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

Area of Science:

• * Electronic structure theory
• * Quantum chemistry
• * Computational physics

Background:

• * The GW approximation is widely used for quasiparticle properties due to its accuracy-cost balance.
• * Its accuracy relies on a cancellation of vertex corrections, which can be disrupted when extending beyond GW.
• * Existing methods often focus on single correlation channels, limiting their scope.

Purpose of the Study:

• * To explore the parquet formalism as a theoretical approach beyond the GW approximation.
• * To present the formal structure of parquet equations and discuss necessary approximations.
• * To assess the accuracy of the parquet approach for molecular systems.

Main Methods:

• * Development and presentation of the formal structure of parquet equations.
• * Coupling of the one-body Green's function, self-energy, and two-body vertex.
• * Implementation and accuracy assessment for principal ionization potentials of small molecules.

Main Results:

• * The parquet formalism treats all two-body scattering channels (electron-hole, particle-particle) simultaneously.
• * Formal structure of the coupled parquet equations is derived.
• * Initial assessment of accuracy for ionization potentials is outlined.

Conclusions:

• * The parquet formalism provides a theoretically rigorous route beyond GW approximation.
• * It offers a balanced treatment of all relevant correlation channels.
• * Further investigation is warranted for its application to complex molecular systems.