264
D. Escudero
the k f and k r decay rates, can ultimately provide access to the quantum yields of
photoluminescence. Further details of these ES decay rate formalisms and recent
examples of its application for TMCs will be presented in Sects. 2.2 and 3.1, respectively. Unfortunately, these investigations are yet scarce and can hardly be applied in
a systematic manner. This is so because the calculation of particularly ES → GS nonradiative rates still pose significant problems, as (i) the actual mechanisms are often
unknown without a prior exploration of the involved PES and (ii) more than one ES
might be involved in these nonradiative decay processes. The possible radiationless
deactivation pathways are schematically shown in Fig. 2. In the weak coupling limit
(Fig. 2a), the PESs of the ES and GS are weakly displaced, so that both surfaces will
only intersect at regions far away from the ES minimum. Therefore, the nonradiative
decay is mainly driven by the overlap between the vibrational wavefunctions of the
ES and the GS, and thus, it is relatively slow and it generally obeys the energy gap
law [31]. This weak coupling limit is found for aromatic hydrocarbons, but also for
strongly emissive molecular systems. In Fig. 2b, the strong coupling limit is depicted,
which is characterized by largely displaced ES and GS minima. Due to these large
displacements, the ES and GS PESs intersect at regions near to the ES minimum,
leading to nonadiabatic photochemical events. These surface crossings are mediated
by conical intersections (CoIns) [32] and provide very efficient funnels for the radiationless deactivation to the GS, which typically occur on a subpicosecond scale
for these molecular systems [3]. The MC states of TMCs do belong to this strong
coupling limit [33]. In a nutshell, if one aims to study the nonradiative processes of
a given molecular system, one should first explore their ES and GS PESs and locate
the relevant stationary points along the deactivation pathways to assess whether the
strong or the weak limit applies. In addition, this situation may become even more
complex due to the population of close-lying ES; see Fig. 2c. In Fig. 2c, ES 1 is
weakly coupled to the GS and it may thus decay back to the GS in a radiative or
nonradiative manner. Conversely, ES 2 is strongly coupled to the GS and it will thus
be exclusively involved in nonradiative processes. This situation is very common
for TMCs, being ES 1 an emissive state of fundamentally MLCT character and ES 2
a MC state that acts as a quencher of photoluminescence [34]. Depending on the
relative energetic alignment between ES 1 and ES 2 , an activation barrier to populate
ES 2 might appear (see E act in Fig. 2), leading to strongly temperature-dependent
nonradiative decay rates. Cyclometalated Ir(III) complexes do usually belong to this
latter scenario [35]. Importantly, these situations require from complex ES kinetic
models, since the involved ESs are thermally equilibrated. In this regard, the development of realistic kinetic models is crucial to attain quantitative determinations of the
photoluminescence quantum yields (PLQY) in these systems. Recent computational
works combining the calculation of ES decay rate constants at the first principles
level with kinetic modeling enabled the calculations of lifetimes and PLQY values
of Ir(III) complexes [36, 37]. These strategies are further elaborated in Sect. 3.1.
The above static approach is best suited to assess the competition between radiative and nonradiative processes occurring at long timescales (i.e., from the nanosecond regime, where fluorescence typically occurs, up to the micro or the millisecond
regime, and thus also covering phosphorescence), and indeed, this approach remains
D. Escudero
the k f and k r decay rates, can ultimately provide access to the quantum yields of
photoluminescence. Further details of these ES decay rate formalisms and recent
examples of its application for TMCs will be presented in Sects. 2.2 and 3.1, respectively. Unfortunately, these investigations are yet scarce and can hardly be applied in
a systematic manner. This is so because the calculation of particularly ES → GS nonradiative rates still pose significant problems, as (i) the actual mechanisms are often
unknown without a prior exploration of the involved PES and (ii) more than one ES
might be involved in these nonradiative decay processes. The possible radiationless
deactivation pathways are schematically shown in Fig. 2. In the weak coupling limit
(Fig. 2a), the PESs of the ES and GS are weakly displaced, so that both surfaces will
only intersect at regions far away from the ES minimum. Therefore, the nonradiative
decay is mainly driven by the overlap between the vibrational wavefunctions of the
ES and the GS, and thus, it is relatively slow and it generally obeys the energy gap
law [31]. This weak coupling limit is found for aromatic hydrocarbons, but also for
strongly emissive molecular systems. In Fig. 2b, the strong coupling limit is depicted,
which is characterized by largely displaced ES and GS minima. Due to these large
displacements, the ES and GS PESs intersect at regions near to the ES minimum,
leading to nonadiabatic photochemical events. These surface crossings are mediated
by conical intersections (CoIns) [32] and provide very efficient funnels for the radiationless deactivation to the GS, which typically occur on a subpicosecond scale
for these molecular systems [3]. The MC states of TMCs do belong to this strong
coupling limit [33]. In a nutshell, if one aims to study the nonradiative processes of
a given molecular system, one should first explore their ES and GS PESs and locate
the relevant stationary points along the deactivation pathways to assess whether the
strong or the weak limit applies. In addition, this situation may become even more
complex due to the population of close-lying ES; see Fig. 2c. In Fig. 2c, ES 1 is
weakly coupled to the GS and it may thus decay back to the GS in a radiative or
nonradiative manner. Conversely, ES 2 is strongly coupled to the GS and it will thus
be exclusively involved in nonradiative processes. This situation is very common
for TMCs, being ES 1 an emissive state of fundamentally MLCT character and ES 2
a MC state that acts as a quencher of photoluminescence [34]. Depending on the
relative energetic alignment between ES 1 and ES 2 , an activation barrier to populate
ES 2 might appear (see E act in Fig. 2), leading to strongly temperature-dependent
nonradiative decay rates. Cyclometalated Ir(III) complexes do usually belong to this
latter scenario [35]. Importantly, these situations require from complex ES kinetic
models, since the involved ESs are thermally equilibrated. In this regard, the development of realistic kinetic models is crucial to attain quantitative determinations of the
photoluminescence quantum yields (PLQY) in these systems. Recent computational
works combining the calculation of ES decay rate constants at the first principles
level with kinetic modeling enabled the calculations of lifetimes and PLQY values
of Ir(III) complexes [36, 37]. These strategies are further elaborated in Sect. 3.1.
The above static approach is best suited to assess the competition between radiative and nonradiative processes occurring at long timescales (i.e., from the nanosecond regime, where fluorescence typically occurs, up to the micro or the millisecond
regime, and thus also covering phosphorescence), and indeed, this approach remains