Myrta Grüning - Academia.edu (original) (raw)

Papers by Myrta Grüning

Nano Letters, 2009

Within the Tamm-Dancoff approximation ab initio approaches describe excitons as packets of electr... more Within the Tamm-Dancoff approximation ab initio approaches describe excitons as packets of electron-hole pairs propagating only forward in time. However, we show that in nanoscale materials excitons and plasmons hybridize, creating exciton-plasmon states where the electron-hole pairs oscillate back and forth in time. Then, as exemplified by the trans-azobenzene molecule and carbon nanotubes, the Tamm-Dancoff approximation yields errors as large as the accuracy claimed in ab initio calculations. Instead, we propose a general and efficient approach that avoids the Tamm-Dancoff approximation, and correctly describes excitons, plasmons and exciton-plasmon states. PACS numbers: 73.20.Mf,71.15.Qe, The Bethe-Salpeter (BS) [1] and the Time-Dependent Density Functional Theory (TDDFT) [2] equations allow the accurate calculation of the polarization function of many physical systems without relying on external parameters. Within these frameworks neutral excitations are described as combination of electronhole (e-h) pairs of a noninteracting system. However for nanoscale materials, the huge number of e-h pairs involved makes the solution of the BS/TDDFT equation extremely cumbersome. Consequently, the increasing interest in the excitation properties of such materials has justified the use of ad-hoc approximations. The most important and widely-used is the Tamm-Dancoff approximation (TDA) where only positive energy e-h pairs are considered. Within the TDA the interaction between e-h pairs at positive and negative (antipairs) energies is neglected, and only one e-h pair is assumed to propagate in any time interval. The main advantage of the TDA is that the non-Hermitian BS/TDDFT problem reduces to a Hermitian problem, that can be solved with efficient and stable iterative methods .

The Journal of Chemical Physics, 2006

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the deriv... more Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potential derived from many-body perturbation theory via the optimized effective potential suggest that improving the exchange-correlation potential approximation can yield a reasonable agreement between the Kohn-Sham band gap and the experimental gap. The results in this work show that this is not the case. In fact, we add to the exact exchange the correlation that corresponds to the dynamical ͑random phase approximation͒ screening in the GW approximation. This accurate exchange-correlation potential provides band structures similar to the local density approximation with the corresponding derivative discontinuity that contributes 30%-50% to the energy gap. Our self-consistent results confirm substantially the results for Si and other semiconductors obtained perturbatively ͓R. W. Godby et al., Phys. Rev. B 36, 6497 ͑1987͔͒ and extend the conclusion to LiF and Ar, a wide-gap insulator and a noble-gas solid.

The Journal of Chemical Physics, 2002

It is well known that shape corrections have to be applied to the local-density ͑LDA͒ and general... more It is well known that shape corrections have to be applied to the local-density ͑LDA͒ and generalized gradient ͑GGA͒ approximations to the Kohn-Sham exchange-correlation potential in order to obtain reliable response properties in time dependent density functional theory calculations. Here we demonstrate that it is an oversimplified view that these shape corrections concern primarily the asymptotic part of the potential, and that they affect only Rydberg type transitions. The performance is assessed of two shape-corrected Kohn-Sham potentials, the gradient-regulated asymptotic connection procedure applied to the Becke-Perdew potential ͑BP-GRAC͒ and the statistical averaging of ͑model͒ orbital potentials ͑SAOP͒, versus LDA and GGA potentials, in molecular response calculations of the static average polarizability ␣, the Cauchy coefficient S Ϫ4 , and the static average hyperpolarizability ␤. The nature of the distortions of the LDA/GGA potentials is highlighted and it is shown that they introduce many spurious excited states at too low energy which may mix with valence excited states, resulting in wrong excited state compositions. They also lead to wrong oscillator strengths and thus to a wrong spectral structure of properties like the polarizability. LDA, Becke-Lee-Yang-Parr ͑BLYP͒, and Becke-Perdew ͑BP͒ characteristically underestimate contributions to ␣ and S Ϫ4 from bound Rydberg-type states and overestimate those from the continuum. Cancellation of the errors in these contributions occasionally produces fortuitously good results. The distortions of the LDA, BLYP, and BP spectra are related to the deficiencies of the LDA/GGA potentials in both the bulk and outer molecular regions. In contrast, both SAOP and BP-GRAC potentials produce high quality polarizabilities for 21 molecules and also reliable Cauchy moments and hyperpolarizabilities for the selected molecules. The analysis for the N 2 molecule shows, that both SAOP and BP-GRAC yield reliable energies i and oscillator strengths f i of individual excitations, so that they reproduce well the spectral structure of ␣ and S Ϫ4 .

Physical Review B, 2009

ABSTRACT The electronic properties of zircon and hafnon, two wide-gap high- kappa materials, are ... more ABSTRACT The electronic properties of zircon and hafnon, two wide-gap high- kappa materials, are investigated using many-body perturbation theory (MBPT) combined with the Wannier interpolation technique. For both materials, the calculated band structures differ from those obtained within density-functional theory and MBPT by (i) a slight displacement of the highest valence-band maximum from the Gamma point and (ii) an opening of the indirect band gap to 7.6 and 8.0 eV for zircon and hafnon, respectively. The introduction of vertex corrections in the many-body self-energy does not modify the results except for a global rigid shift of the many-body corrections.

Nano Letters, 2009

Within the Tamm-Dancoff approximation ab initio approaches describe excitons as packets of electr... more Within the Tamm-Dancoff approximation ab initio approaches describe excitons as packets of electron-hole pairs propagating only forward in time. However, we show that in nanoscale materials excitons and plasmons hybridize, creating exciton-plasmon states where the electron-hole pairs oscillate back and forth in time. Then, as exemplified by the trans-azobenzene molecule and carbon nanotubes, the Tamm-Dancoff approximation yields errors as large as the accuracy claimed in ab initio calculations. Instead, we propose a general and efficient approach that avoids the Tamm-Dancoff approximation, and correctly describes excitons, plasmons and exciton-plasmon states. PACS numbers: 73.20.Mf,71.15.Qe, The Bethe-Salpeter (BS) [1] and the Time-Dependent Density Functional Theory (TDDFT) [2] equations allow the accurate calculation of the polarization function of many physical systems without relying on external parameters. Within these frameworks neutral excitations are described as combination of electronhole (e-h) pairs of a noninteracting system. However for nanoscale materials, the huge number of e-h pairs involved makes the solution of the BS/TDDFT equation extremely cumbersome. Consequently, the increasing interest in the excitation properties of such materials has justified the use of ad-hoc approximations. The most important and widely-used is the Tamm-Dancoff approximation (TDA) where only positive energy e-h pairs are considered. Within the TDA the interaction between e-h pairs at positive and negative (antipairs) energies is neglected, and only one e-h pair is assumed to propagate in any time interval. The main advantage of the TDA is that the non-Hermitian BS/TDDFT problem reduces to a Hermitian problem, that can be solved with efficient and stable iterative methods .

The Journal of Chemical Physics, 2006

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the deriv... more Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potential derived from many-body perturbation theory via the optimized effective potential suggest that improving the exchange-correlation potential approximation can yield a reasonable agreement between the Kohn-Sham band gap and the experimental gap. The results in this work show that this is not the case. In fact, we add to the exact exchange the correlation that corresponds to the dynamical ͑random phase approximation͒ screening in the GW approximation. This accurate exchange-correlation potential provides band structures similar to the local density approximation with the corresponding derivative discontinuity that contributes 30%-50% to the energy gap. Our self-consistent results confirm substantially the results for Si and other semiconductors obtained perturbatively ͓R. W. Godby et al., Phys. Rev. B 36, 6497 ͑1987͔͒ and extend the conclusion to LiF and Ar, a wide-gap insulator and a noble-gas solid.

The Journal of Chemical Physics, 2002

It is well known that shape corrections have to be applied to the local-density ͑LDA͒ and general... more It is well known that shape corrections have to be applied to the local-density ͑LDA͒ and generalized gradient ͑GGA͒ approximations to the Kohn-Sham exchange-correlation potential in order to obtain reliable response properties in time dependent density functional theory calculations. Here we demonstrate that it is an oversimplified view that these shape corrections concern primarily the asymptotic part of the potential, and that they affect only Rydberg type transitions. The performance is assessed of two shape-corrected Kohn-Sham potentials, the gradient-regulated asymptotic connection procedure applied to the Becke-Perdew potential ͑BP-GRAC͒ and the statistical averaging of ͑model͒ orbital potentials ͑SAOP͒, versus LDA and GGA potentials, in molecular response calculations of the static average polarizability ␣, the Cauchy coefficient S Ϫ4 , and the static average hyperpolarizability ␤. The nature of the distortions of the LDA/GGA potentials is highlighted and it is shown that they introduce many spurious excited states at too low energy which may mix with valence excited states, resulting in wrong excited state compositions. They also lead to wrong oscillator strengths and thus to a wrong spectral structure of properties like the polarizability. LDA, Becke-Lee-Yang-Parr ͑BLYP͒, and Becke-Perdew ͑BP͒ characteristically underestimate contributions to ␣ and S Ϫ4 from bound Rydberg-type states and overestimate those from the continuum. Cancellation of the errors in these contributions occasionally produces fortuitously good results. The distortions of the LDA, BLYP, and BP spectra are related to the deficiencies of the LDA/GGA potentials in both the bulk and outer molecular regions. In contrast, both SAOP and BP-GRAC potentials produce high quality polarizabilities for 21 molecules and also reliable Cauchy moments and hyperpolarizabilities for the selected molecules. The analysis for the N 2 molecule shows, that both SAOP and BP-GRAC yield reliable energies i and oscillator strengths f i of individual excitations, so that they reproduce well the spectral structure of ␣ and S Ϫ4 .

Physical Review B, 2009

ABSTRACT The electronic properties of zircon and hafnon, two wide-gap high- kappa materials, are ... more ABSTRACT The electronic properties of zircon and hafnon, two wide-gap high- kappa materials, are investigated using many-body perturbation theory (MBPT) combined with the Wannier interpolation technique. For both materials, the calculated band structures differ from those obtained within density-functional theory and MBPT by (i) a slight displacement of the highest valence-band maximum from the Gamma point and (ii) an opening of the indirect band gap to 7.6 and 8.0 eV for zircon and hafnon, respectively. The introduction of vertex corrections in the many-body self-energy does not modify the results except for a global rigid shift of the many-body corrections.