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3
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0003893794
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Bai, Z, Demmel, J, Dongarra, J, Ruhe, A, van der Vorst, H, Eds, SIAM: Philadelphia, PA
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Templates for the solution of algebraic problems: a practical guide; Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., van der Vorst, H., Eds.; SIAM: Philadelphia, PA, 2000.
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(2000)
Templates for the solution of algebraic problems: A practical guide
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5
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33748639994
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See, for example: a
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See, for example: (a) Del Puerto, M.; et al. Phys. Rev. Lett. 2006, 97, 096401.
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(2006)
Phys. Rev. Lett
, vol.97
, pp. 096401
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Del Puerto, M.1
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12
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67650964169
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The GW0 quasiparticle corrections and the BS spectra are calculated with the yambo code (Marini, A.; Hogan, C.; Grüning, M.; Varsano, D. Comput. Phys. Commun. 2009, 180, 1392), where the algorithm proposed in this work has been implemented.
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(a) The GW0 quasiparticle corrections and the BS spectra are calculated with the yambo code (Marini, A.; Hogan, C.; Grüning, M.; Varsano, D. Comput. Phys. Commun. 2009, 180, 1392), where the algorithm proposed in this work has been implemented.
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13
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68949102855
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The Kohn-Sham basis (local density approximation) is calculated with ABINIT, Gonze, X.; et al. Comput. Mater. Sci. 2002, 25, 478.
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(b) The Kohn-Sham basis (local density approximation) is calculated with ABINIT, Gonze, X.; et al. Comput. Mater. Sci. 2002, 25, 478.
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15
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68949112929
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We have calculated the quasiparticle (QP) corrections for the five highest occupied and four lowest unoccupied states using the GW approximation (GW gap 6.9 eV, Five hundred states have been included to calculate the plasmon pole dielectric function εGG′ (2 Ha cut-off) and the Green function. The energies of the Green functions have been updated up to self consistence using a linear extrapolation for the QP corrections not explicitly computed, In the calculation for the BS spectrum, we included all e-h pairs from the 18 highest occupied and 85 lowest unoccupied states. Two hundred states instead have been included in the static polarization function. We used a cutoff of 0.5 Ha for the screened interaction and of 3 Ha for the exchange component
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GG′ (2 Ha cut-off) and the Green function. The energies of the Green functions have been updated up to self consistence (using a linear extrapolation for the QP corrections not explicitly computed). In the calculation for the BS spectrum, we included all e-h pairs from the 18 highest occupied and 85 lowest unoccupied states. Two hundred states instead have been included in the static polarization function. We used a cutoff of 0.5 Ha for the screened interaction and of 3 Ha for the exchange component.
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16
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68949134492
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NIST Chemistry WebBook; http://webbook.nist.gov/chemistry (accessed February 5, 2009). den Hertog, H. J.; Henkens, C. H.; van Roon, J. H. Recl. Trav. Chim. 1952, 71, 1145. Note that the experimental spectrum is scaled so that the height of the most intense peak coincides with that of the full Hamiltonian calculated spectrum.
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(a) NIST Chemistry WebBook; http://webbook.nist.gov/chemistry (accessed February 5, 2009). den Hertog, H. J.; Henkens, C. H.; van Roon, J. H. Recl. Trav. Chim. 1952, 71, 1145. Note that the experimental spectrum is scaled so that the height of the most intense peak coincides with that of the full Hamiltonian calculated spectrum.
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17
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68949143918
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As a consequence of the difference in the relative intensity of the peaks between the TDA and the full Hamiltonian, the static polarizability R[R (ω) 0, is also affected. Indeed, the TDA underestimates R[R(ω) 0, by about 15% with respect to the full Hamiltonian
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As a consequence of the difference in the relative intensity of the peaks between the TDA and the full Hamiltonian, the static polarizability R[R (ω) 0)] is also affected. Indeed, the TDA underestimates R[R(ω) 0)] by about 15% with respect to the full Hamiltonian.
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21
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68949143919
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When the formation of excitons does not lead to a fundamental change of ground state, H j is positive definite, see ref 15
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When the formation of excitons does not lead to a fundamental change of ground state, H j is positive definite, see ref 15.
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22
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0010610199
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Ehrenfest, H, Seitz, F, Turnbull, D, Eds, Academic Press, New York
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Haydock, R. In Solid State Physics; Ehrenfest, H., Seitz, F., Turnbull, D., Eds.; Academic Press, New York, 1980; Vol. 35, pp 215-294.
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(1980)
Solid State Physics
, vol.35
, pp. 215-294
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Haydock, R.1
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24
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68949084231
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Because of the interplay between H, F and H j, evaluating the H j -inner product does not require extra operation with respect to the standard inner-product.
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Because of the interplay between H, F and H j, evaluating the H j -inner product does not require extra operation with respect to the standard inner-product.
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25
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68949089240
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The proposed approach requires mN2 operations, where m is the number of iterations and N the size of the system. For azobenzene N ∼ 104 and m ∼ 102. Thus, it is much faster and convenient compared to the standard diagonalization, that requires O(N3) operations
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3) operations.
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15544375926
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O'Connell, M. J.; Bachilo, S. M.; Huffman, C. B.; et al. Science 2002, 297, 593.
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(2002)
Science
, vol.297
, pp. 593
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O'Connell, M.J.1
Bachilo, S.M.2
Huffman, C.B.3
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(a) Chang, E.; Busi, G.; Ruini, A.; Molinari, E. Phys. Rev. Lett. 2004, 92, 196401.
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(2004)
Phys. Rev. Lett
, vol.92
, pp. 196401
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Chang, E.1
Busi, G.2
Ruini, A.3
Molinari, E.4
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30
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1642585814
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(b) Spataru, C. D.; Ismail-Beigi, S.; Benedict, L. X.; Louie, S. G. Phys. Rev. Lett. 2004, 92, 077402.
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(2004)
Phys. Rev. Lett
, vol.92
, pp. 077402
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Spataru, C.D.1
Ismail-Beigi, S.2
Benedict, L.X.3
Louie, S.G.4
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(c) Deslippe, J.; Spataru, C. D.; Prendergast, D.; Louie, S. G. Nano Lett. 2007, 7, 1626.
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(2007)
Nano Lett
, vol.7
, pp. 1626
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Deslippe, J.1
Spataru, C.D.2
Prendergast, D.3
Louie, S.G.4
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68949123547
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We have included e-h pairs and antipairs from band 32 to 96 in a window of 15 eV and used cut-offs of 4 and 1 Ha for the V j and W integrals. The 1D Brillouin zone is sampled by 64 k-points. Quasiparticle correction from ref 6
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We have included e-h pairs and antipairs from band 32 to 96 in a window of 15 eV and used cut-offs of 4 and 1 Ha for the V j and W integrals. The 1D Brillouin zone is sampled by 64 k-points. Quasiparticle correction from ref 6.
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33
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68949134491
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Note that our system differs from the experimental one. The latter is far more complex and thus cannot be treated using ab initio methods. In fact, the experimental system consists of a film of aligned bundles of CNTs with an average diameter of 2 nm. In particular the different diameter [2 nm versus ∼0.6 nm of the (8,0) zig-zag CNT] explains the different position of the spectrum onset (the gap is known to decrease with the tube diameter). In spite of these differences, within the full Hamiltonian formulation, the BS equation reproduces well the polarization dependence of the observed photoabsorption spectra.
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Note that our system differs from the experimental one. The latter is far more complex and thus cannot be treated using ab initio methods. In fact, the experimental system consists of a film of aligned bundles of CNTs with an average diameter of 2 nm. In particular the different diameter [2 nm versus ∼0.6 nm of the (8,0) zig-zag CNT] explains the different position of the spectrum onset (the gap is known to decrease with the tube diameter). In spite of these differences, within the full Hamiltonian formulation, the BS equation reproduces well the polarization dependence of the observed photoabsorption spectra.
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