Electron Propagator Self-Energies versus Improved GW100 Vertical Ionization Energies

Abstract

Ab initio electron propagator (EP) methods that are free of adjustable parameters in their self-energy formulae and in the generation of their orbital bases have been applied to the calculation of the lowest vertical ionization energies (VIEs) of the GW100 set. An improved set of standard results accompanied by irreducible representation assignments has been produced indirectly with coupled-cluster singles and doubles plus perturbative triples, i.e., CCSD­(T), total energy differences at initial-state geometries reoptimized (in 28 cases) with the largest applicable point groups. The best compromises of accuracy and efficiency belong to a new generation of EP self-energies, several members of which may be derived from an intermediately normalized, Hermitized super-operator metric. The following diagonal self-energy methods are optimal: opposite-spin non-Dyson second order (os-nD-D2), approximately renormalized partial third order (P3+), approximately renormalized quasiparticle third order (Q3+), and non-Dyson approximately renormalized linear third order version B (nD-L3+B). Their mean absolute errors (MAEs) in electron volts and arithmetic scaling factors expressed in terms of occupied (O) and virtual (V) orbital dimensions are, respectively, (0.18, OV2), (0.14, O2V3), (0.15, O2V3), and (0.11, OV4). The 0.06 eV MAE for the non-diagonal, sixth-power (O2V4) Brueckner doubles, triple-field operator (BD-T1) EP method is exceeded by the 0.1 eV MAE with respect to experiments in seventh-power, ΔCCSD­(T) calculations and indicates that BD-T1 may serve as a direct, spin-symmetry-conserving alternative in the generation of standard results for VIEs of larger, closed-shell molecules.

Electron Propagator Theory of Vertical Electron Detachment Energies of Anions: Benchmarks and Applications to Nucleotides

“…The P3 and P3+ methods have no selection parameters and require O 2 V 3 arithmetic operations. P3+ mean absolute errors were lower than those of the OVGF approach in recent tests. ,,, …”

“…A new generation of self-energy approximations features ring–ladder renormalizations with exchange and retains terms that contain ground-state correlation amplitudes (e.g., first-order double replacements or T 2 (1) ) in the D3, OVGF, P3, and P3+ self-energies. , To derive the renormalized linear third order (RL3) self-energy, a Hermitized, intermediately normalized superoperator metric, defined by [ X | Y ] = 1 2 false( false⟨ HF false| false( X † Y + Y X † false) false( 1 + T 2 false( 1 false) + T 1 false( 2 false) false) false| HF false⟩ + false⟨ HF false| false( 1 + T 2 false( 1 false) + T 1 false( 2 false) false) † false( X † Y + Y X † false) false| HF false⟩ false) has been adopted. This choice suffices to recover the third-order terms that are linear in ground-state correlation amplitudes, but some of them now have different coefficients than in D3.…”

“…Perturbative expressions for the self-energy matrix elements needed in eqs and have been thoroughly analyzed, and systematic approaches for generating all terms through any order in the Møller–Plesset fluctuation potential have been established. , Second-order methods with nondiagonal (ND2) or diagonal (D2) self-energy matrices provide the simplest and usually the largest relaxation and correlation corrections to canonical Hartree–Fock orbital energies . These methods typically underestimate the vertical ionization energies of closed-shell molecules even when the basis sets are saturated. , This defect persists when the 2ph term, which accounts for ground-state correlation, becomes energy-independent in the non-Dyson (nD) version of D2 (nD-D2). , To mitigate this systematic error, the opposite-spin-only (os) versions of D2 and nD-D2 have been introduced. , Although the resulting os-D2 and os-nD-D2 methods have no adjustable parameters, they produce average absolute errors for vertical ionization energies that are less than half those of the D2 and nD-D2 methods (i.e., approximately 0.2 vs 0.5 eV). After completion of a partial integral transformation that requires only N 4 arithmetic operations for each electron binding energy, all four diagonal second-order methods are practically free because they have only OV 2 bottlenecks.…”

“…Diagonal third-order (D3) calculations typically make the opposite error: their overestimates of vertical ionization energies are exacerbated by enlargement of basis sets. , To remedy this deficiency and to estimate the effects of higher-order terms, the three OVGF versions were introduced . Whereas the diagonal self-energy matrix elements of D3 require OV 4 arithmetic operations, the OVGF extensions involve only trivial evaluations of scaling factors.…”

“…Here we avoid orbitals, self-energies, and selection procedures that are based on adjustable parameters and therefore employ a G 0 W 0 version based on canonical Hartree–Fock orbitals and exchangeless Tamm–Dancoff excitations instead of the commonly encountered combination of Kohn–Sham orbitals with exchangeless random-phase-approximation excitations. The resulting HF-TDA- G 0 W 0 self-energy sums exchangeless ring diagrams in all orders of the fluctuation potential and is a simplified version of the two-particle–one-hole Tamm–Dancoff approximation (2ph-TDA), which includes exchange as well as ladder and mixed ring–ladder terms in all orders. ,, …”