"Balancing" the Block Davidson-Liu Algorithm.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Algorithm Development

Background:

• The block Davidson-Liu algorithm is a standard method for solving large eigenvalue problems in electronic structure theory.
• Efficient computation is crucial for large molecular systems in quantum chemistry.
• Current methods can face challenges with convergence and computational cost for large systems.

Purpose of the Study:

• To introduce a simple yet effective modification to the block Davidson-Liu eigenvalue algorithm.
• To enable natural decrease of Krylov search direction norms for improved convergence.
• To enhance computational efficiency in large-scale quantum chemistry calculations.

Main Methods:

• Implementation of a "balancing" modification to the block Davidson-Liu eigenvalue algorithm.
• Application of the modified algorithm to integral-direct configuration interaction singles (CI).
• Integration with time-dependent density functional theory (TD-DFT) calculations.
• Utilizing density-based screening for computational efficiency.

Main Results:

• The balancing modification allows Krylov search direction norms to decrease naturally near convergence.
• Efficient utilization of density-based screening is achieved.
• Speedups of approximately 2x were observed on systems up to 1500 atoms using the TeraChem GPGPU code.
• Negligible loss in accuracy was noted.

Conclusions:

• The balancing modification offers a practical and efficient enhancement to the block Davidson-Liu algorithm.
• This approach significantly accelerates large-scale electronic structure calculations.
• The method demonstrates a favorable balance between computational speed and accuracy for demanding quantum chemistry problems.