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Volumn 91, Issue 15, 2015, Pages

Exploring approximations to the GW self-energy ionic gradients

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EID: 84929094736     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.91.155109     Document Type: Article
Times cited : (40)

References (75)
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    • One has to note, however, that the impact of the functional on the vibrational eigenmodes used to calculate the EPC matrix elements was found to be marginal, the main effect coming from the framework within which the quasiparticle energies are calculated.
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    • This triple-(Equation presented) plus polarization (TZP) basis consists of three shells of (Equation presented) and (Equation presented) orbitals, complemented by one polarization (Equation presented) shell, that is 19 orbitals per carbon atom, for the description of the eigenstates. This basis is larger than the double-(Equation presented) plus polarization (DZP) basis used in Ref. [9], with the inclusion in particular of diffuse (Equation presented) and p orbitals.
    • This triple-(Equation presented) plus polarization (TZP) basis consists of three shells of (Equation presented) and (Equation presented) orbitals, complemented by one polarization (Equation presented) shell, that is 19 orbitals per carbon atom, for the description of the eigenstates. This basis is larger than the double-(Equation presented) plus polarization (DZP) basis used in Ref. [9], with the inclusion in particular of diffuse (Equation presented) and p orbitals.
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    • Notice that in Ref. [5] the interlayer distance between the graphene sheets is 15 a.u. and not 20 a.u. as it is wrongly reported in the paper. Further, Coulomb truncation techniques to avoid layer-layer interactions were not implemented at that time. Our strategy was to follow exactly the same running protocol to compare on equal footing our simplified (Equation presented) treatment to these reference calculations.
    • Notice that in Ref. [5] the interlayer distance between the graphene sheets is 15 a.u. and not 20 a.u. as it is wrongly reported in the paper. Further, Coulomb truncation techniques to avoid layer-layer interactions were not implemented at that time. Our strategy was to follow exactly the same running protocol to compare on equal footing our simplified (Equation presented) treatment to these reference calculations.
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    • For the sake of indication, at the LDA level, the two lowest (Equation presented) and (Equation presented) vibrational modes lead to a (negative) (Equation presented) eV coupling energy, one order of magnitude smaller than the (Equation presented) mode coupling strength.
    • For the sake of indication, at the LDA level, the two lowest (Equation presented) and (Equation presented) vibrational modes lead to a (negative) (Equation presented) eV coupling energy, one order of magnitude smaller than the (Equation presented) mode coupling strength.
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    • Direct comparison with Fig. 2 of Ref. [12] is not possible, since the figure presents the total electron-phonon coupling at wave vector (Equation presented), i.e., all phonon modes are considered and not just (Equation presented) as in this study. The comparison was made directly with the data used in Ref. [12] via personal correspondence.
    • Direct comparison with Fig. 2 of Ref. [12] is not possible, since the figure presents the total electron-phonon coupling at wave vector (Equation presented), i.e., all phonon modes are considered and not just (Equation presented) as in this study. The comparison was made directly with the data used in Ref. [12] via personal correspondence.
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    • We provide for information in Table II the results associated with the (single-shot) COHSEX approach, starting from DFT-LDA eigenstates. Clearly, the EPC coupling energies approach from below the (Equation presented) value with an error not larger than that induced by the evCOHSEX technique. This stems from a cancellation of errors between the COHSEX approximation and the lack of self-consistency which leads to overscreening when building (Equation presented) directly from the DFT-LDA spectrum.
    • We provide for information in Table II the results associated with the (single-shot) COHSEX approach, starting from DFT-LDA eigenstates. Clearly, the EPC coupling energies approach from below the (Equation presented) value with an error not larger than that induced by the evCOHSEX technique. This stems from a cancellation of errors between the COHSEX approximation and the lack of self-consistency which leads to overscreening when building (Equation presented) directly from the DFT-LDA spectrum.
  • 72


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