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Igor Reshetnyak , Lucia Reining

New starting point for the calculation of optical properties. Igor Reshetnyak , Lucia Reining. Outline. State of art methods Comparative analysis of TDLDA & BSE Analysis of the details Resonant only case Conclusions. Commonly used methods. TDDFT. BSE. Ground state. GW. f xc.

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Igor Reshetnyak , Lucia Reining

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  1. New starting point for the calculation of optical properties Igor Reshetnyak, Lucia Reining

  2. Outline • State of art methods • Comparative analysis of TDLDA & BSE • Analysis of the details • Resonant only case • Conclusions

  3. Commonly used methods TDDFT BSE Ground state GW fxc They work in a completely different ways! + e.h.

  4. Comparison of real spectra Codes: Bulk Si, q= 0.75 (1,1,1) c.c. units of 2pi/a = 0.612217 a.u.; Exp. from [1] For Si EELS, the TDLDA & BSE results very similar Are the underlying objects connected? [1] H.C. Weissker et al. Phys. Rev. B, 81:085104, Feb 2010

  5. 4-point equations & Hamiltonian form BSE TDLDA

  6. 4-point equations & Hamiltonian form Formal solution Hamiltonian form Both formulated the same way • Comparative analysis • Mixed methods • Deeper understanding

  7. Underlying stuff Coefficient JDOS(ε) ε, eV ε, eV • For JDOS only difference – GW (scissor) • The vectors in transition space spread over a small range • For TDLDA spread larger than for BSE. Agrees with [2] [2] Z.-h. Yang and C.A. Ullrich Phys. Rev. B, 87:195204, May 2013

  8. Digging into details... Overlaps eigenvector, # Overlap ε, eV eigenvector, # Overlaps happen over a small range But how do we explain similarity in spectra? The JDOS is shifted. Are the eigenvectors making the opposite shift?

  9. Digging into details... • Interference is very important! Cancelations in • Not just , but also S is important

  10. Can we replace parts of BSE by smth? TDLDA BSE, width = dE • The dE required is smaller without coupling • For EELS not particularly good

  11. And for optics? TDLDA BSE, width = dE • The dE required is smaller without coupling • For optical properties should do better Usage for combined methods!

  12. Some good & bad news • Effect of coupling can be very important for large transferred momenta q. • One should not interpret results in a basis with positive energies only • Interference effects important • TDLDA and BSE give similar results for EELS • Space for combined methods & analysis possible

  13. Thank you! Question?

  14. Commonly used methods = = = (1) TDDFT BSE (2) (3) KS DFT GW fxc (1) (2) (3)

  15. Digging into details... (2) • Average shift practically 0 • Nothing specific around ε = 0 • Even if the effect !=0 cannot amount for the shift

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