Efficient calculation of integrals in mixed ramp-Gaussian basis sets

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Algorithm Development

Background:

• Efficient calculation of two-electron integrals is crucial for quantum chemistry.
• Existing all-Gaussian and Slater basis sets have limitations in speed and accuracy for specific properties.

Purpose of the Study:

• To present algorithms for efficient calculation of two-electron integrals using novel mixed ramp-Gaussian basis sets.
• To introduce RampItUp, a Fortran90 implementation of these algorithms.
• To evaluate the potential speed-up and applicability of these new basis sets in quantum chemistry calculations.

Main Methods:

• Development of algorithms for calculating two-electron integrals with ramp-Gaussian basis sets.
• Implementation of these algorithms in a Fortran90 code named RampItUp.
• Comparison of computational timings for Hartree-Fock (HF) calculations using ramp-Gaussian (R-31G) versus all-Gaussian (6-31G) basis sets for large linear molecules.

Main Results:

• The new ramp-Gaussian basis sets show potential for up to 20% speed-up in general HF and DFT calculations.
• Significant speed-ups are observed for core-dependent properties, potentially replacing Slater functions or large Gaussian sets.
• Initial implementation demonstrates approximately 10% speed-up in HF/R-31G compared to HF/6-31G for large linear molecules.

Conclusions:

• The developed algorithms and RampItUp implementation offer a promising approach for accelerating quantum chemistry computations.
• Ramp-Gaussian basis sets provide a viable alternative to traditional basis sets, especially for core-dependent property calculations.
• The methodology's efficiency stems from a reduced number of primitive functions and simpler intermediate integrals.