Parquet theory for molecular systems: Formalism and static kernel parquet approximation

2025/09/03 by Antoine Marie, Pierre-François Loos, Marie, Antoine +2 · 1 voice · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #Advanced Chemical Physics Studies #High-pressure geophysics and materials #Quantum, superfluid, helium dynamics #cond-mat.mtrl-sci #cond-mat.str-el #math-ph #nucl-th #physics.chem-ph

paper · pdf · doi:10.48550/arxiv.2509.03253

openalex publication_date 2025/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The GW approximation has become a method of choice for predicting quasiparticle properties in solids and large molecular systems, owing to its favorable accuracy-cost balance. However, its accuracy is the result of a fortuitous cancellation of vertex corrections in the polarizability and self-energy. Hence, when attempting to go beyond GW through inclusion of vertex corrections, the accuracy can deteriorate if this delicate balance is disrupted. In this work, we explore an alternative route that theoretically goes beyond GW: the parquet formalism. Unlike approaches that focus on a single correlation channel, such as the electron-hole channel in GW or the particle-particle channel in T-matrix theory, parquet theory treats all two-body scattering channels on an equal footing. We present the formal structure of the parquet equations, which couple the one-body Green's function, the self-energy, and the two-body vertex. We discuss the approximations necessary to solve this set of equations, the advantages and limitations of this approach, outline its implementation for molecular systems, and assess its accuracy for principal ionization potentials of small molecular systems.

Citations

• The QUEST Database of Highly-Accurate Excitation Energies
• Why does the GW approximation give accurate quasiparticle energies? The cancellation of vertex corrections quantified
• Fully dynamic G3W2 self-energy for finite systems: Formulas and benchmark
• The GW Approximation: A Quantum Chemistry Perspective
• Accelerating Analytic-Continuation GW Calculations with a Laplace Transformation and Natural Auxiliary Functions
• Quasiparticle Self-Consistent GW-Bethe-Salpeter equation calculations for large chromophoric systems
• The \it victory project v1.0: an efficient parquet equations solver
• GW vertex corrected calculations for molecular systems
• Stochastic GW calculations for molecules
• Large scale GW calculations
• Self-interaction in Green's-function theory of the hydrogen atom
• TheGWmethod
• New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem
• Stationary Entropy Principle and Renormalization in Normal and Superfluid Systems. I. Algebraic Formulation

Cited by

• From Full Dynamic to Pure Static: A Family of GW-Based Approximations

Discussions

• arxiv.org/abs/2509.03253 #compchem [bsky, 5 points, 0 comments]

Related

• Why does the GW approximation give accurate quasiparticle energies? The cancellation of vertex corrections quantified
• Bridging the size gap between density-functional and many-body perturbation theory
• The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap
• Generating functional for the full parquet approximation
• The GW Approximation: A Quantum Chemistry Perspective