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

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

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Commonly used methods TDDFTBSE Ground state f xc GW They work in a completely different ways! + e.h. 3

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

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4-point equations & Hamiltonian form TDLDA BSE 5

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

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Underlying stuff 7 JDOS(ε) 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] 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] ε, eV Coefficient [2] Z.-h. Yang and C.A. Ullrich Phys. Rev. B, 87:195204, May 2013

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8 Digging into details... ε, eV Overlap 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? eigenvector, # Overlaps

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

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

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

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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 12

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13 Thank you! Question?

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(1) TDDFTBSE KS DFT f xc GW (2) (3) 14 Commonly used methods = = (1) =

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

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Optimization of Numerical Atomic Orbitals

Optimization of Numerical Atomic Orbitals

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