Testing Exact Upper Bounds to Exact Exchange.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Exact exchange energy is crucial for accurate Kohn-Sham density functional theory (KS-DFT) but computationally demanding.
• Existing approximations often involve trade-offs between accuracy and computational cost.

Purpose of the Study:

• To present and test novel, nonempirical upper bounds to exact exchange energy.
• To evaluate the performance of these bounds as computationally tractable approximations within KS-DFT.

Main Methods:

• Developed "Rung 3.5" upper bounds by contracting KS one-particle density matrices with model density matrices.
• Utilized the Cauchy-Schwarz inequality to simplify the exchange hole calculation.
• Eliminated the computationally expensive long-range part of the exact exchange hole.

Main Results:

• The developed upper bounds provide a computationally efficient alternative to exact exchange.
• Numerical tests indicate that these bounds underestimate total exchange energies.
• Despite underestimation, other predicted properties show accuracy close to standard hybrid approximations.

Conclusions:

• "Rung 3.5" upper bounds offer a promising approach for reducing the computational cost of KS-DFT.
• These approximations maintain a high level of accuracy for various properties, making them suitable for practical applications.