An Efficient Hartree-Fock Implementation Based on the Contraction of Integrals in the Primitive Basis.

Area of Science:

• Computational Chemistry
• Quantum Chemistry

Background:

• The restricted closed-shell Hartree-Fock (HF) equation is a cornerstone of quantum chemistry for electronic structure calculations.
• Traditional implementations involve computationally intensive integral transformations between different basis sets.

Purpose of the Study:

• To propose and implement a new computational approach for the restricted closed-shell Hartree-Fock equation.
• To enhance computational efficiency by omitting explicit integral transformations.

Main Methods:

• A novel ansatz transforms the density matrix to the primitive basis for contraction with untransformed integrals.
• The Fock matrix's two-electron component is computed and transformed back to the atomic orbital basis.
• Standard techniques like integral prescreening, DIIS acceleration, and differential density are incorporated.
• The program is written in C++ utilizing code generation and Streaming SIMD extensions.

Main Results:

• The new method demonstrates superior performance compared to MOLPRO and TURBOMOLE.
• Computational speedups of up to 5x against MOLPRO and 3x against TURBOMOLE were observed.
• Significant accelerations, up to 55x, were achieved with generalized contracted basis sets.

Conclusions:

• The proposed method offers a computationally efficient alternative for restricted closed-shell Hartree-Fock calculations.
• The approach is particularly effective with generalized radial contraction basis sets.
• The implementation's efficiency and scalability are highlighted by its performance gains.