Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened...

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• The random-phase approximation with second-order screened exchange (RPA+SOSEX) is a model for electron correlation energy.
• RPA+SOSEX accuracy depends on the mean field choice and exhibits high computational scaling (O(n^5) operations, O(n^3) memory).

Purpose of the Study:

• To derive a new algorithm that reduces the computational scaling of RPA+SOSEX.
• To introduce a new self-consistent field method that approximates Brueckner coupled-cluster doubles theory with RPA+SOSEX.

Main Methods:

• Developed a new algorithm based on controlled approximations.
• Introduced a new self-consistent field, termed Brueckner RPA theory.
• Reduced computational scaling to O(n^3) operations and O(n^2) memory.

Main Results:

• The new algorithm comparably reduces the scaling of second-order Møller-Plesset perturbation theory.
• The Brueckner RPA theory demonstrates smaller cost prefactors than RPA+SOSEX.
• Semiempirical model studies on H2 dissociation and Hn rings verified the accuracy and scaling.

Conclusions:

• Brueckner RPA theory offers a computationally efficient alternative to existing methods for electron correlation energy calculations.
• The developed algorithm significantly lowers the computational cost and memory requirements, facilitating studies of larger quantum systems.