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Is the Bethe – Salpeter Formalism Accurate forExcitation Energies? Comparisons with TD-DFT, CASPT2, and EOM-CCSD

View Article: PubMed Central - PubMed

ABSTRACT

2016: Developing ab initioapproaches able to provide accurate excited-stateenergies at a reasonable computational cost is one of the biggestchallenges in theoretical chemistry. In that framework, the Bethe–Salpeterequation approach, combined with the GW exchange-correlationself-energy, which maintains the same scaling with system size asTD-DFT, has recently been the focus of a rapidly increasing numberof applications in molecular chemistry. Using a recently proposedset encompassing excitation energies of many kinds [J. Phys.Chem. Lett., 7, 586–591],we investigate here the performances of BSE/GW. Wecompare these results to CASPT2, EOM-CCSD, and TD-DFT data and showthat BSE/GW provides an accuracy comparable to thetwo wave function methods. It is particularly remarkable that theBSE/GW is equally efficient for valence, Rydberg,and charge-transfer excitations. In contrast, it provides a poor descriptionof triplet excited states, for which EOM-CCSD and CASPT2 clearly outperformBSE/GW. This contribution therefore supports theuse of the Bethe–Salpeter approach for spin-conserving transitions.

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Related in: MedlinePlus

Variation of the excitation energies when changing the functionalfrom M06 to M06-2X at the TD-DFT (top) and BSE/evGW (bottom) levels. The states are ordered as in Table 1. The blue, red, and green histograms correspondto valence, Rydberg, and CT transitions, respectively. The stars indicatethe singlet–triplet transitions.
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fig1: Variation of the excitation energies when changing the functionalfrom M06 to M06-2X at the TD-DFT (top) and BSE/evGW (bottom) levels. The states are ordered as in Table 1. The blue, red, and green histograms correspondto valence, Rydberg, and CT transitions, respectively. The stars indicatethe singlet–triplet transitions.

Mentions: In a second step, we have comparedthe TD-DFT results obtainedwith two functionals, namely, M06 and M06-2X, to the correspondingBSE/evGW values determined starting with the sametwo functionals (see Figure 1 and the SI for the BSE/evGW@M06 values). At the TD-DFT level, going from M06 to M06-2Xtends to significantly upshift the transition energies, as expectedwhen increasing the exact exchange ratio in the functional.It is only for the n → π* transitions of acetaldehyde,acetone, and formaldehyde that the opposite effect is found. On average,the increase attains 0.34 eV and is particularly strong for the twoRydberg transitions as well as for the B-TCNE CT excited state, atrend consistent with literature.34,35 In contrast,the impact of the functional on the TD-DFT n → π* transitionenergies is more limited, which also fits the conclusions of previousreports.36 Let us now turn toward the BSE/evGW results. In this case, an average upshift is also observedbut is much smaller, 0.09 eV on average. This confirms that the partialself-consistent evGW procedure washes out most ofthe functional dependency, and this improvement is particularly impressivefor the π → π*, Rydberg, and CT states that aremuch less sensitive to the starting functional than with TD-DFT. Nevertheless,small variations related to the frozen eigenvectors pertain with BSE/evGW. From Figure 1, one notices that these variations remain sizable for the n → π* transitions; that is, they remain onthe same order of magnitude as with TD-DFT. Comparing the BSE/evGW singlet–singlet and singlet–triplet transitionsin a given compound, one also notices that the latter are more dependenton the selected functional but less dependent than with TD-DFT, aconclusion that is inline with our most recent study.37


Is the Bethe – Salpeter Formalism Accurate forExcitation Energies? Comparisons with TD-DFT, CASPT2, and EOM-CCSD
Variation of the excitation energies when changing the functionalfrom M06 to M06-2X at the TD-DFT (top) and BSE/evGW (bottom) levels. The states are ordered as in Table 1. The blue, red, and green histograms correspondto valence, Rydberg, and CT transitions, respectively. The stars indicatethe singlet–triplet transitions.
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Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5385505&req=5

fig1: Variation of the excitation energies when changing the functionalfrom M06 to M06-2X at the TD-DFT (top) and BSE/evGW (bottom) levels. The states are ordered as in Table 1. The blue, red, and green histograms correspondto valence, Rydberg, and CT transitions, respectively. The stars indicatethe singlet–triplet transitions.
Mentions: In a second step, we have comparedthe TD-DFT results obtainedwith two functionals, namely, M06 and M06-2X, to the correspondingBSE/evGW values determined starting with the sametwo functionals (see Figure 1 and the SI for the BSE/evGW@M06 values). At the TD-DFT level, going from M06 to M06-2Xtends to significantly upshift the transition energies, as expectedwhen increasing the exact exchange ratio in the functional.It is only for the n → π* transitions of acetaldehyde,acetone, and formaldehyde that the opposite effect is found. On average,the increase attains 0.34 eV and is particularly strong for the twoRydberg transitions as well as for the B-TCNE CT excited state, atrend consistent with literature.34,35 In contrast,the impact of the functional on the TD-DFT n → π* transitionenergies is more limited, which also fits the conclusions of previousreports.36 Let us now turn toward the BSE/evGW results. In this case, an average upshift is also observedbut is much smaller, 0.09 eV on average. This confirms that the partialself-consistent evGW procedure washes out most ofthe functional dependency, and this improvement is particularly impressivefor the π → π*, Rydberg, and CT states that aremuch less sensitive to the starting functional than with TD-DFT. Nevertheless,small variations related to the frozen eigenvectors pertain with BSE/evGW. From Figure 1, one notices that these variations remain sizable for the n → π* transitions; that is, they remain onthe same order of magnitude as with TD-DFT. Comparing the BSE/evGW singlet–singlet and singlet–triplet transitionsin a given compound, one also notices that the latter are more dependenton the selected functional but less dependent than with TD-DFT, aconclusion that is inline with our most recent study.37

View Article: PubMed Central - PubMed

ABSTRACT

2016: Developing ab initioapproaches able to provide accurate excited-stateenergies at a reasonable computational cost is one of the biggestchallenges in theoretical chemistry. In that framework, the Bethe–Salpeterequation approach, combined with the GW exchange-correlationself-energy, which maintains the same scaling with system size asTD-DFT, has recently been the focus of a rapidly increasing numberof applications in molecular chemistry. Using a recently proposedset encompassing excitation energies of many kinds [J. Phys.Chem. Lett., 7, 586–591],we investigate here the performances of BSE/GW. Wecompare these results to CASPT2, EOM-CCSD, and TD-DFT data and showthat BSE/GW provides an accuracy comparable to thetwo wave function methods. It is particularly remarkable that theBSE/GW is equally efficient for valence, Rydberg,and charge-transfer excitations. In contrast, it provides a poor descriptionof triplet excited states, for which EOM-CCSD and CASPT2 clearly outperformBSE/GW. This contribution therefore supports theuse of the Bethe–Salpeter approach for spin-conserving transitions.

No MeSH data available.


Related in: MedlinePlus