Chapter 1: TADF Material Design: Photophysical Background and Case Studies Focusing on Cu(I) and Ag(I) Complexesa – Highly Efficient OLEDs

TADF Material Design: Photophysical Background and Case Studies Focusing on Cu(I) and Ag(I) Complexesa

Hartmut Yersin1b Rafał Czerwieniec1 Marsel Z. Shafikov1,2 and Alfiya F. Suleymanova1

1University of Regensburg, Department of Chemistry, Institute of Physical Chemistry, Universitätsstr. 31, Regensburg, D‐93053, Germany

2Ural Federal University, Department of Technology of Organic Synthesis, Institute of Chemical Technology, Mira str. 19, Ekaterinburg, 620002, Russia

1.1 Introduction

Basic research of photophysical and chemical properties of organo‐transition metal compounds was strongly activated by their potential commercial use. This became particularly apparent for classes of compounds that may be applied as emitters in organic light‐emitting diodes (OLEDs) [119] or in light emitting electrochemical cells (LEEC) [7, 2028]. These scientific investigations led to a much deeper understanding of the photophysical principles and of the compound's properties resulting in the development of an enormous number of new materials in part with drastically improved properties for OLED applications [4, 9, 2952]. Improvements were also stimulated in the fields of related functional materials based on metal complexes for sensing of oxygen or temperature [5359] or for photocatalysis [6066].

For luminescent materials to be applied in OLEDs, it is essential that all excitons generated in the emission layer are harvested and converted into photons. Since the statistic ratio of the formed excitons is 1 singlet to 3 triplets [67, 68], special mechanisms that allow to harvest all of them are required, as the two types of excitons show different relaxation properties [67]. Already about 20 years ago, it was discovered that third‐row transition metal complexes, especially those with Ir(III), Pt(II), or Os(II) metal centers, are well suited for such harvesting processes, since the metal centers can induce efficient spin–orbit coupling (SOC) [6977] between the lowest triplet state T1 and higher‐lying singlet states Sn (with n > 1) [1, 9, 11, 12, 67, 6989]. As a consequence, fast intersystem crossing (ISC) to the lowest triplet state of several tens of femtosecond [88, 90] can occur, and relatively high radiative phosphorescent rates from the T1 state to the electronic ground state S0 are induced. These latter rates can become as high as ≈106 s−1 [70, 89, 91]. Therefore, these phosphorescent compounds are frequently denoted as triplet emitters. As a consequence, when applied in OLEDs, these materials can harvest all singlet and triplet excitons in the lowest excited triplet state. Accordingly, the corresponding mechanism is denoted as triplet harvesting effect [69, 78]. Indeed, using, for example, Ir(ppy)3 (with ppy = 2‐phenylpyridinate), OLEDs with almost 100% internal quantum efficiency could be produced [11, 81].

However, these triplet emitter complexes require high‐cost rare metals, and this may become a limiting factor, when OLED lighting goes into mass production [70, 92, 93]. Therefore, an alternative harvesting mechanism that may work with low‐cost materials has been proposed more than one decade ago [94]. This mechanism is based on the molecular effect of thermally activated delayed fluorescence (TADF), according to which also all excitons generated in the emission layer may be harvested. In this situation, however, the emission does not stem from the lowest excited triplet state, but from the thermally activated singlet state S1. Hence, this mechanism has been denoted as singlet harvesting mechanism [9, 30, 31, 37, 40, 56, 70, 92, 9497]. Accordingly, the luminescent materials do not need to contain high SOC‐inducing metal centers (high‐cost materials), since the (thermally activated) singlet state usually carries sufficient allowedness with respect to the transition to the singlet ground state (spin‐allowed transition). Therefore, an efficient path for photon generation becomes available.

Obviously, thermal activation, from the lowest triplet state T1 to the higher‐lying singlet state S1, requires a relatively small energy separation ΔE(S1–T1) between these states. For example, at ambient temperature (T = 300 K), a thermal energy of kBT ≈ 210 cm−1 (26 meV) is available (kB = Boltzmann constant). Hence, as a rule of thumb, efficient thermal activation with fast up‐ISC or reverse intersystem crossing (rISC) is not expected to occur for ΔE(S1–T1) distinctly above 103 cm−1 (≈130 meV). Indeed, such energy separations can be realized with environmentally friendly and low‐cost Cu(I) [4, 9, 27, 3035, 3756, 70, 92, 93, 95105] and Ag(I) [104, 106109] complexes as well as with purely organic molecules [110113].

In this review, we focus on Cu(I) and Ag(I) complexes. For these materials, we have to address three crucial photophysical requirements:

  1. The emitter compounds should exhibit high photoluminescence quantum yields φPL. After an electronic excitation, however, Cu(I) and Ag(I) complexes experience distinct flattening distortions with respect to the ground state geometries [114123]. Usually, such geometry changes are related to an increase of nonradiative deactivation or even result in total quenching of the luminescence by vibrational relaxation. This is induced by a strong increase of the Franck–Condon factors of the low‐lying vibrational modes of the excited electronic state and highly excited vibrational modes of the electronic ground state [124126]. However, these shortcomings may be suppressed to a large extent by rigidifying the molecular structure either by sterically demanding ligands or by a rigid environment. This behavior has already been discussed frequently in the literature [9, 30, 31, 35, 92, 95, 96, 108, 109, 114, 119, 127]. We will address these properties in Sections 1.3 and 1.6. Interestingly, design of a material, a silver complex, with ΦPL of 100% becomes possible by following this strategy of rigidifying the molecular structure (see Refs [108, 109] and Section 1.6).
  2. Well‐designed TADF materials should exhibit relatively small energy separations ΔE(S1–T1). For organo‐transition metal compounds, this is related to the occurrence of metal‐to‐ligand charge‐transfer (MLCT) (and ligand‐to‐ligand charge‐transfer (LL'CT)) states having frontier orbitals, highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), which are spatially largely separated. This leads to a small exchange interaction [128130] between the involved electrons and, hence, to the required small splitting between the singlet S1 and triplet T1 state. In particular, a relatively small ΔE(S1–T1) value is a necessary condition to obtain a short radiative TADF decay time, which is important to maximize the photoluminescence quantum yield ΦPL. Moreover, for use in OLEDs, short decay times are important to minimize roll‐off effects (for example, induced by saturation or triplet‐polaron quenching) and to reduce device stability problems as well as undesired energy transfer processes from the emitter dopant to the host. In Sections 1.3 and 1.4, discussing case studies, we will present Cu(I) compounds and the dependence of photophysical properties on the ΔE(S1–T1) gap.
  3. The TADF properties crucially depend on the allowedness of the S1 → S0 fluorescence that is thermally activated from the lower‐lying triplet state. The reason is that the corresponding radiative rate kr(S1 → S0) also governs the TADF decay time. kr(S1 → S0) should be as large as possible to obtain a short TADF decay time. However, basic quantum chemical considerations show that these rates kr(S1 → S0) and ΔE(S1–T1) correlate. We address this behavior in Section 1.5.

Thus, designing of TADF compounds with short TADF decay time and high emission quantum yield is a challenge. For example, radiative TADF decay times of Cu(I) complexes of less than 3–5 μs have not been reported so far [30, 31, 96]. We will discuss this challenge in several sections of this investigation. In particular, in Section 1.6, where we focus on designing new Ag(I) complexes, we will show how to develop a breakthrough TADF material [108, 109] with a radiative TADF decay time of only 1.4 μs (at φPL = 100%), which is significantly shorter than so far reported.

This chapter is organized as follows: In Section 1.2, we introduce different parameters that have to be addressed for designing efficient TADF materials based on Cu(I) and Ag(I) complexes, and we present the materials studied in this chapter together with selected photophysical data. Sections 1.3 and 1.4 display case studies of Cu(I) complexes with large and small ΔE(S1–T1) energy separation, respectively. Furthermore, we discuss effects of SOC with respect to properties of the lowest triplet state, such as phosphorescence allowedness and zero‐field splitting (ZFS). In Section 1.5, we show on a very simple quantum mechanical basis that the size of the energy gap ΔE(S1–T1) and the allowedness of the singlet S1 → singlet S0 transition are correlated. This result is clearly supported by experimental data. In Section 1.6, we present photophysical properties of a new TADF class of Ag(I) complexes, and we show how an extraordinarily efficient TADF material can be designed. Finally, in a conclusion, we will give a short summary and point to future perspectives.

1.2 TADF, Molecular Parameters, and Diversity of Materials

The molecular TADF effect was already reported more than five decades ago [131, 132]. It can be described by the use of Figure 1.1. By an optical excitation, one usually excites a singlet state, for example, higher‐lying vibrational levels of the S1 state. Subsequently, fast vibrational relaxation of the order of 10−12 s [124] proceeds to lower lying vibrational levels. Then, depending on the class of molecules, prompt fluorescence and/or down‐ISC (as well as nonradiative relaxation to the electronic ground state) can occur. For Cu(I) and Ag(I) complexes, being in the focus of this contribution, ISC from S1 to the T1 state is very effective, since fast ISC occurring in the time range of 3–30 ps has been observed [118, 121, 122, 133, 134]. The individual value does not only depend on molecular properties, for example, on the extent of SOC of higher‐lying singlets to the lowest triplet state, but also on the local environment, such as a fluid or a rigid matrix [134]. In general, a significant prompt fluorescence (S1 → S0) is not detected, instead a very bright long‐lived phosphorescence (T1 → S0) is frequently observed at low temperature [30, 31, 3335, 70, 92, 9597, 135, 136]. At a higher temperature and in a situation of a fast thermal equilibration, population of the higher‐lying singlet state is governed by the Boltzmann distribution. In this context, “fast” means that the down‐ and up‐ISC processes are much faster than the T1 → S0 and S1 → S0 emission decay processes. As a consequence, the emission decays with a single decay time being a weighted average (Eq. 1.1) of the T1 → S0 and S1 → S0 decay processes. Usually, this is fulfilled for Cu(I) and Ag(I) complexes with low‐lying MLCT states. At lower temperatures population of the S1 state due to the Boltzmann thermal distribution is frozen out. For completeness, it is remarked that below T ≈ 15 K, effects of spin–lattice relaxation (SLR) between the triplet substates might strongly slow down relaxation processes [31, 33, 34, 88, 95, 137139]. Consequently, frequently a multiexponential decay (from the different T1 substates to the ground state S0) is observed at very low temperature.

Figure 1.1Illustration of the molecular TADF effect and its use in OLEDs (singlet harvesting). τ(T1) and τ(TADF) are the phosphorescence decay time and the TADF decay time, respectively. k(S1) = kr(S1 → S0) is the radiative rate of the S1 → S0 transition (prompt fluorescence). Up‐ISC is also often denoted as reverse intersystem crossing (rISC).

At higher temperatures, up‐ISC processes efficiently depopulate the triplet T1 state, i.e. the three triplet substates, and populate the singlet S1 state. In particular, if the emission decay time of the T1 state is long, for example, longer than several 100 μs, the phosphorescence is largely “quenched” and almost only the S1 → S0 fluorescence is observed. Because the population of the S1 state is fed from the long‐living triplet state (triplet reservoir), this type of fluorescence is also long living compared with the prompt fluorescence that does not involve a triplet state. Hence, the emission is denoted as TADF.

For completeness, it is mentioned that for several Cu(I) complexes, SOC with respect to the T1 state is significant. In this situation, the TADF process will not fully deplete the T1 state during its much shorter population time, and a combined TADF/phosphorescence is observed. This property is not in the focus of the present contribution, but is discussed in detail in the literature [31, 33, 34, 97].

In the emission layer of an OLED device, the electron‐hole recombination produces excitons of different spin multiplicity, that is, 75% are of triplet and 25% of singlet character [67, 68, 78, 79] (Figure 1.1). These excitons can be trapped in the emitter molecule. Such mechanisms are discussed in Ref. [67]. Subsequently, fast internal conversions, i.e. one singlet path and three triplet paths, populate the S1 and the T1 state, respectively [67]. Then similarly to the behavior after optical excitation, thermal activation takes place. In particular, in a situation of a forbidden T1 → S0 transition and a relatively small ΔE(S1–T1) value, finally almost all excitations are transferred to the lowest excited singlet state, which then exhibits delayed S1 → S0 fluorescence. According to this process, the molecular TADF effect as exploited in an OLED device has been denoted as singlet harvesting mechanism [9, 30, 31, 70, 9496].

As already stressed, the TADF decay time τ(TADF) should be as short as possible (obviously, at a high emission quantum yield), if the emitter is applied in an OLED. To achieve this goal, valuable guidelines can be deduced. Especially, a discussion of the temperature dependence of the emission decay time is helpful. This is easily explained by the use of a model discussion of a simplified molecule with two excited states, a singlet S1 and a triplet T1, being in fast thermal equilibrium, and the electronic ground state S0 (compare Figure 1.1). In this situation, the decay time τ(T) of the luminescent molecule is described by a Boltzmann‐type relation [30] (compare also [140143]):


k(T1) = 1/τ(T1) and k(S1) = 1/τ(S1) are the decay rates with the decay times τ(T1) and τ(S1) of the triplet and singlet excited state, respectively, and ΔE(S1–T1) is the energy separation between the S1 and T1 state. τ(T) represents the experimentally accessible emission decay time at a given temperature. For the subsequent discussion, it is assumed that the molecular parameters τ(T1), τ(S1), and ΔE(S1–T1) are temperature independent and that the splitting of the triplet state into three substates (ZFS) is small, i.e. much smaller than kBT.

Thus, application of Eq. ( 1.1 ) to the measured decay times at different temperatures opens access to the molecular parameters given above. In particular, it becomes possible to determine very small energy separations being much below the attainable spectral resolution. For example, using a slightly modified Eq. ( 1.1 ) energy separations of only a few cm−1 can be resolved despite the fact that the MLCT emission bands are frequently as broad as several thousand cm−1 (compare [9, 31, 95, 97, 140]).

At very low temperature, the exponential terms in Eq. ( 1.1 ) are negligible, and the measured decay time τ(T) displays the phosphorescence decay time τ(T1), while at high temperature (and long τ(T1)), the term containing τ(T1) can be neglected, and one obtains essentially the decay time τ(TADF). In Sections 1.3, 1.4, and 1.6, several case studies, discussing the τ(T) temperature behavior, are presented.

Eq. ( 1.1 ) shows that three parameters crucially determine the emission decay time. These parameters can be deduced from fitting Eq. ( 1.1 ) to the measured emission decay times for a suitable temperature range. If this is carried out for a number of Cu(I) and/or Ag(I) complexes, valuable guidelines for molecular design rules can be extracted. Therefore, a more detailed discussion of the three parameters is illustrative.

Figure 1.2 schematically visualizes the photophysical background of the parameters that govern Eq. ( 1.1 ). For all three cases, subsequently discussed in detail, it is assumed that the respective molecule shows TADF.

Figure 1.2Different strategies for minimizing the emission decay time of TADF compounds for OLED applications. The zero‐field splitting of the T1 state into three substates is not shown in this diagram.

1.2.1 TADF and Phosphorescence

Figure 1.2a displays an energy level diagram of a compound that exhibits significant SOC of the triplet state T1 to a singlet state. Quantum mechanical considerations show that SOC between the triplet state T1 and the singlet state S1 both stemming from the same orbital configuration vanishes [9, 30, 31, 6977]. However, mixing in of different, higher‐lying singlets Sn (with n > 1) can be significant. If so, the triplet state of Cu(I) complexes, for example, exhibits a distinct ZFS of several cm−1 (a few 0.1 meV), and the T1 → S0 transition rate for the phosphorescence can become as large as 5 × 104 s−1 (20 μs) [30, 34, 97, 135, 136]. Accordingly, a second, effective radiative decay channel is opened in addition to the TADF decay path. These combined radiative decay paths can distinctly shorten the ambient temperature emission decay time. In this contribution, we do not focus further on this effect, but compare the literature reports [30, 31, 34, 97, 144].

1.2.2 Minimizing ΔE(S1–T1)

As already addressed, the energy separation ΔE(S1–T1) between the lowest singlet S1 and triplet state T1 should be relatively small (Figure 1.2b). This can be well achieved with Cu(I) and Ag(I) complexes, if the lowest lying excited states are largely of 1,3MLCT character. In this situation, a distinct charge separation between the unpaired electrons can occur. As a consequence, the quantum mechanical exchange interaction [128130] and, hence, also the singlet–triplet splitting becomes small (Section 1.5). Because ΔE(S1–T1) enters in an exponential term in Eq. ( 1.1 ), ΔE(S1–T1) reduction has a dominating effect on the TADF decay time, τ(TADF). However, this seems to be limited, when ΔE(S1–T1) becomes lower than 200–300 cm−1 (25 to ≈40 meV), since at smaller splitting, decrease of the S1–S0 transition rate kr(S1 → S0) might induce an opposite trend and lead to an increase of τ(TADF). (In Section 1.5 it will be shown that ΔE(S1–T1) and kr(S1 → S0) are related to each other.) The variation of ΔE(S1–T1) can be achieved by a suitable molecular design as discussed below in this section and in the case studies presented in the next two sections.

1.2.3 Importance of kr(S1–S0)

The allowedness of the S1 ↔ S0 transition can be expressed, for example, by the radiative fluorescence rate kr(S1 → S0) (Figure 1.2c). According to Eq. ( 1.1 ), this rate also plays an important role at determining the TADF decay time. Frequently, this property is not adequately addressed. The rate should be as high as possible to obtain short TADF decay time. For this requirement also ΔE(S1–T1) should be as small as possible. However, the two photophysical parameters are correlated. Small splitting ΔE(S1–T1) requires a small exchange interaction between the unpaired electrons, at least when both T1 and S1 states are well described by a HOMO–LUMO excitation. For a small exchange interaction, small overlap of HOMO and LUMO is advantageous. At the same time, small HOMO–LUMO overlap leads to a small oscillator strength (small allowedness) of the S1 → S0 transition and, thus, to a small kr(S1 → S0) value and, hence, to a long fluorescence decay time. Indeed, experimental studies on Cu(I) complexes exhibiting TADF reveal that such a correlation exists for a large number of compounds (compare also Section 1.5) [31].

However, it is indicated that a close correlation between these two photophysical properties might not always be so strict. In particular, the S1 state might be modified by a suitable molecular design. For example, quantum mechanical configuration interaction (CI) can be helpful in this respect. This means that a different, higher‐lying singlet state, which is energetically proximate and carries high allowedness (high oscillator strength) with respect to the transition to the electronic ground state, can mix with the S1 state and induce a higher S1 → S0 allowedness. Presumably, this mechanism is important for the Ag(I) complexes discussed in Section 1.6.

Experimental access to the photophysical parameters as discussed above and in Figure 1.2 becomes possible by the use of a fitting procedure of Eq. ( 1.1 ) to the measured values of τ(T) over a large temperature range. The required range depends on the size of ΔE(S1–T1). For example, if ΔE(S1–T1) values are larger than about 700 cm−1 (87 meV), a temperature range of 77 K ≤ T ≤ 300 K might usually be sufficient. However, for smaller splittings, the range has to be extended, for example, to T = 30 K to be able to characterize a compound with a splitting of only ΔE(S1–T1) = 370 cm−1 (compound 2, see Section 1.4) [31, 96]. Moreover, if the splitting of the T1 state into substates of a few cm−1 (a few 0.1 meV) and the corresponding photophysical properties should be addressed, extension of the temperature range to about T = 1.3 K (and application of a slightly modified Eq. 1.1) is required [58, 70, 88, 89, 97, 138, 145].

In Sections 1.3, 1.4, and 1.6, we will present case studies. In these we will show how to develop a deeper understanding of representative compounds. In Table 1.1, for a broader overview, we summarize a selection of photophysical data for a large number of complexes that are addressed in this contribution. The compounds studied were investigated as powder materials. In this respect, it should be remarked that very frequently, the decay behavior measured of powder materials is modified, for example, by processes of energy transfer or triplet–triplet annihilation. However, if the low‐lying charge‐transfer (CT) states of the complexes exhibit geometry distortions also in the relatively rigid crystalline environment, localization (self‐trapping) can occur and prevent energy transfer effects. Thus, the emission of the powder material can display molecular properties. Accordingly, concentration quenching does not occur, and the decay behavior does not show any distinctive feature (such as shortening of decay times) with concentration increase [30, 31, 58, 95].

Table 1.1 Photophysical data based on luminescence measurements of powder materials arranged according to increasing ΔE(S1–T1).

Compound Photophysical data References
ΔE(S1–T1) = 270 cm−1
λmax(300 K) = 511 nm
ΦPL(300 K) = 97%
τ(300 K) = 5 μs
τ(T1 → S0) = 23 μs
τ(S1 → S0) = 570 ns
[31, 38]
ΔE(S1–T1) = 370 cm−1
λmax(300 K) = 535 nm
ΦPL(300 K) = 70%
τ(300 K) = 3.3 μs
τ(T1 → S0) = 1200 μs
τ(S1 → S0) = 180 ns
[43, 96, 146]
ΔE(S1–T1) = 460 cm−1
λmax(300 K) = 506 nm
ΦPL(300 K) = 45%
τ(300 K) = 6.6 μs
τ(T1 → S0) = 250 μs
τ(S1 → S0) = 210 ns
ΔE(S1–T1) = 510 cm−1
λmax(300 K) = 490 nm
ΦPL(300 K) = 65%
τ(300 K) = 4.1 μs
τ(T1 → S0) = 1200 μs
τ(S1 → S0) = 110 ns
ΔE(S1–T1) = 570 cm−1
λmax(300 K) = 464 nm
ΦPL(300 K) = 65%
τ(300 K) = 4.6 μs
τ(T1 → S0) = 290 μs
τ(S1 → S0) = 90 ns
ΔE(S1–T1) = 600 cm−1
λmax(300 K) = 545 nm
ΦPL(300 K) = 35%
τ(300 K) = 3 μs
τ(T1 → S0) = 2200 μs
τ(S1 → S0) = 70 ns
[100, 107]
ΔE(S1–T1) = 630 cm−1
λmax(300 K) = 465 nm
ΦPL(300 K) = 65%
τ(300 K) = 5.6 μs
τ(T1 → S0) = 250 μs
τ(S1 → S0) = 100 ns
ΔE(S1–T1) = 650 cm−1
λmax(300 K) = 464 nm
ΦPL(300 K) = 90%
τ(300 K) = 13 μs
τ(T1 → S0) = 500 μs
τ(S1 → S0) = 170 ns
[9, 95, 147, 148]
ΔE(S1–T1) −a
λmax(300 K) = 575 nm
ΦPL(300 K) = 36%
τ(300 K) = 2 μs
τ(77 K) = 270 μs
τ(S1 → S0
Table 1.7
ΔE(S1–T1) = 640 cm−1
λmax(300 K) = 535 nm
ΦPL(300 K) = 70%
τ(300 K) = 2 μs
τ(T1 → S0) = 1600 μs
τ(S1 → S0) = 32 ns
Table 1.7
ΔE(S1–T1) = 650 cm−1
λmax(300 K) = 537 nm
ΦPL(300 K) = 78%
τ(300 K) = 2.8 μs
τ(T1 → S0) = 890 μs
τ(S1 → S0) = 36 ns
Table 1.6
λmax(300 K) = 562 nm
ΦPL(300 K) = 45%
τ(300 K) = 1.7 μs
τ(T1 → S0) = 475 μs
ΔE(S1–T1) = 650 cm−1
λmax(300 K) = 526 nm
ΦPL(300 K) = 100%
τ(300 K) = 1.4 μs
τ(T1 → S0) = 1570 μs
τ(S1 → S0) = 18 ns
[108, 109]
ΔE(S1–T1) = 720 cm−1
λmax(300 K) = 555 nm
ΦPL(300 K) = 55%
τ(300 K) = 11 μs
τ(T1 → S0) = 84 μs
τ(S1 → S0) = 160 ns
ΔE(S1–T1) = 740 cm−1
λmax(300 K) = 475 nm
ΦPL(300 K) = 76%
τ(300 K) = 11 μs
τ(T1 → S0) = 34 μs
τ(S1 → S0) = 160 ns
[34, 149]
ΔE(S1–T1) = 786 cm−1
λmax(300 K) = 512 nm
ΦPL(300 K) = 57%
τ(300 K) = 11 μs
τ(T1 → S0) = 343 μs
τ(S1 → S0) = 79 ns
ΔE(S1–T1) = 830 cm−1
λmax(300 K) = 519 nm
ΦPL(300 K) = 88%
τ(300 K) = 24 μs
τ(T1 → S0) = 110 μs
τ(S1 → S0) = 190 ns
[30, 41]
ΔE(S1–T1) = 930 cm−1
λmax(300 K) = 485 nm
ΦPL(300 K) = 92%
τ(300 K) = 8.3 μs
τ(T1 → S0) = 42 μs
τ(S1 → S0) = 40 ns
[96, 150]
ΔE(S1–T1) = 940 cm−1
λmax(300 K) = 468 nm
ΦPL(300 K) = 99%
τ(300 K) = 9.4 μs
τ(T1 → S0) = 34 μs
τ(S1 → S0) = 47 ns
ΔE(S1–T1) = 980 cm−1
λmax(300 K) = 480 nm
ΦPL(300 K) = 93%
τ(300 K) = 15 μs
τ(T1 → S0) = 1100 μs
τ(S1 → S0) = 45 ns
ΔE(S1–T1) = 1000 cm−1
λmax(300 K) = 530 nm
ΦPL(300 K) = 80%
τ(300 K) = 14 μs
τ(T1 → S0) = 240 μs
τ(S1 → S0) = 40 ns
[92, 151]
ΔE(S1–T1) = 1000 cm−1
λmax(300 K) = 447 nm
ΦPL(300 K) = 90%
τ(300 K) = 22 μs
τ(T1 → S0) = 450 μs
τ(S1 → S0) = 80 ns
[95, 148]
ΔE(S1–T1) = 1070 cm−1
λmax(300 K) = 467 nm
ΦPL(300 K) = 95%
τ(300 K) = 15 μs
τ(T1 → S0) = 50 μs
τ(S1 → S0) = 41 ns
ΔE(S1–T1) = 1170 cm−1
λmax(300 K) = 455 nm
ΦPL(300 K) = 66%
τ(300 K) = 9.5 μs
τ(T1 → S0) = 49 μs
τ(S1 → S0) = 14 ns
ΔE(S1–T1) = 1300 cm−1
λmax(300 K) = 436 nm
ΦPL(300 K) = 45%
τ(300 K) = 20 μs
τ(T1 → S0) = 610 μs
τ(S1 → S0) = 10 ns
[70, 95, 148]

ΔE(S1–T1) and τ(S1 → S0) values result from fitting procedures. A prompt fluorescence of the S1 state has not been observed directly.

Similar ΔE(S1–T1) values are expected to occur for all Ag(phen‐substituted)(P2‐nCB) complexes displayed in this table.

Investigated as [Cu(tmbpy)(pop)](BF4) powder.

Investigated as [Cu(dmp)(phanephos)](PF6) powder.

Source: Ref. [31]. Reproduced with permission of Elsevier.

1.3 Case Study: TADF of a Cu(I) Complex with Large ΔE(S1–T1)

The luminescence properties of TADF compounds depend strongly on the energy separation between the lowest excited singlet and triplet state. In this case study, we discuss properties of Cu(dmp)(phanephos)+ 21 (with dmp = 2,9‐dimethyl‐1,10‐phenanthroline and phanephos = 4,12‐bis(diphenylphosphino)‐[2.2]‐paracyclophane) (Figure 1.3).

Figure 1.3Chemical formula and frontier orbitals of Cu(dmp)(phanephos)+ 21 obtained for the DFT‐optimized triplet state (T1) geometry. The calculations were performed at the B3LYP/def2‐SVP level of theory [152, 153]. Hydrogen atoms are omitted for clarity. HOMO and LUMO exhibit distinctly different spatial distributions. The HOMO is mainly composed of the copper 3d and phosphorus sp3 atomic orbitals, while the LUMO represents essentially a π* orbital of the dmp ligand.

1.3.1 DFT and TD‐DFT Calculations

Quantum mechanical density functional theory (DFT) computations reveal that for this compound, the lowest excited states result dominantly from HOMO to LUMO transitions from metal and phosphorus orbitals to dmp ligand orbitals [92] (Figure 1.3). Accordingly, the excited states have significant admixtures of 1,3MLCT character. This assignment is also supported by the photophysical investigations as discussed below. Time‐dependent density functional theory (TD‐DFT) calculations, carried out in the T1 state geometry, allow us to estimate an energy separation between the singlet and triplet MLCT states of ΔE(S1–T1) ≈ 0.22 eV. Since TD‐DFT computations give energies of vertical transitions between Franck–Condon states, the calculated ΔE(S1–T1) value is overestimated as demonstrated experimentally (see below) but allows us to expect an occurrence of TADF at ambient temperature.

1.3.2 Flattening Distortions and Nonradiative Decay

An MLCT transition in Cu(I) complexes often leads to flattening distortions of the molecule in the excited state relative to the ground state geometry [114, 116122, 154, 155]. Such distortions are usually connected with an increase of non‐radiative deactivations or even quenching of the emission due to a strong increase of the Franck–Condon factors of the low‐lying vibrational modes of the excited state and the highly excited vibrational modes of the electronic ground state [124126]. Thus, engineering of a highly emissive compound requires that such geometry changes are minimized. This can be achieved by using matrix materials characterized by cages of rigid microenvironments. In a different approach, the excited state distortions can also be reduced or even largely suppressed at the molecular level.

Cu(dmp)(phanephos)+ 21 represents an example of a Cu(I) complex in which the excited state distortions are hindered owing to a rational molecular design. In particular, the diphosphine phanephos with a wide P–Cu–P bite angle of 116° [92] forms a rigid “semicage” for the metal ion coordinated by the second ligand (Figure 1.4). Methyl groups in the 2‐ and 9‐positions of dmp exert steric demands that further hinder flattening distortions. Thus, mutual steric interactions of the chelating ligands strongly reduce flattening distortions and as a consequence radiationless relaxations.

Figure 1.4Perspective drawing of Cu(dmp)(phanephos)+ 21 (enantiomer R) resulting from X‐ray crystallography studies.

Source: Ref. [92]. Adapted with permission of the Royal Society of Chemistry.

Indeed, Cu(dmp)(phanephos)+ 21 displays intense green‐yellow luminescence at ambient temperature even in solution (Figure 1.5). For instance, in dichloromethane (DCM) the quantum yield ΦPL is 40% (Table 1.2). With this ΦPL value and the measured decay time of τ(CH2Cl2, 300 K) = 10 μs, the nonradiative rate knr can be estimated, using the relation


Figure 1.5Ambient temperature absorption and emission spectra of Cu(dmp)(phanephos)+ 21 recorded in diluted (c ≈ 3 × 10−5 M−1) DCM solution (solid lines) and as [Cu(dmp)(phanephos)](PF6) powder (dashed line). LC and MLCT denote ligand centered (π–π*) and metal‐to‐ligand charge‐transfer (d–π*) transitions, respectively.

Source: Ref. [92]. Adapted with permission of the Royal Society of Chemistry.

Table 1.2 Luminescence properties of [Cu(dmp)(phanephos)](PF6) 21 in dichloromethane, PMMA (poly(methyl methacrylate)), and as powder.

T = 300 K T = 77 K
λmax (nm) τ (μs) ΦPL (%) kr (s−1) knr (s−1) λmax (nm) τ (μs) ΦPL (%) kr (s−1) knr (s−1)
CH2Cl2 558 10 40 4.0 × 104 6.0 × 104 548 130 60 4.6 × 103 3.1 × 103
PMMA 535 20 65 3.3 × 104 1.8 × 104 567 170 60 3.5 × 103 2.4 × 103
Powder 530 14 80 5.7 × 104 1.4 × 104 562 240 70 2.9 × 103 1.3 × 103

Source: Ref. [92]. Reproduced with permission of Royal Society of Chemistry.

The resulting rate of knr = 6.0 × 104 s−1 represents one of the smallest knr values found for Cu(I) complexes in liquid solution so far [31]. This proves the validity of the molecular design strategy applied to Cu(dmp)(phanephos)+ 21. The excited state distortions and, thus, the extent of nonradiative relaxation can further be reduced by increasing the rigidity of the environment. Using the ΦPL and τ data summarized in Table 1.2, the rates knr for a polymer matrix and a solid sample are found to be of knr = 1.8 × 104 s−1 (poly(methyl methacrylate), PMMA) and knr = 1.4 × 104 s−1 (powder), respectively. Interestingly, the changes of knr induced by the strongly different matrix rigidities are distinctly less than one order of magnitude. This is regarded as being relatively small, and it indicates that the excited state distortions are already partly suppressed at the level of molecular structure.

The discussed trend is also reflected by the small extent of spectral changes observed for the emission spectra. The emission maximum at T = 300 K of compound 21 is found at λmax = 558 nm in DCM. For the compound doped in PMMA, it lies at λmax = 535 nm and at 530 nm for a powder sample, respectively. Accordingly, the largest blue shift Δλmax (fluid solution → powder) amounts to Δλ(max) = 28 nm (≈950 cm−1, 118 meV) only. For comparison, for the blue‐green emitting Cu(pop)(pz2BH2) 25, Δλ(max) was found to be as large as 99 nm (≈4200 cm−1) [95]. In the latter case, the large shift is related to the more flexible molecular structure that enables significant flattening distortions in the MLCT excited states. In compound 21, such distortions are largely suppressed due to the large bite angle and bulky phanephos ligand.

1.3.3 TADF Properties

As expected for a TADF material, the emission decay time τ is strongly dependent on temperature (Table 1.2). Upon heating from T = 77 K to ambient temperature, the decay time becomes about one order of magnitude shorter with the quantum yield remaining approximately equally high. Thus, the change of τ is connected to a change of the radiative decay rate kr. This rate is determined according to the following relation:


In Table 1.2, radiative decay rates are given for different environments and temperatures. In particular, for the powder material kr amounts to 2.9 × 103 s−1 at T = 77 K and increases with temperature increase to 5.7 × 104 s−1 at ambient temperature, i.e. by a factor of almost 20. Thus, different emission mechanisms are active in the two temperature regimes.

The temperature dependence of the decay time is studied in more detail for a powder sample (Figure 1.6). Between 20 K and about 120 K, the decay time is almost constant and as long as τ ≈ 240 μs (plateau). The assignment of this emission to a T1 → S0 phosphorescence is straightforward. Obviously, in this plateau range no other decay mechanism is activated (thermal energy at ≈120 K amounts to ≈83 cm−1 or ≈10 meV). However, with further temperature increase, a steep decrease of the decay time is observed, which is due to the increase of the radiative decay rate kr as discussed above. This change is related to a growing involvement of the higher‐lying S1 singlet state with its much higher decay rate of the transition to the electronic ground state S0. The S1 state is thermally activated from the lower‐lying T1 state. Hence, the ambient temperature emission represents (largely) a TADF (see also below). It exhibits a decay time of τ(TADF) = 14 μs at 300 K.

Figure 1.6(a) Emission decay time of [Cu(dmp)(phanephos)](PF6) 21 powder versus temperature. The emission was excited with a pulsed UV laser at λexc = 355 nm (pulse width 7 ns) and detected at λdet = 550 nm. The solid line represents a fit of Eq. ( 1.1 ) to the experimental data fixing the phosphorescence decay time τ(T1) = 240 μs (plateau at 20 K < T < 120 K). The resulting fit parameters are ΔE(S1–T1) = 1000 cm−1 and τ(S1) = 40 ns. τ(TADF) = 14 μs is the decay time dominated by the delayed fluorescence at ambient temperature. (b) Energy level diagram for Cu(dmp)(phanephos)+. The radiative rate for the S1 → S0 transition kr(S1 → S0) was determined according to Eq. (1.3) assuming τ(S1) = 40 ns (fit) and ΦPL = 80% (measured at ambient temperature). The energy of the T1 → S0 0–0 transition is estimated from the high‐energy flank of the 77 K emission spectrum (not reproduced).

Source: Ref. [92]. Reproduced with permission of Royal Society of Chemistry.

The temperature dependence of τ = τ(T), as displayed in Figure 1.6a, can be interpreted in terms of a three states kinetic model involving the electronic ground state S0, the lowest triplet state T1, and the lowest excited singlet state S1, as expressed by Eq. ( 1.1 ). By fitting this equation to the measured decay times and inserting the measured decay time τ(T1) = 240 μs (plateau at 20 K < T < 120 K), values of τ(S1) = 40 ns and ΔE(S1–T1) = 1000 cm−1 are obtained. The value of ΔE(S1–T1) = 1000 cm−1 corresponds well to the spectral blue shift of 1070 cm−1 observed for the emission maximum with temperature increase from T = 77 K (λmax = 562 nm) to 300 K (λmax = 530 nm) (Table 1.2). This correspondence between the activation energy and the spectral shift upon temperature increase represents a further support for the assignment of the ambient temperature emission as TADF.

For completeness, it is remarked that the emission at ambient temperature frequently does not only represent TADF but also contains some T1 → S0 (phosphorescence) contribution. (Prompt fluorescence is not observed due to fast ISC of the order of a few tens of picoseconds [118, 122, 133, 134, 154, 156158].) According to Refs [33, 97], the intensity ratio (S1)I(T1) can be expressed by




one obtains


kr(I), kr(II), and kr(III) are the rates of transitions from the triplet substates I, II, and III of the lowest triplet state (T1) to the ground state (S0), respectively. kr(T1) = kr(T1 → S0) represents the average transition rate from the three triplet substates to the ground state. We will return to the average decay properties later in Section 1.4 (compare Eq. 1.9). kr(S1) = kr(S1 → S0) is the transition rate from the lowest excited singlet state (S1) to the ground state, and ΔE(S1T1) is the energy gap between states S1 and T1 (compare [31, 33]). For Cu(dmp)(phanephos)+ 21 at T = 300 K with ΔE(S1–T1) = 1000 cm−1 (fit, Figure 1.6b), kr(S1) = 2 × 107 s−1 (fit), and kr(T1) = 2.9 × 103 s−1 (measured at 77 K; Table 1.2), one obtains I(S1)/I(T1) ≈ 20. Thus, the emission spectrum at ambient temperature is clearly dominated by TADF (≈95% TADF, ≈5% phosphorescence from T1).

1.3.4 Radiative S1 → S0 Rate, Absorption, and Strickler–Berg Relation

The radiative rate kr(S1) for the electronic transition between the excited singlet state S1 and the ground state S0 can be determined independently from an analysis of the absorption spectrum [92]. According to Figure 1.7, the absorption peak of lowest energy centered at ≈26 300 cm−1 (380 nm) and showing a slight spectral overlap with the emission is assigned to the S0 → S1 transition. Thus, a (radiative) transition rate for the related emission S1 → S0 can be estimated using the well‐known Strickler–Berg relation between the radiative decay rate of the spontaneous emission and the strength of the corresponding absorption [159]. Accordingly, kr(S1) can be expressed as


where c is the speed of light in vacuum, NA is the Avogadro number, and n is the refractive index of the medium. displays the reciprocal of the mean value of the third power of the fluorescence energy (cm−1) (weighted with the emission intensity at each value of the spectrum). The integral represents the absorption strength of the S0 → S1 band. is the molar absorption (extinction) coefficient at a given energy . If is approximated by the third power of the emission maximum , Eq. 1.5 can be rewritten as


with const ≈ 2.88 × 10−12 s−1 mol cm.

Figure 1.7Absorption spectrum of Cu(dmp)(phanephos)+ 21 in CH2Cl2 at ambient temperature. (Compare Figure 1.5.) The red‐shaded area approximates the lowest absorption. The integrated intensity is determined to 3.7 × 105 cm2 mol−1. The vertical line at 22 670 cm−1 represents the calculated energy of the S0 → S1 MLCT transition with a relatively small oscillator strength of f = 0.0621. The TD‐DFT calculation was performed for the ground state optimized geometry at the B3LYP/def2‐SVP level of theory.

Source: Ref. [92]. Adapted with permission of Royal Society of Chemistry.

From an integration of the lowest energy absorption band estimated by the shaded area as shown in Figure 1.7, a value of  = 3.7 × 105 cm2 mol−1 is obtained. Thus, for  = 17 500 cm−1 (emission maximum in CH2Cl2 at ambient temperature and with n = 1.42), a spontaneous fluorescence rate of kr(S1 → S0) ≈ 1.2 × 107 s−1 is obtained. With respect to the different approximations made, this value corresponds reasonably well to the fluorescence decay rate of kr(S1 → S0) ≈ 2 × 107 s−1 as determined from the temperature dependence of the emission decay time as discussed above (Figure 1.6).

The value of kr lying in the range of 1–2 × 107 s−1 corresponds to a moderately allowed transition, as it is expected for a S0 → 1MLCT transition. The moderate allowedness of this transition is also reflected in the value of the small oscillator strength resulting from TD‐DFT calculations (Figure 1.7). For the optimized singlet ground state geometry at the B3LYP/def2‐SVP level of theory, the oscillator strength for the S0 → S1 transition of ƒ = 0.0621 is obtained [92]. With a simple relation, the radiative rate can be estimated according to [124]:


where is the energy (in wave numbers) corresponding to the maximum wavelength of absorption. With the calculated value of f = 0.0621 and the S0 → S1 transition energy of 22 670 cm−1, a radiative rate of 3 × 107 s−1 is estimated, being in agreement with the value of kr(S1 → S0) = 2 × 107 s−1 as determined experimentally.

With respect to the approximations made applying the different and independent methods, the kr(S1 → S0) values (2 × 107 s−1 from the decay time analysis, 1.2 × 107 s−1 from the absorption strength analysis, and 3 × 107 s−1 from a TD‐DFT approach) are in good agreement. This is an important result, since it strongly supports the TADF assignment with respect to the involvement of the singlet S1 state in the emission process at ambient temperature. Moreover, it is concluded that the geometry changes that still take place upon excitation do not significantly alter the S1 → S0 transition rate determined for the relaxed geometry (from emission properties) as compared with the rate determined for the unrelaxed molecular geometry (from absorption).

1.4 Case Study: TADF of a Cu(I) Complex with Small ΔE(S1–T1)

As already addressed, Cu(I) complexes display a large variety of TADF properties. In particular, this is related to a large range of energy separations ΔE(S1–T1) between the lowest singlet and triplet state being larger than 103 cm−1 (120 meV) or as small as a few hundred cm−1. In Section 1.3, a complex with a relatively large ΔE(S1–T1) was presented. In the present case study, we will focus on a complex characterized by a small ΔE(S1–T1) value and discuss related TADF properties.

1.4.1 DFT and TD‐DFT Calculations

In Figure 1.8, frontier orbital plots of Cu(dppb)(pz2Bph2) 2 (with dppb = 1,2‐bis(diphenylphosphino)benzene and pz2Bph2 = diphenylbis(pyrazolylborate)) are reproduced together with the complex' chemical structure. The HOMO is derived from a metal 3d atomic orbital with significant contributions from the coordinating phosphorus and nitrogen atoms, whereas the LUMO is localized on the o‐phenylene ring of the dppb ligand. Thus, similarly to Cu(dmp)(phanephos)+ 21, the orbitals display distinctly different spatial distributions, and the related HOMO → LUMO excitations are of CT character. It can be further shown by TD‐DFT calculations that the lowest excited singlet state S1 and the triplet state T1 are of more than 90% of HOMO–LUMO character [96]. Due to the distinct involvement of the metal, these states are assigned to largely represent 1MLCT and 3MLCT states, respectively. The significant spatial separation of HOMO and LUMO allows us to predict a relatively small exchange interaction and, thus, a small singlet–triplet energy separation ΔE(S1–T1). Indeed, TD‐DFT calculations in the triplet state optimized geometry give a small value of ΔE(S1–T1) = 72 meV (≈580 cm−1), estimated as the energy difference between vertical S0 → S1 and S0 → T1 transitions [96] (Table 1.3), as being three times smaller than the value calculated for Cu(dmp)(phanephos)+ 21. Again, the ΔE(S1–T1) value calculated as the energy difference between the computed vertical excitations is overestimated. The experimentally determined activation energy amounts to ΔE(S1–T1) = 370 cm−1 (46 meV).

Figure 1.8Chemical formula and contour plots of the HOMO and LUMO of Cu(dppb)(pz2Bph2) 2 resulting from DFT calculations for the triplet state geometry at the B3LYP/def2‐SVP level of theory. The frontier orbitals exhibit distinctly different spatial distributions. The HOMO is mainly composed of the copper 3d and phosphorus sp3 atomic orbitals, while the LUMO represents a π* orbital of the dppb ligand. Compare [96].

Table 1.3 Vertical transition energies, oscillator strengths, and main orbital contributions of selected electronic transitions of Cu(dppb)(pz2Bph2) 2 resulting from TD‐DFT calculations for the optimized triplet state geometry (T1 state) at the B3LYP/def2‐SVP level of theory.

Transition Energy (eV) Oscillator strength Main contribution
S0 → T1 1.303 0
S0 → T2 1.926 0
S0 → T3 2.404 0
S0 → T4 2.601 0
S0 → T5 2.681 0
S0 → S1 1.375 0.0016
S0 → S2 2.033 0.0038
S0 → S3 2.623 0.0547
S0 → S4 2.746 0.0253
S0 → S5 2.814 0.0727
S0 → S6
2.848 0.0102

The lowest S0 → Sn transition of HOMO−n → LUMO character that contains different Cu‐3d character than the HOMO and that can exhibit SOC to the T1 state is marked (see text).

aSOC to T1 possible.

Source: Refs [31, 96]. Reproduced with permission of Elsevier.

According to the spatial separation of the molecular orbitals involved in the transition between the electronic ground state S0 and the lowest excited singlet state S1 (1MLCT), it can be predicted that the transition dipole moment and, thus, the oscillator strength of the transition is relatively small. Indeed, TD‐DFT calculations performed for the T1 geometry at the B3LYP/def2‐SVP level of theory result to f = 0.0016, being more than one order of magnitude smaller than the value 0.0201 calculated for the S0 → S1 transition of complex [Cu(dmp)(phanephos)]+ 21. Further results of TD‐DFT calculations are presented in Table 1.3 that are later used to explain effects of SOC in complex 2.

1.4.2 Emission Spectra and Quantum Yields

Emission properties of Cu(dppb)(pz2Bph2) 2 were studied for powder samples over a wide temperature range from T = 1.5 to 300 K. Figure 1.9 displays representative emission spectra. Emission maxima, quantum yields, and decay times are collected in Table 1.4.

Figure 1.9Luminescence spectra of Cu(dppb)(pz2Bph2) 2 powder recorded at different temperatures.

Source: Ref. [96]. Reproduced with permission of American Chemical Society.

Table 1.4 Emission data for a powder sample of Cu(dppb)(pz2Bph2) 2.

Temperature (K) λmax (nm) ΦPL (%) τ (μs) kr (s−1)a knr (s−1) a
300 535    70 3.3 210 × 103 9 × 104
 80 535 ≈100b 300 3.3 × 103
 30 548 ≈100b 1200 8.3 × 102

akr and knr are determined by the use of Eqs. (1.2) and ( 1.3 ), respectively.

bIt is assumed that the quantum yield ΦPL at T = 30 K amounts to 100%, as determined experimentally at T = 77 K.

Source: Ref. [96]. Reproduced with permission of American Chemical Society.

The compound shows intense green‐yellow luminescence at all temperatures in the investigated range of 1.5–300 K, with quantum yields ΦPL of 70% at ambient temperature and about 100% at T = 77 K. The spectra are broad and unstructured, which correlates with the predicted MLCT character of the corresponding electronic transitions. With temperature increase to T ≥ 30 K, only a small blue shift is observed with the emission maximum λ(max) shifting from 548 nm at 1.5 K (not shown) and 30 K to 535 nm at 80 and 300 K. This is a consequence of the thermal activation of the TADF decay path via the higher‐lying S1 state above T ≈ 50 K (see below).

1.4.3 The Triplet State T1 and Spin–Orbit Coupling

The emission spectra do not display distinct changes with temperature change. However, the decay kinetics varies drastically even at very low temperature (below T = 20 K). This is related to the properties of the triplet state and its substates. Therefore, before discussing effects of thermal activation of the singlet state, the TADF effect, we want to focus on triplet state properties.

At T = 1.5 K, the decay curve is distinctly nonmonoexponential. The decay curve can be fitted with a bi‐exponential function with the time constants of 7.7 ms and 470 μs (Figure 1.10). These different decay constants are assigned to emissions from the three individual triplet T1 substates I, II, and III with τI ≈ τII = 7.7 ms and τIII = 470 μs, respectively. It is remarked that for Cu(I) complexes, frequently a bi‐exponential decay behavior is observed and not a tri‐exponential one as expected for three triplet substates [57, 88, 160, 161]. This is due to the fact that the decay times of two substates are often very similar [33, 9597]. Theoretical calculations based on SOC‐TD‐DFT (ADF2014) computations support this assignment [162].

Figure 1.10(a) Emission decay curve of Cu(dppb)(pz2Bph2) 2 at 1.5 K recorded for a powder sample after pulsed excitation at λexc = 372 nm and with signal detection at λdet = 550 nm. (b) Energy level scheme showing the triplet substates and the related decay paths at T = 1.5 K at vanishing fast equilibration.

Source: Ref. [96]. Reproduced with permission of American Chemical Society.

At low temperature of T = 1.5 K, these T1 substates are not thermally equilibrated due to slow SLR [57, 88, 137, 160, 161]. This behavior is related to small ZFSs of the T1 state of less than 1 or 2 cm−1 (0.1 or 0.2 meV) [9, 57, 70, 88, 160, 161]. Such a small ZFS value is a consequence of weak SOC of the T1 substates with higher‐lying states. Furthermore, the emission decay time of τ(T1) = 1200 μs (at 30 K) is extremely long if compared with Cu(dmp)(phanephos)+ 21 (Section 1.3) and many other Cu(I) complexes [9, 31, 33, 35, 40, 42, 46, 50, 70, 92, 9598, 100, 135, 163, 164]. Again, this is a consequence of the weak SOC with respect to the lowest triplet state.

Obviously, the (weak) allowedness of the T1 → S0 transition is not dominantly related to the SOC constant of copper, which is with ζ = 857 cm−1 [165] not very small. More important is the extent of mixing of energetically higher‐lying singlet state(s). In a very simplified perturbational approach, the radiative rate can be described by [31, 69, 70, 166]:


HSO is the SO operator. E(Sm) and E(T1) are the (unperturbed) energies of the (pure) singlet state Sm and the (pure) triplet state T1, respectively. In this simple model, it is assumed that one higher‐lying singlet state Sm couples dominantly to the state T1, i.e. to at least one T1 triplet substate. is the dipole matrix element with the dipole operator .

A discussion of the energy denominator and its size is particularly helpful. Presumably, SOC with the energetically most proximate singlet state of adequate character represents a leading contribution to the radiative rate. Therefore, Eq. 1.8 shows only one mixing singlet state, being the state Sm, although several other singlet states may additionally contribute to the allowedness of the T1 → S0 transition.

Quantum mechanical considerations show that SOC between a triplet state T1 and a singlet state S1 that both stem from the same orbital configuration, for example, from the HOMO → LUMO excitation, is negligible as for efficient SOC different d orbitals must be involved in the coupling states [9, 30, 31, 6972, 75, 167].

The TD‐DFT calculations presented above for compound 2 show that the energetically nearest singlet state that involves another d orbital than the T1 state is the singlet state S6. It originates from the HOMO − 1 → LUMO electronic transition. According to Table 1.3, the energy separation that is responsible for dominant SOC amounts to ΔE(S6−T1) = 1.545 eV (≈12 500 cm−1) (ΔE(HOMO − (HOMO−1)) = 1.4 eV). As a consequence of this large energy denominator (Eq. 1.8), the triplet state does not experience effective SOC with state S6. Hence, the phosphorescence decay time is expected to be very long. Indeed, this is found for compound 2 with τ(T1 → S0) = 1200 μs. For comparison, the phosphorescence decay time of a compound that exhibits a much smaller energy denominator is given. For example, Cu2Cl2(N^P)2 18 with an energy separation between HOMO and HOMO−1 (that involve different d orbitals) amounts to only 0.378 eV (3000 cm−1) [31, 97]. Since this HOMO−1 → LUMO excitation essentially defines the S2 state, the energy separation to the T1 state is much smaller than for compound 2. Accordingly, the mixing of S2 and T1 becomes distinctly stronger (Eq. 1.8), and, hence, the triplet decay time amounts to only τ(T1 → S0) = 43 μs [31, 97]. Thus, the T1 → S0 allowedness of compound 18 is by a factor of almost 30 higher than found for compound 2.

The size of the squared dipole matrix element with the dipole operator is also of importance for the radiative rate kr(T1 → S0) (or more exactly for the rate of the individual triplet substate that mixes with Sm). The corresponding value is proportional to the oscillator strength or the molar absorption coefficient of the singlet–singlet transition S0 → Sm, whereby Sm is the singlet state that can mix with the T1 state via SOC [69, 72]. With respect to the corresponding allowedness, it is referred to Table 1.3.

For completeness, it is remarked that literature discussions frequently assume dominating SOC between T1 and S1. However, for compound 2, the corresponding energy separation is very small amounting to only ΔE(S1–T1) = 370 cm−1 (see below). As a consequence, relatively strong SOC would be expected to occur. Above, it has been demonstrated that this is not the case. Obviously, the simple literature approach is not suited.

1.4.4 Temperature Dependence of the Emission Decay Time and TADF

Let us focus on the temperature dependence of the emission decay time. With temperature increase, the SLR processes become faster (presumably according to a Raman process of SLR [137, 138, 160]), resulting in a fast thermalization of the three T1 substates. At sufficiently high temperature, e.g. above T = 10 or 20 K, an average emission decay time τav is normally observed as expressed by Eq. 1.9 [9, 33, 57, 70, 88, 95, 96, 137, 139, 161]:


Inserting the decay times of τI ≈ τII = 7.7 ms and τIII = 470 μs, as determined at T = 1.5 K, one obtains τav = 1250 μs. Almost the same value of τ(T1) = 1200 μs (monoexponential decay) is measured at T = 30 K (Figure 1.11). Thus, the assignments of the decay times we made above are validated.

Figure 1.11(a) Emission decay profiles of Cu(dppb)(pz2Bph2) 2 (powder) at 30, 80, and 300 K recorded after pulsed excitation at λexc = 378 nm and detected at λdet = 540 nm. (b) Emission decay time τ versus temperature. The solid line represents a fit of Eq. ( 1.1 ) to the experimental τ(T) values fixing τ(T1) = 1.2 ms as measured at T = 30 K. The fit parameters are τ(S1) = 180 ns and ΔE(S1–T1) = 370 cm−1, respectively. (c) Energy level diagram of Cu(dppb)(pz2Bph2) 2. Both competing emission processes are marked: Phosphorescence with a decay time of τ(T1) = 1.2 ms dominating the photophysical behavior at temperatures below about 50 K and TADF determining the emission properties at higher temperatures with a measured decay time at 300 K of 3.3 μs (with the emission quantum yield of ΦPL = 70%).

Source: Ref. [96]. Reproduced with permission of American Chemical Society.

Figure 1.11 displays emission decay curves and the temperature dependence of the decay time for the range of 20 K ≤ T ≤ 300 K. From T = 20 K to about 40 K, the decay time remains constant (plateau) with τ(T1) = 1200 μs. With further temperature increase, the decay time decreases drastically to τ(80 K) = 300 μs and τ(300 K) = 3.3 μs. The plot of the measured τ values versus temperature has a characteristic form of an s‐shaped curve similar to the one obtained for Cu(dmp)(phanephos)+ 21 (Figure 1.6a) but with the point of maximum slope shifted from 180 to 70 K for compound 2. The radiative rate kr, determined by the use of Eq. ( 1.3 ), rises from the low‐temperature value of kr(30 K) = 8.3 × 102 s−1 to kr(80 K) = 3.3 × 103 s−1, and to kr(300 K) = 2.1 × 105 s−1, respectively (Table 1.4). The latter value represents a rate increase by a factor of 250 as compared with the kr(30 K) value. This drastic increase of the radiative rate combined with the spectral blue shift of 13 nm with temperature increase (Figure 1.9) is explained by an involvement of a higher‐lying state that carries a higher radiative rate, hence demonstrating the occurrence of TADF.

An analysis of the decay time data according to the Boltzmann‐type Eq. ( 1.1 ) leads to an activation energy of ΔE(S1–T1) = 370 cm−1 and a prompt fluorescence decay rate of kr(S1 → S0) = 3.9 × 106 s−1 (taking the emission quantum yield of ΦPL = 70% as measured at 300 K into account) (Figure 1.11).1 Again, it is stressed that the prompt fluorescence could not be observed directly in our experiments conducted with nanosecond time resolution. This agrees with measured ISC time of the order of several picoseconds [118, 122, 134, 154, 156158]. The resulting energy level diagram and the relevant rates are summarized in Figure 1.11c.

The value of ΔE(S1–T1) = 370 cm−1 represents one of the smallest splitting values found so far [31, 96]. Accordingly, Cu(dppb)(pz2Bph2) 2 shows a very short TADF decay time of τ(TADF) = 3.3 μs, being one of the shortest values reported so far for Cu(I) complexes (compare Section 1.6).

The experimental characterization of the luminescence behavior of Cu(dppb)(pz2Bph2) 2 supports the predictions based on model calculations, as developed above. According to the distinct spatial separation of the orbitals involved in the lowest excited states, the (formal) fluorescence decay time of τ(S1) = 180 ns (calculated from kr(S1 → S0) = 3.9 × 106 s−1 and ΦPL = 70%) is relatively long for a spin‐allowed transition. For instance, it is about four times longer than the decay time of the S1 state as determined for Cu(dmp)(phanephos)+ 21 (Section 1.3). A large difference of the τ(S1) lifetimes could be predicted by the TD‐DFT calculations, as the oscillator strength of the corresponding S0 → S1 transition (calculated for the T1 state geometry), being 0.0016 for Cu(dppb)(pz2Bph2) 2 (Table 1.3), is more than an order of magnitude smaller than calculated for Cu(dmp)(phanephos)+ 21 with f = 0.0201 (Section 1.3).

Interestingly, the case studies presented in Sections 1.3 and 1.4 focusing on two complexes with very different allowedness of the S1 ↔ S0 transitions is displayed inversely in the size of the energy splitting ΔE(S1–T1). For Cu(dmp)(phanephos)+ 21, it amounts to 1000 cm−1 (120 meV), while for Cu(dppb)(pz2Bph2) 2 a value of 370 cm−1 (46 meV) is found. This important relation will be addressed in Section 1.5.

Moreover, the photophysical studies presented in Sections 1.3 and 1.4 reveal an important practical conclusion concerning the assignments of emission processes. Both compounds show a phosphorescence plateau at low temperatures, at T < 120 K in the case of Cu(dmp)(phanephos)+ 21 with ΔE(S1–T1) = 1000 cm−1 and at T < 50 K in the case of Cu(dppb)(pz2Bph2) 2 with ΔE(S1–T1) = 370 cm−1, respectively. At ambient temperature, the emission of both compounds represents TADF. Importantly, in many laboratories only two temperature regimes of T = 300 K (ambient temperature) and T = 77 K (boiling point of nitrogen) are easily accessible. Therefore, characterization of new compounds is usually performed at these two temperatures. Based on these results, preliminary conclusions concerning the character of the emissive states and the emission mechanism(s) are drawn. For Cu(dmp)(phanephos)+ 21, with the measured decay time of τ(77 K) = 240 μs (plateau range between 20 and 120 K) and τ(300 K) = 14 μs, respectively, the emissions at low temperature and at ambient temperature would be assigned correctly as phosphorescence from the T1 state and as TADF, respectively. For Cu(dppb)(pz2Bph2) 2 with τ(77 K) = 300 μs and τ(300 K) = 3.3 μs, a similar assignment would not be correct. As shown in Figure 1.11, the phosphorescence decay time τ(T1) = 1200 μs (plateau for T ≤ 40 K) is four times longer than found at 77 K. Thus, the emission at 77 K cannot be assigned as phosphorescence. On the contrary, it represents mainly delayed fluorescence (TADF) even at T = 77 K. The ratio of TADF to phosphorescence is estimated (by the use of Eq. (1.4c)) to 75% : 25%. Correspondingly, the emission spectra recorded at T = 77 K and 300 K are not shifted with respect to each other as for the two temperatures, the spectral maxima of compound 2 are found at 535 nm. Thus, conclusions made on the basis of 77 K and ambient temperature measurements must be taken with care. The risk of possible misinterpretation is particularly large when the energy separation ΔE(S1–T1) is small.

1.5 Energy Separation ΔE(S1–T1) and S1 → S0 Fluorescence Rate

In Section 1.2, it was already shortly discussed that a reduction of the energy separation between the lowest singlet S1 and triplet T1 state is connected with a decrease of the radiative singlet–singlet rate kr(S1 → S0). This relation has also been addressed in the two previous sections based on case studies. Since both photophysical parameters crucially determine the TADF behavior, in particular, the TADF decay time, we want to focus in this section on a simple model that may explain this relation.

1.5.1 Experimental Correlation Between ΔE(S1–T1) and kr(S1 → S0) for Cu(I) Compounds

During the last years, the ΔE(S1–T1) energy separations and the S1 → S0 fluorescence decay times have been determined for a large number of Cu(I) compounds that show TADF. Both parameters result from fit procedures by the use of Eq. ( 1.1 ). For two compounds, this has been discussed in detail in Sections 1.3 and 1.4. It is stressed again that the prompt fluorescence was not observed directly, but the corresponding kr(S1 → S0) rate could be determined. In Table 1.5, adapted from Ref. [31], we summarize the corresponding data for Cu(I) compounds. The fitting procedure leads to the formal (prompt) decay time τ(S1) or to the rate k(S1 → S0). From this information and by the use of the measured photoluminescence quantum yield (ΦPL), one can easily determine the radiative rate kr(S1 → S0) applying Eq. ( 1.3 ).

Table 1.5 Energy separation ΔE(S1–T1) and radiative rate kr(S1 → S0) determined by fitting procedures applying Eq. ( 1.1 ) to experimental decay time data. τ(S1) is the (formal) prompt fluorescence decay time and ΦPL the emission quantum yield.

Source: Ref. [31]. Adapted with permission of Elsevier.

Compound ΔE(S1−T1) (cm−1) τ(S1) (ns) ΦPL (300 K) kr(S1 → S0) (106 × s−1) References
1 Cu2I2[MePyrPHOS)(Pph3)2  270 570 0.97 1.7 [30]
2 Cu(dppb)(pz2Bph2)  370 180 0.70 3.9 [96]
3 [Cu(μ‐Cl)(PNMe2)]2  460 210 0.45 2.1 [33]
4 [Cu(μ‐Br)(PNMe2)]2  510 110 0.65 5.9 [33]
5 [Cu(μ‐I)(PNMe2)]2  570  90 0.65 7.2 [33]
6 Cu2Cl2(dppb)2  600  70 0.35 5.0 [107]
7 [Cu(μ‐I)(PNpy)]2  630 100 0.65 6.5 [33]
8 Cu(pop)(pz2BPh2)  650 170 0.9 5.3 [9, 95]
14 Cu(tmbpy)(pop)+  720 160 0.55 3.4 [35]
15 (IPr)Cu(py2‐BMe2)  740 160 0.76 4.8 [34]
16 [Cu(PNPtBu)]2  786  79 0.57 7.2 [46]
17 Cu2I2(MePyrPHOS)(dpph)  830 190 0.88 4.6 [30]
18 Cu2Cl2(N^P)2  930  40 0.92 23 [97]
19 CuCl(Pph3)2(4‐Mepy)  940  47 0.99 21 [98]
21 Cu(dmp)(phanephos)+ 1000  40 0.80 20 [92]
22 Cu(pop)(pz4B) 1000  80 0.9 11 [95]
23 CuBr(Pph3)2(4‐Mepy) 1070  41 0.95 23 [98]
24 CuI(Pph3)2(4‐Mepy) 1170  14 0.66 47 [98]
25 Cu(pop)(pz2BH2) 1300  10 0.45 45 [70, 95]

In Figure 1.12, the kr(S1 → S0) data are plotted versus ΔE(S1–T1). It is obvious that with decreasing energy splitting, the allowedness of the S1 → S0 transition decreases drastically. For example, if compound 25 is compared with compound 1, ΔE(S1–T1) decreases from 1300 to 270 cm−1, while the allowedness of the S1 → S0 transition decreases by a factor of about 26. In a simple consideration, using Eq. ( 1.1 ), it can be seen that the TADF decay time will not become shorter, when ΔE(S1–T1) reaches 300 to 200 cm−1 (≈40 or 25 meV). Such a minimum decay time lies in the range of several microsecond [168], at least for the type of Cu(I) compounds discussed here.

Figure 1.12Radiative decay rate kr(S1–S0) plotted versus ΔE(S1–T1) for different Cu(I) complexes that show TADF at ambient temperature (data from Table 1.5). The fit curve represents an exponential function as guide for the eye.

Source: Ref. [31]. Reproduced with permission of Elsevier.

1.5.2 Quantum Mechanical Considerations

In this section, we want to illustrate on a simple quantum mechanical basis, following [31], why a small energy separation ΔE(S1–T1) between the lowest singlet S1 and triplet T1 state is related to a fast radiative rate of the S1 → S0 transition, i.e. a small kr(S1 → S0) value. Let us assume that S1 and T1 can be described by a one‐electron transition from HOMO ϕH to LUMO ϕL. In this situation, simple expressions can be given for the radiative rate kr(S1–S0) (= kr(S1 → S0)) and the energy splitting ΔE(S1–T1).

The radiative rate may be obtained from the transition dipole moment , which is approximately given by


is the dipole vector and e is the electron charge.

Thus, the radiative rate can be expressed by (see Ref. [169], p. 159), [31]:


with the numerical constant C = 16π3/(3ε0hc3), wherein ε0 is the vacuum permittivity, h is Planck's constant, and c is the velocity of light. ν = ΔE(S1–S0)/h is the transition frequency and n the refractive index.

The energy separation ΔE(S1–T1) can be expressed in this approximation by twice the exchange integral KHL for HOMO and LUMO (see Ref. [[130], p. 86]) giving






It is an important result that both the exchange interaction and hence the energy splitting ΔE(S1–T1) (Eq. (1.13)) as well as the radiative rate (Eq. (1.12)) depend quadratically on the product of ϕH(r)ϕL(r) or the squared overlap of HOMO and LUMO.2 Accordingly, it becomes obvious that ΔE(S1–T1) and kr(S1 → S0) correlate. A small HOMO–LUMO overlap implies small ΔE(S1–T1) and small kr(S1 → S0). This relation is schematically illustrated in Figure 1.13.

Figure 1.13Schematic illustration of the relation between energy splitting ΔE(S1–T1) and the radiative decay rate kr(S1–S0) on the spatial overlap of HOMO and LUMO.

Source: Ref. [31]. Reproduced with permission of Elsevier.

The simple qualitative model presented above allows us to understand the experimental results as displayed in Figure 1.12. The model's basic assumption is that the low‐lying singlet S1 and triplet T1 states, originating from the HOMO → LUMO excitation, are energetically well separated from higher‐lying energy states. Accordingly, in the scope of this material class (or this model), we cannot reduce the TADF decay time distinctly below a few microsecond. However, the simple model, being valid for the compounds shown in Table 1.5, does not contain mixing of the singlet state S1 with a higher‐lying singlet state that carries high oscillator strength with respect to the transition to the electronic ground state. In principle, such mixing, induced by CI, might significantly increase the radiative rate of the lowest singlet–singlet transition without strongly altering the energy splitting ΔE(S1–T1). Presumably, such Cu(I) complexes may be developed in the future. In Section 1.6, we will address this challenge shortly again.

1.6 Design Strategies for Highly Efficient Ag(I)‐Based TADF Compounds

In contrast to Cu(I) complexes, TADF materials based on Ag(I) are rarely reported [104, 106109, 171]. This is related to the higher oxidation potential of Ag+ compared with Cu+ [171]. Accordingly, the 4d orbitals of Ag(I) complexes lie mostly energetically below ligand‐centered (LC) orbitals. As a consequence, low‐lying states of 3LC character determine the emission properties [106, 172175]. Thus, Ag(I) complexes often do not exhibit TADF, but long‐lived phosphorescence and sometimes even slow ISC [174]. Therefore, designing Ag(I) complexes that show TADF represents an optimization task. In this respect, it is required to destabilize the energetically lower‐lying 4d orbitals by an organic ligand with good electron‐donating ability. This may be attainable with electron‐donating bidentate phosphine ligands. Indeed, it has already been demonstrated that this strategy is successful. For example, Ag2Cl2(dppb)2 20 represents a blue light‐emitting material that shows efficient TADF with ΦPL = 97%, though with a relatively long decay time of τ(TADF, 300 K) = 15 μs (Table 1.1) [107]. Another attractive ligand is nido‐carborane‐bis‐(diphenylphosphine) (P2‐nCB) [176]. It coordinates via phosphine groups and, thus, induces substantial electron‐donating character. Additionally, electron donation is strongly enhanced by the negative charge of the nido‐carborane moiety. Suitable complexes can be built using the (P2‐nCB) ligand in combination with 1,10‐phenanthroline (phen) or substituted phen ligands. Accordingly, a series of neutral Ag(I) complexes, referring to the numbers from 9 to 13, is obtained (Table 1.1) [108, 109]. In this section, we want to focus on these Ag(phen)(P2‐nCB)‐type compounds and to demonstrate key steps for designing a material that shows TADF behavior. Interestingly, by this strategy an efficiency breakthrough is reached [108, 109].

1.6.1 Ag(phen)(P2‐nCB): A First Step to Achieve TADF

DFT and TD‐DFT calculations give an insight into electronic properties of Ag(phen)(P2‐nCB) 9. The chemical structure as well as HOMO and LUMO plots are displayed in Figure 1.14. The calculations were performed for the optimized triplet T1 state geometry. From the TD‐DFT approach, it is indicated that the states S1 and T1 are dominated by HOMO → LUMO electronic transitions by 96% and 94%, respectively. Analysis of the frontier orbitals shows that the HOMO is mainly localized on the phosphines and the silver ion, whereas the LUMO is localized on the phen ligand. Accordingly, both states may be assigned to be of (metal + ligand L) to ligand L′ charge‐transfer (1,3MLL′CT) character. The small overlap of HOMO and LUMO suggests the occurrence of a small exchange interaction between the unpaired electrons and, thus, a small ΔE(S1–T1) splitting. From TD‐DFT calculations the energy gap of ΔE(S1–T1) = 1070 cm−1 (133 meV) can be estimated from the energy difference between vertical electron transitions S0 → S1 and S0 → T1. This agrees approximately with the value of 725 cm−1 (90 meV) roughly estimated from the shift of the emission peak maxima upon cooling (see below). Hence, this Ag(I) complex represents an interesting TADF candidate.

Figure 1.14Chemical structure formula and calculated (M062X/def‐2SVP) frontier orbital isosurface contour plots (iso‐value = 0.05) for Ag(phen)(P2‐nCB) 9. The calculations were carried out for the gas phase optimized (M06/def‐2SVP) T1 state geometry.

Source: Ref. [109]. Reproduced with permission of Elsevier.

Figure 1.15 displays emission and absorption spectra of Ag(phen)(P2‐nCB) 9. The absorption peak of low molar extinction (3020 M−1 cm−1) near 400 nm is assigned to the S0 → S1 (1MLL′CT) transition, while the structures of higher allowedness and higher energy are ascribed to LC transitions. (Compare also the TD‐DFT results shown in the SI of Ref. [109].) The emission spectral bands are broad and unstructured as usually found for CT transitions. With temperature reduction from T = 300 to 40 K, a red shift of the peak maximum of the powder material from 575 to 600 nm (25 nm corresponding to 725 cm−1 or 90 meV) is observed. Such a behavior agrees well with the occurrence of TADF at 300 K. At ambient temperature, the emission stems dominantly from the singlet state S1, while at T = 40 K, the TADF process is frozen out and only the lower‐energy phosphorescence from the T1 state occurs.

Figure 1.15Emission and absorption spectra of Ag(phen)(P2‐nCB) 9 at different temperatures. The absorption spectrum is measured with a dichloromethane (DCM) solution of ≈10−5 M concentration at 300 K (black line). The emission spectra are shown in colored lines (λexc = 410 nm). The PMMA film was doped with ≈1 wt% of compound 9.

Source: Ref. [109]. Reproduced with permission of Elsevier.

For completeness, it is noted that the slight red shift of the ambient temperature emission of the PMMA‐doped emitter 9, as compared with the powder material, is related to the lower rigidity of the PMMA film given by the emitter's environment. A corresponding behavior has already been discussed for Cu‐based TADF compounds in Sections 1.3 and 1.4 as well as in the literature [31, 95].

1.6.2 Emission Quenching in Ag(phen)(P2‐nCB)

It is of particular importance for application of emitters in OLEDs that the photoluminescence quantum yield of the emitter should be as high as possible. However, for Ag(phen)(P2‐nCB), the values amount only to ΦPL(powder, 300 K) = 36% and ΦPL(PMMA doped, 300 K) = 26%, respectively (Table 1.6).3 Therefore, it is of interest to understand why emission quenching is distinctly effective for this compound.

Table 1.6 Photophysical data that govern TADF properties of a series of Ag(I) complexes.

Ag(phen)(P2‐nCB) 9 Ag(mbp)(P2‐nCB) 10 Ag(dmp)(P2‐nCB) 11 Ag(dbp)(P2‐nCB) 13
ΦPL(300 K) 36% 70% 78% 100%
ƒ(S1 → S0)a 0.0258 0.0478 0.0423 0.0536
kr(S1 → S0)b 2.2 × 107 s−1 2.2 × 107 s−1 5.6 × 107 s−1
τr(TADF, 300 K)c 5.3 μs 2.9 μs 3.2 μs 1.4 μs
ΔE(S1–T1)d 640 cm−1 650 cm−1 650 cm−1
λmax (300 K) 575 nm 535 nm 537 nm 526 nm

aTD‐DFT calculated (M062X/def2‐SVP) oscillator strength based on gas phase optimized (M06/def2‐SVP) T1 state geometries.

bRadiative decay rate of the prompt fluorescence determined from the fit of Eq. ( 1.1 ) to experimental decay times at various temperatures.

cRadiative decay time measured at 300 K, essentially representing TADF.

dEnergy gap between the lowest excited singlet and triplet states as determined from the fit of Eq. ( 1.1 ) to experimental decay times over a temperature range of 30 ≤ T ≤ 300 K.

Source: Refs [108, 109]. Reproduced with permission of American Chemical Society.

For Cu(I) complexes, it is well known that flattening distortions occur upon excitation of MLCT states (Section 1.3 and see Refs [31, 114, 117, 118, 121, 122, 177]). A similar behavior is also expected to be relevant for Ag(I) complexes. DFT geometry optimizations (M06/def2‐SVP) show that the molecule in the lowest excited (relaxed) triplet state T1 of Ag(phen)(P2‐nCB) 9 is distinctly twisted toward planarization as compared with the ground state geometry. This distortion cannot be characterized by one simple parameter, but in a rough description, one may take the change of the angle Δϕ between two planes placed into the molecular core of the complex (Figure 1.16). Related to such a distortion, the potential energy surfaces of the involved energy states are shifted significantly with respect to each other. This leads to an increase of the Franck–Condon factors between higher‐lying vibrational states of the electronic ground state S0 and the lower‐lying vibrational states of the excited state. The larger the Franck–Condon factors, the more efficient are non‐radiative relaxation processes [124126]. Indeed, the emission quantum yield of compound 9 with a large value of Δϕ ≈ 35° amounts only to ΦPL = 36%, although the compound sits in a rigid crystalline (powder) environment.

Figure 1.16Schematic visualization of the geometry change between the electronic ground state S0 and the triplet state T1. Only the coordination core around the Ag ion is shown. The angles refer to the inclination between the P–Ag–P (orange) and the N–Ag–N (blue) planes. The charge transfer excitation induces a flattening distortion characterized by a model parameter of Δϕ ≈ 35°. The calculations were carried out on the M06/def2‐SVP level of theory for the gas phase conditions.

Source: Ref. [109]. Reproduced with permission of Elsevier.

These considerations lead to the suggestion to rigidify the emitter's structure by introducing intramolecular steric hindrances. Such an approach has already been successfully applied [9, 30, 31, 35, 92, 108, 109, 114, 119, 127]. (Compare also Section 1.3.) We will discuss this procedure in the next section, applying it to Ag(R‐phen)(P2‐nCB), with R representing a substitution.

1.6.3 Sterical Hindrance. Tuning of the Emission Quantum Yield up to 100%

Several Ag(I) complexes comprising the P2‐nCB ligand in combination with a phenanthroline ligand, in each case differently substituted at the positions 2 and 9, are displayed in Table 1.6. The photophysical investigations show that with more bulky substituents on the phenanthroline ligand, the nonradiative decay rate decreases, and, hence, the photoluminescence quantum yield increases. For example, an increase from ΦPL = 36% found for Ag(phen)(P2‐nCB) 9 with an unsubstituted phen ligand to ΦPL = 100% for Ag(dbp)(P2‐nCB) 13 with the 2,9‐di‐n‐butyl phenanthroline ligand is observed [108, 109]. The calculated model parameter Δϕ, describing coarsely the flattening angle, correlates with this photophysical behavior, as was expected. Without sterical hindrance, the Δϕ parameter amounts to ≈35°, while for the compounds with sterical hindrance, the angle change is about three times smaller. For Ag(dbp)(P2‐nCB) 13, for example, the Δϕ parameter amounts only to ≈12°. (Compare Figures 1.16 and 1.17.) According to the significantly lower geometry change upon CT excitation, the emission quantum yield increases drastically (Table 1.6).

Figure 1.17Schematic visualization of the geometry change between the electronic ground state S0 and the triplet state T1. Only the coordination core around Ag is shown. The angles refer to the inclination between the P–Ag–P (orange) and the N–Ag–N (blue) planes. The charge‐transfer excitation induces a flattening distortion characterized by a model parameter Δϕ ≈ 12°. The geometry optimizations were carried out for gas phase conditions at the M06/def2‐SVP level of theory. (Compare Figure 1.16.)

Source: Ref. [109]. Adapted with permission of Elsevier.

The TD‐DFT calculations (M062X/def2‐SVP) carried out for the optimized T1 state geometry reveal another important variation in the series of complexes shown in Table 1.6. The oscillator strength ƒ(S0 → S1) of the S1 → S0 electronic transition increases from ƒ = 0.0258 for Ag(phen)(P2‐nCB) 9 to ƒ = 0.0536 for Ag(dbp)(P2‐nCB) 13, i.e. by a factor of more than two [109]. At the first sight, the reason for this increase is not obvious. However, in a computational model, as presented in Ref. [109], it can be shown that TD‐DFT calculations carried out for Ag(phen)(P2‐nCB) 9, fixed to the T1 state geometry of Ag(dbp)(P2‐nCB) 13, gives the S0 → S1 oscillator strength of ƒ = 0.0687. This value is even higher than the value, calculated for compound Ag(dbp)(P2‐nCB) 13 itself. Obviously, the effect of the complex geometry on the S1 → S0 oscillator strength is superior to the electronic influence of the substituents on positions 2 and 9 of the 1,10‐phenanthroline ligand [109].

The increase of the calculated oscillator strength of the series of Ag(I) complexes should also be displayed in the experimentally determined radiative rate (that is, proportional to the oscillator strength). Indeed, the radiative rates kr(S1 → S0) (Table 1.6) show a similar increase as is seen, for example, when Ag(mbp)(P2‐nCB) with kr(S1–S0) = 2.2 × 107 s−1 is compared with Ag(dbp)(P2‐nCB) with kr(S1–S0) = 5.6 × 107 s−1.

In summary, the drastic increase of the emission quantum yield in the series of Ag(I) complexes arranged in Table 1.6 is induced by two different effects: (i) Increasing sterical hindrance strongly reduces nonradiative relaxation. (ii) In parallel, the 2,9‐substitutions stabilize a complex geometry that leads to a high radiative rate. Both effects are responsible in a very favorite way for attaining the high emission quantum yield of ΦPL = 100% for Ag(dpb)(P2‐nCB).

For completeness, we also calculated the S0 → S1 oscillator strengths for Cu(I) complexes with the same ligands. For example, TD‐DFT calculation (M062X/def2‐SVP) carried out for compound Cu(dbp)(P2‐nCB) in gas phase for the T1 state geometry (M06/def2‐SVP) gives an oscillator strength value of ƒ = 0.0660, while the value for the corresponding Ag(dbp)(P2‐nCB) complex amounts to f = 0.0536. Obviously, the change of allowedness affected by replacement of Ag(I) through Cu(I) is not very distinct.4

Guided by this result, it seems to be justified to relate properties based on oscillator strengths of the S1 ↔ S0 transitions of Ag(I) complexes to trends that are observed for Cu(I) complexes. In particular, comparison to the relation between the energy splitting ΔE(S1–T1) and the radiative rate kr(S1–S0), as displayed in Figure 1.12 (Section 1.5) for Cu(I) complexes, elucidates an interesting result. Inserting the data found for Ag(dbp)(P2‐nCB) with ΔE(S1–T1) = 650 cm−1 and kr(S1–S0) = 5.6 × 107 s−1 (Table 1.6), it becomes obvious that these data do not fit. The rate of the Ag(I) complex is about one order of magnitude higher than expected from the relation shown in Figure 1.12. This result is highly interesting, since it indicates how to develop new materials that break the restrictions imposed by the simple quantum mechanical model presented in Section 1.5. Apparently, the singlet state S1 wave function of the discussed Ag(I) complexes are not simply given by the HOMO–LUMO excitation, but are distinctly modified by configurational interaction. This means that higher‐lying singlet states, resulting from other configurations, mix and thus induce significantly larger S1 → S0 transition rates. Further quantum mechanical investigations have to be carried out in this respect. Nevertheless, these results represent a guideline for the development of materials with shorter TADF decay time, as it has already been demonstrated for Ag(dbp)(P2‐nCB) 13 [108].

1.6.4 Detailed Characterization of Ag(dbp)(P2‐nCB)

The TADF properties of Ag(dbp)(P2‐nCB) 13 are highly attractive due to its photoluminescence quantum yield of ΦPL = 100% and the very short decay time of τ(TADF) = 1.4 μs. Therefore, in this section, we will focus on a detailed characterization of the compound's emission properties.

The lowest excited singlet S1 and triplet T1 states predominantly originate from the HOMO → LUMO transition (92%), slightly less than found for Ag(phen)(P2‐nCB) 9. The HOMO is mainly composed of silver (13%) and phosphorus (47%) orbitals, while the LUMO represents a π* orbital of the dbp ligand (Figure 1.18). Thus, we can assign the two lowest excited states as 1,3(MLL′CT) states with L and L′ representing P2‐nCB and dbp, respectively. According to the TD‐DFT calculations carried out for the optimized T1 state geometry of Ag(dbp)(P2‐nCB) 13, the energy separation ΔE(S1–T1) can be estimated to 0.15 eV (≈1200 cm−1). This represents an upper bound that is obtained from vertical excitations of S0 → S1 and S0 → T1 transitions, respectively. The calculated value is largely in agreement with the experimentally determined activation energy of ΔE(S1–T1) = 650 cm−1 (see below).

Figure 1.18Chemical structure formula and calculated (M062X/def2‐SVP) isosurface contour plots (iso‐value = 0.05) of the frontier orbitals of Ag(dbp)(P2‐nCB) 13. The calculations were carried out for the gas phase optimized (M06/def2‐SVP) T1 state geometry.

Source: Ref. [108]. Reproduced with permission of American Chemical Society.

The n‐butyl substitutions at the 2,9‐positions of the phen ligand lead to a distinct sterical hindrance with respect to a geometry change upon the CT excitation. DFT computations show that this flattening distortion is much less expressed than found for Ag(phen)(P2‐nCB). (Compare Figures 1.16 and 1.17.) As a consequence, it is expected that the emission quantum yield of the more rigid complex Ag(dbp)(P2‐nCB) 13 is higher than that of Ag(phen)(P2‐nCB), as already discussed above and as experimentally found.5

Figure 1.19 displays the emission spectra of Ag(dbp)(P2‐nCB) 13. The spectra are broad and unstructured as expected for CT transitions. Even cooling to T = 1.5 K does not lead to any better resolution (not shown). However, application of methods based on the temperature dependence of the emission decay time reveals additional information, as will be demonstrated below. For the powder material, a blue shift is observed with temperature increase from T = 40 K (T1 emission) to T = 300 K (S1 emission) of Δλ = 14 nm corresponding to 490 cm−1 (60 meV). This value fits approximately to the activation energy of ΔE(S1–T1) = 650 cm−1 (80 meV) as determined below. However, it is noted that the emission spectra represent transitions between Franck–Condon states, and therefore the shift of emission spectra is not very reliable to assess the ΔE(S1–T1) gap, especially when the excited states are of CT character.

Figure 1.19Emission spectra of Ag(dbp)(P2‐nCB) 13. The measurements were carried out under different conditions, as marked in the diagram. Concentrations: PMMA: c ≈ 1 wt%, dissolved in dichloromethane (DCM): c ≈ 10−5 M. λexc = 410 nm.

Source: Ref. [108]. Reproduced with permission of American Chemical Society.

Detailed information on the electronic structure and the relevant decay processes can be obtained from time‐resolving measurements, as already shown in previous sections. Figure 1.20a shows almost monoexponential emission decay curves measured at different temperatures. In Figure 1.20b, the decay times are plotted versus temperature. In the temperature range of 20 K ≤ T ≤ 60 K, a constant value of 1570 μs is observed (plateau). With this value and the low‐temperature emission quantum yield of ΦPL(77 K) = 87% (Table 1.7), one can determine the radiative rate to kr(40 K) = 5.5 × 102 s−1 (applying Eq. ( 1.3 ), whereby it is assumed that the quantum yield at T = 40 K is the same as the measured one at T = 77 K). With temperature increase to T = 300 K, the decay time decreases drastically to τ(300 K) = 1.4 μs (at ΦPL = 100%). Accordingly, the radiative rate increases by a factor of about 1300 to kr(300 K) = 7.1 × 105 s−1. Obviously, such a change has to be related to the involvement of different electronic transitions at low and high temperature, respectively. At low temperature, the emission is a phosphorescence from the T1 state, and at ambient temperature it represents TADF from the S1 state.

Figure 1.20(a) Luminescence decay curves of Ag(dbp)(P2‐nCB) 13 powder measured at different temperatures. (b) Luminescence decay time (τ) plotted versus temperature. The values of k(S1 → S0) = 5.6 × 107 s−1 (18 ns) and ΔE(S1–T1) = 650 cm−1 result from a fit of Eq. ( 1.1 ) to the experimental τ(T) data, with τ(T1) fixed to 1570 μs as determined directly for T < 60 K (plateau). λexc = 378 nm, diode laser PB‐375 L, and pulse width = 100 ps.

Source: Adapted with permission from Ref. [108]. Copyright © 2017, American Chemical Society.

Table 1.7 Emission data for Ag(I) complexes as powder materials and doped in PMMA measured at different temperatures.

Ag(phen)(P2‐nCB) 9 Ag(mbp)(P2‐nCB) 10 Ag(dmp)(P2‐nCB) 11 Ag(dbp)(P2‐nCB) 13
Powder PMMA Powder PMMA Powder PMMA Powder PMMA
λmax(300 K) 575 nm 577 nm 535 nm 555 nm 537 nm 540 nm 526 nm 535 nm
ΦPL(300 K) 36% 26% 70% 58% 78% 75% 100% 85%
τ(300 K) 2.0 μs 2.0 μs 2.8 μs 1.4 μs
kr(300 K) 1.8 × 105 s−1 3.5 × 105 s−1 2.8 × 105 s−1 7.1 × 105 s−1
knr (300 K) 3.2 × 105 s−1 1.5 × 105 s−1 0.79 × 105 s−1 <0.21 × 105 s−1 b)
ΦPL(77 K) 15% 70% 68% 87%
τ(77 K) 270 μs 1390 μs 804 μs 1300 μs
kr(77 K) 5.6 × 102 s−1 5 × 102 s−1 8.5 × 102 s−1 6.7 × 102 s−1
knr(77 K) 3.1 × 103 s−1 2.2 × 102 s−1 3.9 × 102 s−1 1 × 102 s−1
τ(T1, 40 K) 1600 μs 885 μs 1570 μs
kr(S1 → S0)a 2.2 × 107 s−1 2.8 × 107 s−1 5.6 × 107 s−1
ΔE(S1–T1) a 640 cm−1 650 cm−1 650 cm−1

aDetermined from the fit of experimental luminescence decay times according to Eq. ( 1.1 ), measured for a powder sample at different temperatures.

Determined assuming 3% error for the measured ΦPL value, which would allow ΦPL = 97%.

The monoexponentiality of the decay curves indicates fast thermalization between the involved energy states due to fast up‐ and down‐ISC and small inhomogeneities (small variations of ΔE(S1–T1)) of the compounds in the powder material. In this situation, the emission decay time τ(T) of a molecular system of two excited energy states, T1 and S1, can be expressed by Eq. ( 1.1 ). The fit of this equation to the experimental data (Figure 1.20b) gives the activation energy of ΔE(S1–T1) = 650 cm−1 (80 meV) and the radiative rate of the prompt fluorescence of kr(S1 → S0) = 5.6 × 107 s−1. Formally, this value corresponds to a fluorescence decay time of τ(S1) = 18 ns. However, the related prompt fluorescence is not directly observed, since the processes of ISC from S1 to T1 are about three orders of magnitude faster (compare Ref. [118, 121, 133]) [134].

The experimental value of k(S1–S0) = 5.6 × 107 s−1 found for the prompt fluorescence rate is remarkably large. Cu(I) complexes investigated so far (and that have comparable ΔE(S1–T1) splittings) exhibit only rates that are one order of magnitude smaller [31]. (See Section 1.5, Figure 1.12.) Thus, the high (prompt) fluorescence rate can be identified as a key feature that leads to the exceptionally fast TADF decay time of Ag(dbp)(P2‐nCB). This behavior fits perfectly to the large oscillator strength that is calculated for the S1 → S0 transition. (Compare the discussion presented above in this section.)

Photophysical data for Ag(dbp)(P2‐nCB) 13 are summarized in Table 1.7 and in an energy level diagram shown in Figure 1.21. Herein, the material's properties are highlighted: At low temperature (T < 60 K), one observes only long‐living phosphorescence as the T1 → S0 transition decays with τ = 1570 μs. Such a long phosphorescence decay time is not unusual for Ag(I) or Cu(I) compounds [31, 33, 96, 107, 178]. It displays the spin forbiddenness of this transition. The reason is that SOC to singlet states is weak. According to the discussion presented in Refs [108, 109], the next higher‐lying singlet state (S4) that exhibits a different 4d orbital character than the T1 state and that can induce SOC (following general quantum mechanical rules) [7077] is energetically far (ΔE(S4–T1) = 1.57 eV). Therefore, the singlet character mixed into the T1 state is very small. As already mentioned in Section 1.4, SOC via the S1 state can be neglected.

Figure 1.21Energy level diagram and decay times/rates for Ag(dbp)(P2‐nCB) 13 powder. Frequently, up‐ISC is also denoted as reverse ISC (rISC).

Source: Ref. [108]. Adapted with permission of American Chemical Society.

With temperature increase, the S1 state is populated according to the thermal energy kBT. As a consequence, the decay time decreases and a spectral blue shift is observed. This represents the TADF effect. The corresponding activation energy, as determined from the decay time plot (Figure 1.20b), amounts to ΔE(S1–T1) = 650 cm−1. This energy separation is not very small (compare compound 2, Section 1.4), but the S1 → S0 transition rate is much higher than for any other organometallic TADF material (with comparable ΔE(S1–T1) values). Thus, the TADF decay time drops to the record value of τ(TADF, 300 K) = 1.4 μs. Moreover, the Ag(I) complex represents the first TADF material with a radiative decay time comparable to those of Ir(III) complexes [1, 69, 70, 86, 89] that have become famous for OLED applications.

This short TADF decay time or the related very large radiative decay rate of kr(TADF, 300 K) = 7.1 × 105 s−1 is responsible for the high quantum yield of ΦPL = 100%, measured at T = 300 K. For completeness, it is mentioned that the quantum yield at T = 77 K amounts to only ΦPL(77 K) = 87%, since at that temperature the decay time is with τ(77 K) = 1300 μs relatively long, leading to a radiative rate of only kr(77 K) = 6.7 × 102 s−1. Using Eq. ( 1.2 ), the nonradiative rate for this temperature is determined to knr = 1 × 102 s−1. Thus at 77 K, the non‐radiative process can moderately compete with the radiative process. But at ambient temperature, the TADF rate predominates by about three orders of magnitude. Hence, nonradiative processes are no longer relevant.

1.7 Conclusion and Future Perspectives

In this chapter, we study TADF material design based on photophysical properties investigated for a large number of compounds, in particular, with respect to OLED applications. Especially, we focus on photoluminescence properties and on the crucial requirement of designing materials that exhibit short emission decay times (high radiative rates), obviously at high emission quantum yields. The decay time should be as short as possible in order to minimize nonradiative quenching, saturation effects, and, in particular, chemical reactions that might occur in the excited state. Thus, short TADF decay time will help to increase the OLED device lifetime. Here, we discuss important molecular or photophysical parameters and analyze their impact on the TADF decay time. For example, it is well known that the energy separation ΔE(S1–T1) between the lowest excited singlet state S1 and triplet state T1 should be as small as possible. Accordingly, we present detailed photophysical properties of two case studies referring to materials that exhibit a large ΔE(S1–T1) value of 1000 cm−1 (120 meV) and a small one of 370 cm−1 (46 meV), respectively. From these studies – extended by investigations of photophysical properties of many other Cu(I) TADF compounds – we can show, however, that small ΔE(S1–T1) is not a sufficient requirement for short TADF decay time. High allowedness of the transition between the emitting S1 state and the electronic ground state S0, expressed by the radiative rate kr(S1 → S0), is also very important. This has often been disregarded. However, mostly small ΔE(S1–T1) is related to a small kr(S1 → S0). As a consequence, a reduction of τ(TADF) to below a few microsecond might be problematic. This relation results from an investigation of a large number of Cu(I) complexes and basic quantum mechanical considerations. However, these studies are based on a situation, in fact a very frequent one, in which the involved states, S1 and T1, stem from the same HOMO–LUMO excitation. Other higher‐lying singlet states from which the S1 → S0 transition might borrow allowedness are energetically too far from the S1 state. However, new materials can be designed for which this disadvantage is not prevailing. Very probably, the new TADF compound, Ag(dbp)(P2‐nCB), represents such an example. Indeed, we obtained a TADF record material with τ(TADF) = 1.4 μs at 100% emission quantum yield, as discussed in Section 1.6.

As a consequence, it is an important issue for future developments of TADF materials with even shorter decay times to focus on the different effects of (i) reducing the overlap of HOMO and LUMO, which leads to a smaller exchange interaction (small ΔE(S1–T1)) and (ii) to provide other energetically low‐lying singlet states from which the S1 → S0 transition can borrow oscillator strength. For completeness, it is remarked that a different strategy to reduce the emission decay time can also be successful. It has been shown that an increase of SOC with respect to the T1 state, leading to an increase of the T1 → S0 phosphorescence rate, will open another radiative decay path. In this situation, the phosphorescence decay path is added to the TADF path [144]. Accordingly, the overall emission decay time is also significantly reduced [31, 97].

For completeness, it is mentioned that similar design rules (with the exception of increasing the phosphorescence decay rate) are also valid for purely organic TADF materials. Thus, recently it was possible to develop compounds by minimizing even a residual donor-acceptor hyper-conjugation. These compounds show extremely small ΔE(S1–T1) values of ≤10 cm−1 (≈1 meV) (≪kBT at ambient temperature) and that carry sufficient S1 → S0 allowedness to result in a decay time regime of only a few 100 ns. Interestingly, at this small energy separation, thermal activation is not a key property. All excitons that populate the triplet state (75%) are transferred directly by ISC to the singlet state S1 (that is populated independently by 25%). This new mechanism of Direct Singlet Harvesting will lead us to beyond TADF and might be successful for next generation OLED applications [179181]. An equivalent design strategy as developed for the organic materials could also be successful for organometallic TADF materials in future.


The authors thank the German Ministry of Education and Research for financial support in the scope of the cyCESH project (FKN 13N12668). R.C. thanks the European Research Council (ERC) for support in the framework of the MSCA RISE Project no. 645628. M.Z.S. thanks Professor Duncan Bruce (York) and the University of York for their help with computational facilities. Moreover, we thank our cooperation partners for fruitful collaborations. This includes the research groups of Prof. Dr. Chensheng Ma (Shenzhen University, China), Prof. Dr. Wai‐Ming Kwok (Hong Kong Polytechnic University, Hong Kong), and Prof. Dr. Thomas A. Niehaus (Claude Bernard University, Lyon, France). In addition, we acknowledge the German Academic Exchange Service (DAAD) and the Bavaria California Technology Center (BaCaTec) for giving us the opportunity to establish and maintain our collaborations.


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