Wave Function Perspective and Efficient Truncation of Renormalized Second-Order Perturbation Theory

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Second-order Green's function perturbation theory (GF2) and Møller-Plesset perturbation theory (MP2) are standard methods for calculating electron correlation.
• These methods can suffer from divergences and limitations in describing strongly correlated systems.
• Existing approaches often rely on continuous variables, grids, or explicit Green's functions, increasing computational complexity.

Purpose of the Study:

• To develop a novel, computationally efficient approach to renormalized second-order Green's function perturbation theory (GF2).
• To formulate GF2 entirely in terms of static quantities and wave functions, avoiding continuous variables and explicit Green's functions.
• To enable accurate description of strong correlation effects beyond the capabilities of MP2.

Main Methods:

• Renormalized second-order Green's function perturbation theory (GF2) formulated using static quantities and wave functions.
• Iterative incorporation of MP2 diagrams by coupling the system to auxiliary degrees of freedom.
• Compression of auxiliary space conserving spectral moments for rigorous O(N^5) scaling.
• Application to the G1 test set for energetic accuracy.

Main Results:

• The developed GF2 approach avoids divergences and limitations of MP2 and its orbital-optimized variants.
• Rigorous O(N^5) computational scaling is achieved through auxiliary space compression.
• Accurate energetics for strongly correlated systems are obtained by modifying only the third spectral moment.
• The method provides a qualitative description of stronger correlation effects.

Conclusions:

• The novel GF2 formulation offers a computationally tractable and accurate method for electronic structure calculations.
• It effectively captures strong correlation effects without the need for full dynamical self-energy descriptions.
• This approach represents a significant advancement in computational quantum chemistry for challenging systems.