Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators

Abstract

We present a general scheme of range-separated hybrid functionals in which the mixing parameters of Fock exchange are fully nonempirical and determined solely from the dielectric function.We showthat the full dielectric dependence leads to an unscreened Fock exchange in the short range, while in the long range the Fock exchange is correctly screened by the macroscopic dielectric constant. The range separation is obtained by fitting to the calculated static dielectric function in the long-wavelength limit. The resulting hybrid functional accurately accounts for electronic and structural properties of various semiconductors and insulators spanning a wide range of band gaps. We present a general scheme of range-separated hybrid functionals in which the mixing parameters of Fock exchange are fully nonempirical and determined solely from the dielectric function. We show that the full dielectric dependence leads to an unscreened Fock exchange in the short range, while in the long range the Fock exchange is correctly screened by the macroscopic dielectric constant. The range separation is obtained by fitting to the calculated static dielectric function in the long-wavelength limit. The resulting hybrid functional accurately accounts for electronic and structural properties of various semiconductors and insulators spanning a wide range of band gaps.

Assessing model-dielectric-dependent hybrid functionals on the antiferromagnetic transition-metal monoxides MnO, FeO, CoO, and NiO

“…Despite these differences, we find that singleshot DD0-RSH-CAM and DSH0 perform almost equally and both hybrid functionals outperform conventional hybrid functionals for the band gaps with the smallest MAPE compared to experimental gaps. This is in line with the finding reported in [34,35] based on a large dataset of conventional insulators and semiconductors. In fact, for the TMOs series DD0-RSH-CAM and DSH0 yield band gaps in excellent agreement with experiment and are capable to qualitatively predict the band gaps, a feat that is not even achieved by the G 0 W 0 @ For better comparison with experimental spectra, the calculated DOS are broadened by a Gaussian with 0.5 eV full width at half maximum.…”

“…In contrast to what is observed in [34,35]-namely, that self-consistent DD-RSH-CAM or DSH perform almost equally well as the single-shot counterparts for the considered data sets-here we find that self-consistency deteriorates the results with a significant overestimation of band gaps due to underestimated dielectric constants (see figure 3). Moreover, it was found in [34] that self-consistent DD-RSH-CAM delivers slightly better numbers compared to DD0-RSH-CAM (MAPE = 7.3% versus MAPE = 7.9%, respectively), which is apparently in contrast with the results obtained in [35] where self-consistent DSH was found to yield a MAPE nearly twice as large as DSH0 (9% against 5%, respectively).…”

“…In contrast to what is observed in [34,35]-namely, that self-consistent DD-RSH-CAM or DSH perform almost equally well as the single-shot counterparts for the considered data sets-here we find that self-consistency deteriorates the results with a significant overestimation of band gaps due to underestimated dielectric constants (see figure 3). Moreover, it was found in [34] that self-consistent DD-RSH-CAM delivers slightly better numbers compared to DD0-RSH-CAM (MAPE = 7.3% versus MAPE = 7.9%, respectively), which is apparently in contrast with the results obtained in [35] where self-consistent DSH was found to yield a MAPE nearly twice as large as DSH0 (9% against 5%, respectively). However, a closer inspection of the data in [34,35] shows that oxide compounds such as Cu 2 O, In 2 O 3 , ZnO, TiO 2 , and MgO show larger errors compared to the other members of the considered data set for self-consistent DD-RSH-CAM and DSH [34,35], suggesting that self-consistent DD-RSH-CAM and DSH might not be suitable for the prescription of the band gaps of oxides.…”

Assessing model-dielectric-dependent hybrid functionals on the antiferromagnetic transition-metal monoxides MnO, FeO, CoO, and NiO

“…Despite these differences, we find that singleshot DD0-RSH-CAM and DSH0 perform almost equally and both hybrid functionals outperform conventional hybrid functionals for the band gaps with the smallest MAPE compared to experimental gaps. This is in line with the finding reported in [34,35] based on a large dataset of conventional insulators and semiconductors. In fact, for the TMOs series DD0-RSH-CAM and DSH0 yield band gaps in excellent agreement with experiment and are capable to qualitatively predict the band gaps, a feat that is not even achieved by the G 0 W 0 @ For better comparison with experimental spectra, the calculated DOS are broadened by a Gaussian with 0.5 eV full width at half maximum.…”

“…In contrast to what is observed in [34,35]-namely, that self-consistent DD-RSH-CAM or DSH perform almost equally well as the single-shot counterparts for the considered data sets-here we find that self-consistency deteriorates the results with a significant overestimation of band gaps due to underestimated dielectric constants (see figure 3). Moreover, it was found in [34] that self-consistent DD-RSH-CAM delivers slightly better numbers compared to DD0-RSH-CAM (MAPE = 7.3% versus MAPE = 7.9%, respectively), which is apparently in contrast with the results obtained in [35] where self-consistent DSH was found to yield a MAPE nearly twice as large as DSH0 (9% against 5%, respectively).…”

“…In contrast to what is observed in [34,35]-namely, that self-consistent DD-RSH-CAM or DSH perform almost equally well as the single-shot counterparts for the considered data sets-here we find that self-consistency deteriorates the results with a significant overestimation of band gaps due to underestimated dielectric constants (see figure 3). Moreover, it was found in [34] that self-consistent DD-RSH-CAM delivers slightly better numbers compared to DD0-RSH-CAM (MAPE = 7.3% versus MAPE = 7.9%, respectively), which is apparently in contrast with the results obtained in [35] where self-consistent DSH was found to yield a MAPE nearly twice as large as DSH0 (9% against 5%, respectively). However, a closer inspection of the data in [34,35] shows that oxide compounds such as Cu 2 O, In 2 O 3 , ZnO, TiO 2 , and MgO show larger errors compared to the other members of the considered data set for self-consistent DD-RSH-CAM and DSH [34,35], suggesting that self-consistent DD-RSH-CAM and DSH might not be suitable for the prescription of the band gaps of oxides.…”

Nonempirical hybrid functionals for band gaps of inorganic metal-halide perovskites

“…This deviation is in line with previous results in the literature on other materials [27,32]. The consideration of range-separated functionals reduces the mean average deviation to 0.20 eV, confirming thereby that the use of this type of functional leads to a higher accuracy [30,32]. Global hybrid functionals fulfilling Koopmans' condition also yield band gaps in good agreement with our GW references, as indicated by the mean average deviation of 0.20 eV.…”

“…The dielectric-dependent approach based on global functionals yields a mean average deviation of 0.35 eV with respect to the GW references. This deviation is in line with previous results in the literature on other materials [27,32]. The consideration of range-separated functionals reduces the mean average deviation to 0.20 eV, confirming thereby that the use of this type of functional leads to a higher accuracy [30,32].…”

Assessing model-dielectric-dependent hybrid functionals on the antiferromagnetic transition-metal monoxides MnO, FeO, CoO, and NiO

“…Despite these differences, we find that singleshot DD0-RSH-CAM and DSH0 perform almost equally and both hybrid functionals outperform conventional hybrid functionals for the band gaps with the smallest MAPE compared to experimental gaps. This is in line with the finding reported in [34,35] based on a large dataset of conventional insulators and semiconductors. In fact, for the TMOs series DD0-RSH-CAM and DSH0 yield band gaps in excellent agreement with experiment and are capable to qualitatively predict the band gaps, a feat that is not even achieved by the G 0 W 0 @ For better comparison with experimental spectra, the calculated DOS are broadened by a Gaussian with 0.5 eV full width at half maximum.…”

“…In contrast to what is observed in [34,35]-namely, that self-consistent DD-RSH-CAM or DSH perform almost equally well as the single-shot counterparts for the considered data sets-here we find that self-consistency deteriorates the results with a significant overestimation of band gaps due to underestimated dielectric constants (see figure 3). Moreover, it was found in [34] that self-consistent DD-RSH-CAM delivers slightly better numbers compared to DD0-RSH-CAM (MAPE = 7.3% versus MAPE = 7.9%, respectively), which is apparently in contrast with the results obtained in [35] where self-consistent DSH was found to yield a MAPE nearly twice as large as DSH0 (9% against 5%, respectively).…”

“…In contrast to what is observed in [34,35]-namely, that self-consistent DD-RSH-CAM or DSH perform almost equally well as the single-shot counterparts for the considered data sets-here we find that self-consistency deteriorates the results with a significant overestimation of band gaps due to underestimated dielectric constants (see figure 3). Moreover, it was found in [34] that self-consistent DD-RSH-CAM delivers slightly better numbers compared to DD0-RSH-CAM (MAPE = 7.3% versus MAPE = 7.9%, respectively), which is apparently in contrast with the results obtained in [35] where self-consistent DSH was found to yield a MAPE nearly twice as large as DSH0 (9% against 5%, respectively). However, a closer inspection of the data in [34,35] shows that oxide compounds such as Cu 2 O, In 2 O 3 , ZnO, TiO 2 , and MgO show larger errors compared to the other members of the considered data set for self-consistent DD-RSH-CAM and DSH [34,35], suggesting that self-consistent DD-RSH-CAM and DSH might not be suitable for the prescription of the band gaps of oxides.…”

Nonempirical hybrid functionals for band gaps of inorganic metal-halide perovskites

“…This deviation is in line with previous results in the literature on other materials [27,32]. The consideration of range-separated functionals reduces the mean average deviation to 0.20 eV, confirming thereby that the use of this type of functional leads to a higher accuracy [30,32]. Global hybrid functionals fulfilling Koopmans' condition also yield band gaps in good agreement with our GW references, as indicated by the mean average deviation of 0.20 eV.…”

“…The dielectric-dependent approach based on global functionals yields a mean average deviation of 0.35 eV with respect to the GW references. This deviation is in line with previous results in the literature on other materials [27,32]. The consideration of range-separated functionals reduces the mean average deviation to 0.20 eV, confirming thereby that the use of this type of functional leads to a higher accuracy [30,32].…”

Assessing model-dielectric-dependent hybrid functionals on the antiferromagnetic transition-metal monoxides MnO, FeO, CoO, and NiO

“…Despite these differences, we find that singleshot DD0-RSH-CAM and DSH0 perform almost equally and both hybrid functionals outperform conventional hybrid functionals for the band gaps with the smallest MAPE compared to experimental gaps. This is in line with the finding reported in [34,35] based on a large dataset of conventional insulators and semiconductors. In fact, for the TMOs series DD0-RSH-CAM and DSH0 yield band gaps in excellent agreement with experiment and are capable to qualitatively predict the band gaps, a feat that is not even achieved by the G 0 W 0 @ For better comparison with experimental spectra, the calculated DOS are broadened by a Gaussian with 0.5 eV full width at half maximum.…”

“…In contrast to what is observed in [34,35]-namely, that self-consistent DD-RSH-CAM or DSH perform almost equally well as the single-shot counterparts for the considered data sets-here we find that self-consistency deteriorates the results with a significant overestimation of band gaps due to underestimated dielectric constants (see figure 3). Moreover, it was found in [34] that self-consistent DD-RSH-CAM delivers slightly better numbers compared to DD0-RSH-CAM (MAPE = 7.3% versus MAPE = 7.9%, respectively), which is apparently in contrast with the results obtained in [35] where self-consistent DSH was found to yield a MAPE nearly twice as large as DSH0 (9% against 5%, respectively).…”

“…In contrast to what is observed in [34,35]-namely, that self-consistent DD-RSH-CAM or DSH perform almost equally well as the single-shot counterparts for the considered data sets-here we find that self-consistency deteriorates the results with a significant overestimation of band gaps due to underestimated dielectric constants (see figure 3). Moreover, it was found in [34] that self-consistent DD-RSH-CAM delivers slightly better numbers compared to DD0-RSH-CAM (MAPE = 7.3% versus MAPE = 7.9%, respectively), which is apparently in contrast with the results obtained in [35] where self-consistent DSH was found to yield a MAPE nearly twice as large as DSH0 (9% against 5%, respectively). However, a closer inspection of the data in [34,35] shows that oxide compounds such as Cu 2 O, In 2 O 3 , ZnO, TiO 2 , and MgO show larger errors compared to the other members of the considered data set for self-consistent DD-RSH-CAM and DSH [34,35], suggesting that self-consistent DD-RSH-CAM and DSH might not be suitable for the prescription of the band gaps of oxides.…”

Nonempirical hybrid functionals for band gaps of inorganic metal-halide perovskites

“…This deviation is in line with previous results in the literature on other materials [27,32]. The consideration of range-separated functionals reduces the mean average deviation to 0.20 eV, confirming thereby that the use of this type of functional leads to a higher accuracy [30,32]. Global hybrid functionals fulfilling Koopmans' condition also yield band gaps in good agreement with our GW references, as indicated by the mean average deviation of 0.20 eV.…”

“…The dielectric-dependent approach based on global functionals yields a mean average deviation of 0.35 eV with respect to the GW references. This deviation is in line with previous results in the literature on other materials [27,32]. The consideration of range-separated functionals reduces the mean average deviation to 0.20 eV, confirming thereby that the use of this type of functional leads to a higher accuracy [30,32].…”