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We report on ab initio calculations of the first-order corrections in the screened interaction W to the random-phase approximation polarizability and to the GW self-energy, using a noninteracting Green’s function, for silicon and diamond. It is found that the first-order vertex and self-consistency corrections to the polarizability largely compensate each other. This does not hold, however, for the first-order corrections to the GW gap. For silicon the compensation between the first-order vertex and self-consistency correction contributions to the gap is only about 35%, while for diamond it is even absent. The resulting gap values are significantly and systematically too large, the direct gaps for silicon and diamond being 0.4 eV and 0.7 eV larger than their GW values, respectively. The success of GW in predicting electronic properties of, e.g., silicon and diamond can therefore apparently not be understood in terms of ‘‘small’’ corrections to GW to first order in W using a noninteracting Green’s function. @S0163-1829~98!01819-0# I. INTRODUCTION One of the most successful methods of describing exchange-correlation effects in ab initio calculations is the random-phase approximation ~RPA! GW approach, where the ~irreducible! polarizability P is calculated in the RPA and the self-energy S is calculated to first order in the dynamically screened interaction W. 1,2 It is remarkable in this connection that non-self-consistent RPA GW calculations lead to quasiparticle ~QP! band gaps that are in excellent agreement with experiment in the case of a large group of semiconductors if the starting point is chosen to be the density-functional theory ~DFT! in the local-density approximation ~LDA!. Henceforth we will call this non-selfconsistent RPA GWapproach ‘‘standard GW.’’ The inherent assumption that higher-order corrections can be neglected is, however, far from obvious. The inclusion of vertex ( V) and so-called self-consistency ~SC! corrections to S and P has been studied by a number of researchers, mainly for the homogeneous electron gas. Hubbard 3 introduced the corrections to the RPA by means of a local-field factor ~not to be confused with the so-called local-field effects to be introduced later on!. In the electron gas case much effort has gone into obtaining expressions for local-field factors in the dielectric function; see, for instance, Refs. 2 and 4. DuBois, 5 whose work can be considered as an extension to the work of Gell-Mann and Brueckner, 6,7 stresses the importance of taking into account all polarizability diagrams of the same order in the Wigner-Seitz radius r s . He noticed the significant cancellation between V and SC corrections in the high-density limit. Geldart and Taylor 8 found a similar compensation for the static polarizability. They attempted to construct a local-field factor that includes SC corrections. Mahan and Sernelius, 9 using the local-field factor approach, concluded that the effects of V corrections to the bandwidth of the homogeneous electron gas nearly cancel when added to both the self-energy and the polarizability, as was already predicted by Rice. 10

physical review. b, condensed matter

First-order corrections to random-phase approximation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>GW</mml:mi></mml:math>calculations in silicon and diamond

First-order corrections to random-phase approximationGWcalculations in silicon and diamond