Fully Dynamic G3W2 Self-Energy for Finite Systems: Formulas and Benchmark

Area of Science:

• * Electronic structure theory
• * Quantum chemistry
• * Solid-state physics

Background:

• * Hedin's GW self-energy is a widely used, accurate approximation for electronic quasiparticle energies.
• * Vertex corrections aim to improve the accuracy of the GW approximation.
• * Previous attempts at improving GW have focused on various vertex corrections.

Purpose of the Study:

• * To derive, analyze, and benchmark the complete second-order term (G3W2) in the screened Coulomb interaction for finite systems.
• * To present analytic formulas for G3W2, including an imaginary frequency counterpart for larger molecules.
• * To evaluate the accuracy of G3W2 against established benchmarks for valence and core quasiparticle energies.

Main Methods:

• * Derivation and implementation of the G3W2 self-energy, incorporating all time orderings of three Green's functions (G) and two screened Coulomb interactions (W).
• * Evaluation of G3W2 on standard benchmarks: GW100, Acceptor 24, and Core 65.
• * Analysis of the relationship between G3W2 and the static screened second-order exchange (SOSEX) approximation, leading to the proposal of 2SOSEX.

Main Results:

• * G3W2 and its approximations do not outperform one-shot G0W0 with a suitable starting point for quasiparticle energies.
• * Quasi-particle self-consistent GW calculations show marginal improvement in HOMO energies when G3W2 is included.
• * The improvement in self-consistent calculations is attributed to the update of the screened Coulomb interaction, causing a sign change in vertex corrections.

Conclusions:

• * The computationally intensive G3W2 self-energy offers limited improvement over simpler GW methods for many applications.
• * Self-consistent updates to the screened Coulomb interaction are crucial for observing any benefits from vertex corrections.
• * Future research may focus on more efficient approximations or specific systems where G3W2 provides a more significant advantage.