experimentally. Nevertheless, the application of TD-DFT to spectroscopic problems generally implies two major approximations: the use of the adiabatic approximation (i.e., only a frequency-independent exchange and correlation kernel is
applied) and the selection of an adequate exchange-correlation functional (XCF).
These two drawbacks limit the final accuracy of the results obtained and numerous
works have been devoted to the appraisal of the most suited XCF [24], as well as to
schemes going beyond linear-response TD-DFT [5, 25] in the framework of the
simulation of optical spectra. Despite these limits, TD-DFT clearly remains the
most applied theory for evaluating the spectral properties of “real-life” structures
and this popularity can be ascribed to the simplicity and speed of use of this singlereference approach and also to the modeling of environmental effects which can be
achieved with several theories [26, 27]. This general statement is particularly true
for solvation effects for which a panel of refined models is now accessible [28–32].
In this chapter we summarize several recent advances in the TD-DFT spectroscopy field with a focus on recent works dealing with 0–0 energies, for which a
protocol is detailed in Sect. 2. We next present the results of several benchmarks
performed for these 0–0 energies (Sect. 3) before going through a series of
examples obtained in the dye chemistry field (Sect. 4).
2 Protocol to Determine the 0–0 Energies
In this section we present a popular approach to compute the 0–0 energies with
TD-DFT. This also allows us to define a series of different energies which are
subsequently used, and to propose an easy-to-follow protocol to obtain all the
relevant parameters which are represented in Fig. 1, in which R
GS and R
ES stand
for the optimal geometries of the ground- and excited-states, respectively, whereas
E
GS and E
ES are the total energies of these two states. Following [15], we first
explain the more straightforward gas-phase situation before extending the protocol
to the condensed phase.
2.1 Gas Phase
In the gas phase, the vertical absorption can simply be defined as the difference
between the ES and GS energies at the optimal ground-state geometry,
E
vertÀa
¼ E
ES R
GS
À
Á À E
GS R
GS
À
Á ;
ð1Þ
whereas the vertical fluorescence is the corresponding data estimated at the optimal
geometry of the relevant excited-state,
Computational Molecular Electronic Spectroscopy with TD-DFT
349
applied) and the selection of an adequate exchange-correlation functional (XCF).
These two drawbacks limit the final accuracy of the results obtained and numerous
works have been devoted to the appraisal of the most suited XCF [24], as well as to
schemes going beyond linear-response TD-DFT [5, 25] in the framework of the
simulation of optical spectra. Despite these limits, TD-DFT clearly remains the
most applied theory for evaluating the spectral properties of “real-life” structures
and this popularity can be ascribed to the simplicity and speed of use of this singlereference approach and also to the modeling of environmental effects which can be
achieved with several theories [26, 27]. This general statement is particularly true
for solvation effects for which a panel of refined models is now accessible [28–32].
In this chapter we summarize several recent advances in the TD-DFT spectroscopy field with a focus on recent works dealing with 0–0 energies, for which a
protocol is detailed in Sect. 2. We next present the results of several benchmarks
performed for these 0–0 energies (Sect. 3) before going through a series of
examples obtained in the dye chemistry field (Sect. 4).
2 Protocol to Determine the 0–0 Energies
In this section we present a popular approach to compute the 0–0 energies with
TD-DFT. This also allows us to define a series of different energies which are
subsequently used, and to propose an easy-to-follow protocol to obtain all the
relevant parameters which are represented in Fig. 1, in which R
GS and R
ES stand
for the optimal geometries of the ground- and excited-states, respectively, whereas
E
GS and E
ES are the total energies of these two states. Following [15], we first
explain the more straightforward gas-phase situation before extending the protocol
to the condensed phase.
2.1 Gas Phase
In the gas phase, the vertical absorption can simply be defined as the difference
between the ES and GS energies at the optimal ground-state geometry,
E
vertÀa
¼ E
ES R
GS
À
Á À E
GS R
GS
À
Á ;
ð1Þ
whereas the vertical fluorescence is the corresponding data estimated at the optimal
geometry of the relevant excited-state,
Computational Molecular Electronic Spectroscopy with TD-DFT
349