Vertex corrections to the polarizability do not improve the GW approximation for the ionization potential of molecules

Abstract

The $GW$ approximation is based on the neglect of vertex corrections, which appear in the exact self-energy and the exact polarizability. Here, we investigate the importance of vertex corrections in the polarizability only. We calculate the polarizability with equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD), which rigorously includes a large class of diagrammatically-defined vertex corrections beyond the random phase approximation (RPA). As is well-known, the frequency-dependent polarizability predicted by EOM-CCSD is quite different and generally more accurate than that predicted by the RPA. We evaluate the effect of these vertex corrections on a test set of 20 atoms and molecules. When using a Hartree-Fock reference, ionization potentials predicted by the $GW$ approximation with the RPA polarizability are typically overestimated with a mean absolute error of 0.3 eV. However, those predicted with a vertex-corrected polarizability are typically underestimated with an increased mean absolute error of 0.5 eV. This result suggests that vertex corrections in the self-energy cannot be neglected, at least for molecules. We also assess the behavior of eigenvalue self-consistency in vertex-corrected $GW$ calculations, finding a further worsening of the predicted ionization potentials.

arXiv comment8 pages, 4 figures; results and discussion revised

References in corpus (18)

• The GW method
• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• Fully selfconsistent GW calculations for molecules
• Quasiparticle GW calculations for solids, molecules and 2D materials
• Unified description of ground and excited states of finite systems: the self-consistent GW approach
• A Benchmark of GW Methods for Azabenzenes: Is the GW Approximation Good Enough?
• First-principles GW calculations for DNA and RNA nucleobases
• Quasi-Particle Self-Consistent $GW$ for Molecules
• Benchmark of GW approaches for the GW100 testset
• On The Relation Between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation
• Vertex corrections in localized and extended systems
• Converged GW quasiparticle energies for transition metal oxide perovskites
• Quasiparticles in Neon using the Faddeev Random Phase Approximation
• Simple vertex correction improves GW band energies of bulk and two-dimensional crystals
• Random-phase approximation excitation energies from approximate equation-of-motion ring coupled-cluster doubles
• A Finite-field Approach for $GW$ Calculations Beyond the Random Phase Approximation
• Faddeev Random Phase Approximation for Molecules
• $GW$ self-screening error and its correction using a local density functional

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