The weak orthogonality functional in explicitly correlated pair theories

Area of Science:

• Quantum chemistry
• Computational physics
• Electronic structure theory

Background:

• Explicitly correlated methods (e.g., R12, Gaussian geminal) are advancing.
• A key difference lies in handling many-electron integrals.
• Weak orthogonality functional and resolution of the identity are crucial components.

Purpose of the Study:

• To analyze the conflict between the weak orthogonality functional and the strong orthogonality constraint.
• To propose an improved weak orthogonality functional.
• To provide recommendations for integral evaluation in explicitly correlated methods.

Main Methods:

• Examination of the weak orthogonality functional and resolution of the identity.
• Development of a new weak orthogonality functional.
• Analysis of the electronic cusp and strong orthogonality constraint.

Main Results:

• The standard weak orthogonality functional conflicts with the electronic cusp description and strong orthogonality.
• An improved weak orthogonality functional is proposed, ensuring near-orthogonality of pair functions to occupied orbitals.
• The strong orthogonality functional with resolution of the identity achieves 95%-98% accuracy in total correlation energy.

Conclusions:

• The proposed improved weak orthogonality functional resolves existing conflicts.
• For applications needing 95%-98% accuracy, the strong orthogonality functional with resolution of the identity is recommended for three- and four-electron integrals.