Linear-scaling implementation of the direct random-phase approximation

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of electronic structure is crucial for understanding molecular properties.
• Traditional methods for methods like direct random-phase approximation (dRPA) and Møller-Plesset perturbation theory (MP2) scale poorly with system size.
• The development of linear-scaling algorithms is essential for tackling larger molecular systems.

Purpose of the Study:

• To implement a linear-scaling direct random-phase approximation (dRPA) for closed-shell molecular systems.
• To extend linear-scaling algorithms to the second-order screened exchange extension of dRPA and second-order Møller-Plesset (MP2) methods.
• To enable accurate electronic structure calculations for significantly larger molecules than previously possible.

Main Methods:

• An incremental scheme based on a local correlation method was employed.
• Extensive use of local natural orbitals to reduce the size of local correlation domain basis sets.
• Utilization of natural auxiliary functions to reduce auxiliary basis set size and three-center Coulomb integral lists.

Main Results:

• A linear-scaling implementation of dRPA for closed-shell molecules was successfully developed.
• Linear-scaling algorithms were also presented for dRPA's screened exchange extension and MP2 variants.
• Benchmark calculations demonstrated the method's ability to handle molecules with over 1000 atoms and 10,000 basis functions on a single processor.

Conclusions:

• The developed approach significantly reduces computational cost, enabling accurate electronic structure calculations for large molecular systems.
• The method provides substantial savings in computation time through efficient basis set and integral list management.
• This work opens new possibilities for studying complex molecular systems using advanced quantum chemical methods.