An overlap fitted chain of spheres exchange method

Area of Science:

• Computational chemistry
• Quantum mechanics
• Electronic structure theory

Background:

• The RIJCOSX SCF procedure approximates exchange terms using a hybrid analytic-numeric approach.
• The "chain of spheres" (COS) algorithm is a key component of RIJCOSX, performing partial analytic integration.
• Minimizing numerical errors in COS is crucial for improving computational efficiency and accuracy.

Purpose of the Study:

• To enhance the efficiency of the "chain of spheres" (COS) algorithm within the RIJCOSX SCF procedure.
• To minimize numerical errors in the COS approximation of exchange integrals.
• To achieve chemical accuracy with reduced computational cost.

Main Methods:

• Implemented a fitting matrix, Q, based on Friesner's work to align numerical and analytic overlap matrices.
• Systematically tested various grid setups to evaluate the impact of the fitting procedure.
• Compared results against fully analytic methods and the original COS approximation.

Main Results:

• The fitting procedure significantly reduces the grid sizes needed for chemical accuracy.
• Achieved chemical accuracy for total and reaction energies with approximately 30% speedup for single point energies.
• Geometry optimizations showed slight accuracy reductions but remained within inherent theoretical framework errors.

Conclusions:

• The enhanced COS algorithm with the fitting matrix Q improves computational efficiency and accuracy.
• Reduced grid requirements lead to faster calculations without compromising essential accuracy.
• The method offers a favorable balance between speed and precision for quantum chemical computations.