Renormalized Singles Green’s Function in the T-Matrix Approximation for Accurate Quasiparticle Energy Calculation

Abstract

We combine the renormalized singles (RS) Green's function with the T-matrix approximation for the single-particle Green's function to compute quasiparticle energies for valence and core states of molecular systems. The G RS T 0 method uses the RS Green's function that incorporates singles contributions as the initial Green's function. The G RS T RS method further calculates the generalized effective interaction with the RS Green's function by using RS eigenvalues in the T-matrix calculation through the particle−particle random phase approximation. The G RS T RS method provides significant improvements over one-shot methods G 0 T 0 and G 0 W 0 as demonstrated in calculations for GW100 and CORE65 test sets. It also systematically eliminates the dependence of G 0 T 0 on the choice of density functional approximations. For valence states, the G RS T RS method provides excellent accuracy, which is better than that of G 0 T 0 and G 0 W 0 . For core states, the G RS T RS method identifies correct peaks in the spectral function and significantly outperforms G 0 T 0 on core-level binding energies (CLBEs) and relative CLBEs.

Benchmark of $\boldsymbol{GW}$ Methods for Core-Level Binding Energies

“…One way to reduce the underscreening is to include corrections for the electron correlation in the RS Hamiltonian, which is dominated by exchange interactions. An alternative strategy is to compensate the underscreening by including vertex corrections, e.g., to use the T-matrix formalism, 29,69,70 where the two-point screened interaction W is replaced with a four-point effective interaction T . However, methods such as the T-matrix are computationally much more expensive than GW due to their higher complexity.…”

“…68 We also used the RS Green's function in the T-matrix approximation (G RS T RS ) in a similar manner as in G RS W RS . 69 The T-matrix method scales formally as O(N 6 ) with respect to system size N , 69,70 with reduced scaling possible using effective truncation of the active space. 71 In addition to the high computational cost, the performance of G RS T RS for core-levels is not particularly impressive.…”

“…The error with respect to experiment is 1.5 eV for absolute and 0.3 eV for relative CLBEs. 69 In the present work, we focus thus on RS GW approaches for core-levels.…”

Static and Dynamic Bethe-Salpeter Equations in the $T$-Matrix Approximation

“…Alternatives to GW do exist. For example, the T -matrix (or Bethe-Goldstone) approximation, first introduced in nuclear physics, [10][11][12][13][14] then in condensed matter physics, [15][16][17][18][19][20][21][22][23] and more recently in quantum chemistry, 24,25 sums to infinity the ladder diagrams from the particle-particle (pp) channel and is justified in the low-density or strongly-correlated regime. [13][14][15]26 While the two-point screened interaction W is the cornerstone of GW, the T -matrix approximation relies on a more complex (four-point) effective interaction -the so-called T matrixyielding the following self-energy:…”

Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods

“…47,48 In addition to obvious irregularities in potential energy surfaces that hampers the accurate determination of properties such as equilibrium bond lengths and harmonic vibrational frequencies, 40,41 one direct consequence of these discontinuities is the difficulty to converge (partially) self-consistent GW calculations as the self-consistent procedure jumps erratically a) Electronic mail: loos@irsamc.ups-tlse.fr from one solution to the other even if convergence accelerator techniques such as DIIS are employed. 39,49,50 Note in passing that the present issues do not only appear in GW as the T -matrix [51][52][53][54] and second-order Green's function (or second Born) formalisms [55][56][57][58][59][60][61][62][63][64][65] exhibit the same drawbacks.…”