Spin-flip luminescence

In molecular photochemistry, charge-transfer emission is well understood and widely exploited. In contrast, luminescent metal-centered transitions only came into focus in recent years. This gave rise to strongly phosphorescent CrIII complexes with a d3 electronic configuration featuring luminescent metal-centered excited states which are characterized by the flip of a single spin. These so-called spin-flip emitters possess unique properties and require different design strategies than traditional charge-transfer phosphors. In this review, we give a brief introduction to ligand field theory as a framework to understand this phenomenon and outline prerequisites for efficient spin-flip emission including ligand field strength, symmetry, intersystem crossing and common deactivation pathways using CrIII complexes as instructive examples. The recent progress and associated challenges of tuning the energies of emissive excited states and of emerging applications of the unique photophysical properties of spin-flip emitters are discussed. Finally, we summarize the current state-of-the-art and challenges of spin-flip emitters beyond CrIII with d2, d3, d4 and d8 electronic configuration, where we mainly cover pseudooctahedral molecular complexes of V, Mo, W, Mn, Re and Ni, and highlight possible future research opportunities.

Most prominently, this occurs in Fe II complexes where efficient relaxation via low-energy MC states had precluded long MLCT lifetimes and phosphorescence for a long time [12][13][14][15][16][17][18][19][20]. An octahedral Fe II complex with tridentate N^N^N ligands showed a 3/5 MC lifetime of >1.6 ns and sensitized 1 O 2 [15] and an iron(II) complex with a hexadentate tren(py) 3 ligand reduces quinones by photoinduced electron 1 3 transfer from its 5 MC state (tren(py) 3 = tris(2-pyridyl-methyliminoethyl)amine) [18]. An excited 3 CT state lifetime of 3 ns was achieved by an iron(II) complex with strongly covalent Fe-N amido bonds due to a high barrier for the 3 MC/ 3 CT interconversion [21]. Most recently, the first emissive mononuclear Fe II complex has been reported [22]. It shows NIR-II luminescence in the range of 1030-1600 nm originating from a 3 MLCT state with a lifetime of 1 ns in benzene solution at room temperature.
Rare examples of d 6 complexes showing luminescent 3 MC states were presented with [Co III (CN) 6 ] 3and more recently with a hexacarbene Co III complex [23,24]. The strongly σ-donating ligands imposed a very high ligand field splitting. This raised the energy of MC states so they can act as long-lived emissive excited states [24].
A fundamentally different type of phosphorescence from MC states appears in octahedral d 3 -Cr III complexes. Instead of interconfigurational states with occupied antibonding orbitals, associated emissive MC states feature the same electronic configuration as the ground state (t 2g ) 3 , but differ by a single flipped electron spin. Hence, this luminescence from intraconfigurational states was named 'spin-flip emission'. Although Cr III complexes have been known for many years, a conceptual breakthrough toward intense spin-flip emission led to an increased interest in the past six years [11,[25][26][27][28][29].
Beyond the d 3 electronic configuration, spin-flip emission is also conceivable in octahedral d 2 , d 4 and d 8 complexes, but examples are much less prevalent in the literature than for d 3 complexes. In this review, we outline the theoretical frame required to understand spin-flip luminescence with respect to ligand field theory, symmetry, intersystem crossing (ISC) and relaxation pathways using various well-described Cr III complexes. We also show how emission energies can be tuned in these systems over a range of 5800 cm -1 , and which applications exploit their unique excited state properties. Finally, we summarize the advances of the field with special emphasis on the often-undervalued central ions V II , V III , Cr IV , Mo III , W III , Mn IV , Re IV and Ni II . While spin-flip emission has been observed in many solids doped with suitable transition metal ions [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] and many lanthanide complexes show emissive metal-centered ff-transitions [47][48][49], this review focuses on mononuclear molecular systems with d-block transition metal ions.

Implications from ligand field theory
Ligand field theory is a powerful tool to understand and design spin-flip emitters. In an octahedral ligand field the five degenerate d-orbitals split into two sets, three lower t 2g and two higher e g * orbitals (O h notation), which differ in energy by the ligand field splitting ∆ O [50,51]. The ligand field concomitantly leads to splitting of the atomic terms of the central metal forming ligand field terms of different symmetries. The energies of these terms in dependence of ∆ O are visualized in Tanabe-Sugano (TS) diagrams and depend on ∆ O as well as the Racah parameters B and C (Fig. 1) [52,53]. While both B and C describe the interelectronic repulsion, the parameter C only affects the energies of states with multiplicities lower than the maximum for a given electronic configuration (for example those of the doublet states in d 3 ions) [54]. The relative state energies in a TS diagram depend on the ratio C/B which is often arbitrarily set to 4.0 but in reality varies between complexes [55]. Figure 1 shows the TS diagrams for octahedral d 2 , d 3 , d 4 and d 8 complexes [52,53]. These electronic configurations feature a set of intraconfigurational states with low energy at high ∆ O (e.g., 2 E and 2 T 1 for d 3 , O h notation with g/u omitted). These intraconfigurational states possess a nearly unchanged electron distribution compared to the ground state, e.g., (t 2g ) 3 for the 4 A 2 state in d 3 . This has two consequences: their energy is essentially ligand field-independent (Eqs. 1 and 2) and they show a geometry close to the ground-state geometry (nested states, 2 E/ 2 T 1 states in Fig. 2, weak coupling limit). In contrast, the occupation of orbitals of different energies in interconfigurational states like the 4 T 2 and 4 T 1 states in d 3 ions (Eqs. 3 and 4) or charge-transfer states results in horizontally shifted and broad potential wells ( 4 T 2 state in Fig. 2, strong coupling limit). Consequently, this shift can lead to enhanced non-radiative relaxation to the ground state and broader emission bands, while spin-flip emission is typically very sharp [56].
In general, the transition energies from the ground state to excited MC states with the highest possible multiplicity like 4 T 2 and 4 T 1 in the d 3 electron configuration can be described with ∆ O and the Racah parameter B (Eqs. 3 and 4), while those with lower multiplicity like the 2 E and 2 T 1 states also require the Racah parameter C (Eqs. 1 and 2) [50,57]. It should be noted that Eqs. 1 and 2 were generated by assuming C/B = 4 for the calculation of the configurational interaction terms as multiples of B 2 /∆ O [50,57]. For exact solutions, the reader is referred to Ref. [58].
As discussed in more detail below, tuning of the excited MC state energies via the ligand field strength ∆ O is well understood and heavily exploited in the design of spin-flip emitters (see Sect. 3.1). Yet designing systems with tailored Racah parameters B and C and thus spin-flip phosphorescence energy is difficult (see Sect. 4). Similarly, to achieve MLCT emission from Fe II complexes, many studies focused on imposing a high ligand field splitting ∆ O to raise the MC states as potential deactivating states above the MLCT states [10,19,59]. Recently, a new design strategy featured increased metal-ligand covalency leading to decreased interelectronic repulsion, which counteracted the lower ∆ O and yielded an excited state lifetime of 3 ns of a pseudo-octahedral iron(II) complex [21].
While ligand field theory and the derived TS diagrams are useful to identify certain trends, they come with some limitations: (1) The diagrams refer to a perfectly octahedral coordination geometry. (2) Spin-orbit coupling (SOC) and hence mixing of states with different multiplicity is neglected. (3) Both a lower symmetry of the ground state and SOC lead to splitting of degenerate ligand field terms. (4) TS diagrams reflect the state energies at the ground-state geometry (Franck-Condon state) and neglect excited state energy lowering by excited state distortion. (5) CT states are not considered but can sometimes play an important role in the photodynamics of spin-flip emitters as discussed below.

Prerequisites for strong spin-flip emission
In this section, parameters influencing spin-flip emission and excited state relaxation pathways are discussed using d 3 -Cr III complexes as instructive and well-explored examples.

Strong ligand field splitting to avoid relaxation via MC states
Spin-flip phosphorescence is favored when the spin-flip states are the lowest energy excited states, even though it is a spin-forbidden process. As discussed in the previous (4)  [60,61]. This limits overlap with ligand orbitals, which is referred to as a low intrinsic ligand field strength [62]. For d 3 ions in an octahedral ligand field, the 4 T 2 state rises above the 2 E and 2 T 1 states with increasing ∆ O (Fig. 1b). For Cr III ions this could not be fully achieved using traditional ligands like en or tpy with their homoleptic complexes showing only weak spin-flip phosphorescence ([Cr III (en) 3 ] 3+ Cr1 3+ : Φ = 0.0062%, [Cr III (tpy) 2 ] 3+ Cr2 3+ : Φ < 0.001%; en = 1,2-ethylenediamine, tpy = 2,2';6',2"-terpyridine; Scheme 1, Table 1) [63,64]. These ligands form five-membered chelate rings with the metal ion which leads to substantial deviation of 7°-11° from perfectly octahedral geometry (∠(N-Cr-N) = 90° or 180°) and a weak σ-orbital overlap [56,65]. As a result, Cr1 3+ and Cr2 3+ only reach the first 4 T 2 -2 E crossing point in the TS diagram (Fig. 1b). Weakly luminescent Cr III (acac) 3 Cr3 serves to discuss the effects of a small ∆ O (acac -= acetylacetonato, Scheme 1, Table 1). For Cr3, quantum chemical calculations placed the 4 T 2 state close to the 2 T 1 state in the FC region, i.e., close to the first quartet-doublet crossing point 4 T 2 -2 E in the TS diagram (Fig. 1b), leading to a high density of states. Furthermore, large SOC constants of 100-170 cm -1 were calculated between the 4 T 2 and 2 T 1 states [66]. This is in agreement with El Sayed' rule stating that SOC between two states is large when a change in spin multiplicity is accompanied by a change in orbital angular momentum. The orbital character changes during ISC from the 4 T 2 state with (t 2g ) 2 (e g *) 1 to the 2 T 1 state with (t 2g ) 3 (e g *) 0 electron configuration [67]. Consequently, wavepacket simulations predicted an ultrafast 4 T 2 → 2 T 1 ISC for Cr3 [66]. In fact, fs-transient absorption studies with ligand field excitation revealed ISC with ISC < 100 fs, that competes with vibrational cooling (VC) in the 4 T 2 state. An experimental time constant of = 1.1(1) ps was assigned to VC in the doublet states state [68].
Apart from facilitating ISC, a small energy separation between 4 T 2 and 2 E/ 2 T 1 states enables back-intersystem crossing (bISC) from the doublet manifold to the 4 T 2 state [69]. This results in low phosphorescence quantum yields and a low photostability of the complexes, since the 4 T 2 state with its (t 2g ) 2 (e g *) 1 electronic configuration is Jahn-Teller distorted and potentially dissociative [25,70,71].
A conceptual breakthrough was achieved with [Cr III (ddpd) 2 ] 3+ Cr4 3+ (ddpd = N,N'-dimethyl-N,N'-dipyridin-2-ylpyridine-2,6-diamine, Scheme 1, Table 1) showing a very strong and long-lived dual emission in the near-infrared (NIR, 738 and 775 nm, Φ = 11%, = 899 µs) after 4 A 2 → 4 LMCT or 4 A 2 → 4 T 2 excitation at 435 nm [25]. In Cr4 3+ , the tridentate tpy-like ligand was formally expanded by NMe bridges leading to six-membered chelate rings with almost perfectly octahedral coordination with respect to the [CrN 6 ] coordination polyhedron. The resulting very strong ligand field raised the 4 T 2 state to the level of the 2 T 2 state, close to the second quartet-doublet crossing point 4 T 2 -2 T 2 in the TS diagram ( Fig. 1b) [72]. At this crossing point with roughly degenerate 4 T 2 and 2 T 2 states at the FC geometry, ISC from the 4 T 2 state to the 2 T 2 state might be facilitated by a high density of doublet states [67] as well as a large SOC constant of 42 cm -1 between the 4 T 2 (1) and 2 T 2 (2) states as calculated using multi-reference methods [73]. Furthermore, the internal conversion (IC) 2 T 2 → 2 E/ 2 T 1 might be faster than the bISC process 2 T 2 → 4 T 2 resulting in efficient population of the emissive 2 E/ 2 T 1 states. In fact, after excitation to the 4 T 2 states, fast ISC and vibrational cooling (VC) populate the thermalized doublet states 2 E/ 2 T 1 within = 3.5 ps [74]. The significant 2 E-4 T 2 energy gap of the relaxed excited states of 7100 cm -1 effectively prevents bISC and enables radiative relaxation (k Ph ) to the ground state [25]. Cr4 3+ is called 'Molecular Ruby' because of its optical properties reminiscent of the gemstone ruby (Al 2 O 3 :Cr 3+ ) [25]. The nickname was recently adapted for the emerging class of strongly luminescent Cr III complexes [25,28,73].

Relaxation via CT states
Aside from interconfigurational MC states, CT states need to be considered as relaxation pathways in spin-flip emitters as well. Complexes of V II , Cr III and Mn IV all feature a d 3 electronic configuration. However, due to the different oxidation state of the central metal ions, low-energy MLCT and LMCT states can arise in V II and Mn IV complexes,  (Fig. 1b) and energies of the Franck-Condon (FC) states. Radiative (phosphorescence k Ph and fluorescence k Fl ) and non-radiative decay pathways (back-intersystem crossing k bISC , dissociation k diss and internal conversion k IC ) and exemplary microstates of the relevant states are depicted [56] 1 3 respectively (see below for more details) [42,89]. For Cr III , CT states are of relatively high energy (e.g., the superposition of 4 LMCT and 4 T 2 absorption bands at 435 nm in Cr4 3+ [25]) or they can be avoided altogether in the region of the 4 T 2 absorption as demonstrated with [Cr III (bpmp) 2 ] 3+ Cr5 3+ and [Cr III (tpe) 2 ] 3+ Cr6 3+ (bpmp = 2,6-bis(2-pyridylmethyl) pyridine, tpe = 1,1,1-tris(pyrid-2-yl)ethane; Scheme 1, Table 1) [73,78]. Since low-energy CT states or their admixture to spin-flip states as in [V II (bpy) 3 ] 2+ (bpy = 2,2'-bipyridine) may act as relaxation pathways for long-lived spinflip states [89], the relative energies of ligand and central metal orbitals need to be taken into account when designing ligands for spin-flip emitters.

Symmetry
The intraconfigurational spin-flip transition is governed by two selection rules: it is a spin-forbidden process and additionally Laporte's rule applies, which forbids electronic transitions between wave functions of the same parity [90]. In centrosymmetric [Cr III (CN) 6 ] 3-Cr7 3the combination of Laporte and spin selection rules leads to very long-lived emission ( = 3.45 ms) in frozen solution at 77 K with a low radiative rate constant of k Ph = 25 s -1 (Scheme 1, Table 1) [80,91]. Irradiation of Cr7 3in aqueous solution can lead to ligand substitution [70]. The tripodal chelating ligand tpe imposes inversion symmetry on [Cr III (tpe) 2 ] 3+ Cr6 3+ (Scheme 1, Table 1) resulting in a record lifetime of 4.5 ms in DClO 4 /D 2 O at room temperature while retaining a high phosphorescence quantum yield of 8.2% [78]. Due to the

Cr7
(L = CN, n Cr15 inversion symmetry, the extinction coefficient for the 4 A 2 → 4 T 2 transition is very low ( = 30 M -1 cm -1 , Laporte forbidden), as is the radiative rate constant of the NIR phosphorescence (k Ph = 18 s -1 , Laporte and spin-forbidden) [78]. On the other hand, the coordinating nitrogen atoms in the ddpd complex Cr4 3+ are arranged around a center of symmetry [CrN 6 ] but the overall symmetry is lower due to the orientation of the pyridine rings (point group D 2 ). This allows for a faster radiative decay k Ph and thus leads to a shorter lifetime of 899 µs [25]. Lower symmetry also lifts the degeneracy of the E and T states, which influences band shape and transition energy of the spin-flip luminescence [27,72]. The radiative rate k Ph increases by removing the center of inversion from Cr6 3+ to Cr4 3+ lifting Laporte's rule [78].

Multi-phonon relaxation
The low energy of the doublet states in Cr III -based spinflip emitters (typically 12,800-15,000 cm -1 ) [94] enables non-radiative decay via energy transfer to vibrational overtones of nearby X-H oscillators (X = C, N, O) [95]. This constitutes a major obstacle for efficient molecular emitters with organic ligands but not for oxidic materials such as ruby. By almost quantitative deuteration of the ligand in [Cr III ([D 9 ]-ddpd) 2 ] 3+ [D 18 ]-Cr4 3+ , a record quantum yield of 30% could be achieved (Table 1) [79]. This effect is due to the lower energy of the C-D fundamental mode (≈2200 cm -1 ) and its overtones compared to C-H vibrations (≈3000 cm -1 ). To deactivate the excited doublet state in the deuterated Molecular Ruby, energy transfer to a higher vibrational overtone ( 6 ) with a lower 0 → 6 extinction coefficient is necessary than with C-H oscillators ( 4 + 5  [73]. Clearly, the C-H oscillators closest to the Cr III center (d ≈ 3.0 Å) affect the multiphonon energy transfer the most, while the more distant oscillators play only a minor role due to the d -6 dependence of the corresponding rate constant [95].

Solvent effects and counter ions
Apart from deuteration effects discussed in the previous section, solvents, salt additives and the counter ions of the complexes can influence their photophysical properties.
Absorption/emission profiles and lifetimes of the bpy complex Cr8 3+ remained unchanged in non-aqueous solvents like MeOH, MeCN, dimethylformamide (DMF) and ethylene glycol [96]. Yet, the 4 T 2 → 2 E ISC efficiency decreased in these solvents [97]. The emission lifetime of the cyanido complex Cr7 3correlated with solvent polarity [91], while the emission of the en complex Cr1 3+ remained unaffected by the presence of MgCl 2 up to 5.2 M [98].
Cr4[BF 4 ] 3 forms a contact ion pair with one [BF 4 ]anion on average in acetonitrile solution, due to the high charge of the complex cation [99]. In fact, the counter ions of Cr4 3+ affect the phosphorescence lifetime and quantum yield [100]. In acetonitrile solution, Φ increased from 5.2% with chloride anions to 13.6% with tetrakis(3,5-bis(trifluoromethyl)phenyl)borate [BArF 24 ] -. This change was attributed to reduced self-quenching when employing bulky anions. However, tetraphenylborate [BPh 4 ]led to lower quantum yields of 9.2% likely due to the introduction of additional C-H oscillators close to the Cr III center in contact ion pairs enabling multiphonon relaxation (see above). The counter ions affected lifetime and quantum yield in parallel. Thus, only the nonradiative relaxation pathways from the long-lived 2 E/ 2 T 1 states were influenced by the anions, while the fast evolution from initially excited 4 T 2 or 4 LMCT states to the doublet manifold (ISC, VC, IC) remained unaffected [100].
The Molecular Ruby Cr5 3+ features acidic methylene bridges in the ligand due to the high positive charge. Deprotonation of Cr5 3+ is reversible and forms a non-emissive complex. Therefore, addition of an acid is required to prevent deprotonation and to harvest the full luminescence potential of Cr5 3+ . The acidic protons also lead to a stronger interaction with solvent molecules and counter ions via hydrogen bonding. As a result, in deaerated D 2

3 4 Tuning emission energy in Molecular Rubies
In charge-transfer emitters (LMCT, MLCT, LL'CT), it is straightforward to tune excited state energies for example by introducing electron-donating or -withdrawing substituents on the ligand [101][102][103]. Methods for tuning the energy of metal-centered spin-flip states are not so obvious [27,73,88]. Their energies depend on the nephelauxetic effect, i.e., the covalency of the metal-ligand bond and the Racah parameters B and C [50,57]. The archetypical Molecular Ruby Cr4 3+ and many of its congeners emit in the NIR-I spectral region between 720 and 780 nm [25,27,28,64,78,85]. By increasing the metal-ligand covalency with a monoanionic carbazolato ligand in [Cr III (dpc) 2 ] + Cr13 + (dpc -= 3,6-di-tert-butyl-1,8-di(pyridine-2-yl)-carbazolato; Scheme 1, Table 1), the emission band shifted to the NIR-II peaking at 1067 nm in frozen solution at 77 K [87]. The high covalency of the bond between Cr III and the anionic ligand (B = 470-550 cm -1 ) decreased the repulsion of the d electrons and led to an unprecedentedly low energy of the spin-flip emission. However, an admixed 2 LMCT state in Cr13 + increased the excited state distortion which facilitated non-radiative relaxation to the ground state leading to a low quantum yield of Φ < 0.00089% and a relatively short lifetime of 1 = 1.4 µs (88%) and 2 = 6.3 µs (12%) at 77 K. In addition, it is plausible to assume that multi-phonon relaxation of the excited state (see above) plays a significant role because the NIR-II emission band might have a large spectral overlap with the absorption bands of the ligands' aromatic C-H overtones [87]. Similarly a low-energy phosphorescence at 910 nm was found for fac-Cr III (ppy) 3 Cr14 (ppy = anion of 2-phenylpyridine; Scheme 1, Table 1), an isostructural analog of the famous CT emitter Ir III (ppy) 3 , with a lifetime of 9.5 µs in 2-MeTHF (2-MeTHF = 2-methyltetrahydrofuran) at room temperature. At 77 K, the maximum shifted to 890 nm with shoulders at 910 and 1020 nm and a lifetime of 48 µs. The low quantum yield of 0.03% at room temperature in dichloromethane solution was rationalized with multiphonon quenching via C-H oscillators of the ligands, trigonal distortion in the excited state reminiscent of [Cr III (bpy) 3 ] 3+ Cr8 3+ and self-quenching enabled by intermolecular -and CH-interactions of this neutral complex Cr14 [88].
A theoretical upper limit of the emission energy can be derived from ligand field theory using the Racah parameter B of the central metal ion. Assuming C/B = 4.0, a 2 E energy of 19.5 B is predicted for an octahedral d 3 complex [58]. With B = 918 cm -1 for the free Cr 3+ ion [50], this corresponds to 17,900 cm -1 (559 nm). The doublet state energies are also determined by the ratio C/B. This is nicely demonstrated by ruby (Al 2 O 3 :Cr 3+ ) which features a highly ionic metal ligand bond with B = 822 cm -1 but due to the low ratio C/B = 3.2 merely shows red emission at 694 nm (14,400 cm -1 ) [105].
An alternative strategy to ligand design for the tuning of the emission energy is changing the central metal ion. A lower charge and/or extended d-orbitals as in 4d/5d transition metals result in a lower interelectronic repulsion. Consequently, highly charged central ions like Mn IV (B = 1064 cm -1 ) [50] should in principle lead to high spinflip energies. However, in the end the covalence of the metal-ligand bond is the decisive factor, which needs to be considered for each complex individually. A more detailed discussion can be found in Sect. 6.

Applications
The phosphorescence of Cr III emitters is quenched by triplet dioxygen 3 O 2 via doublet-singlet Dexter-type energy transfer forming 1 O 2 with 61% quantum yield in the case of Cr4 3+ . This excited state reactivity allows utilizing Cr4 3+ as an optical oxygen sensor and as photosensitizer for the α-cyanation of aliphatic amines via 1 O 2 /trimethylsilylcyanide [25,74].
The complex Cr12 3+ (Scheme 1, Table 1) was successfully employed as a photoredox catalyst in radical cationic [4 + 2] cycloaddition reactions [106]. Photoexcited Cr12 3+ is reductively quenched by the substrate (e.g., trans-anethol). The resulting radical cation reacts with a diene like isoprene. Interestingly, the catalysis requires the presence of O 2 likely functioning as an electron shuttle. Oxygen can oxidize Cr12 2+ to regenerate the photocatalyst Cr12 3+ and to form superoxide. Finally, superoxide reduces the cationic intermediate after reaction of the oxidized alkene and the diene yielding the [4 + 2] cycloaddition product [86,107]. This catalytic scheme strongly benefits from the very long excited state lifetime of 13 µs of Cr12 3+ in CH 3 NO 2 even under aerobic conditions [86].
Cr4 3+ shows dual phosphorescence from its doublet states at 738 and 775 nm at room temperature because these two states are in thermal equilibrium with an energy difference of 650-700 cm -1 [108]. Thus, the complex was employed as a self-referenced ratiometric optical temperature sensor [108,109].
Hydrostatic pressures for example in diamond anvil cells are usually measured optically via the shift in emission energies of ruby's R 1 /R 2 lines (approx. -0.77(3) and -0.84(3) cm -1 kbar -1 ) [110,111]. Interestingly, for Cr4[BF 4 ] 3 much larger shifts of -14.8 and -9.5 cm -1 kbar -1 were found for the low-and high-energy emission, respectively, in aqueous solution, in methanol and in the solid state. The large barochromic effect is explained by subtle changes in the coordination geometry of the complex induced by high pressures [72,112].
The key figure for quantification is the dissymmetry factor g lum representing the excess of left-handed polarized over right-handed polarized light intensity I L and I R (Eq. 5). The physical description of g lum (Eq. 5) includes the electronic and magnetic transition dipole moments |µ ab | and |m ba |, Fig. 3 Structures of a ligands L 1 and L 2 , b binuclear Cr III -Ln III complexes and c trinuclear Cr III -Ln III -Cr III complexes [114][115][116] with red, green and blue colors used for carbon atoms on different ligands; chromium colored in yellow; lanthanide in violet; nitrogen colored in gray; oxygen colored in orange; hydrogen atoms were omitted for clarity 1 3 respectively, as well as the angle ab between the two vectors. Equation 5 shows that a high dissymmetry factor g lum is expected for transitions a → b which are spin-forbidden (low |µ ab |) and magnetic dipole allowed (high |m ba |) [125]. Both conditions are met by the 2 E → 4 A 2 transition in Molecular Rubies yielding outstanding |g lum | values of 0.09 for Cr4 3+ and 0.20 for [Cr III (dqp OMe ) 2 ] 3+ Cr16 3+ (Scheme 1, Table 1) [29,122]. Dissymmetry factors as high as this are rarely achieved with CT emitters and usually necessitate the use of lanthanide complexes exploiting metal-centered ff-transitions [123,125,126].

Spin-flip emitters based on other transition metals and electronic configurations
This section highlights spin-flip emissive complexes of 3d, 4d and 5d metal ions with suitable d electron configurations. with red and blue colors used for carbon atoms on different ddpd ligands to clarify each ligand's helicity; chromium colored in green; nitrogen colored in gray; hydrogen atoms were omitted for clarity [122]
A weak, structured emission was found for [V III (urea) 6 ] 3+ V1 3+ at 77 K in the solid state peaking at 992, 1010, 1011 and 1187 nm ( Table 2) [140][141][142]. Trigonal Jahn-Teller distortion splits the 3 T 1 ground state by 1400 cm -1 to 3 A 1 and 3 E states. This ground-state splitting of octahedral d 2 metal complexes is a key difference to d 3 spin-flip emitters with their orbitally non-degenerate 4 A 2 ground state (Fig. 1a,b). In V III complexes, the total luminescence intensity is distributed to a large number of possible spin-flip transitions 1 T 2 / 1 E → 3 T 1 with differing energies [143].
[V III (ddpd) 2 ] 3+ V2 3+ is the first V III complex showing NIR luminescence at room temperature in solution (Scheme 2, Table 2). This was achieved by using the strong -donor ddpd that has been previously employed in the first Molecular Ruby [25,62]. The ligand field splitting is so large that the complex is located well above the first crossing point ( 1 T 2 , 1 E)/ 3 T 2 , placing the spin-flip states below the interconfigurational 3 T 2 states in the TS diagram (Fig. 1a). When excited at 306 nm, V2 3+ shows a weak NIR-II phosphorescence peaking at 982, 1088 and 1109 nm in solution at 298 K. The bands were assigned to the spin-flip transitions from 1 T 2 / 1 E to the split 3 T 1 ground state. A quantum yield of 0.00018% was found for this NIR-II emission in CD 3 CN at room temperature. Low energy excitation at 620 nm is less efficient in populating the metal-centered 1 T 2 / 1 E states. In butyronitrile at 77 K, the luminescence decayed biexponentially with lifetimes of 1 = 790 ns (93%) and 2 = 8800 ns (7%). In addition to the NIR-spin-flip emission, blue fluorescence possibly originating from a 3 LMCT state was detected at 396 nm in CD 3 CN at 298 K with a high quantum yield of 2.1%. This dual emissive behavior was rationalized with an inefficient ISC and fast spin-allowed IC and fluorescence. In contrast to Cr4 3+ , non-radiative deactivation of the lowenergy 1 T 2 / 1 E spin-flip states via multiphonon relaxation (electronic-to-vibrational energy transfer to vibrational overtones of C-H oscillators) unexpectedly does not play a significant role as evidenced by the very similar lifetimes and quantum yields of the non-deuterated and perdeuterated vanadium(III) complexes [62,79]. The low quantum yield can then be attributed to a poor ISC efficiency and efficient non-radiative decay pathways beyond multiphonon relaxation. Possibly the inefficient ISC may be caused by the low density of acceptor states in the singlet manifold as Δ O in V2 3+ lies below the second triplet-singlet crossing point 1 A 1 / 3 T 2 in the TS diagram (Fig. 1a) [62].
NIR-II spin-flip emission was also detected for the heteroleptic complex mer-V III Cl 3 (ddpd) V3 (Scheme 2, Table 2) in the solid state at room temperature with bands at 1102, 1219 and 1256 nm and a phosphorescence lifetime of 0.5 µs [144]. Ligand deuteration significantly increased the phosphorescence lifetime to 3.4 µs. Transient absorption spectroscopy showed that the long-lived singlet states are populated after = 1.4 ps, which is an upper limit for the time constant of the ISC. Trajectory surface hopping simulations within a linear vibronic coupling model arrived at a similar value of 1.7 ± 0.3 ps [145]. Interestingly, under hydrostatic pressure V3 showed a hypsochromic shift by + 10 cm -1 kbar -1 Scheme 2 Structures of luminescent V III and Cr IV complexes [62,128,130,131,142,144] 1 3 in contrast to the bathochromic shifts found for Cr4 3+ . This positive shift was rationalized by the combined effect of changes in singlet energy and ground state splitting under pressure [144].
Spin-flip emission occurs also in five-coordinate V III {(C 6 F 5 ) 3 tren}(CN t Bu) V4 ({(C 6 F 5 ) 3 tren} 3-= 2,2',2''tris[(pentafluorphenyl)amido]trimethylamine; Scheme 2, Table 2) which was proposed as an optically addressable molecular quantum bit candidate [128]. In this coordination geometry, a 3 A ground state and 3 E and 1 E MC excited states arise (Fig. 5a). Excitation at 640 nm assigned as a spin-allowed 3 A → 3 E transition yielded a 1 E → 3 A emission around 1240 nm in 2-MeTHF at 77 K and in single crystals. No emission was detected at room temperature in fluid solution. Long lifetimes of 11.1 and 3.0 µs were measured of single crystals of V4 at 4 K and at room temperature, respectively, substantiating the assignment of the emission as phosphorescence. ISC was found to occur within < 4.2 ps followed by VR with a time constant of 26 ps [128]. The rather slow ISC compared to V3 [144] or Cr III (acac) 3 Cr3 (Scheme 1) [68,146] was attributed to restrictions of vibrational modes along the ISC reaction coordinate imposed by the rigid substituted tren ligand [128].
The TS diagram of tetrahedral d 2 complexes is analogous to the octahedral d 8 case (Figs. 1d and 5b). Hence spinflip emission from a 1 E → 3 A 2 transition could be achieved with a high ligand field splitting in tetrahedral d 2 complexes [147]. In fact, tetrahedral Cr IV complexes with anionic alkyl or aryl ligands Cr17-Cr22 emit between 897 and 1025 nm at 4 K and were proposed as optically addressable qubit candidates (Scheme 2, Table 2) [130,131]. For the investigation, the complexes Cr18-Cr22 were diluted in isostructural Sn IV host lattices while a Sn IV (2,4-dimethylphenyl) 4 lattice was used for Cr IV (CH 2 CPh 3 ) 4 Cr17 (CH 2 CPh 3 -= 2,2,2-triphenyleth-1-yl). A resulting incompatibility with this host lattice in Cr17 served to explain its broad emission compared to the extremely narrow bandwidths obtained for Cr18-Cr22. Because of the stronger nephelauxetic effect in the aryl complexes Cr20-Cr22, their emission is of lower energy than in the alkyl derivatives Cr17-Cr19 [131]. The phosphorescence lifetimes of Cr20-Cr22 in the host lattices at 4 K were determined as 3.3, 5.7 and 6.9 µs, respectively [130].

d 3 -Mo III , WIII, VII, Mn IV and Re IV
Luminescent molecular Cr III complexes have been known for a long time with many reviews covering this substance class [56,63,143,155,156,158]. In contrast to Cr III , luminescent complexes of Mo III and W III were hardly investigated. To our knowledge, ten emissive molecular Mo III complexes and only one emissive W III complex were reported in three publications [159][160][161]. This is probably due to the fact that Mo III and W III complexes are less stable than Cr III complexes despite their (t 2g ) 3 electronic configuration [162]. It was suggested that the higher ionic radii facilitate decomposition via seven-coordinate intermediates or that decomposition may be catalyzed by byproducts with different oxidation states [162]. In general, intermediate oxidation states like + III are more difficult to stabilize in 5d and 6d transition metal complexes resulting in complexes sensitive to oxidation [163,164].

Fig. 5
Schematic energy-level ordering and exemplary microstates in a trigonal-bipyramidal V III complex V4 and b tetrahedral Cr IV complexes Cr17-Cr22 (Scheme 2, Table 2) [128,130,147] Mo7-Mo9 (Me 3 [9] Table 3) [160,161]. Multiphonon relaxation via C-H oscillators of the ligands or solvent molecules might play an important role in the deactivation of the excited states. Another reason for the poor quantum yields measured for Mo7-Mo9 might be that despite the high SOC in Mo III [165], ISC could be slow due to a low density of doublet states in the region of the initially excited 4 T 2 state at the FC geometry. For W III Cl 3 (Me 3 [9]aneN 3 ) W1 (Scheme 3, Table 3) the emission peaked at 1400 nm, but the complex was too unstable for a more detailed investigation [161]. The trend of the energies going from Cr III to Mo III and W III can be explained with respect to the weaker interelectronic repulsion in this series (Cr 3+ : B = 918 cm -1 , Mo 3+ : B = 610 cm -1 ) [50,161].
Investigations of novel Mo III and W III emitters may offer insights on the effects that very high ligand field splittings Δ O have on the efficiency of the ISC processes and the radiative and non-radiative rates for the spin-flip state relaxation. Applying the lessons learned from the Molecular Rubies might help in the design and synthesis of stable Mo III and W III complexes with strong emission in the NIR-II spectral region.
Vanadium(II) complexes also feature a d 3 electronic configuration and are thus potential candidates for spinflip emission similar to Cr III . The Racah parameter B(V 2+ ) = 766 cm -1 of the free ion is lower compared to B(Cr 3+ ) = 918 cm -1 [50] indicating lower doublet energies for V II complexes [89]. However, the lower oxidation state also leads to a lower intrinsic ligand field splitting Δ O [171]. In addition, a relatively facile oxidation of V 2+ to V 3+ may generate low-energy MLCT states. In fact, early studies on tris(bidentate)vanadium(II) complexes using bpy, bpy derivatives and phen V5 2+ -V8 2+ (Scheme 4) concluded that their lowest excited states have 4 MLCT character. These complexes featured excited state lifetimes in the low nanosecond region and no luminescence [172]. The excited state assignment was recently called into question and a mixed 2 MC/ 2 MLCT state was proposed instead based on Scheme 3 Structures of luminescent Mo III and W III complexes [159][160][161]  MeCN 1380 -- [170] electrochemical, quantum chemical and transient absorption studies [89]. The partial 2 MLCT character leads to geometric distortion facilitating non-radiative decay compared to Cr III complexes with their nested doublet excited states [25].  [173]. Complexes of the heavier homologues Nb II and Ta II are rare and no spin-flip emission has been reported to date [137,[174][175][176][177][178].
To the best of our knowledge, [ n Bu 4 N] 2 [Re IV X 6 ] (X = Cl, Br) [ n Bu 4 N] 2 Re1 and [ n Bu 4 N] 2 Re2 (Scheme 5, Table 3) present the only emissive molecular Re IV complexes in solution reported so far [160,170]. Excitation at 360 and 414 nm in MeCN leads to NIR-II phosphorescence at 1340 and 1380 nm, respectively. For Re1 2-, lifetimes of 80 and 140 ns and an estimated upper limit of 0.02% for the quantum yield were reported [160,170]. Re2 2showed a phosphorescence lifetime of 40 ns and photosolvation upon LMCT excitation with UV light [179]. Analogous to the Mo III and W III cases, the extended 5d orbitals and low interelectronic repulsion in Re IV lead to high-energy 4 T 2 states and very low lying doublet states. The challenges accompanied with the heavier group 6 metal ions outlined above apply for Re IV as well.

d 4 -Cr II , Mo II , WII, Mn III and Re III
The d 4 complexes are a special case among the electronic configurations discussed in this section. Depending on Δ O , they can be high-spin or low-spin, resulting in dramatically different energy-level ordering (Fig. 1c). States of three different multiplicities (singlet, triplet, quintet) become relevant. Spin-flip emission is only conceivable in lowspin d 4 complexes. A very high Δ O (≫ 38 B for C/B = 4) is required to establish the spin-flip states 1 T 2 and 1 E as the lowest excited states below the high-spin state 5 E (Fig. 1c) [58]. The d 4 configuration is different from the others since deactivation of the potential spin-flip state via a 1 T 1 → 5 E transition would entail a change of the total spin of ΔS = 2 instead of just 1. However, while efficient ISC processes with ΔS = 2 are relatively rare, they cannot be excluded [180,181]. Another challenge in this electronic configuration might be that the 5 E high-spin state always lies below the lowest triplet MC state 3 E. A relaxation cascade 3 E → 1 T 2 / 1 E after 3 T 1 → 3 E excitation is thus probably impeded by non-radiative deactivation of the 3 E state via the 5 E state similar to certain d 6 -Fe II complexes [19]. Therefore, in a potential d 4 spin-flip emitter, the 1 T 2 and 1 E states need to be populated via other routes, e.g., CT states. Finally, similar to the d 2 electron configuration, the 3 T 1 ground state of the lowspin d 4 electron configuration is orbitally degenerate giving rise to Jahn-Teller distortions (Fig. 1a,c). Overall, spin-flip emission from d 4 transition metal complexes has not been achieved yet for molecular systems. In principle complexes  [182,183]. The reduced Molecular Ruby [Cr II (ddpd) 2 ] 2+ Cr4 2+ shows spin-crossover at room temperature and dark excited states with microsecond lifetimes [184]. Further preparative and handling challenges for divalent group 6 metal ions include their sensitivity to oxidation, dimerization or cluster formation [185][186][187][188][189][190].
Other candidates for d 4 spin-flip emission are, e.g., Mn III , Tc III and Re III . However, known emissive Mn III complexes only show luminescence from ligand-centered transitions [191][192][193][194]. While octahedral Tc III and Re III complexes are quite common [195,196], to the best of our knowledge no spin-flip emission has been reported so far.
Due to the very high Δ O required for spin-flip emission in the d 4 case, complexes of 4d and 5d transition metal ions seem to be promising candidates.

d 8 -Ni II , Pd II and Pt II
In an octahedral ligand field, d 8 ions like Ni II possess a 3 A 2 ground state, a 3 T 2 excited state and a 1 E spin-flip state (Fig. 1d). Compared to the other d electron configurations, the 1 E state in d 8 is unique because the spin-flip occurs in the e g * orbitals with -instead of -symmetry. Interestingly, the 1 E state consists of an unpaired and a spin-paired microstate (Fig. 1d). Population of the spin-paired microstate might lead to excited state Jahn-Teller distortion facilitating nonradiative decay to the ground state.
In principle, a strong ligand field could raise the 3 T 2 state above the 1 E state and enable spin-flip phosphorescence. Octahedral Ni II complexes with strong donor ligands like phen, tpm, bpy, tpy and ddpd (Ni1 2+ -Ni5 2+ ; tpm = tris(pyrid-2-yl)methane; Scheme 6) show ligand field splittings of 17-18B which are close to the 3 T 2 / 1 E crossing point in the TS diagram (Fig. 1d) [129,[197][198][199][200][201], while homo-and heteroleptic complexes with poly(pyrazolyl) methane ligands showed a lower Δ O of 11-15B [202]. Absorption spectroscopy revealed that the 3 T 2 and 1 E states are not sufficiently separated with 1 E transitions detected as shoulders on the 3 T 2 bands. In this case, the spin-forbidden 3 A 2 → 1 E absorptions are enhanced by intensity borrowing from the nearby 3 T 2 band [201]. The lowest energy adiabatic state is strongly anharmonic due to coupling with components of the 3 T 2 state via SOC which reduces the spin-flip character [203]. In summary, a ligand field splitting Δ O ≫ 18B is necessary to bring spin-flip luminescence within reach [200]. However, as the classical example of [Ni II (CN) 4 ] 2illustrates, a square-planar coordination geometry with a singlet ground state is favored with very strong ligands [204]. Thus, a balance between these two extremes is necessary for spin-flip emission.
It was reported that Ni1 2+ and Ni2 2+ are emissive in the solid state at 150 K [129]. However, these findings have been called into question since the reported emission bands for Ni1 2+ and Ni2 2+ are almost superimposable, which is unlikely considering their different symmetry [143].
The heavier homologues Pd II and Pt II prefer a square-planar coordination geometry due to their high intrinsic ligand field splitting [185]. Pseudooctahedral complexes of Pd II and Pt II are very rare and often require sophisticated ligands to avoid the formation of a square-planar geometry [205][206][207][208][209][210]. No spin-flip phosphorescence in these types of complexes was reported to date.

Conclusion
The numerous examples of spin-flip luminescent complexes in this review substantiate that metal-centered states can be more than just non-radiative relaxation pathways for chargetransfer states, but that spin-flip chromophores constitute a useful class of phosphorescent complexes complementary to charge-transfer chromophores. A deeper understanding of the requirements for efficient spin-flip emission has given rise to the emerging class of highly luminescent Cr III complexes (Molecular Rubies) and the first luminescent V III complexes. This marks substantial progress in the ongoing endeavor to establish photoactive complexes based on earthabundant metals as sustainable alternatives to precious or rare earth metal complexes [11,19,158]. In this context, circularly polarized luminescence is a promising application Scheme 6 Structures of Ni II complexes discussed in the manuscript 1 3 of enantiopure chiral spin-flip emitters, which makes full use of their unique excited state properties [123].
This review also highlighted many open venues for more fundamental research. It is still a challenge to tune the relative energies of the relevant states to achieve, e.g., highenergy spin-flip emission. In addition, the role of the density of high-energy 2 T 2 doublet states for efficient intersystem crossing in excited Cr III complexes remains unclear to this date. 4d and 5d complexes of Mo III , W III or Re IV offer ideal conditions to study d 3 spin-flip emission beyond the second quartet-doublet crossing point in the Tanabe-Sugano diagram. For some metal ions like Ni II , reports on spin-flip emission are limited to doped solids [46], while convincing evidence in molecular systems is lacking. Here, it remains a challenge to establish a sufficiently high ligand field splitting that separates the initially excited interconfigurational states and the intraconfigurational spin-flip states without resulting in a square-planar coordination geometry.

Acknowledgements
The authors would like to thank Prof. Dr. Christian Reber, Dr. Christoph Förster and Nathan Roy East for constructive criticism of the manuscript. Parts of this research were conducted using the supercomputer ELWETRITSCH and advisory services offered by the Technical University of Kaiserslautern (https:// elwe. rhrk. uni-kl. de/), which is a member of the AHRP.
Author contributions WRK conceptualized the article, performed the literature search and wrote the article. JM provided support in writing of the article. KH provided the idea and general concept for the article and critically revised the work. All authors read and approved the final manuscript.
Funding Open Access funding enabled and organized by Projekt DEAL. Financial support from the Deutsche Forschungsgemeinschaft [DFG, Priority Program SPP 2102 "Light-controlled reactivity of metal complexes" (HE 2778/13-1)] is gratefully acknowledged. W. R. K. is grateful to the Chemical Industry Funds for a Kekulé Fellowship.
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