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Abstract
The GW method in its most widespread variant takes, as an input, Kohn-Sham (KS) single particle energies and single particle states and yields results for the single-particle excitation energies that are significantly improved over the bare KS estimates. Fundamental shortcomings of density functional theory (DFT) when applied to excitation energies as well as artifacts introduced by approximate exchange-correlation (XC) functionals are thus reduced. At its heart lies the quasi-particle (qp) equation, whose solution yields the corrected excitation energies and qp-wave functions. We propose an efficient approximation scheme to treat this equation based on second-order perturbation theory and self-consistent iteration schemes. We thus avoid solving (large) eigenvalue problems at the expense of a residual error that is comparable to the intrinsic uncertainty of the GW truncation scheme and is, in this sense, insignificant.
Highlights
A convenient theoretical tool to study interacting electron systems in condensed matter theory is the Green’s function (G).[1,2] There are two reasons for its popularity
For the density functional theory (DFT) part the PBE functional was used.[73]. We found it helpful to initialize the self-consistency cycles of higher-order approximations with the estimates obtained from lower-order ones: initial guesses to obtain the diagonal approximation, zn(0), have been the bare KS energies εnKS: the second-order cycle (result zn(2)) was initialized with zn(0)
At the heart of any G0W0 calculation is the solution of the quasi-particle equation
Summary
A convenient theoretical tool to study interacting electron systems in condensed matter theory is the (causal) Green’s function (G).[1,2] There are two reasons for its popularity. For molecular systems, G0W0 energies employing (nonselfconsistent) single-shot approximations to the quasi-particle equation (and starting from a semilocal functional) acquire significant corrections, on the order of 1 eV, when including self-consistency on the pole positions; by contrast, corrections on the orbitals (probed by off-diagonal terms), in most cases, appear less relevant. A strong impact of off-diagonal terms in Σ might be expected in charge-transfer compounds, where the amount of charge transfer is controlled by level alignment and hybridization.[69] In this case, the ground-state charge density may differ significantly from KS-LDA or KS-GGA estimates, so that wave function updates should be very important to understand the ground-state structure This situation typically arises with open-shell molecules or in the presence of degeneracies.] In order to illustrate quantitative aspects, we consider two examples: benzene and acrolein. Off-diagonal corrections, in most cases, are quantitatively negligible within the test set of molecules that we have studied
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