Attacking the integral transformation bottleneck: A fast orbital-optimization algorithm with sub-cubic computational...

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Seniority-zero wavefunctions offer a computationally tractable approach to quantum chemistry problems.
• Traditional methods for optimizing these wavefunctions can be computationally demanding, limiting their application to larger systems.

Purpose of the Study:

• To develop an efficient orbital-optimization algorithm for seniority-zero wavefunctions.
• To reduce the computational cost associated with quantum-chemical calculations.
• To enable the accurate prediction of molecular properties for large and complex systems.

Main Methods:

• Devised an orbital-optimization algorithm tailored for seniority-zero wavefunctions.
• Utilized one- and two-electron reduced density matrices to avoid four-index integral transformations.
• Employed rank-three tensors and exploited spatial locality and sparsity for computational efficiency.
• Implemented a direct inversion in the iterative subspace scheme for accelerated convergence.

Main Results:

• Achieved sub-cubic scaling with system size, significantly reducing computational resource consumption.
• Successfully optimized large linear oligomer chains and hydrogen clusters with up to 1391 orbitals.
• Demonstrated the algorithm's efficacy using pECCD as the seniority-zero wavefunction.
• Obtained accurate predictions for molecular properties of ozone, ethylene's rotational barrier, and organic reaction isomerization energies.

Conclusions:

• The developed algorithm provides a computationally efficient and scalable method for seniority-zero wavefunction optimization.
• This approach enables accurate quantum-chemical calculations on larger molecular systems than previously feasible.
• The method shows promise for predicting molecular properties and benchmarking against conventional quantum-chemical techniques.