Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• The construction of the exact exchange matrix (K) is a bottleneck in hybrid density functional theory (DFT).
• Increased computational efficiency is highly desirable for practical applications of DFT.
• Existing methods like integral-direct and resolution of the identity (RI)-K can be computationally intensive.

Purpose of the Study:

• To present a novel framework for computing a compressed exchange matrix.
• To improve the efficiency of calculating exact exchange energy, gradients, and DIIS error vectors.
• To demonstrate the practical advantages of this framework in quantum chemical calculations.

Main Methods:

• Framework for computing a compressed exchange matrix with one index in the molecular orbital basis and the other in the atomic orbital basis.
• Integration of the compressed exchange matrix framework with the resolution of the identity (RI) approximation, termed occupied orbital RI-K (occ-RI-K).
• Utilizing the direct inversion of the iterative subspace (DIIS) algorithm for convergence acceleration.

Main Results:

• The occ-RI-K method demonstrates well-behaved convergence in conjunction with DIIS.
• Computed energetics using occ-RI-K are highly accurate, matching conventional RI-K results.
• Significant speedups were achieved: 14× over conventional algorithms and 3.3× over RI-K for a large graphene fragment.

Conclusions:

• The developed occ-RI-K framework offers a substantial increase in computational efficiency for hybrid DFT.
• This method maintains excellent accuracy for energetics, making it a viable alternative to existing approaches.
• The framework shows great potential for accelerating large-scale quantum chemical computations.