for molecular integrals.

Main Methods:

• Application of Sidi's nonlinear D transformation to two-center overlap integrals.
• Development of a new algorithm based on the D transformation for high accuracy.
• Testing the algorithm on molecular multicenter integrals including B functions and Slater-type functions.

Main Results:

• The D transformation significantly improves the convergence of highly oscillatory integrals.
• The developed algorithm demonstrates high accuracy and efficiency compared to quadrature rules, Levin's u transform, and Wynn's epsilon-algorithm.
• Numerical results confirm the effectiveness of the D transformation for various molecular integrals.

Conclusions:

• Sidi's D transformation is highly effective for evaluating two-center overlap integrals.
• The new algorithm offers a significant advancement in the accurate and efficient computation of molecular integrals.
• This method provides a robust tool for complex quantum chemistry calculations.