Efficient Calculation of Molecular Integrals over London Atomic Orbitals

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of molecular properties in strong magnetic fields requires gauge-origin invariant methods.
• London atomic orbitals (LAOs) provide a framework for gauge-origin invariant calculations.
• Efficient evaluation of electron repulsion integrals (ERIs) is crucial for computational feasibility.

Purpose of the Study:

• To implement and compare algorithms for evaluating ERIs over Gaussian-type LAOs under strong magnetic fields.
• To assess the efficiency of generalized McMurchie-Davidson (MD), Head-Gordon-Pople (HGP), and Rys quadrature schemes.
• To develop a robust and efficient method for ERI evaluation applicable to a wide range of magnetic field strengths.

Main Methods:

• Implementation of generalized McMurchie-Davidson (MD), Head-Gordon-Pople (HGP), and Rys quadrature algorithms for ERIs.
• Evaluation of ERIs using Gaussian-type LAOs at arbitrary magnetic field strengths.
• Numerical comparison of algorithm efficiencies based on angular momentum and basis set type (primitive and contracted).

Main Results:

• The Rys quadrature implementation avoids high-precision arithmetic and interpolation, allowing seamless application across magnetic field strengths.
• No single algorithm (MD, HGP, Rys) is universally optimal for all angular momenta.
• A mixed scheme, selecting the most efficient algorithm per shell quartet, demonstrates significant efficiency gains over exclusive use of any single algorithm.

Conclusions:

• A mixed computational scheme for ERI evaluation over Gaussian-type LAOs in strong magnetic fields offers superior efficiency.
• The developed methods facilitate accurate quantum chemical calculations in the presence of intense magnetic fields.
• This work provides a more computationally tractable approach to studying molecular systems under extreme magnetic conditions.