modeled with adiabatic TD-DFT [33, 82–93]. Indeed, the TD-DFT transition
energies are too large (by ca. 0.3–1.0 eV) in cyanines, and this conclusion has
been reached through comparisons of both TD-DFT’s E
vertÀa with their highlycorrelated wavefunction counterparts [82, 87] and TD-DFT’s E
AFCP with experimental references for fluoroborate emitters [88, 89]. More puzzling is the fact that
the errors seem to be almost independent of the selected XCF and that this error is
not related to a multi-determinant nature. The fundamental reasons explaining this
failure of TD-DFT have been given in [90–92, 94, 95] and summarized in a recent
account [93]. A pragmatic approach to obtain accurate E
AFCP is to apply (13)
selecting an appropriate variant of the CIS(D), ADC(2) or CC2 approaches as the
wavefunction method [47, 96]. Examples of applications of such mixed approach
are given in Sect. 4.
3.3.2 Energy and Geometry of Charge-Transfer States
One generally denotes as CT states, states in which the photon absorption or
emission induces a strong displacement of the electronic density, i.e., when the
electron and the hole are spatially separated. For those CT ES, it is now well
recognized that both pure and global hybrid XCF including a small fraction of
exact exchange tend to deliver (much) too small E
vertÀa , E
vertÀ f , and E
AFCP [97–
100]. For instance, Dreuw and Head-Gordon have shown that LDA [101], BLYP
[59, 60], and B3LYP [52] XCF yield errors of 1 eV or more for the
bacteriochlorophyll-spheroidene dyad. Within the adiabatic TD-DFT approximation, this error can be strongly reduced by using a range-separated hybrid XCF, e.g.,
CAM-3LYP [54], LC-BOP [102], or ωB97-X [103] which restores a correct
interaction between the electron and the hole [104–107] and therefore provides
an efficient answer to the CT challenge.
Additionally, the TD-DFT determination of the R
ES can be problematic for CT
ES. Tozer was the first to unravel the qualitatively incorrect PES obtained for
4-(dimethylamino)-benzonitrile with B3LYP [108]. Indeed, this popular XCF predicts that the twisted ES, in which the NMe 2 terminal group becomes perpendicular
to the central phenyl ring, is more stable than the corresponding planar geometry,
whereas accurate wavefunction theories yield the opposite conclusion (more stable
planar structure). As for the transition energies, the use of range-separated hybrid
XCF restores a physically correct behavior. Similar conclusions to that of Tozer
have been obtained for several other compounds [15, 109, 110] and it indicates that
one should be particularly cautious when interpreting dual-fluorescence originating
from an equilibrium between planar and twisted intramolecular CT.
In short, for CT states, both the structures and transition energies are more
accurately evaluated using range-separated hybrid XCF.
360
D. Jacquemin and C. Adamo
energies are too large (by ca. 0.3–1.0 eV) in cyanines, and this conclusion has
been reached through comparisons of both TD-DFT’s E
vertÀa with their highlycorrelated wavefunction counterparts [82, 87] and TD-DFT’s E
AFCP with experimental references for fluoroborate emitters [88, 89]. More puzzling is the fact that
the errors seem to be almost independent of the selected XCF and that this error is
not related to a multi-determinant nature. The fundamental reasons explaining this
failure of TD-DFT have been given in [90–92, 94, 95] and summarized in a recent
account [93]. A pragmatic approach to obtain accurate E
AFCP is to apply (13)
selecting an appropriate variant of the CIS(D), ADC(2) or CC2 approaches as the
wavefunction method [47, 96]. Examples of applications of such mixed approach
are given in Sect. 4.
3.3.2 Energy and Geometry of Charge-Transfer States
One generally denotes as CT states, states in which the photon absorption or
emission induces a strong displacement of the electronic density, i.e., when the
electron and the hole are spatially separated. For those CT ES, it is now well
recognized that both pure and global hybrid XCF including a small fraction of
exact exchange tend to deliver (much) too small E
vertÀa , E
vertÀ f , and E
AFCP [97–
100]. For instance, Dreuw and Head-Gordon have shown that LDA [101], BLYP
[59, 60], and B3LYP [52] XCF yield errors of 1 eV or more for the
bacteriochlorophyll-spheroidene dyad. Within the adiabatic TD-DFT approximation, this error can be strongly reduced by using a range-separated hybrid XCF, e.g.,
CAM-3LYP [54], LC-BOP [102], or ωB97-X [103] which restores a correct
interaction between the electron and the hole [104–107] and therefore provides
an efficient answer to the CT challenge.
Additionally, the TD-DFT determination of the R
ES can be problematic for CT
ES. Tozer was the first to unravel the qualitatively incorrect PES obtained for
4-(dimethylamino)-benzonitrile with B3LYP [108]. Indeed, this popular XCF predicts that the twisted ES, in which the NMe 2 terminal group becomes perpendicular
to the central phenyl ring, is more stable than the corresponding planar geometry,
whereas accurate wavefunction theories yield the opposite conclusion (more stable
planar structure). As for the transition energies, the use of range-separated hybrid
XCF restores a physically correct behavior. Similar conclusions to that of Tozer
have been obtained for several other compounds [15, 109, 110] and it indicates that
one should be particularly cautious when interpreting dual-fluorescence originating
from an equilibrium between planar and twisted intramolecular CT.
In short, for CT states, both the structures and transition energies are more
accurately evaluated using range-separated hybrid XCF.
360
D. Jacquemin and C. Adamo