Fast Evaluation of Two-Center Integrals over Gaussian Charge Distributions and Gaussian Orbitals with General...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Algorithm Development

Background:

• Traditional ab initio integration techniques can be computationally intensive.
• Existing methods for computing integrals and derivatives have limitations in generality and efficiency.

Purpose of the Study:

• To develop efficient algorithms for computing two-center integrals and their derivatives.
• To provide a general method applicable to various interaction kernels and Gaussian charge distributions.
• To offer a computationally feasible alternative for quantum chemistry and molecular modeling.

Main Methods:

• Adaptation of the McMurchie-Davidson Recurrence Relation (MDRR).
• Integration with analytical properties of solid harmonic transformations.
• Application to fully contracted auxiliary kernel integrals.

Main Results:

• Algorithms demonstrate high efficiency for general interaction kernels and angular momenta.
• A large Coulomb matrix (4894 × 4894) was computed in 50 ms on a Q2'2018 notebook CPU.
• The method obviates intermediate recurrences, simplifying computation.

Conclusions:

• The presented algorithms provide a significant speed-up for integral and derivative computations.
• This technique is suitable for semiempirical and first-principles quantum chemistry.
• The formalism is also applicable to classical force fields and model potentials for electrostatic interactions.