Static correlation beyond the random phase approximation: dissociating H2 with the Bethe-Salpeter equation and...

Area of Science:

• Quantum chemistry
• Computational condensed matter physics

Background:

• The dissociation limit of molecules like H2 is challenging for standard electronic structure methods.
• Accurate calculation of correlation energy is crucial for describing molecular properties.

Purpose of the Study:

• To evaluate various approximations for the correlation energy of H2 at dissociation.
• To assess the performance of Hedin's equations-based methods and the Bethe-Salpeter equation (BSE).

Main Methods:

• Derivation of correlation energies from the density response function.
• Application of Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), and BSE.
• Utilizing a Hubbard model for exact analytical comparisons.
• Ab initio calculations and exact diagonalization.

Main Results:

• Response functions from Hedin's equations (RPA, TDHF, BSE, Time-Dependent GW) correctly reproduce the H2 dissociation limit.
• BSE significantly enhances correlation energies over RPA and TDHF at intermediate distances.
• The Hubbard model validates ab initio findings, confirming BSE's improvement despite its breakdown at dissociation.

Conclusions:

• Hedin's equations-based methods, particularly BSE, offer accurate descriptions of H2 correlation energy, even at dissociation.
• BSE provides substantial improvements for intermediate binding distances compared to RPA and TDHF.
• The study highlights the importance of irreducible response functions for accurate dissociation limit descriptions.