Radical Reactivity of the Biradical [⋅P(μ‐NTer)2P⋅] and Isolation of a Persistent Phosphorus‐Cantered Monoradical [⋅P(μ‐NTer)2P‐Et]

Abstract The activation of C−Br bonds in various bromoalkanes by the biradical [⋅P(μ‐NTer)2P⋅] (1) (Ter=2,6‐bis‐(2,4,6‐trimethylphenyl)‐phenyl) is reported, yielding trans‐addition products of the type [Br−P(μ‐NTer)2P−R] (2), so‐called 1,3‐substituted cyclo‐1,3‐diphospha‐2,4‐diazanes. This addition reaction, which represents a new easy approach to asymmetrically substituted cyclo‐1,3‐diphospha‐2,4‐diazanes, was investigated mechanistically by different spectroscopic methods (NMR, EPR, IR, Raman); the results suggested a stepwise radical reaction mechanism, as evidenced by the in‐situ detection of the phosphorus‐centered monoradical [⋅P(μ‐NTer)2P‐R].< To provide further evidence for the radical mechanism, [⋅P(μ‐NTer)2P‐Et] (3Et⋅) was synthesized directly by reduction of the bromoethane addition product [Br‐P(μ‐NTer)2P‐Et] (2  a) with magnesium, resulting in the formation of the persistent phosphorus‐centered monoradical [⋅P(μ‐NTer)2P‐Et], which could be isolated and fully characterized, including single‐crystal X‐ray diffraction. Comparison of the EPR spectrum of the radical intermediate in the addition reaction with that of the synthesized new [⋅P(μ‐NTer)2P‐Et] radical clearly proves the existence of radicals over the course of the reaction of biradical [⋅P(μ‐NTer)2P⋅] (1) with bromoethane. Extensive DFT and coupled cluster calculations corroborate the experimental data for a radical mechanism in the reaction of biradical [⋅P(μ‐NTer)2P⋅] with EtBr. In the field of hetero‐cyclobutane‐1,3‐diyls, the demonstration of a stepwise radical reaction represents a new aspect and closes the gap between P‐centered biradicals and P‐centered monoradicals in terms of radical reactivity.


Introduction
Open-shell singlet biradical(oid)s, such as [ * P(μ-NTer) 2 P * ] (1; Scheme 1) with a biradical character of 25 %, [1] are molecular species with a spin density of exactly zero at any point in space, [2] even though the two radical electrons tend to avoid each other. [3] There are many classifications and names for biradicals (diradical, biradicaloid, etc.); [4] however, throughout this paper we will only use the term biradical since the transitions between open-shell singlet biradical!biradicaloid! closed-shell singlet species are smooth in terms of electronic interaction. [5,6] Depending on the strength of the antiferromagnetic coupling between the electrons and therefore on the degree of biradical character, singlet biradicals usually feature a reactivity that lies between typical closed-shell and radical species. [3,[7][8][9][10][11][12] That is, biradicals can undergo pericyclic, concerted reactions, or step-wise, radical-type reactions.

Bromoalkane addition: Synthesis of 1,3-substituted cyclo-1,3-diphospha-2,4-diazanes
We started this project with addition reactions between biradical 1 and a series of bromoalkanes (Scheme 1), affording addition products 2, so-called 1,3-substituted cyclo-1,3-diphospha-2,4-diazanes. Over the course of the addition, the CÀ Br bond of the bromoalkane is cleaved and the bromine atom is attached to one phosphorus atom and the organic substituent to the other. The dominant product of the reaction was always the trans-addition product ( Figure 1).
1,3-Dibromo-cyclo-diphosphadiazane 4 could also be synthesized directly by reacting 1 with dry bromine in benzene at ambient temperature, however, yielding a mixture of the cisand trans-isomer in a ratio of 2 : 7 (δ[ 31 P] = 243.9 for cis-and 277.9 ppm for trans-4). After crystallization, almost pure trans-4 (97 % trans isomer) was obtained. 4 has not been reported before and completes the series of 1,3-dihalogen-cyclo-1,3diphospha-2,4-diazanes (formal dihalogen addition products of 1). [36][37][38] 31 P NMR shifts of all dihalogen addition products are compiled in Table 1. The 31 P NMR shift increases towards heavier halogens, so the data of 4 fits in with the data of the other adducts. The molecular structure of 4 as determined by single crystal X-ray diffraction is shown in Figure 2. It reveals a planar N 2 P 2 ring system and typical PÀ Br single bond lengths (2.311(1) Å).
All addition products 2 (see above) could be crystallized and fully characterized (see the Supporting Information). After repeated recrystallization the bromoalkane adducts 2 still contained small impurities, mainly trans-4. Corresponding NMR spectra can be found in the Supporting Information. As depicted in Figure 1, the molecular structures were determined by single-crystal X-ray diffraction and reveal slightly puckered N 2 P 2 ring systems (in contrast to 4) with somewhat shortened NÀ P single bonds (1.70-1.78 Å, cf. Σr cov (PÀ N) = 1.82 Å [39] ).

Mechanistic studies for the reaction of biradical 1 with EtBr
Although only small amounts of 1,3-dibromo-cyclo-1,3-diphosphadiazane 4 were found in all reactions of 1 with bromoalkanes, this observation prompted us to further investigate the mechanism of the formation of 1,3-substituted cyclo-1,3diphospha-2,4-diazanes (2), since only a radical mechanism (Scheme 3) should allow the formation of 4. Moreover, concerted addition of RÀ Br to 1 should always give the cis-products of 2, but we observed only the trans-products. To answer these questions, a series of kinetic studies were performed along with EPR studies for the addition reaction of EtBr giving 2 a.
First, the reaction of 1 with EtBr was traced by 31 P NMR spectroscopy. Spectra were recorded over several days in shorter intervals at the beginning and longer ones towards the end of the experiment. The reaction rate was determined by modeling second order kinetics to the experimental data as illustrated in Figure 3. In particular, the in situ NMR spectra (see the Supporting Information) display the appearance and  Table S4 in the Supporting Information. disappearance of several small signals, including the abovementioned by-product [BrP(μ-NTer) 2 PBr] (4). Thus, the byproducts were attributed to typical chain-termination reactions (see also Computational Studies below).
Considering the evidence for a radical mechanism, the reaction of EtBr with 1 was repeated in the presence of azobis(isobutyronitrile) (AIBN; Figure S12). To compare the outcomes of the addition reaction with and without radical starter, two batches of 2 a were prepared, one with and one without the use of AIBN, but otherwise under exactly the same conditions. A reaction temperature of 60°C was chosen to activate AIBN. After 2 h, 31 P NMR spectra were recorded. The ratio of biradical 1 (starting material) to addition product 2 a was 2 : 7 with AIBN and 2 : 3 without AIBN ( Figure S12), indicating a significant acceleration (x2.5) of the addition reaction upon addition of AIBN. Only a radical reaction mechanism can explain this acceleration.
To finally prove that the addition of EtBr is indeed a radical reaction, in situ EPR spectra (red graph in Figure 4) were recorded during the reaction. The spectrum displays a doublet (g = 2.003) with a large hyperfine coupling constant (a( 31 P) = 59 G) due to the coupling of an unpaired electron with a phosphorus nucleus. This and the disappearance of the signal once the reaction is completed suggests the presence of a phosphorus-centered radical intermediate during the reaction.
To elucidate the identity of this intermediate radical, we tried to generate both the bromine-substituted radical 3Br * and the Et-substituted radical 3Et * directly (Scheme 3). When the dibromine adduct 4 ([BrP(μ-NTer) 2 PBr]) is treated with magnesium, always biradical 1 ([ * P(μ-NTer) 2 P * ]) is formed, while the reduction of the EtBr adduct 2 a leads to the persistent radical 3Et * that can be isolated in substance (see below). The recorded EPR spectrum of 3Et * is virtually identical to the spectrum taken from the reaction solution of 1 + EtBr (Figure 4), so that we have a direct proof that 3Et * forms in situ as intermediate.
Also, DFT computations (see the Supporting Information for further details) indicated that the phosphorus-centered radical intermediate is the ethyl substituted radical 3Et * (Scheme 3). The EPR parameters calculated for 3Et * in silico are in good agreement with the experimental data (gray graph in Figure 4). Additionally, calculations on the other possible, brominesubstituted radical intermediate 3Br * hint at a different, more complicated EPR coupling pattern, not at all in alignment with the experimental data.
Spin density computations of 3Et * also confirm it as a phosphorus-centered radical. The Mulliken spin density is mainly localized at P1 (0.70); while only small values are computed for N1 (0.043) and N2 (0.045), respectively ( Figure 5).

Chemistry-A European Journal
Research Article doi.org/10.1002/chem.202200624 sium worked nicely and the PÀ Br bond was reductively cleaved within 2 h, yielding after recrystallization the desired, dark red, persistent phosphorus-centered radical 3Et * in good yields (83 %). The presence of the molecular radical 3Et * in the solid state was unequivocally proven by single crystal X-ray diffraction ( Figure 6). Surprisingly, the oxygen-and moisture-sensitive radical 3Et * is stable for long periods as a solid when stored sealed in an ampoule under inert gas. Thermally, decomposition only begins above its melting point of 195°C. These properties, together with its good solubility in many organic solvents, allowed a full characterization (see the Supporting Information) and suggest an interesting follow-up chemistry for radical 3Et * .
EPR spectra of a solution of a crystalline sample of 3Et * (black graph in Figure 4) are virtually identical with the in situ EPR signal during the formation of 2 a in the reaction of 1 with EtBr (small "side bands" in the in situ spectrum are attributed to impurities as they did not change over time, see above). Thus, we conclude that 3Et * is in fact an intermediate in the addition of EtBr to 1. The measured EPR parameters (g = 2.003, A = 59 G) are in alignment with other literature-known P-centered radicals. [74] Also note the different scales of the two measurements depicted in Figure 4 with an intensity difference of six orders of magnitude, showing the difference in concentration between a sample of the pure compound and the in situ measurement.
The UV-vis spectrum of 3Et * shows a distinct absorption band at 399 nm ( Figure S8), responsible for the dark red color of the compound. DFT calculations indicate that the red color is caused by a combination of excitations, in particular the excitation of the unpaired electron at P1 into a π* orbital of the Ter substituents (see the Supporting Information for TD-DFT data and NTO transformation, Figures S23 and S24).
Persistent radical [75] 3Et * belongs to the class of P-centered radicals (Scheme 5). Since the discovery of the first persistent radical (triphenylmethyl) by Gomberg in 1900, [76] considerable advances have been made in persistent radical chemistry and radicals such as TEMPO (2,2,6,6-tetramethylpiperidin-1-yl)oxyl) have found widespread applications in organic chemistry. [77] However, only very few phosphorus-centered persistent radicals that can be isolated as a solid are known. An overview with examples of neutral phosphorus radicals that could be structurally characterized is presented in Scheme 5. Phosphoruscentered radicals are known to activate various small molecules, such as P 4, [78,79] chalcogens , [79,80] CS 2 and CO 2.

Scheme 5.
Selected examples of neutral, persistent P-centered radicals. [74,[83][84][85] formation of a 1 : 1 mixture of trans-2 a and [EtP(μ-NTer) 2 PEt] (5 a) as shown by 31 P NMR studies (trans-2 a: 229.2/255.2 ppm; cis/trans-5 a: 225.2/266.7 ppm). The formation of trans-2 a is consistent with the result of the reaction of biradical 1 with EtBr, where only trans-2 a was obtained, but not 5 a. Still, the formation of 5 a in the reaction of 3Et * with EtBr is not surprising, since in this instance there is a very large concentration of the 3Et * radical in solution at the beginning of the reaction, which can react directly with another Et * radical that is formed upon reaction of EtBr with 3Et * (see reaction 4 in Scheme 7, below), finally yielding [EtP(μ-NTer) 2 PEt] (5 a). In contrast, the formation of 5 a is very unlikely in the reaction of biradical 1 with EtBr, as 3Et * is only formed as a lowconcentrated intermediate in this case. From these combined experimental (and theoretical) studies, we can summarize that in the reaction of biradical 1 with EtBr, persistent radical 3Et * occurs as an intermediate, indicating a radical mechanism for the addition reaction.

Computational studies
From the experimental studies on the mechanism of the EtBr addition to biradical 1, several questions arose, such as why is the radical mechanism preferred over a concerted mechanism (Scheme 3) or which radicals form preferentially? To answer these questions, DFT and coupled cluster calculations on kinetics and thermodynamics were performed (see the Supporting Information for details). Furthermore, to account for the open-shell biradical character of biradical 1 along the reaction pathway, Complete Active Space SCF (CASSCF) methods were applied. The orbitals of the active space and their contributions are listed in Table S5. To account for dynamic correlation, the CASSCF reference wavefunctions were subjected to multireference perturbation calculations, using the Fully Internally Contracted N-Electron Valence State Perturbation Theory (FIC-NEVPT2). [91][92][93] Model system. To obtain an initial idea of possible reaction pathways, the model reaction of [ * P(μ-NH) 2 P * ] (1 H ) with MeBr was investigated. Therefore, a variety of nudged elastic band (NEB) [94][95][96][97][98] and relaxed potential energy surface (PES) scans were performed at the UPBEÀ D3/def2-SVP [99] level of theory using ORCA 4.2.1 [61,67] or Gaussian 09, [68] respectively. Different orientations of the starting materials and configurations of the product were considered. We could not locate a transition state for a concerted mechanism (e. g., analogous to the addition of H 2 to the singlet biradical [ * P(μ-NTer) 2 P * ], Scheme 2). [35,100,101] All results pointed towards a stepwise (i. e., radical) mechanism of the reaction, in agreement with experimental observations. In   Table S6.

Chemistry-A European Journal
Research Article doi.org/10.1002/chem.202200624 particular, our model computations implied that the formal abstraction of a Br * radical from the bromoalkane by the singlet biradical initiated the radical chain reaction (see also section "Real system" below). It was therefore of special interest to investigate this first reaction step in more detail (Scheme 6).
Therefore, this initiation reaction (resulting in a radical chain reaction, see below and Scheme 6) is an intrinsically biradical process with a steadily decreasing singlet-triplet gap and an increasing biradical character (Figures 7 and 8). At the end of the reaction, when only the two separate radicals 3 H Br * and CH 3 * are present, the singlet and triplet states are degenerate, that is, two separate doublet species are present. Along the path on the singlet PES, no barrier is found but the formation of the two doublet species is endergonic. For the separated molecules 1 H and MeBr, the biradical character (about 25 %) is attributed exclusively to the radical electrons at the two P atoms in 1 H (as represented by the blue isosurfaces of the local nondynamic correlation function [102][103][104] depicted in Figure 8). The biradical character increases dramatically over the course of the reaction, while one of the associated radical electrons shifts across the bromine atom to the methyl-C atom. Note that the tetraradical character (Figure 8), although low throughout the process, reaches a maximum at about d(CÀ Br) = 2.5 Å, where the CÀ Br and PÀ Br bond orders are roughly equal (Figure 9), indicating a small admixture of a Lewis-type structure of the type * P(μ-NH) 2 P * ⋯Br * ⋯Me * (see also Table S5 for a depiction of the active orbitals).
Real system. Possible radical reaction steps were computed using the actual molecular structures (i. e., including the Ter and Et substituents). The relevant steps are listed in Scheme 7 (a full set of all possible reactions can be found in Table S6). In agreement with our computations on the model system (see above), we identified the abstraction of Br * from EtBr by the biradical [ * P(μ-NTer) 2 P * ] (1) as the probable initiation reaction in an endergonic process (Δ R G°= 103 kJ mol À 1 ) yielding 3Br * . The formation of the ethyl-substituted radical 3Et * in this first step is thermodynamically significantly less favored (Δ R G°= 149 kJ mol À 1 , cf. reactions 1 and 2 in Scheme 7). In this sense, the initiation reaction(s) may be understood as the "reaction barrier" for the radical process (cf. Scheme 8). Radical 3Br * now has different reactions channels it can follow: i) 3Br * can react with the free Et * radical to give the (experimentally observed) final trans product 2 a in a highly exergonic reaction (Δ R G°= À 186.5 kJ mol À 1 , reaction 8 in Scheme 7). Therefore, the overall reaction 1 + EtBr ! trans-2 a becomes energetically favored with À 83.5 kJ mol À 1 (reaction 9 in Scheme 7). However, this termination reaction is rather unlikely because the concentration of free Et * radicals is very small compared to the concentration of EtBr. ii) 3Br * can further react with EtBr affording the experimentally observed by-product 4 and Et * (Δ R G°= + 31.9 kJ mol À 1 , reaction 5). The actual reaction turnover proceeds through addition of the free Et * radical (which is   [102][103][104] (iso = 0.0025) at the points indicated in red. Figure 9. Change in the PÀ Br, CÀ Br, and P'À C bond orders along the MEP of the initiation reaction (using a model system). The CÀ Br bond order decreases (corresponding to the bond being broken), while the PÀ Br bond order increases smoothly. The interaction between the two radical centers (P', C) in the product is slightly antibonding throughout the reaction. initially generated by reactions 2 and 5 as discussed above) to the biradical [ * P(μ-NTer) 2 P * ] (1), leading to the spectroscopically observed intermediate [ * P(μ-NTer) 2 P-Et] (3Et * ) in an exergonic reaction (Δ R G°= À 106.6 kJ mol À 1 , reaction 3). Radical 3Et * then reacts with another equivalent of EtBr to the product [Br-P(μ-NTer) 2 P-Et] (2 a) and a new Et * radical (Δ R G°= + 23.1 kJ mol À 1 , reaction 4). The free Et * radical can then repeat the reaction cascade outlined above (Scheme 8). All termination reactions are highly exergonic (Scheme 7 and Table S6).
Why is the radical 3Et * the crucial intermediate (which we do observe experimentally), but not the bromine-substituted radical 3Br * , which forms at the beginning of the reaction? This can be explained when considering the possible reactions of both radical species 3Et * and 3Br * with EtBr (e. g., reaction 4 in Scheme 7): The reaction of 3Br * with EtBr leads preferentially to the side product 4 (+ 31.9 kJ mol À 1 , reaction 5), while the reaction 3Br * + EtBr!2a + Br * is thermodynamically unfavored (+ 69.9 kJ mol À 1 , Table S6). In contrast, the formation of the product 2 a from 3Et * and EtBr (+ 23.1 kJ mol À 1 , reaction 4) is much more likely than the formation of the hypothetical byproduct [Et-P(μ-NTer) 2 P-Et] (5 a, + 98.6 kJ mol À 1 ), which was not observed experimentally (see above). Thus, formation of the final reaction product 2 a via the intermediate 3Et * corresponds to the minimum energy path on the potential energy surface.
As outlined above, the by-product [Et-P(μ-NTer) 2 P-Et] (5 a) could in fact be generated when isolated 3Et * was treated with EtBr. This is also in line with our computed radical reaction steps (Scheme 7 and Table S6). In this case, 5 a is likely formed by the termination reaction 3Et * + Et * (À 157.7 kJ mol À 1 , reaction 6), owing to the very large concentration of 3Et * , which is at least six orders of magnitude larger than the concentration of the intermediately formed 3Et * in the reaction of 1 with EtBr. Thus, in the latter case, the same termination reaction is very unlikely to happen.
Finally, compared to cis-2 a, the formation of trans-2 a is energetically more favored by À 24.3 kJ mol À 1 (cf. reactions 9 and 10 in Scheme 7). This fact is best understood by looking at reaction 4 in Scheme 7. The formation of trans-2 a is associated with a Gibbs energy of + 23.1 kJ mol À 1 , while the analogous reaction to the cis-2 a product requires + 47.7 kJ mol À 1 (Table S6). Since these radical reaction steps are equilibrium reactions, it is understandable that the formation of trans-2 a is thermodynamically significantly favored, which explains the exclusively observed formation of trans-2 a. It is also worth noting that a solution of pure trans-2 a does not isomerize to cis-2 a.

Conclusion
We have demonstrated the radical reactivity of the biradical [ * P(μ-NTer) 2 P * ] (1) for addition reactions of bromoalkanes. This approach represents a new synthesis route to asymmetrically substituted 1,3-substituted cyclo-1,3-diphospha-2,4-diazanes. Extensive experimental and theoretical studies revealed [ * P(μ-NTer) 2 PEt] (3Et * ) as a radical intermediate for the addition process of ethyl bromide to 1. With the direct synthesis of 3Et * , it was possible to obtain a hitherto unknown persistent phosphorus-centered radical that can be generated on a large scale and stored for a long time under inert gas. It was possible to fully characterize 3Et * , inter alia by EPR spectroscopy, singlecrystal X-ray diffraction and UV-vis spectroscopy. Reactivity studies of 3Et * with EtBr demonstrated its application in smallmolecule activation processes, and we believe that it has the potential to open a new field of activation chemistry involving phosphorus, due to its relatively high thermal stability and good accessibility.

Experimental Section
All experiments were carried out under oxygen-and moisture-free conditions in an inert argon atmosphere using standard Schlenk or dry-box techniques. Experimental details including synthetic protocols, spectroscopic data and computational details can be found in the Supporting Information.
Deposition Numbers 2068187 (for 2 a), 2068188 (for 2 b), 2068189 (for 2 c), 2107762 (for 2 d), 2068190 (for 3Et * ), 2069052 (for 4) contain the supplementary crystallographic data for this paper. These data are provided free of charge by the joint Cambridge Crystallographic Data Centre and Fachinformationszentrum Karlsruhe Access Structures service.