Effective one-particle energies from generalized Kohn–Sham random phase approximation: A direct approach for computing and analyzing core ionization energies

Abstract

Generalized-Kohn-Sham (GKS) orbital energies obtained self-consistently from the random phase approximation energy functional with a semicanonical projection (spRPA) were recently shown to rival the accuracy of GW quasiparticle energies for valence ionization potentials. Here, we extend the scope of GKS-spRPA correlated one-particle energies from frontier-orbital ionization to core orbital ionization energies, which are notoriously difficult for GW and other response methods due to strong orbital relaxation effects. For a benchmark consisting of 23 1s core electron binding energies (CEBEs) of second-row elements, chemical shifts estimated from GKS-spRPA one-particle energies yield mean absolute deviations from experiment of 0.2 eV, which are significantly more accurate than the standard GW and comparable to Δ self-consistent field theory without semiempirical adjustment of the energy functional. For small ammonia clusters and cytosine tautomers, GKS-spRPA based chemical shifts capture subtle variations in covalent and noncovalent bonding environments; GKS-spRPA 1s CEBEs for these systems agree with equation-of-motion coupled cluster singles and doubles and ADC(4) results within 0.2–0.3 eV. Two perturbative approximations to GKS-spRPA orbital energies, which reduce the scaling from O(N6) to O(N5) and O(N4), are introduced and tested. We illustrate the application of GKS-spRPA orbital energies to larger systems by using oxygen 1s CEBEs to probe solvation and packing effects in condensed phases of water. GKS-spRPA predicts a lowering of the oxygen 1s CEBE of approximately 1.6–1.7 eV in solid and liquid phases, consistent with liquid-jet X-ray photoelectron spectroscopy and gas phase cluster experiments. The results are rationalized by partitioning GKS-spRPA electron binding energies into static, relaxation, and correlation parts.

Accurate Absolute and Relative Core-Level Binding Energies from GW

“…38,39 The few existing studies for molecular core excitations give a mixed first impressions since anything between 0.5 eV 17 and 10 eV deviation from experiment has been reported. 30,40 In this work, we show how reliable and highly accurate core-level BEs can be obtained from GW and explain why large deviations from experiment were reported earlier. We also present a GW benchmark set for 1s core states complementary to the popular GW100 benchmark set 41 for valence excitations.…”

“…30, 40 and 54, for such a spectral function leads to uncontrollable results, which partly explains the large deviation of the reported results from experiment. 30,40 Furthermore, the linearization error increases rapidly with increasing binding energy and may already amount to 0.5 eV for deeper valence states, as shown in Ref. 32.…”

“… 30 Good accuracy for deep states was reported for a recently introduced direct approach based on effective one-particle energies from the generalized KS random phase approximation. 31 However, the application of these higher level methods is restricted to small- or medium-sized systems due to unfavorable scaling with the system size and large computational prefactors.…”

“…Previous GW core-level studies for small molecules 31 , 41 reported G 0 W 0 calculations performed on top of generalized gradient approximation (GGA) or hybrid functionals with a low amount of exact exchange. Our analysis presented in this Letter demonstrates that those studies cannot have found the QP solution because their spectral function would look like the yellow spectrum in Figure 1 c. Linearizing the QP equation by a Taylor expansion to first-order around ε n , as done for such a spectral function in refs ( 31 ), ( 41 ), and ( 63 ), leads to uncontrollable results, which partly explains the large deviation of the reported results from experiment. 31 , 41 Furthermore, the linearization error rapidly increases with increasing BE and may already amount to 0.5 eV for deeper valence states, as shown in ref ( 33 ).…”

“…As shown Figure 1(f), G 0 W 0 @PBE0 still suffers from a large transfer of spectral weight to the satellites. Previous GW core-level studies for small molecules 30,40 reported G 0 W 0 calculations performed on top of generalized gradient approximation (GGA) or hybrid functionals with a low amount of exact exchange. Our analysis presented in this article demonstrates that those studies cannot have found the QP solution because their spectral function would look like the yellow spectrum in Figure 1(c).…”