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Oneparticle Green’s functions obtained from the selfconsistent solution of the Dyson equation can be employed in the evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry selfconsistent algorithms cannot be easily deployed for the Green’s function methods because of a nonconvex grand potential functional and a nonidempotent density matrix. Moreover, the optimization problem can become more challenging due to the inclusion of correlation effects, changing chemical potential, and fluctuations of the number of particles. In this paper, we study acceleration techniques to target the selfconsistent solution of the Dyson equation directly. We use the direct inversion in the iterative subspace (DIIS), the leastsquared commutator in the iterative subspace (LCIIS), and the Krylov space accelerated inexact Newton method (KAIN). We observe that the definition of the residual has a significant impact on the convergence of the iterative procedure. Based on the Dyson equation, we generalize the concept of the commutator residual used in DIIS and LCIIS and compare it with the difference residual used in DIIS and KAIN. The commutator residuals outperform the difference residuals for all considered molecular and solid systems within both GW and GF2. For a more »
 Publication Date:
 NSFPAR ID:
 10363554
 Journal Name:
 The Journal of Chemical Physics
 Volume:
 156
 Issue:
 9
 Page Range or eLocationID:
 Article No. 094101
 ISSN:
 00219606
 Publisher:
 American Institute of Physics
 Sponsoring Org:
 National Science Foundation
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