Rational Design of Persistent Phosphorus-Centered Singlet Tetraradicals and Their Use in Small-Molecule Activation

Abstract

Biradicals are important intermediates in the process of bond formation and breaking. While main-group-element-centered biradicals have been thoroughly studied, much less is known about tetraradicals, as their very low stability has hampered their isolation and use in small-molecule activation. Herein, we describe the search for persistent phosphorus-centered tetraradicals. Starting from an s-hydrindacenyl skeleton, we investigated the introduction of four phosphorus-based radical sites linked by an N–R unit and bridged by a benzene moiety. By varying the size of the substituent R, we finally succeeded in isolating a persistent P-centered singlet tetraradical, 2,6-diaza-1,3,5,7-tetraphospha-s-hydrindacene-1,3,5,7-tetrayl (1), in good yields. Furthermore, it was demonstrated that tetraradical 1 can be utilized for the activation of small molecules such as molecular hydrogen or alkynes. In addition to the synthesis of P-centered tetraradicals, the comparison with other known tetraradicals as well as biradicals is described on the basis of quantum mechanical calculations with respect to its multireference character, coupling of radical electrons, and aromaticity. The strong coupling of radical electrons enables selective discrimination between the first and the second activations of small molecules, which is shown by the example of H₂ addition. The mechanism of hydrogen addition is investigated with parahydrogen-induced hyperpolarization NMR studies and DFT calculations.

Introduction

Biradicals are molecules with two radical electrons in two nearly degenerate orbitals.¹⁻⁴ A classification of biradicals is possible, for example, on the basis of the electron exchange coupling constant (J),⁵ which describes the interaction between the two radical electrons (Figure 1, top). Molecular systems, in which the radical electrons do not interact with each other (J = 0), are called dis-biradicals and are in spectroscopic terms two-doublet species.⁶ When the electrons do interact with each other (J ≠ 0), a biradicaloid is formed where the electrons couple either antiferromagnetically (singlet species, J < 0) or ferromagnetically (triplet species J > 0).^6,7 However, there is no exact value for J, which separates biradicaloids from dis-biradicals and closed-shell molecules. For simplicity, the term biradical is used in this article, and unless otherwise stated, it refers to biradicaloids. The same applies to the term tetraradical referring to tetraradicaloids.

Figure 1.

Classification of symmetrical bi-⁶ and tetraradicals⁸ by means of electron exchange coupling constants J (antiferromagnetic coupling: negative J; ferromagnetic coupling: positive J). A green circle corresponds to an atom with one radical electron.

Extending the biradical concept, tetraradicals are molecules with four radical electrons in four nearly degenerate orbitals. Here, the interaction between the four radical electrons can be completely described by six electron exchange coupling constants. To simplify such systems, the discussion is restricted here to symmetrical tetraradicals, in which two biradicals are connected by a linker and in which the interactions can be described by only two electron exchange coupling constants (Figure 1, J₁ = coupling within a biradical unit, J₂ = coupling between the two biradical units, where |J₁| ≥ |J₂|).

With these restrictions, three different types of tetraradicals can be distinguished by considering the coupling constants (Figure 1, bottom): (a) Dis-tetraradicals, in which no interaction between the electrons occurs at all (J₁ = J₂ = 0, four-doublet species); (b) bis(biradicaloids), in which there is no interaction between the two sets of biradicaloids (J₂ = 0), and depending on the coupling within the biradical fragments either a singlet (J₁ < 0) or a two-triplet species (J₂ > 0) can be present; and (c) tetraradicaloids, in which there is an interaction between the electrons of both biradical units and the species either adopts a singlet (J₁ and/or J₂ < 0) or quintet state (J₁ and J₂ > 0).

Stable cyclic biradicals have been in the focus of preparative chemistry^7,9−12 since the synthesis of the first stable heterocyclobutene-1,3-diyl by Niecke and co-workers in 1995.¹³ Their unique reactivity with respect to bond activation is in between radicals and closed-shell molecules.¹⁴ For example, the activation of small molecules such as dihydrogen,¹⁵⁻²⁰ chalcogens,²¹⁻²³ halogenated alkanes,²⁴⁻²⁸ and molecules with double and triple bonds (e.g., CO,²³ HCCH^28,29) by cyclic main-group-element-centered biradicals has been demonstrated in many studies.^5,7,10

Heteroatom-centered cyclic tetraradicals, on the other hand, have been the subject of only a few publications so far (Scheme 1).^28,30,31 Conceptually, tetraradicals can be constructed by linking two biradicals (vide supra), as illustrated in Scheme 1. For example, our group was able to synthesize the tetraradical B by bridging two P-centered heterocyclopentane-1,3-diyls A with a methylenediphenyl linker.²⁸ Since the non-conjugated linker does not allow any interaction between the two biradical units, it has to be considered as a bis(biradicaloid), showing the same reactivity and properties as the single, uncatenated biradicaloid A. Bertrand and co-workers were able to link two boron-centered heterocyclobutane-1,3-diyls³⁰C with a para- and meta-substituted benzene (Scheme 1). Interestingly, para-substitution results in the formation of the tetraradical para-D, while the meta-substituted isomer, meta-D, forms a closed-shell species with transannular boron–boron bonds at ambient temperatures.³² It should be noted that also tetraradical para-D forms a closed-shell butterfly species with two boron–boron bonds at slightly elevated temperatures. DFT calculations of meta- and para-D showed that both biradical units interact significantly via the conjugated linker. The interaction in meta-D is smaller than in para-D, which was given as a possible reason for the exclusive observation of the closed-shell species meta-D.⁸ Besides main-group-element-centered tetraradicals B and para-D, some further—however less related—compounds like cluster-³¹ or organic aminoxyl-³³⁻³⁶ and aminyl-based³⁷ as well as C-centered^31,38−42 tetraradicals are known.

Scheme 1. Known Main-Group-Element-Centered Tetraradicals (B,²⁸para-D³²), Synthesized by Linking Biradical Structural Motifs (A,²⁸C,³⁰ and E(43)).

We were intrigued by the idea to extend the structural motif of the recently published azadiphosphaindane-1,3-diyl (E, Scheme 1)⁴³ to the tetraradical 1, in which all radical electrons are part of a condensed, aromatic 14π electron ring system. Two questions were of interest in the synthesis: First, how bulky must the steric hindrance be to prevent dimerization or oligomerization of the tetraradical, because this would lead to closed-shell systems? And second, is it possible to use these tetraradicals for the stepwise activation of small molecules? Through the interaction between the radical sites, when using the benzene linker, we hoped to achieve a kinetic separation between the addition of a first and second equivalent of a small molecule to the formal biradical units in 1. For bis(biradicaloids), no kinetic separation between the two activation steps is expected due to the missing interaction and large spatial separation, so that both biradical subunits react independently.

Results and Discussion

Synthesis

To form a type 1 tetraradical, several aspects must be considered in the design. First, it needs sufficiently large steric protection, which can be tuned via the substituent at the nitrogen atom. Second, it needs suitable precursors for the construction of two PNP units connected to the central benzene ring. To this end, we identified 1,2,4,5-tetrakis(dichlorophosphino)benzene 2 (Scheme 2) as suitable starting material. Tetraphosphane 2 was recently published by our group and is easily prepared in very good yield (91%) by complete chlorination of the corresponding tetraphosphane with PCl₅.⁴⁴

Scheme 2. Synthesis of Differently Substituted 2,6-Diaza-1,3,5,7-tetraphospha-s-hydrindacene-1,3,5,7-tetrayls (1R).

Their stability toward oligomerization depends on the steric demand of the substituent R (= Ter, EMind), as depicted on the right.

Synthesis of Starting Materials

With tetrakis(dichlorophosphino)benzene 2 in hand, double ring closure on both sides of the benzene ring was attempted by reaction with two equivalents of a primary amine, H₂N-R, in a dehydrochlorination reaction (Scheme 2; R = Ter, ^tBuBhp, Mes*, and EMind; Ter = 2,6-dimesitylphenyl,^45,46tBuBhp = 2,6-bis(benzhydryl)-4-tert-butylphenyl,^43,47 Mes* = 2,4,6-tri-tert-butylphenyl,⁴⁸ and EMind = 1,1,7,7-tetraethyl-3,3,5,5-tetramethyl-s-hydrindacenyl).⁴⁹⁻⁵¹ In the case of the Ter and EMind substituents, this reaction led to the formation of the tricyclic, 4-fold chlorinated ring system 3R in good yields (3Ter: 62%, 3EMind: 78%), whereas the Mes* and ^tBuBhp derivatives were only formed in low yields and/or could not be isolated in acceptable purity (cf. Supporting Information (SI), p S44 ff.).

Both 3Ter and 3EMind are thermally very stable up to about 360–380 °C. They dissolve well in CH₂Cl₂, from which colorless single crystals were obtained (Figure 2). Interestingly, for 3Ter, the trans isomer is found (the two chlorine atoms on each side are trans to the two on the other side), while for 3EMind all chlorine atoms are on one side of the three condensed rings, resulting in the formation of a cis isomer in the crystal. In both compounds, the central benzene ring remains planar, while the two outer five-membered rings are notably puckered (envelope conformation). This effect is much more pronounced in 3EMind. The mean P–C (3Ter: 1.821(2), 3EMind: 1.825(3) Å) and P–N bonds (3Ter: 1.706(3), 3EMind: 1.715(4) Å) are in the typical range of polarized single bonds (cf. ∑r_cov.(C–P) = 1.86 Å, ∑r_cov.(N–P) = 1.82 Å).⁵² As expected, the ³¹P NMR spectra showed a singlet signal at 143 (3Ter) and 145 ppm (3EMind), respectively.

Figure 2.

Molecular structures of 3Ter (top) and 3EMind (bottom) in the crystal (T = 203 K, ellipsoids at 50% probability). Selected bond lengths [Å] and angles [deg]: 3Ter: P1–Cl1 2.102(1), P1–P2 2.964(1), P1–C1 1.821(2), P2–Cl2 2.084(1), P2–C2 1.821(2), N1–P1–P2–C2–160.6(2), symmetry code: (′) = 1–x, 1–y, 1–z; 3EMind: P4–Cl4 2.0981(8), P3–Cl3 2.1089(7), P2–Cl2 2.1066(7), P1–Cl1 2.0954(7), P4–C4 1.828(2), P3–C3 1.822(2), P2–C6 1.820(2), P1–C1 1.831(2), P3–P4 2.9733(7), P1–P2 2.9642(7), P1–N1–P2 119.57(7), P3–N2–P4 120.32(7), N1–P1–P2–C6–159.4(1), C3–P3–P4–N2–164.3(1).

Attempted Synthesis of 1Ter: Isolation of the Dimer 4Ter

The reduction of 3Ter with elemental zinc dust in tetrahydrofuran (THF) did not lead to the desired tetraradical 1Ter but selectively to a dimer (4Ter, Scheme 2) as unequivocally proven by single-crystal X-ray diffraction (SCXRD) (Figure 3).

Figure 3.

Molecular structure of 4Ter in the crystal. Ellipsoids are set at 50% probability (123 K). Selected distances [Å]: P3–P4 2.943(1), P5–P6 2.928(1), P1–C10 1.945(3), P2–P5 2.3364(9), P7–C8 1.703(3), P8–C9 1.714(3), P5–C11 1.802(3), P6–C12 1.817(3), P6–C3 1.942(3), C6–C7 1.625(3).

Interestingly, the reaction mixture turned green at the start, the color of the targeted tetraradical (see below), but then slowly changed to brown. Yellow single crystals of 4Ter could be isolated from this brown solution. It was not possible to isolate the green intermediate, which is probably 1Ter, but it could be trapped by derivatization (vide infra). Dimer 4Ter decomposes above 180 °C in the solid state and is long-term stable in solution at ambient temperatures, as shown by NMR experiments. In the ³¹P{¹H} NMR spectrum, 4Ter features an AA′BB′XX′YY′ spin system due to its C₂ symmetry (see Figure S19). However, the NMR spectrum is simplified by the fact that there is only one larger coupling constant (³J(P3,P6) = ³J(P1,P8) = 25 Hz, assignment as depicted in Figure 3). The divalent P atoms (δ(P4/P7) = 273 ppm; δ(P3/P8) = 280 ppm) are significantly deshielded in comparison to the trivalent P atoms (δ(P2/P5) = 120 ppm; δ(P1/P6) = 136 ppm), and their chemical shifts are similar to those of structurally related compounds (cf. E: 285 ppm in Scheme 1).⁴³ By means of temperature-dependent ³¹P{¹H} NMR measurements we investigated whether 4Ter can dissociate into its tetraradical monomers (1Ter). Above 100 °C, decomposition of 4Ter occurred, but formation of the monomeric 1Ter was not observed (see Figure S20).

Yellow crystals of 4Ter crystallized in the triclinic space group P1̅ with one molecule and three cocrystallized solvent molecules in the unit cell. As depicted in Figure 3, dimer 4Ter is generated by the formation of one P–P, two C–P, and one C–C single bond between the two monomeric units, the desired tetraradical 1Ter, thus forming a cage compound in a very unusual addition reaction. In cage compound 4Ter, two ethylene units are oriented orthogonally to each other and linked at four points via chains of two atoms. The parent hydrocarbon compound (tricyclo[5.5.0.0^4,10]dodeca-1(7),4(10)-diene) corresponding to this structural motif has not been isolated so far.⁵³ The bonds between the atoms connecting the monomeric units (d(P2–P5) = 2.3364(9) Å, d(P1–C10) = 1.945(3) Å, d(P6–C3) = 1.942(3), d(C6–C7) = 1.625(3) Å) are all elongated by approximately 0.1 Å, compared to the sum of the covalent radii for the corresponding single bonds (∑r_cov.(P–P) = 2.22 Å, ∑r_cov.(C–P) = 1.86 Å, ∑r_cov.(C–C) = 1.50 Å).⁵² In addition, dimerization also removes the planarity of the monomer, since the three condensed rings are no longer aromatic (cf. planar structure of 1EMind, see below). Therefore, all rings involved in the dimerization (red and blue rings in Figure 3) are significantly puckered (red: 25.3(2)°, along P6···P5; blue: 37.2(2)°, along C7···C10), while the third ring remains nearly planar (green: 2.4(3)°, along P5···P8). The C–P bond lengths in this planar five-membered ring (d(C–P) = 1.711(3) Å) indicate double bonds (∑r_cov.(P=C) = 1.69 Å).⁵² This new bonding situation that arises during dimerization is shown in Scheme 2. It is worthy to note that a comparable type of trimerization was previously observed in the attempted synthesis of the Ter derivative of biradical E.⁴³ Thus, the steric demand of the Ter substituent is apparently not sufficient to stabilize these bi/tetraradical structures.

Trapping of Tetraradical 1Ter

Since we observed the in situ formation of tetraradical 1Ter at the beginning of the reaction (green color, ³¹P NMR shift at 287 ppm), we investigated the possibility of trapping it by adding an alkyne during the reduction process of 3Ter with zinc dust. In previous studies, we have shown that cyclic four- and five-membered P-centered biradicals can readily add alkynes such as tolan.^6,7,22 For example, it was demonstrated that tolan is a suitable trapping reagent for unstable biradicals of the type [^•E(μ-NTer)]₂ (E = Sb, Bi),⁵⁴ bridging two radical centers in a formal [2+2] addition. Indeed, in situ generated 1Ter is also capable of activating tolan. When zinc is added to the chlorinated species 3Ter (Scheme 3), a new compound is slowly formed as observed by ³¹P NMR experiments (δ(³¹P) = 100 (s)), which, after recrystallization from THF, leads to the deposition of colorless crystals. SCXRD revealed the formation of the double addition product 5Ter (Figure 4). Although evidence (green color, ³¹P NMR data, vide infra) for in situ generation of 1Ter is available, we do want to stress that the synthesis of 5Ter is not direct proof of the presence of 1Ter, as it is also conceivable that the reduction of the P–Cl units proceeds stepwise, forming only a biradical in the first step, followed by direct addition of tolan.

Scheme 3. Trapping of Tetraradical 1Ter by Addition of Tolan.

Figure 4.

Molecular structure of 5Ter in the crystal. Ellipsoids are set at 50% probability (123 K). Selected distances [Å] and angles [deg]: P1–C1 1.857(2), P1–C7 1.885(2), P2–C2 1.845(2), P1–P2 2.7877(7), P2–C8 1.879(2), P3–C4 1.865(2), P3–C22 1.878(2), C7–C8 1.344(3), C22–C21 1.347(3), P2–C8–C7 114.0(2), P3–C22–C21 111.4(1).

The tolan addition product 5Ter is thermally stable up to over 360 °C and then decomposes. No reversible elimination of tolan was observed. The molecular structure of 5Ter in the crystal proves that the two outer five-membered rings are strongly bent upon addition of tolan and incorporate only single bonds (Figure 4). The central six-membered ring remains planar and the former C–C triple bonds of the two added tolan molecules are now in the region of double bonds (C7–C8: 1.344(3), C22–C21: 1.347(3), cf. ∑r_cov.(C=C) = 1.34 and ∑r_cov.(C≡C) = 1.2 Å).⁵²

Synthesis of Tetraradical 1EMind

The synthesis of the tetraradical 1EMind was achieved by reduction of 3EMind with elemental zinc dust in THF at ambient temperatures in a rather slow reaction. Upon addition of the reducing agent, the colorless solution of 3EMind immediately turned green (Figure 5).

Figure 5.

Addition of elemental zinc powder to a solution of 3EMind leads to the formation of the intensively green colored tetraradical 1EMind. The reduction was carried out in the glovebox in an argon atmosphere.

However, complete conversion was detected only after 6 days according to ³¹P NMR studies. The course of the reduction process could easily be traced by ³¹P NMR spectroscopy, where the singlet signal of 3EMind slowly disappeared at 145 ppm, while a new singlet signal at 289 ppm appeared and became more intense. Crystallization of 1EMind from benzene after separation of ZnCl₂ yielded remarkably temperature stable (T_dec. = 365 °C) green crystals in gram scale in good yields (η = 67%). The UV–vis spectrum of 1EMind showed two absorption bands in the visible region (λ_max = 396 and 667 nm), which explain the green color (Figure 5). In the ³¹P{¹H} NMR spectrum, 1EMind shows a single sharp resonance at 289 ppm (cf. biradical E: 285 ppm)⁴³ and is EPR silent, suggesting a singlet ground state (see Electronic Structure section).

The solid-state structure was determined by SCXRD (Figure 6). 1EMind crystallized in the triclinic space group P1̅ with one centrosymmetric molecule and four cocrystallized benzene molecules in the unit cell (Figure 6). There are no significant intermolecular interactions in the solid-state structure. In contrast to 4Ter, the annulated tricyclic ring system is planar. The EMind substituents are oriented almost orthogonally to the tricyclic ring system (∠ = 83.1(4)°). All C–C bond lengths are in the range between 1.400(3) (C1–C3′) and 1.449(3) Å (C1–C2), indicating partial double bond character (cf. ∑r_cov.(C–C) = 1.50, ∑r_cov.(C=C) = 1.34 Å).⁵² The P–C bonds (d(P1–C1) = 1.752(2) and d(P2–C2) = 1.751(2) Å) are slightly longer than a typical P–C double bond (cf. ∑r_cov.(P=C) = 1.69 Å)⁵² but significantly shorter than a single bond (cf. ∑r_cov.(P–C) = 1.86 Å), indicating some double-bond character, in agreement with the Lewis resonance scheme of 1 (see Electronic Structure section). The transannular P1···P2 distance amounts to 2.9702(9) Å, which is much too long for a covalent P–P interaction (cf. ∑r_cov.(P–P) = 2.2 Å),⁵² but significantly shorter than the sum of the van der Waals radii (cf. ∑r_vdW(P···P) = 3.8 Å).⁵⁵ Together with the computed electronic structure of 1 (see Electronic Structure section), this is indicative of a singlet biradical-type interaction between each pair of P atoms, as expected for a tetraradical of type 1.

Figure 6.

Molecular structure of 1EMind in the crystal. Ellipsoids are set at 50% probability (123 K). Selected bond lengths [Å] and angles [deg]: P2–P1 2.9702(9), P2–C2 1.751(2), P1–C1 1.752(2), N1–P1 1.694(2), N1–P2 1.698(2), C1–C2 1.449(3), C2–C3 1.400(3), C3′–C1 1.400(3), P1–N1–P2 122.3(1), C1–P1–N1 93.14(9), C2–P2–N1 93.11(9), C2–C1–P1 115.8(1), C1–C2–P2 115.7(1), N1–P1–P2–C2 179.9(1), P1–C1–C2–C3 179.8(2). Symmetry code (′): (1–x, 1–y, 2–z).

Theoretical Aspects of Tetraradical vs Dimer Formation

To gain access to the desired stable tetraradical 1R, the sterically demanding substituent at the nitrogen had to be modified, since in the case of R = Ter we could only isolate the dimer (see above, section on Synthesis). The steric requirement of a suitable candidate must be large enough to stabilize the tetraradical against dimerization, but small enough to allow activation of small molecules (see below, section on H₂Activation). Varying the substituent is very time consuming from a preparative point of view, so we decided to perform quantum mechanical calculations at the PBE-D3/def2-TZVP⁵⁶⁻⁵⁸ level of theory to select a suitable substituent for synthesis after we found that 1Ter dimerizes, making isolation of 1Ter impossible. For this reason, we examined theoretically four different bulky substituents (R = Ter, EMind, Mes*, and Oma; Scheme 4) in more detail in terms of steric requirements and thermodynamics of dimerization.

Scheme 4. Gibbs Free Energies (Δ_RG°) in Toluene (SMD Solvation Model)⁵⁹ for the Dimerization of 1R to 4R, Calculated at PBE-D3/def2-TZVP Level of Theory.

Steric Influence

Good measures of the bulkiness of a substituent are the cone angle⁶⁰⁻⁶² and the concept of buried volume,⁶³⁻⁶⁵ which can be used to rationalize and illustrate steric hindrance of the substituent in 1R. The calculated cone angles⁶⁶ in 1R (computed at the optimized N–C distance, see SI) increase along the series R = Ter (222°) < EMind (246°) < Mes* (265°) = Oma (265°). A similar situation was found for the buried volumes. When the center of the transannular P–P axis is chosen as the spherical center in the computation of the buried volume, the radical centers (region between 2 and 3 Å) are best sterically shielded in 1R for R = Oma (32.6%) > Mes* (30.9%) > EMind (27.5%) > Ter (24.2%).

Interestingly, this order changes with increasing spherical radius, as can be seen in Figure 7 (see also SI, Table S8). At a large radius > 4 Å, the steric shielding of the terphenyl substituent becomes significantly larger compared to the other three substituents, which now have similar values (see SI, Table S7). However, the steric shielding at large sphere radii seems to be of secondary importance for the stability of the tetraradicals 1R with respect to dimerization.

Figure 7.

Buried volume as a function of the sphere radius in 1R (R = Ter, EMind, Mes*, and Oma).

Thermodynamics of Dimerization

In agreement with experiment, the dimerization of 1Ter to 4Ter in toluene (SMD solvation model)⁵⁹ is considerably exergonic at the level of theory applied (Δ_RG° = −75.1 kJ/mol, Scheme 4). However, for all three other substituents, the monomer is energetically preferred over the dimer. From these thermodynamic considerations in combination with the studies on steric influences, we decided to use the EMind substituent for the preparation of 1 since the starting materials, in particular the amine EMindNH₂, can be easily prepared (see SI, p S34 ff).

Electronic Structure of Tetraradical 1

The electronic structure of the tetraradical was studied using both a proton-substituted model system (1H) as well as the actual system 1EMind (optimized at the PBE-D3/def2-TZVP⁵⁶⁻⁵⁸ level of theory). As the EMind substituent is oriented orthogonally to the ring plane of the central annulated ring system and therefore does not allow delocalization of the π electron system into the substituent, the results obtained for 1H and 1EMind do not deviate significantly. Thus, for reasons of clarity, we will discuss only the results for the model system here; further information about 1EMind can be found in the SI (p S77 ff).

NBO Picture

NBO analysis finds Lewis representation I (Scheme 5) as the energetically most favorable Lewis structure for 1H. Structure I describes a P-centered tetraradical with a benzene linker that has six delocalized π electrons. Together with one lone pair of electrons on both nitrogen atoms and the four radical electrons at the P atoms, all of which are localized in p-atomic orbitals, this results in a total of 14 π electrons. No formal charges are needed. The formal radical electrons are localized in two π*(P–P) NBOs (Figure S30), in agreement with the CASSCF wave function (vide infra). The biradical subunits in 1H may therefore be classified as type-II biradicals according to the scheme of Abe,⁵ analogously to other known P-centered biradicals.^{16,23,28,43,67} Other important Lewis structures are those in which one five-membered ring is a formal biradical, whereas the remaining two rings are described using C=C, P=C, or P=N double bonds (Lewis formulas of type II and III; for a depiction of the corresponding NLMOs = Natural localized molecular orbital, see Figure S30). The delocalization of the lone pair on the N atom leads to formal charges and thus to zwitterionic character.

Scheme 5. Formal Lewis Representations of 1H Derived from NBO/NLMO Analysis.

Lone pairs are omitted for clarity. Only one Lewis structure per type is shown. Due to symmetry there are two type I, eight type II, and two type III structures. The radical electrons are localized in a π*-type orbital, which is indicated by the dotted lines.

MO Picture

First, we investigated the order of electronic spin and excited states of the tetraradical to verify the singlet ground state postulated on the basis of the sharp NMR resonances of 1EMind and absence of signals in the EPR spectrum. In general, for a system with four electrons in four (frontier) orbitals, there are 20 possible singlet as well as 15 triplet states and one quintet state. For the description of 1H we performed NEVPT2⁶⁸⁻⁷⁰/CAS(14,12)⁷¹⁻⁷⁹/def2-TZVP^58,80 calculations, which take into account all π-orbitals of the central ring system. According to these calculations, 1H possesses a singlet ground state. The first excited state is the triplet state with ΔE_ST = E_S – E_T = −93 kJ/mol (1EMind: – 92 kJ/mol), which is significantly lower than in E^tBuBhp (ΔE_ST = −126 kJ/mol).⁴³Table 1 contains the first 10 excited states of 1H including the quintet state in their energetic order. The quintet state is clearly above the ground state with ΔE_SQ = −311 kJ/mol (1EMind: −313 kJ/mol). This clearly differs from an ideal tetraradical (or dis-tetraradical), in which the first six states (2× singlet, 3× triplet, 1× quintet) are degenerate, and indicates that the radical electrons of 1H are rather strongly coupled. The interaction of two radical electrons (i, j) in polyradicals can be described by the electron-exchange coupling constants J_ij, which result from the phenomenological Heisenberg–Dirac–van Vleck Hamiltonian^81,82 (Ŝ = spin operator):

1

Table 1. Exited States of Model System 1H (NEVPT2/CASSCF(14,12)/def2-TZVP).

excited state	term symbol	ΔE [eV]	ΔE [kJ/mol]
ground state	1Ag	0.00	0
1	3B2u	0.97	93
2	3B3g	1.59	154
3	1B2u	1.95	188
4	1Ag	2.66	256
5	3B1u	2.84	274
6	3B3g	3.00	290
7	1B3g	3.11	300
8	3B2u	3.11	300
9	1B3g	3.16	305
10	5Ag	3.22	311

The larger the value of J, the stronger the interaction between two electrons. A positive value indicates a ferromagnetic coupling, while a negative value indicates antiferromagnetic coupling. To describe systems of four electrons, a maximum of six coupling constants is needed. However, 1H can be described by only three coupling constants due to its D_2h symmetry (vide supra).

In general, compound 1H can be understood as a benzene, formally substituted by four radical units. By analogy with the work of Head-Gordon, Casanova, and co-workers,^8,83 the coupling constant between the radical centers in ortho position to each other is called σ (short), in meta position μ (medium), and in para position λ (long-range coupling). The relationship between the energies of the excited states (Table 1) and the coupling constants can be derived from eq 1 and is shown in Table 2 (a derivation can be found in the SI, p S89 ff). Using a least-square fit, the coupling constants for 1H can be obtained (Figure 8). They can be compared to the respective ortho-, meta-, and para-couplings of other bi- and tetraradically substituted benzenes.

Table 2. Energetic Dependency of the Electron Exchange Coupling Constants σ, μ, and λ.

state	symbol	Erel. =
Q1	Ag	–σ/2 – μ/2 – λ/2
T3	B1u	–σ/2 + μ/2 + λ/2
S1	Ag	–σ/2 + μ + λ
T2	B3g	+σ/2 + μ/2 – λ/2
T1	B2u	+σ/2 – μ/2 + λ/2
S0	Ag	+3/2σ

Figure 8.

Electron exchange coupling constants in 1H, E^tBuBhp, meta-D, and para-D in kJ/mol. 1H: NEVPT2/CASSCF(14,12)/def2-TZVP, E^tBuBhp: value taken from ref (43), meta-D and para-D: values taken from ref (8).

In 1H, σ = −149.9 kJ/mol (1EMind: −150.8 kJ/mol), which shows a strong antiferromagnetic coupling between the radical electrons within each of the five-membered rings, similar to that in the five-membered biradical E^tBuBhp (−126.2 kJ/mol) and also on the same order of magnitude as found in the four-membered rings of the tetraradicals meta-D (−97.5 kJ/mol) and para-D (−94.4 kJ/mol). The meta-coupling μ = 13.8 kJ/mol (1EMind: 14.4 kJ/mol) is the only ferromagnetic coupling in 1H and similar to the meta-coupling in meta-D (5.0 kJ/mol). The para-coupling λ = −46.5 kJ/mol (1EMind: –49.9 kJ/mol) shows a significant antiferromagnetic interaction between the electrons of the two formal biradicals and is slightly larger than in para-D (−31.1 kJ/mol). Thus, it can be concluded that there are significant couplings between all radical electrons of 1H, and these couplings are similar to analogous coupling pathways in E^tBuBhp, meta-D, and para-D.

Excursus: How to Understand the Tetraradical Character

Another way to characterize tetraradicals and, in particular, quantify the polyradical character is to examine the occupancy of the LUNO (biradical character; LUNO = lowest unoccupied natural orbital) and LUNO+1 (tetraradical character). Before we come to discuss these values for 1H, however, we want to explain the relationship between the two values by using a simple model system of four hydrogen atoms in D_∞h symmetry. It should be noted that the model is only loosely connected to the tetraradical 1H (D_2h symmetry), but it is an intuitive model for tetraradicals in general, especially if they are to be understood as molecules with two biradical subunits. The system is defined by two variables, a, the distance between an outer H atom and its neighboring H atom, and b, the distance between the inner H atoms (Figure 9). Variation of a and b changes the interaction between the hydrogen atoms and thus n(LUNO) and n(LUNO+1). The occupancies were determined by simple CASSCF(4,4) calculations and are illustrated in Figure 9 as a function of a at three distances b (b = 0.8, 2.2, 5.0 Å).

Figure 9.

Bi- [n(LUNO)] and tetraradical character [n(LUNO+1)] in a chain of four H atoms in D_∞h symmetry at different distances a and b.

The following conclusions and trends can be derived from this: (i) Smalla and b: closed-shell system with minimal bi- and tetraradical character. (ii) Increasinga at smallb (0.8 Å): H₂ molecule in the middle, with radical hydrogen atoms on the outside, moving away from each other; the biradical character increases to perfect biradical; the tetraradical character remains small due to the strong interaction between the inner H atoms. (iii) Increasinga at mediumb (2.2 Å): The initial situation describes two H₂ molecules with medium distance to each other (minimal bi- and tetraradical character); with increasing a, the bi- and tetraradical character increase together, but the tetraradical character is limited at larger a by the interaction of the central H atoms; the final state describes two biradicals with significant interaction between each other. (iv) Increasinga at largeb (5.0 Å): Parallel dissociation of two separated H₂ molecules, biradical character = tetraradical character due to missing interaction between the biradical units. (v) Largea and b: maximum bi- and tetraradical character; no interaction between the H atoms, all valence orbitals are degenerate.

From these simple considerations it follows that the biradical character limits the tetraradical character, so discussing both values independently is not meaningful. The system of four H atoms can be transferred to the systems described in the Introduction, in which there are two sets of biradicals whose interaction depends on the type of linker (e.g., length, conjugation of the electrons, etc.).

Tetraradical Character of 1

In order to describe the bi- and tetraradical character of 1H, a CASSCF(4,4) calculation, which does not take into account the dynamic correlation within the π-system, was performed. The orbitals of the active space are shown in Figure 10. HONO and HONO–1 (HONO = highest occupied natural orbital) describe a transannular antibonding situation between the P atoms within each five-membered ring, while LUNO and LUNO+1 are transannular bonding. The LUNO has an occupancy of 0.26 (26% biradical character, Table 3); the LUNO+1, of 0.19 (19% tetraradical character). The biradical character is significantly increased compared to E^tBuBhp (18%, CASSCF(2,2)),⁴³ which shows that the ring extension to 1H has a clear influence on the multireference character. This would not be the case if two biradicals were linked to form a bis(biradicaloid). The amount of biradical character is similar to nonaromatic P-centered biradicals such as [P(μ-NTer)]₂ (28%) or A (28%, Scheme 1)⁴³ By linear combination of the delocalized CASSCF(4,4) orbitals φ, localized orbitals χ are obtained (Figure 10), which show that the radical electrons are mainly localized at the P atoms, so that it is justified to speak of a P-centered tetraradical.

Figure 10.

Delocalized and localized frontier orbitals of 1H (CASSCF(4,4)/def2-TZVP).

Table 3. Occupation Numbers n of the LUNO, LUNO+1, and LUNO+2 to Quantify the Bi- and Tetraradical Character for 1H in Comparison with E.

compound	active space	n(LUNO)	n(LUNO+1)	n(LUNO+2)
Ea	CASSCF(2,2)	0.18
	CASSCF(10,9)	0.21	0.09	0.09
1H	CASSCF(4,4)	0.26	0.19
	CASSCF(14,12)	0.32	0.19	0.09

^aValues taken from ref (43).

Additionally, the occupation numbers n(LUNO) and n(LUNO+1) of 1H were determined using a CASSCF(14,12) calculation that describes all π-orbitals of the central ring system and the electrons contained therein (Table 3). In contrast to the CASSCF(4,4) calculation, dynamic and nondynamic correlation in the π-system are thus considered. The dynamic correlation leads to a significant increase in the occupation of the LUNO, while the occupation of LUNO+1 remains unaffected. The small LUNO+2 occupation (<10%) shows that a description of the system as tetraradical is sufficient due to the negligible hexaradical character, which is mainly attributable to dynamic correlation.

Aromaticity of 1

The influence of the π-system on the multireference character as well as the strong antiferromagnetic coupling of the radical electrons prompted us to investigate the aromaticity of 1H, which we would like to discuss on the basis of magnetic parameters (magnetically induced ring current,^84,85 NICS values⁸⁶⁻⁸⁸). Benzene and EH are used as comparison in this discussion (data of further compounds see SI p S98 f).^43,89 The current density susceptibilities of benzene, EH, and 1H are visualized in Figure 11 by streamline plots. All compounds show a clear diatropic ring current surrounding the ring systems above and below the ring plane, which is typical for aromatic compounds. By integration of the current density along vertical ring sections to the respective ring center, the net induced ring current can be derived (Table 4).^84,85,90,91

Figure 11.

Streamline plot of the current density susceptibility⁸⁴ for benzene (a), EH (b), and 1H (c).

Table 4. Net Induced Currents and NICS(1)_zz Values of Benzene, EH, and 1H^a.

	C6H6	EH	1H
net induced current [nA/T]	12.1	13.5 (⬟)	13.2 (⬟)
		11.2 (⬟)	13.5 (⬟)
NICS(1)zz [ppm]	–30.2	–31.1 (⬣)	–29.5 (⬣)
		–24.9 (⬢)	–29.4 (⬢)

^aFor fused ring systems, values are given for the five-membered (⬟) and six-membered part (⬢). Further information can be found in the SI, p S98 f.^43,89

According to these computations, the ring currents are very similar (>11 nA/T) and positive in all rings, which means that the diatropic part prevails over the paratropic one.⁸⁴ The opposite is true for antiaromatic compounds (negative sign), while nonaromatic compounds have ring currents around 0 nA/T. The determined NICS(1)_zz values between −24.9 and −31.1 also indicate the aromaticity of the compounds considered (Table 4; for NICS(0), NICS(0)_zz, and NICS(1) see SI, p S98).⁴³

H₂ Activation

Theoretical Aspects

Metal-free activation of molecular hydrogen is an important challenge in molecular chemistry and succeeded in seminal works, for example, by conversion with FLPs,⁹² CAACs,⁹³ or multiple bonds of heavy elements.⁹⁴ For 1EMind, first reactivity studies toward molecular hydrogen were carried out, with the aim to chemically prove the existence of the interactions between the two biradical units discussed above. We began our investigations with calculations in which the H₂ activation occurs analogously to known four-,¹⁵⁻¹⁷ five-,¹⁷ and six-membered¹⁸⁻²⁰ biradicals via the addition of H₂ to the radical centers. In contrast to these biradicals, tetraradical 1EMind enables not only the activation of one equivalent of H₂ under the formation of 6 but additionally the activation of a second equivalent of H₂ (syn-7H and anti-7H, Scheme 6).

Scheme 6. Activation of One Equivalent of H₂ by the Tetraradical 1 Led to the Formation of 6; Additionally, the Diadducts syn-7 Were Formed Depending on the Reaction Temperature and Pressure of H₂.

The calculations for the model system 1H show (Table 5) that the addition of the first equivalent of H₂ is strongly exergonic (Δ_RG° = −52.2 kJ/mol), whereas the addition of the second equivalent is only slightly exergonic (Δ_RG°: syn-7H = −12.4, anti-7H = −12.7 kJ/mol). The activation barrier for the first activation step is 80.0 kJ/mol, while that for the second reaction step is significantly higher (Δ_RG^⧧: syn-7H = 104.3, anti-7H = 103.6 kJ/mol). The differences in the energy profiles for the first and second activation steps indicate that there is a significant interaction between the radical centers of 1H. The formal removal of a biradical unit reduces the biradical character from 26% in 1H (CASSCF(4,4), cf. Table 3) to 17% in 6H (CASSCF(2,2), see SI p S90) and thus the reactivity toward molecular hydrogen. In contrast, for a bis(biradicaloid), the energy profiles for the first and the second activation would be identical. In the model system, steric effects are reduced as much as possible due to the smallest possible substituent (R = H) and the smallest possible molecule to be activated (H₂).

Table 5. Δ_RG^⧧ and Δ_RG° (DLPNO-CCSD(T)/def2-TZVP) for the Activation of H₂ by 1EMind and 6EMind (Values in Parentheses for 1H and 6H, Respectively).

reaction
from	to	ΔRG⧧ [kJ/mol]	ΔRG° [kJ/mol]
1 + H2	6	100.9 (80.0)	–37.7 (−52.2)
6 + H2	syn-7	118.1 (104.3)	–2.4 (−12.4)
6 + H2	anti-7	119.5 (103.6)	–1.3 (−12.7)

The calculations for the EMind-substituted tetraradical (1EMind) show larger activation barriers and decreased energy gains, indicating that hydrogen activation is made more difficult upon introduction of bigger substituents. This is due to bending of the ring system during H₂ addition, which leads to an energetically disfavored spatial proximity of the two EMind substituents. The reactions are predicted to proceed in a concerted mechanism as [2+2] cycloadditions, which may be nicely rationalized by the HOMO–LUMO interactions shown in Figure 12, analogous to the H₂ activation with [P(μ-NTer)]₂.¹⁵

Figure 12.

Schematic representation of the interaction of the frontier MOs of the model system 1H (D_2h symmetry) and H₂ (D_∞h).

Experimental Aspects

To validate the calculations (e.g., with regard to the postulated mechanism) and to select suitable reaction conditions for the synthesis of 6EMind and 7EMind, NMR investigations were carried out. First, an NMR tube with a solution of 1EMind was pressurized with 5 bar H₂ at 67 °C for 20 min. The ³¹P and ¹H NMR spectra of the experiment showed a 75% conversion to 6EMind (Figure 13), with ³¹P resonances at 287 ppm (P_Y) and 58 ppm (P_X). The subsequent increase in the temperature to 87 °C led to an almost complete conversion after 10 min time. The corresponding ¹H and ³¹P NMR spectra fit well to an AA′BB′XX′YY′ spin system (A, B = ¹H; X, Y = ³¹P) based on calculated values (PBE-D3/def2-TZVP). Coupling constants > |10 Hz| can be found between H_A–P_X (183 Hz) and P_X···P_X′ (−26 Hz; for all exptl. and calcd. parameters see SI, p 68 ff).

Figure 13.

Experimental and simulated ¹H and ³¹P NMR spectra of 6EMind. The resonances of P_Y and P_Y′ appear as a singlet and are not shown here.

The hydrogen activation was then repeated with parahydrogen (para-H₂), the spin-0 isomer of H₂, inside a 9.4 T NMR spectrometer. In this case, a concerted activation would lead to a several orders of magnitude signal enhancement of the NMR resonances (¹H and ³¹P) due to the strong nuclear spin hyperpolarization. This phenomenon,⁹⁵⁻⁹⁷ generally known as parahydrogen-induced polarization (PHIP),^98,99 has already been used by us to verify concerted reaction mechanisms for the activation of H₂ by other biradicals (e.g., [P(μ-NTer)]₂, A).^17,100Figure 14 shows ³¹P NMR spectra of the resulting hyperpolarized species after para-H₂ activation (5 bar) by 1EMind and 6EMind at 67 and 97 °C, respectively. At 67 °C, only the resonances of hyperpolarized 6EMind* are visible (Figure 14a). For comparison, a simulated thermal spectrum is also presented in the figure to highlight qualitative amplitude alternations in the XX′ ³¹P NMR multiplet of 6EMind (see Figure 13 for the notation). The observation of PHIP-enhanced resonances in this experiment proves the concerted reaction mechanism of H₂ activation by 1EMind. In turn, the experiment at 97 °C showed that 6EMind also activates H₂ in a concerted manner, since the two isomers of the double addition product, syn-7EMind and anti-7EMind, were also hyperpolarized by PHIP (Figure 14b). As from the NMR point of view both species have the same symmetry, it cannot be elucidated directly from the NMR spectra which of the two sets of XX′ ³¹P NMR resonances centered at 58.4 and 57.9 ppm corresponds to which isomer of 7EMind. The tentative assignment of signals in Figure 14 is based on calculated shifts (see SI, p S72 ff). It is worth noting, however, that syn-7EMind and anti-7EMind most likely interconvert into each other since their resonances drifted apart (ca. 0.5 ppm) when the sample was cooled to room temperature, indicating the presence of dynamic exchange at 97 °C. In addition, this para-H₂ experiment revealed a significant distortion of the thermal signal multiplet corresponding to 6EMind, implying that some portion of this compound was converted into the hyperpolarized form, 6EMind*, via the reversible dissociation into 1Emind and H₂ at 97 °C.

Figure 14.

³¹P NMR spectra measured during para-H₂ activation by (a) 1EMind and (b) 6EMind at 67 and 97 °C, respectively. A 5 bar para-H₂ pressure was used in the experiments. (a) The formation of hyperpolarized 6EMind* was observed in the reaction of 1EMind and para-H₂. A simulated thermal spectrum of 6EMind is depicted to show the qualitative alternation of the XX′ ³¹P multiplet (see Figure 13) with the hyperpolarization. (b) The reaction of 6EMind and para-H₂ resulted in hyperpolarized syn-7EMind* and anti-7EMind* species. In addition, 6EMind itself became slightly hyperpolarized. The resonances of syn-7EMind and anti-7EMind drifted apart under cooling to 25 °C, likely indicating the chemical exchange between the isomers. For the sake of simplicity, “EMind” was omitted from the endings of the compound names in the figure. Asterisk (*) denotes hyperpolarized species, HP = hyperpolarized, TH = thermal.

The conditions for the attempted synthesis and isolation of 6EMind and 7EMind were chosen on the basis of the NMR experiments. Thus, 6EMind is formed exclusively at moderate H₂ pressures and low temperatures, whereas 7EMind is present only in small amounts at high temperatures, so that the pressure of H₂ must be increased significantly to achieve a higher reaction conversion.

6EMind was therefore synthesized in the reaction of 1EMind in toluene with H₂ (10 bar) at 65 °C within 2.5 h (alternatively with 1 atm H₂ at ambient temperature within 4 weeks) and was crystallized as yellow crystals from 1,2-dichlorobenzene. The solid-state structure was determined by SCXRD. 6EMind crystallized in the triclinic space group P1̅ with two molecules and two cocrystallized solvent molecules in the unit cell (Figure 15). Compared to the structure of 1EMind, the H₂-substituted five-membered ring in 6EMind is strongly altered, while the unsubstituted ring remains almost unchanged. The first ring is bent along the P atoms (along P1···P2: 30.6°), and the C–P distances are in the range of single bonds (d(C1–P1) = 1.825(1), d(C6–P2) = 1.832(1) Å, cf. Σr_cov.(C–P) = 1.86 Å),⁵² whereas the second still biradical ring is almost planar (along P3···P4: 0.7(5)°) and the C–P distances are in the range of a double bond (d(C3–P3) = 1.737(1), d(C4–P4) = 1.739(1) Å, cf. ∑r_cov.(P=C) = 1.69 Å).⁵² Furthermore, the H₂ addition leads to a shortening of the transannular P–P distance (d(P1–P2) = 2.9350(6) vs d(P3–P4) = 2.9566(6) Å).

Figure 15.

Molecular structure of 6EMind in the crystal. Ellipsoids are set at 50% probability (173 K). Selected bond lengths [Å] and angles [deg]: C1–P1 1.825(1), C6–P2 1.832(1), C3–P3 1.737(1), C4–P4 1.739(1), P1–P2 2.9350(6), P3–P4 2.9566(6), C1–P1–P2–N1 150.06(9), C3–P3–P4–N2 179.6(1).

The formation of 6EMind is reversible, in agreement with the para-H₂ NMR experiments. Thus, 6EMind turned green in the solid at 120 °C, the color of 1EMind. An analysis of a sample of 6EMind heated to 120 °C for 1 h in a vacuum showed a significant re-formation of the tetraradical 1EMind as evidenced by ³¹P NMR spectroscopy.

Our attempts to isolate the doubly substituted compounds syn-7EMind and anti-7EMind were not successful. The hydrogenation of 1EMind (50 bar H₂, 100 °C in toluene) over a period of 3 h resulted in the formation of a mixture of 6EMind (76%), syn-7EMind (12%), and anti-7EMind (12%, determined by ³¹P{¹H} NMR spectroscopy). The ratio of the diadducts (7EMind) could not be increased by extending the reaction time to 48 h, so the reaction was already in equilibrium after 3 h.

Conclusion

In summary, we report the successful synthesis of 1R, an isolable singlet tetraradicaloid species with radical centers localized at the four P atoms. Theoretical and experimental investigations of different substituents show that EMind is a suitable substituent for the stabilization of 1R, whereas the Ter-substituted derivative dimerizes to the unusual cage compound 4Ter. The tetraradical 1EMind is a compound stable at high temperatures (T_dec. = 365 °C) and can be synthesized in gram scale. Theoretical studies indicate that the radical electrons interact with each other to a considerable extent. Despite the coupling of the radical electrons, 1EMind has a significant bi- (26%) and tetraradical character (19%) according to CASSCF(4,4) calculations and is aromatic. The interaction of the radical electrons additionally affects the reactivity of 1EMind. In the reaction with H₂, the addition of the first equivalent is much quicker than the second. The hydrogen activation proceeds in a concerted [2+2] cycloaddition, which has been proven by PHIP-NMR studies.

Experimental Section

Experimental section, preparation of starting materials and compounds, structure elucidation, additional spectroscopic details, and computational details can be found in the Supporting Information.

Computations were carried out using Gaussian09,¹⁰¹ ORCA 4.2.1¹⁰² or ORCA 5.0.3,¹⁰³ and the standalone version of NBO 6.0.^104−107

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.3c03928.

• Additional experimental information, computational details (PDF)

The authors declare no competing financial interest.