Electronically Excited States of Free Radicals

Abstract

Formation of the excited doublet (D) and quartet (Q) states of free radicals under their photoexcitation is discussed. The relative positions of the D and Q states are compared to the positions of the photoexcited states of organic molecules (Jablonsky diagram). A number of representative cases of the excited states of free radicals detected by their transient absorption or emission are presented. A special case of the population having the lowest Q state in some radicals is discussed. A spin–statistical factor in the reactions of Q and D is debated.

1. Introduction

Organic compounds are used in chemistry and exist in everyday life. They consist of organic molecules. The vast majority of these molecules exist in a singlet state S₀. Upon the absorption of light, a molecule reaches an excited S₁ state. S₁ can undergo intersystem crossing (ISC) and populate the lowest triplet state T₁. These processes are presented in the Jablonsky diagram [1,2] (Figure 1). Singlet states are “close shells”; they have two electrons with opposite spins on each occupied molecular orbital (MO). A triplet state has two single-occupied MO (SOMO) with parallel spins. That way, the spin angular momentum of the singlet states is s = 0; for the T state, s = 1 (The spin multiplicity is 2s + 1. The spin multiplicity is presented as a superscript in a state notation).

The Jablonsky diagram is described in detail in textbooks on photochemistry [1,2]. Such books and review articles present all of the processes occurring in excited states, as well as the known rare exceptions to the diagram [1,2]. Figure 1 presents only the absorption of a light quantum and the intersystem crossing (ISC) to the T₁ state initiated by spin–orbit coupling (SOC) [3]. The probabilities of the occurrences of the processes in the excited states of molecules obviously vary from 0 to 1.

2. Doublets and Quartets

Organic free radicals (R^•) are species with an “open shell”. They have at least one SOMO. The spin state of R^• is s = 1/2, and such states are called doublets (D). Radicals with three one-electron orbitals exist in a quartet electronic state (Q), which has s = 3/2. Free radicals are important intermediates in many photoinduced reactions. There are cases when radicals absorb light and produce excited D₁ or Q₁ states; see below. Obviously, the chemical reactivity of the photoexcited radicals (molecules) is different from that in D₀- (S₀-) states [4].

Synthesized stable organic π-radicals have been recently reported, which are especially interesting for applications in organic light-emitting devices (OLED) due to their possibility of providing a quantum yield of luminescence of 1.0 [5]. This is one of the modern reasons for studying photoexcited free radicals.

It is logical to assume an analog of the Jablonsky scheme (Figure 1) for free radicals. SOC mixes D₁ and Q; see Figure 1. All other processes (luminescence, internal conversion, and vibrational relaxation) take place in photoexcited molecules and radicals. Luminescence from the D₁ (Q₁) state is named in the literature as fluorescence (phosphorescence), apparently due to an analogy with such processes in molecules.

Stable free radicals (R^•) are usually colored, whereas the parent compounds (RH) are colorless. That means that D₁ lies close in energy to D₀, namely 180–300 kJ/mol above D₀ (Figure 1). For example, colorless 2,4,6-tri-tert-butyl phenol has a longwave absorption maximum at λ = 280 nm (370 kJ/mol), whereas the corresponding phenoxyl radical (blue aroxyl) has an analogous value λ = 626 nm (190 kJ/mol). A similar bathochromic shift of the absorption maximum holds between a parent compound (say, a ketone, a quinone) and its radical R^• (a ketyl radical, a semiquinone) formed by hydrogen abstraction.

Q₁ may have a higher energy than D₁; see Figure 2.

The formation of Q₁ requires three unpaired electrons with parallel spins, which may increase the energy of the excited R^•* compared to that of D₁ (The formation of T₁ in molecules requires only two unpaired electrons with parallel spins. The dominant role of the Pauli effect leads to a lower energy of T₁ compared to S₁ in the majority of cases [1,2]). Thus, in a number of cases, Q₁ can be populated only after primary excitation into D₂ or D₃; see Figure 2.

Fast internal conversion (IC) from a higher D₂₍₃₎ to a lower D₁ should lead to a low probability of the population in Q₁. This assumption allowed the authors of [2] to draw conclusions about the insignificant role of Q₁ in the photochemistry of radicals. However, there have been many reports of the experimental detection of Q₁ (Section 3 below). The observation of a relatively long-lived R^•* leads to the assumption that R^•* is in a Q₁ state; see Section 3 below.

3. Excited Neutral Radicals

This brief review article does not aim to review most of the reported cases of R^•* studies. We will focus on liquid solutions of polyatomic organic radicals and radical ions at room temperature. This section presents some instructive and exemplary results of such research. Chemical transformations of R^•*, except a reaction with dioxygen (Section 5), are beyond the scope of this brief article.

The excited states are usually detected by their emission spectra or transient absorption spectra.

However, we will start with a seminal publication [6] that reported a D₀ ← Q₁ phosphorescence of a decacyclene radical anion in a solid state at 77 K. It was assumed that Q₁ was above D₁, and the luminescence was phosphorescence. The Q₁ electronic state of this anion at 77 K was confirmed by transient magnetic resonance [7]. Photoexcited radical ions are considered in Section 4.

High-spin molecular objects are of great interest due to their potential applications in molecular magnets. It has been stated that some labile dehydrophenylnitrenes are in the ground Q state [8]. Quantum chemical calculations of the ground and excited states of several dehydrophenylnitrenes allowed the authors to obtain their geometry and distinguish between the Q and D states of these species [8]. The studied dehydrophenylnitrene system demonstrates that a fine competition between ferromagnetic Q- and antiferromagnetic D states coupling of electron spins takes place. With a single electron orbital being orthogonal to two coplanar orbitals, the relative orientation of the latter orbitals determines which mode of electron coupling prevails; see Scheme 1.

The D₁ state of benzophenone ketyl radical in a benzene solution at room temperature was observed by laser flash photolysis with time-resolved (TR) ESR and absorption spectroscopy [9]. The lifetime of this D₁ was ~2 ns [9]. It is assumed that a photoexcitation of the ketyl into D₂ led to ISC into Q₁ ← D₂ [9]. (Q₁ was positioned above D₁; see Figure 2). It seems that, in the case of the studied ketyl, ISC successfully competed with the D₁ ← D₂. The lifetime of Q₁ is relatively long, namely ~2 μs [9]. As expected, D₀ ← Q₁ is a relatively long process compared to D₀ ← D₁ in the same ketyl radical under the same conditions.

The ketyl radical of benzophenone and of its derivative were studied by two-color laser flash photolysis [10]. The first ns pulse (λ_ex =266 or 355 nm) generated ketyl radicals the usual way: hydrogen abstraction from a solvent. The second ps pulse (λ_ex = 532 nm) excited ketyls into D₁. The transient absorption and fluorescence of D₁ were measured. The lifetime of D₁ in the studied solvents varied from 0.5 to 5 ns [10]. It was noticed that D₁ had a high dipole moment of 7–10 D, which led to a significant solvent effect on D₁ [10].

Many of the compounds reported in [5] were large, stable organic radicals that emit fluorescence. Stable aroxyl (substituted phenoxyl) radicals have demonstrated transient absorption in liquid solvents in flash photolysis experiments [11]; see Figure 3. However, the fluorescence of galvinoxyl and other aroxyls has not been observed [12].

Photoexcitation was performed by UV light (λ_ex = 260–380 nm) [11]. Quite similar spectra were observed in propan-1-ol. The spectra (Figure 3) were tentatively ascribed to the Q₁ state of the aroxyls due to their relatively long lifetime (~10 μs) [11].

The D_9,10 ← D₀ transitions were observed under further study of the photochemistry of galvinoxyl with fs flash photolysis (λ_ex = 400 nm) [12]. However, a long-lived absorption very similar to that presented in Figure 3a was ascribed to the anions of glavinoxyl and galvinoxylate. The formation of anions in a nonpolar solvent (Figure 3) is doubtful. The photochemistry of galvinoxyl deserves further study.

Phosphoresce D₀ ← Q₁ was observed for phosphaethynyl radicals in solid argon [13]. The scheme of the electronic levels for this radical follows Figure 1, and the lifetime of the emission is ~0.1 s [13].

Electron spin polarization and magnetic field effects have been investigated in photoexcited organic molecules that are chemically tethered to radical fragments (nitroxyls and others) [14,15]. With TR ESR, electron spin polarization was observed in the D₁ and Q₁ states after photoexcitation of a large stable radical [15].

Scaiano, Johnson et al. performed a cycle of investigations on photoexcited transient radicals such as diphenylmethyl and others [16,17,18]. The radicals were generated by a laser pulse; after a short delay, the second laser pulse excited the produced radicals [16,17]. A fluorescence from D₁ was apparently observed in these experiments. The lifetime of fluorescence varied from 5 to 400 ns for polyatomic radicals in liquid non-viscous solvents at room temperature [16]. The constant k_q of quenching an excited state by dioxygen (Section 5) obtained for several R^•* [16,17,19] testified to the occurrence of Reactions (1) or (2) in the D₁ state; see Section 5. The lifetime of photoexcited diphenylmethyl radicals in common non-viscous solvents is 250 ns at 300 K [16,17]. Once more, this R^•* is in a D₁ state [16].

The excitation of perchlorodiphenylmethyl radical (PDM^•) at λ_ex = 530 nm leads to the population of D₁ (lifetime τ = 31 ns), from which emission is observed (ϕ_fl = 1.0 × 10⁻³) [20]. This state is quenched by electron donors and acceptors at a rate at or close to the diffusion control and at much slower rates by dioxygen and hydrogen atom donors. The fragmentation of PDM^• (ϕ_dec = 0.06) occurs from a higher excited doublet (D_n, n ≥ 2), producing intermediates that are trapped [20]. See [20] for details of the chemical reactions.

The excitation of perchlorotriphenylmethyl radical (PTM^•) at λ_ex = 532 nm leads to an excited doublet, the D₁ state (lifetime τ = 7 ns) [21]. The lifetime of this state is insensitive to dioxygen, electron acceptors, and hydrogen-donating solvents. Electron donors triphenylamine, N,N-dimethylaniline, and thianthrene quench PTM^•* at diffusion-controlled rates. The cyclization of PTM^• to form the perchloro-9-phenylfluorenyl radical occurs with a quantum efficiency of ϕ_cyc = 0.3 under λ_ex = 365 nm irradiation [21].

Ns and ps laser flash photolysis allowed to observe Q₁ ← D₁ ISC of flavin radicals in DNA photolyase [22]. Thus, the electronic levels in this radical follow Figure 1; see [22] for details. The lifetime of the studied D₁ (Q₁) is 100 ps (1 μs) in an aqueous solution at room temperature [22].

Paramagnetic free radicals are efficient quenchers of the excited states of molecules [1,2]. It was observed in experiments with stable aroxyl radicals that self-quenching occurs in solutions [11]:

R^•* + R^• → 2 R^•

(1)

4. Excited Radical Ions

Electronically excited radical cations and radical anions have been the subject of a number of experimental and theoretical investigations.

Stilbene (Sb) radical anions and radical cations were studied by pulse radiolysis and laser flash photolysis [23]. There were four species under investigation, namely cis- and trans-Sb^•(+/−)*. It was stated that the D₂ of these species was observed [23].

Table 1. Properties of stilbene radical anions and radical cations in the D₂ state: lifetime (τ), rate constants of internal conversion (k_ic) and isomerization (k_i), quantum yield of isomerization (ϕ_i), and excitation energies (E) ¹ [23].

Radical-Ion	τ, ns	kic × 10−8, s−1	ki × 10−9, s−1	ϕi	E, kJ/mol
trans-Sb•−*	2.5 ± 1.0	4.0 ± 1.6	0	0	202
cis-Sb•−*	1.5 ± 0.4	5.6 ± 1.7	1.0 ± 0.3	0.14 ± 0.05	189
trans-Sb•+*	0.24 ± 0.05	41 ± 11	0	0	223
cis-Sb•+*	0.12 ± 0.03	29 ± 7	4.1 ± 1.0	0.49 ± 0.12	210

¹ In DMF at room temperature. See [23] for additional details.

below summarizes most of the data obtained in this work:

Radical cations of polycyclic aromatic hydrocarbons (PAH) play an important role in different processes and in the environment—in particular, in astronomy [24]. PAH are easily ionized, producing radical cations PAH^•+. As expected, the absorption spectra of PAH^•+ are red-shifted towards the spectra of the parent PAH [24]. The excited states of 51 different PAH^•+ were studied with the time-dependent density functional theory [24]. The vertical excitation energies and oscillating strengths of PAH^•+ and even of PAH^•− were obtained. π ← π transitions between individual π-orbitals in radical ions of PAH were considered [24].

Biphotonic laser photoexcitation (λ_ex = 248 nm) of different aromatic compounds (biphenyl, naphthalene, perylene, and others) and several amines in oxygenated polar solvents have led to the corresponding radical cation R^•+ [25]. R^•+ have obviously red-shifted spectra compared to the parent compounds and are absorbed in the visible and NIR regions. A prompt irradiation of R^•+ with a second harmonic Nd:YAG laser (λ_ex = 532 nm) led to the excited R^•+* [25]. The studied R^•+* had a lifetime ranging from hundreds of fs to tens of ps at room temperature. The nature of R^•+* is not discussed [25]; it is probably the D₁₍₂₎ states.

In general, excited states of multiple radicals of radical ions in the D_n state have very short lifetimes (see Section 2 and Section 3) as a result of their low-lying excited state energies (energy gap law) [26,27,28].

A study of the dynamics of the ground state recovery of the perylene radical cation (Pe^•+), of the perylene radical anion (Pe^•−), and of the anthraquinone radical anion (AQ^•−) was shown in [29]. Complete or partial regeneration took place after a picosecond photoexcitation of the corresponding radical ion. In boric acid glass, the excited state lifetime of Pe^•+ was 35 ± 3 ps, while in concentrated sulfuric acid, it was smaller than 15 ps, the time resolution of the experimental setup [29]. The excited state lifetime of Pe^•+, Pe^•−, and AQ^•− generated by a photoinduced intermolecular electron transfer reaction in acetonitrile was shorter than 15 ps [29].

It is well known that molecules in excited states essentially change their redox properties [1,2]. Not surprisingly, the same holds true for radical ions. Wasielewski et al. studied the redox properties of radical anions in excited doublet states [26,27]. The radical anions of aromatic diimides have been assumed recently to be participants in different photoinduced electron transfers. The photoexcitation of these radical anions produces powerful reducing agents [26]. However, the properties of the π^*-excited D states of these radical anions remain obscure. The radical anions of three complex aromatic imides with increasingly larger π systems, namely N-(2,5-di-tert-butylphenyl)phthalimide, N-(2,5-di-tert-butylphenyl)-1,8-naphthalimide, and N-(2,5-di-tert-butylphenyl)perylene-3,4-dicarboximide, as well as the three corresponding aromatic diimides [26], were produced by electrochemical reduction of the neutral molecules. The radical anions of these imides and diimides demonstrated intense visible and weaker NIR absorption bands corresponding to their D_n ← D₀ transitions [26]. The excited states of the radical anions were generated by fs excitation (λ_ex = 840 nm) into these absorption bands. Excitation of the first two radical anions mentioned above led to their decomposition, whereas excitation of the third imide and three diimides yielded transient spectra of their D_n ← D₁ transitions. The lifetimes of the observed D₁ states of the radical anions were all less than 600 ps and increased as the D₀–D₁ energy gap increased [26]. These results imposed constraints on the use of these excited radical anions as electron donors in electron transfer systems targeted at molecular electronics and solar energy utilization [26].

Three photoexcited cyanoanthracenes radical anions, including the radical-anion of 9,10-dicyanoanthracene, were produced by photoinduced electron transfer in liquid using femtosecond spectroscopy [30]. All three excited radical ions had 3–5 ps lifetimes due to efficient non-radiative deactivation to the ground state. The excited state of these radical anions was D₁. It is suggested that a short lifetime of D₁ does not preclude photochemical applications of cyanoanthracene radical anions [30].

It was observed that the 10-phenyl-10H-phenothiazine radical cation (PTZ^•+) had a manifold of excited D states accessible using visible NIR light [27]. PTZ^•+ could serve as super-photooxidants with excited state potentials in excess of +2.1 V vs. SCE [27]. The photoexcitation of PTZ^•+ in acetonitrile with λ_ex = 517 nm laser pulse populated a D_n excited D state that decayed first to the unrelaxed lowest electronic excited state, D₁’ (τ < 0.3 ps), followed by relaxation to D₁ (τ = 10.9 ± 0.4 ps) [27]. D₁ finally decayed to D₀ (τ = 32.3 ± 0.8 ps) [27]. To probe the oxidative power of PTZ^•+* D_n states, PTZ^•+ was covalently linked to each of three hole acceptors: perylene, 9,10-diphenylanthracene, and 10-phenyl-9-anthracenecarbonitrile, which have oxidation potentials of 1.04, 1.27, and 1.6 V vs. SCE, respectively [27]. In all three cases, photoexcitation wavelength-dependent ultrafast hole transfer occurred from the D_n, D₁’, or D₁ of PTZ^•+* to the three acceptors. The high oxidative power of the D_n state of PTZ^•+* will enable applications using this chromophore as a superoxidant for energy-demanding reactions [27].

The quantum chemical calculations (restricted coupled cluster with perturbative triples method) were used to calculate the equilibrium geometries and excitation energies of the hitherto unknown Q states in diacetylene-, triacetylene-, and benzene radical cations [31]. Spectroscopic data for the D states obtained with the same approach were found to be in good agreement with the experiment [31]. In diacetylene and triacetylene cations, there were Q states that were close to the minimum energies of the corresponding D₁ states [31].

The kinetics of the radical cations of perylene (PE^•+), tetracene (TE^•+), and thianthrene (TH^•+), as well as the radical anions of anthraquinone (AQ^•−) and tetracenequinone (TQ^•−), formed by γ irradiation in low-temperature matrices (PE^•+, TH^•+, AQ^•−, and TQ^•−) or by oxidation in sulfuric acid (PE^•+, TE^•+, and TH^•+) were investigated using picosecond spectroscopy [32]. The longest ground state recovery time measured was 100 ps. It is not surprising that the excited state lifetime of PE^•+ is substantially longer in low temperatures than in sulfuric acid. The data suggest that both PE^•+* and TE^•+* probably decay by a reversible charge transfer reaction [32]. TQ^•− demonstrates fluorescence [32]. Most probably, the studied radical ions are photoexcited in the doublet state.

Electron acceptor methyl viologen (N,N′-dimethyl-4,4′-bipyridine, abbreviated MV²⁺) plays an important role in redox reactions (MV²⁺ ↔ MV^•+ [33]). Femtosecond pump-probe spectroscopy was used to investigate the excited state dynamics of the electrochemically generated MV^•+ in an acetonitrile solution [34]. Excitation of the D₁ ← D₀ transition at λ_ex = 730 nm led to rapid relaxation (700 fs), generating two intermediates in the transient absorption spectra [34]. The longer-lived intermediate, with a lifetime of 16 ps, could be assigned to a vibrationally excited ground state of MV^•+. Its absorption spectrum was very similar to the ground state spectrum of MV^•+ in both shape and extinction coefficients but red-shifted by ~810 cm⁻¹ [34]. The shorter-lived transient decayed with a characteristic time of τ = 1.0 ± 0.1 ps and was possibly also a vibrationally excited ground state. Thus, these results show that the excited D₁ state of MV^•+* in an acetonitrile solution relaxes on the fs time scale via at least one long-lived (τ = 16 ps) vibrationally excited ground state [34].

The study [35] provides evidence that the photoexcited radical cation of guanine in DNA participates in chemical reactions.

5. Quenching of Photoexcited Radicals by Dioxygen

The majority of free radicals (especially C-centered alkyl, aromatic benzyl, and others) react with dioxygen at rates controlled by diffusion in a solution. The same is expected for highly reactive R^•*. The rate of a diffusion-controlled reaction estimated by the Debye formula is k_diff ≈ 7 × 10⁹ M⁻¹·s⁻¹ at room temperature (T) and a solvent viscosity of η = 1 cP [36]. In the case of a reagent with a non-zero spin, the expected rate constant of the diffusion reaction is lower: k_q = σ k_diff, where σ is the spin–statistical factor [19,36]. There are two types of quenching of R^•*−, physical and chemical [19]:

ⁿR^•* + ³O₂ → ²R^• + ¹O₂ (¹∆_g)

(2)

ⁿR^•* + ³O₂ → ²RO₂^•

(3)

Photoexcited R^•* can be in the D₁ state (n = 2) or in the Q₁ state (n = 4). It is easy to obtain that, for Reactions (2) and (3), σ = 1/3 and 1/6 for n = 2 (D₁) and n = 4 (Q₁), respectively. Thus, one can expect k_q ≈ 2 × 10⁹ (1 × 10⁹) M⁻¹·s⁻¹ for the quenching of R^•* for D₁ (Q₁) in Reactions (1) or (2) under T and η mentioned above (It is known that k_diff ~ η⁻¹; the rate constant of a reaction with fast-diffusing O₂ may have higher k_diff-values than those predicted by the Debye formula).

6. Conclusions

The main elementary photophysical processes in the excited free radicals are depicted in Figure 1 and Figure 2. There is an analogy with the relevant photophysical processes in molecules (Figure 1), but the photophysics of R^•* are more complex (Figure 2). Usually, D₁ or Q₁ were observed in the experiments by their emission or absorption spectra. Additional TR ESR experiments would make such assignments more reliable. Quantum chemical calculations should help in the identification of R^•*, their electronic nature and their structure as well.

It is possible to conclude that the Q₁ state has a much longer life than the D₁ state of the same radical. It is obvious that D₀ ← Q₁ transition occurs with a change in the spin multiplicity and is analogous to S₀ ← T₁ ISC or phosphorescence in molecules.

Stable nitroxyl radicals (TEMPO and others) have been widely used in chemistry research as antioxidants and as photostabilizers of polymers for many decades. To the best of our knowledge, there are no experimental data on the excited states of nitroxyls.

There are tens of colored stable free radicals that are commercially available or can be synthesized. The photochemistry of a small portion of them has been studied; see some examples in Section 3 and Section 4 above. Stable radicals are valuable and convenient objects for the study of their excited states and their transformations. The first triphenylmethyl free radical discovered by Gomberg in 1900 was in equilibrium with its corresponding dimer [37]. Once more, to the best of our knowledge, there are no experimental data on the excited state of the first radical.

The high reactivity of photoexcited radicals and radical ions may find applications, such as the decomposition of environmental pollutants and light energy conversion [38]. However, a detailed picture of excited radical ions provided by spectroscopy require further clarification, especially the nature of the excited states. Laser flash photolysis (from μs to fs) and other spectroscopic and quantum-chemical calculations will shed light on the nature and reactivity of such excited species. These multidisciplinary studies will help us obtain detailed understandings of the chemistry of the higher excited states and excited intermediates [38,39].

It would be of interest to compare ESR spectra of radicals in the ground and in excited states to compare hyperfine coupling constants (HFC) and g factors. It will give information on the geometrical structure of R^•*.

It is expected that a relatively long lifetime (~10 μs) in solvents at room temperature signified that R^•* is in the Q₁ state.

The measured numerical values of the rate constant k_q of quenching R^•* by O₂ give a hint as to the nature of a spin state of R^•*.