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Benchmarking the Bethe-Salpeter Formalism on a Standard Organic Molecular Set.

Jacquemin D, Duchemin I, Blase X - J Chem Theory Comput (2015)

Bottom Line: It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional.On average, the Bethe-Salpeter scheme based on self-consistent GW calculations comes close to the best time-dependent DFT calculations with the PBE0 functional with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute deviation compared to TD-PBE0 (theoretical best estimates) with a tendency to be red-shifted.We also observe that TD-DFT and the standard adiabatic Bethe-Salpeter implementation may differ significantly for states implying a large multiple excitation character.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire CEISAM - UMR CNR 6230, Université de Nantes , 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France ; Institut Universitaire de France , 103 bd St. Michel, 75005 Paris Cedex 5, France.

ABSTRACT

We perform benchmark calculations of the Bethe-Salpeter vertical excitation energies for the set of 28 molecules constituting the well-known Thiel's set, complemented by a series of small molecules representative of the dye chemistry field. We show that Bethe-Salpeter calculations based on a molecular orbital energy spectrum obtained with non-self-consistent G 0 W 0 calculations starting from semilocal DFT functionals dramatically underestimate the transition energies. Starting from the popular PBE0 hybrid functional significantly improves the results even though this leads to an average -0.59 eV redshift compared to reference calculations for Thiel's set. It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional. On average, the Bethe-Salpeter scheme based on self-consistent GW calculations comes close to the best time-dependent DFT calculations with the PBE0 functional with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute deviation compared to TD-PBE0 (theoretical best estimates) with a tendency to be red-shifted. We also observe that TD-DFT and the standard adiabatic Bethe-Salpeter implementation may differ significantly for states implying a large multiple excitation character.

No MeSH data available.


Histograms showing the number of transitions as a function of thedifference in energy (eV) with respect to the theoretical TBE-2 bestestimates data for (a) BSE/G0W0@PBE0, (b) TD-PBE0, and (c) BSE/GW@PBE0results for all states in the Thiel set. The red arrows indicate the21Ag statesin hexatriene and octatetraene.
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fig8: Histograms showing the number of transitions as a function of thedifference in energy (eV) with respect to the theoretical TBE-2 bestestimates data for (a) BSE/G0W0@PBE0, (b) TD-PBE0, and (c) BSE/GW@PBE0results for all states in the Thiel set. The red arrows indicate the21Ag statesin hexatriene and octatetraene.

Mentions: Forthe full set of excited-states, we obtained a deviation between theBSE/evGW@PBE and BSE/evGW@PBE0 estimateslimited to 0.08 eV with a very large correlation coefficient (0.9979).Similar to that for the individual chemical families analyzed above,the use of self-consistency not only decreases the dependence to theoriginal Kohn–Sham eigenvalues but also drastically diminishesthe discrepancy with TD-PBE0 that amounts to 0.18 eV for BSE/evGW@PBE0 compared with 0.44 eV for BSE/G0W0@PBE0. In Table 4 and Figure 8, we providea statistical analysis considering all families. Clearly, the non-self-consistentBSE/G0W0@PBEscheme is very unsatisfying with a large MAE (0.615 eV) and a quasi-systematicunderestimation of the reference transition energies. Nevertheless,this popular approach provides the trends accurately (r = 0.980). The results obtained with the self-consistent BSE andTD-PBE0 approaches are rather similar with MAEs of 0.253 and 0.232eV, respectively, and equivalent correlation coefficients, thoughthe BSE/evGW@PBE0 dispersion appears slightly tighterin Figure 8. It remains that TD-PBE0 providesa trifling MSE, whereas BSE/evGW@PBE0 underestimatesthe TBE-2 values by −0.142 eV on average. As we show below,this underestimation can be partly ascribed to the most compact moleculesin the set. We also highlight that the very good performance of TD-DFTreported in Table 4 and Figure 8 is related to the selection of the XC PBE0 functional shownto be one of the most accurate for Thiel’s set.24 Indeed, at the bottom of Table 4, we provide comparisons with the results of a previous TD-DFTbenchmark. Obviously, the statistical data obtained for TD-PBE0 israther independent of the selection of the TZVP or aug-cc-pVTZ atomic basis set. It is also clear that both TD-CAM-B3LYPand TD-PBE yield significantly less accurate results for Thiel’sset. This also illustrates the advantage of the BSE/evGW scheme that is free of such XC “optimization”.


Benchmarking the Bethe-Salpeter Formalism on a Standard Organic Molecular Set.

Jacquemin D, Duchemin I, Blase X - J Chem Theory Comput (2015)

Histograms showing the number of transitions as a function of thedifference in energy (eV) with respect to the theoretical TBE-2 bestestimates data for (a) BSE/G0W0@PBE0, (b) TD-PBE0, and (c) BSE/GW@PBE0results for all states in the Thiel set. The red arrows indicate the21Ag statesin hexatriene and octatetraene.
© Copyright Policy - editor-choice
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4504186&req=5

fig8: Histograms showing the number of transitions as a function of thedifference in energy (eV) with respect to the theoretical TBE-2 bestestimates data for (a) BSE/G0W0@PBE0, (b) TD-PBE0, and (c) BSE/GW@PBE0results for all states in the Thiel set. The red arrows indicate the21Ag statesin hexatriene and octatetraene.
Mentions: Forthe full set of excited-states, we obtained a deviation between theBSE/evGW@PBE and BSE/evGW@PBE0 estimateslimited to 0.08 eV with a very large correlation coefficient (0.9979).Similar to that for the individual chemical families analyzed above,the use of self-consistency not only decreases the dependence to theoriginal Kohn–Sham eigenvalues but also drastically diminishesthe discrepancy with TD-PBE0 that amounts to 0.18 eV for BSE/evGW@PBE0 compared with 0.44 eV for BSE/G0W0@PBE0. In Table 4 and Figure 8, we providea statistical analysis considering all families. Clearly, the non-self-consistentBSE/G0W0@PBEscheme is very unsatisfying with a large MAE (0.615 eV) and a quasi-systematicunderestimation of the reference transition energies. Nevertheless,this popular approach provides the trends accurately (r = 0.980). The results obtained with the self-consistent BSE andTD-PBE0 approaches are rather similar with MAEs of 0.253 and 0.232eV, respectively, and equivalent correlation coefficients, thoughthe BSE/evGW@PBE0 dispersion appears slightly tighterin Figure 8. It remains that TD-PBE0 providesa trifling MSE, whereas BSE/evGW@PBE0 underestimatesthe TBE-2 values by −0.142 eV on average. As we show below,this underestimation can be partly ascribed to the most compact moleculesin the set. We also highlight that the very good performance of TD-DFTreported in Table 4 and Figure 8 is related to the selection of the XC PBE0 functional shownto be one of the most accurate for Thiel’s set.24 Indeed, at the bottom of Table 4, we provide comparisons with the results of a previous TD-DFTbenchmark. Obviously, the statistical data obtained for TD-PBE0 israther independent of the selection of the TZVP or aug-cc-pVTZ atomic basis set. It is also clear that both TD-CAM-B3LYPand TD-PBE yield significantly less accurate results for Thiel’sset. This also illustrates the advantage of the BSE/evGW scheme that is free of such XC “optimization”.

Bottom Line: It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional.On average, the Bethe-Salpeter scheme based on self-consistent GW calculations comes close to the best time-dependent DFT calculations with the PBE0 functional with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute deviation compared to TD-PBE0 (theoretical best estimates) with a tendency to be red-shifted.We also observe that TD-DFT and the standard adiabatic Bethe-Salpeter implementation may differ significantly for states implying a large multiple excitation character.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire CEISAM - UMR CNR 6230, Université de Nantes , 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France ; Institut Universitaire de France , 103 bd St. Michel, 75005 Paris Cedex 5, France.

ABSTRACT

We perform benchmark calculations of the Bethe-Salpeter vertical excitation energies for the set of 28 molecules constituting the well-known Thiel's set, complemented by a series of small molecules representative of the dye chemistry field. We show that Bethe-Salpeter calculations based on a molecular orbital energy spectrum obtained with non-self-consistent G 0 W 0 calculations starting from semilocal DFT functionals dramatically underestimate the transition energies. Starting from the popular PBE0 hybrid functional significantly improves the results even though this leads to an average -0.59 eV redshift compared to reference calculations for Thiel's set. It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional. On average, the Bethe-Salpeter scheme based on self-consistent GW calculations comes close to the best time-dependent DFT calculations with the PBE0 functional with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute deviation compared to TD-PBE0 (theoretical best estimates) with a tendency to be red-shifted. We also observe that TD-DFT and the standard adiabatic Bethe-Salpeter implementation may differ significantly for states implying a large multiple excitation character.

No MeSH data available.