Prescreening and efficiency in the evaluation of integrals over ab initio effective core potentials

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Evaluating integrals over effective core potentials (ECPs) is computationally intensive.
• Existing methods can be inefficient and scale poorly with system size.

Purpose of the Study:

• To develop novel, efficient schemes for prescreening and evaluating integrals over ECPs.
• To improve the accuracy and reduce the computational cost of quantum chemistry calculations.

Main Methods:

• Developed new prescreening schemes providing rigorous bounds on integral values.
• Implemented a systematic rescaling procedure to minimize approximation errors.
• Devised a numerically stable recursive integration routine, avoiding expensive quadratures.

Main Results:

• The new screening provides bounds within 10% of true values, reducible to 0.1% error via rescaling.
• The recursive integration routine avoids costly quadrature methods.
• Tests on silver clusters using coupled clusters with single and double excitations and perturbative triple calculations showed no loss in accuracy.
• Significant reductions in computational scaling with system size were observed.

Conclusions:

• The new schemes offer a substantial speedup (approx. 40x) compared to traditional quadrature methods.
• These advancements enable more accurate and efficient quantum chemical calculations, particularly for larger systems.
• The methods are robust and maintain accuracy while improving computational performance.