3.1 AFCP Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
3.2 Band Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
3.3 Challenging Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
4 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
4.1 Organic Electronic Chromophores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
4.2 Inorganic Dyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
4.3 Fluoroborate Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
4.4 ESIPT and Dual Emitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
4.5 Caging Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
4.6 Charge-Transfer Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
1 Introduction
By analyzing the continuously increasing number of quantum chemistry works
relying on Time-Dependent Density Functional Theory (TD-DFT) [1–5], it appears
that the vast majority of TD-DFT’s applications are devoted to the modeling of the
most widely available excited-state (ES) properties, namely optical spectra. One
can roughly split these works into two major categories. In the first, which contains
the majority of the TD-DFT investigations, the so-called vertical approximation is
applied, i.e., a frozen ground-state (GS) geometry is considered and transition
energies are determined without accounting for vibrational couplings [6]. This
approach is computationally very efficient, allows one to characterize the nature
of the relevant excited-states, and has been successfully used to design dyes or to
understand environmental effects, albeit the vertical energies cannot be experimentally measured in most cases. However, more and more works of the second
category, looking for well-grounded theory-measurement comparisons, have
recently appeared. These studies, which imply higher computational efforts than
their vertical counterparts, aimed at determining the 0–0 energies and/or
vibrationally-resolved spectra [7–17]. Indeed, on the one hand, the 0–0 energies
can be directly measured in the gas-phase for small molecules, or taken as the
crossing point between absorption and emission curves (AFCP: absorption/fluorescence crossing point) in the experimental spectra of large solvates species [13],
whereas, on the other hand, vibronic couplings give access to both band shapes and
absolute intensities, which can also be directly correlated with measurements. The
calculation of these properties implies the determination of the ES Hessian. Thanks
to the development and implementation of analytic first and second derivatives [18–
22], TD-DFT has indeed become an efficient approach to explore the potential
energy surfaces (PES) of the ES in large compounds, the accuracy obtained being in
most cases reasonable, at least close to the Franck–Condon point [23]. TD-DFT can
therefore not only be used to probe the nature of the ES responsible for the
absorption and fluorescence spectra but also provide many other properties, e.g.,
ES geometries and dipole moments, which are difficult (or costly) to measure
348
D. Jacquemin and C. Adamo
3.2 Band Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
3.3 Challenging Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
4 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
4.1 Organic Electronic Chromophores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
4.2 Inorganic Dyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
4.3 Fluoroborate Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
4.4 ESIPT and Dual Emitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
4.5 Caging Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
4.6 Charge-Transfer Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
1 Introduction
By analyzing the continuously increasing number of quantum chemistry works
relying on Time-Dependent Density Functional Theory (TD-DFT) [1–5], it appears
that the vast majority of TD-DFT’s applications are devoted to the modeling of the
most widely available excited-state (ES) properties, namely optical spectra. One
can roughly split these works into two major categories. In the first, which contains
the majority of the TD-DFT investigations, the so-called vertical approximation is
applied, i.e., a frozen ground-state (GS) geometry is considered and transition
energies are determined without accounting for vibrational couplings [6]. This
approach is computationally very efficient, allows one to characterize the nature
of the relevant excited-states, and has been successfully used to design dyes or to
understand environmental effects, albeit the vertical energies cannot be experimentally measured in most cases. However, more and more works of the second
category, looking for well-grounded theory-measurement comparisons, have
recently appeared. These studies, which imply higher computational efforts than
their vertical counterparts, aimed at determining the 0–0 energies and/or
vibrationally-resolved spectra [7–17]. Indeed, on the one hand, the 0–0 energies
can be directly measured in the gas-phase for small molecules, or taken as the
crossing point between absorption and emission curves (AFCP: absorption/fluorescence crossing point) in the experimental spectra of large solvates species [13],
whereas, on the other hand, vibronic couplings give access to both band shapes and
absolute intensities, which can also be directly correlated with measurements. The
calculation of these properties implies the determination of the ES Hessian. Thanks
to the development and implementation of analytic first and second derivatives [18–
22], TD-DFT has indeed become an efficient approach to explore the potential
energy surfaces (PES) of the ES in large compounds, the accuracy obtained being in
most cases reasonable, at least close to the Franck–Condon point [23]. TD-DFT can
therefore not only be used to probe the nature of the ES responsible for the
absorption and fluorescence spectra but also provide many other properties, e.g.,
ES geometries and dipole moments, which are difficult (or costly) to measure
348
D. Jacquemin and C. Adamo