Self-consistent solution of the Dyson equation for atoms and molecules within a conserving approximation

Area of Science:

• Quantum chemistry
• Condensed matter physics

Background:

• Accurate calculation of electronic properties is crucial for understanding atomic and molecular behavior.
• Existing methods may not always satisfy fundamental conservation laws or the virial theorem.

Purpose of the Study:

• To develop and apply a self-consistent Green's function method for calculating electronic properties.
• To ensure that calculated observables adhere to macroscopic conservation laws and the virial theorem.
• To extend the method for finite temperature and nonequilibrium systems.

Main Methods:

• Calculation of self-consistent Green's functions using a conserving self-energy approximation.
• Application of the finite temperature formalism on the imaginary time axis.
• Utilizing the extended Koopmans' theorem for ionization potential calculations.

Main Results:

• Green's functions were successfully calculated for atoms and diatomic molecules.
• Observables derived from the Green's functions were shown to agree with conservation laws (particle number, momentum, energy).
• Agreement with the virial theorem and consistent total energy calculations were achieved.

Conclusions:

• The self-consistent Green's function method provides a robust framework for accurate electronic structure calculations.
• The method's adherence to conservation laws and theorems enhances its reliability.
• The formalism is adaptable for studying finite temperature and nonequilibrium phenomena.