Hybrid gausslet/Gaussian basis sets.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Accurate electronic structure calculations are crucial for understanding molecular properties.
• Standard Gaussian basis sets face challenges in accurately describing electron-electron cusp conditions.
• Existing methods often struggle with computational scaling for large systems.

Purpose of the Study:

• To introduce a novel hybrid gausslet/Gaussian basis set approach.
• To enhance accuracy near atomic nuclei while maintaining computational efficiency.
• To develop corrections for basis set incompleteness, particularly for electron-electron cusp.

Main Methods:

• Developed hybrid basis sets combining gausslets and Gaussian functions.
• Orthogonalized Gaussian functions to the existing orthonormal gausslet basis.
• Introduced approximations to maintain the diagonal property of the two-electron Hamiltonian for efficient scaling.
• Implemented corrections to the Hamiltonian to enforce exact properties and address basis set incompleteness.
• Performed Hartree-Fock and full configuration interaction (full-CI) calculations on two-electron systems and a hydrogen chain.

Main Results:

• Achieved highly accurate results for two-electron systems, reaching complete basis set limits with micro-Hartree accuracy.
• Demonstrated significant improvements in describing electron-electron cusp conditions.
• Showcased efficient computational scaling of the new basis set approach.
• Observed comparable accuracy for Hartree-Fock calculations on a ten-atom hydrogen chain.

Conclusions:

• The hybrid gausslet/Gaussian basis set approach offers a promising route to high accuracy in electronic structure calculations.
• The developed corrections effectively address basis set incompleteness, especially concerning electron-electron cusps.
• This method provides a computationally efficient and accurate alternative for quantum chemistry applications.