Introduction

The exchange of skeletal sp2 carbon atoms in polyaromatic hydrocarbons (PAHs) with heavier p-block elements reduces the HOMO-LUMO gap, which has attracted the interest of many researchers in chemistry, physics, and materials science. For example, group 14/15 elements have been used in the synthesis of congeners of naphthalene, anthracene, phenanthrene, and [7]helicene1,2,3,4,5,6,7,8,9,10,11,12. Although most heavier congeners of PAHs are unstable, designing appropriate peripheral substituents enables isolation under ordinary conditions and characterization of the physical properties of the π-electron systems. We used fluoroalkyl groups at the peri positions to stabilize 9-phosphaanthacene3,13,14, which enabled chromatographic purification and characterization of physical properties including fluorescence and crystalline polymorphs15. Notably, the synthetic procedures of peri-trifluoromethylated 9-phosphaanthracenes can be applied for extensions of the π-electron system of 9-phosphaanthracene16 and the synthesis of thienoacenes including fused phosphinine (a phosphorus analog of pyridine)17.

Considering the importance of the radical reactions of anthracene from the perspectives of bioactivity, combustion science, and environmental science18,19,20,21, we previously analyzed the radical reaction of a peri-trifluoromethylated 9-phosphaanthracene via muon spin rotation, relaxation, and resonance (µSR) spectroscopy22. A positive muon (µ+) is an elementary particle classified as a lepton. High-intensity, spin-polarized beams of muons are available at several accelerator facilities around the world. In most insulating materials, a positive muon can capture an electron during the radiolysis process and form a muonium (Mu = [µ+e−]), which behaves chemically like a light isotope of hydrogen. The light H-atom surrogate Mu can add to the unsaturated parts in the organic molecule and produce a muoniated paramagnetic species. The muon hyperfine coupling constants (hfcs) of the muoniated radicals produced by the addition of Mu to organic compounds are considerably smaller than those of Mu itself (4463.3 MHz) because the unpaired electron is delocalized over multiple atoms23,24,25,26. The muon hfc and the hfcs of other nuclei in the radical with nuclear spin I > 0 can be used to map the distribution of the unpaired electron and determine the structure of the radical. To date, muoniated radicals have been produced not only by the reaction of Mu with ordinary organic compounds such as benzenes, alkenes, alkynes, and aldehydes/ketones27,28,29 but also by reactions with heavier congeners including imines, carbenes, and cyclobutane-1,3-diyls30,31,32.

In our previous µSR study of a peri-trifluoromethylated 9-phosphaanthracene22, we observed the regioselective addition of Mu to sp2-type phosphorus, affording the single paramagnetic species, which was in sharp contrast with anthracene33 and the acyclic phosphaalkenes producing the mixtures of the muonium (Fig. 1a)34,35,36. Notably, the hfc parameters of the muoniated 9-phosphaanthracene indicated a planar tricyclic system because the increased zero-point energy due to the muon of 1/9th mass of the proton cancels the trifluoromethyl effect. These findings suggest that µSR could clarify the unveiled characteristics of organic molecules as well as muon(ium) via chemical processes including H-surrogates and heavier PAHs.

We recently synthesized several π-extended derivatives of 9-phosphaanthracene. Figure 1b is a formula of 12-phosphatetraphene 1 as a π-extended phosphaanthracene16. The highly π-conjugated tetracyclic system in 1 would be promising for producing uniquely delocalized paramagnetic structures by capturing radicals; thus, 1 should be attractive for producing transient paramagnetic molecules via the muon isotope effect leading to the planar π-delocalized molecular skeleton. In this study, observation of muoniated 1 via µSR experiments was attempted, and the muonium radical was structurally characterized via DFT calculations. The amount of the sample seemed to be insufficient for µSR, but as a result, the use of a dilute solution sample 1 was advantageous for characterizing the considerable reactivity with muonium. The temperature dependence of the muoniated radical containing the planar 12-phosphatetraphene skeleton and the reaction dynamics of the addition of muonium were also investigated.

Fig. 1
figure 1

(a) Reaction of a peri-trifluoromethylated 9-phosphaanthracene with muonium (Mu). (b) Chemical formula of 12-phosphatetraphene 1 for this µSR study.

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Materials and methods

A total of 120 mg of 1 was prepared according to the synthetic procedures in the literature16. A solution sample of 0.060 M (1 M = 1 mol dm–3) 1 was prepared by using 4.0 mL degassed tetrahydrofuran (THF) in a glovebox. The THF solution was packed in the cell shown in Fig. 2.

Fig. 2
figure 2

A solution sample of 1 in degassed THF (0.060 M) sealed in a µSR sample cell.

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The µSR measurements were performed at TRIUMF on the M15 beamline with the Helios spectrometer. The µSR techniques and their applications in chemistry have been extensively reviewed23,24,27,28,29,30,31,32.

Density functional theory (DFT) calculations were performed via the Gaussian09 software package37. Hydrogen was used instead of muonium in the structure optimization. The normally optimized structure did not consider the isotope effect of muon increasing the zero-point energy and was revised to include the muonium radical of 9-phosphaanthracene22. The flat tetracyclic skeleton was maintained during the calculation. Conventional structural modifications involving increasing the bond length and angles around the muonium were attempted as the empirical vibrational averaging but were unsuccessful in simulating the experimental results.

Results and discussion

µSR of a peri-trifluoromethylated 12-phosphatetraphene

TF-µSR measurements were performed on a 0.060 M THF solution of 1. It was expected that a 0.060 M solution sample of 1 would be too dilute to observe any muoniated radical by µSR. However, to our surprise and delight, a pair of signals due to a single type of muoniated radical was observed, as shown in Fig. 3a. The signals were confirmed to be real, as they shifted appropriately between measurements made in two different applied magnetic fields. The peak at + 36 MHz reflects the real peak at around − 36 MHz (ν12), consistent with Figure S4 of νµ = 196 MHz in a 1.44 T transverse field. The amplitude of the ν12 signal increased dramatically with increasing temperature (Fig. 3b).

Fig. 3
figure 3

(a) A Fourier transformed TF-µSR spectrum of a 0.060 M THF solution of 1 that was exposed to a beam of µ+ at 309 K in a 0.86 T transverse magnetic field. A strong diamagnetic resonance of muon (vµ) appears at 117 MHz, and one pair of paramagnetic signals v12 and v43 means Aµ = 306.472 ± 0.010 MHz. The paramagnetic signal v43 is small because of the time resolution of the spectrometer. The peak at 0 MHz marked with * is an artefact due to the Fourier transform. (b) The v12 signal in the Fourier transformed TF-µSR spectra of a 0.060 M THF solution of 1 in a 0.86 T transverse magnetic field as a function of temperature. The inset graph shows the temperature dependence of the amplitude of the v12 signal determined from fits in the time domain.

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To observe a muoniated radical with TF-µSR, there must be efficient transfer of spin polarization from Mu to the muoniated radical. In the high magnetic field, this is approximately

$$P=\frac{{{\lambda ^2}}}{{{\lambda ^2}+\delta {\omega ^2}}}$$
(1)

where λ is the addition rate of Mu and equals kMu[1], where kMu is the second order Mu addition rate constant, [1] is the concentration of 1, and δω = ωMu – ωR is the difference in precession frequencies in Mu and the radical. The physical interpretation is that the muon spins in Mu dephase prior to the reaction; if the rate is too slow or the field is too high, then muon polarization is lost. In the case of 9-phosphaanthracene, the muoniated radical was observed when a 0.16 M solution was used22, and the more dilute conditions were inappropriate for observing the paramagnetic signals. In most relevant µSR studies of the phosphorus congeners of alkenes, 0.5 M solutions were used for observing the muonium adducts34,35,36. To observe a muoniated radical with a concentration of 0.06 M, the rate constant of addition has to be ~ 1010 M–1 s–1, which is approaching the diffusion-controlled limit (1010~1011 M–1 s–1)24,38. The increase in the amplitude of the radical signal is consistent with an increase in the diffusion coefficients of Mu and 1 due to the increasing temperature and decreasing viscosity of the THF solvent (Fig. 3b inset). As far as the authors know, comparable diffusion parameters on the regioselective muoniation at the P = C-containing molecule have never been reported.

In high magnetic fields, only the 1↔2 and 3↔4 transitions can be observed:

$$\:{\upsilon\:}_{12}=\:{\nu\:}_{\text{D}}\:\--\:\frac{1}{2}{A}_{\mu\:\:}$$
(2)
$$\:{\upsilon\:}_{43}=\:{\nu\:}_{\text{D}}+\:\frac{1}{2}{A}_{\mu\:\:}$$
(3)

where νD is the precession frequency of muons in diamagnetic environments (closed shell: 135.53 MHz/T), and Aµ is the muon hfc. Aµ can be readily determined from the difference of the two radical precession signals, or if the higher frequency cannot be observed owing to the time resolution of the spectrometer, Aµ can be determined from v12 and vD. Aµ is 306.969 ± 0.014 MHz at 298 K.

The hfcs of other nuclei can be measured via muon avoided level-crossing resonance (µLCR, alternatively referred to as avoided level-crossing muon spin resonance or ALC-µSR). In µLCR measurements, both the muon’s spin and the magnetic field are oriented parallel to the muon’s momentum. The muon’s polarization is proportional to the asymmetry, which is the difference in the time-integrated number of positrons measured in the forward and backward directions divided by the total. Under most applied fields, the muon’s spin does not evolve with time. However, there are certain magnetic fields where the spin states of the radical are nearly degenerate, which causes a mixing of the spin states. If the mixed states involve different muon spin orientations, there is a partial loss of spin polarization at the resonance field. In solution, resonances are only observed between spin states where M, which is the sum of the spin quantum numbers of the muon (µ), electron (e), and nucleus (k), does not change. These are called ΔM = 0 or Δ0 resonances. The resonance occurs at a magnetic field according to Eq. (4):

$$\:{B}_{\text{L}\text{C}\text{R}}^{{\varDelta\:}_{0}}\:=\:\frac{1}{2}\left[\frac{{A}_{\mu\:}\--{A}_{k}}{{\gamma\:}_{\mu\:}\--{\gamma\:}_{k}}\--\frac{{A}_{\mu\:}+{A}_{k}}{{\gamma\:}_{e}}\right]$$
(4)

where γµ, γk, and γe refer to the gyromagnetic ratios of the muon, the nucleus k, and the electron, respectively. Ak is the hyperfine coupling constant of nucleus k.

The µLCR spectra of the 0.060 M THF solution of 1 are shown in Fig. 4a. There is a Δ0 resonance at 750.6 ± 0.2 mT at 298 K. We know that this Lorentz-like resonance is not due to protons as the resulting proton hfc would be too large (~ 166 MHz). The addition of Mu at the secondary unsaturated carbons (positions 6 and 7 of 1) would generate relatively preferable benzyl-type radicals16. These radicals have a CHMu methylene group, and with a muon hfc of ~ 307 MHz the value of the proton hfc should be ~ 80 MHz (see Fig. 5d and the Supporting Information). Radicals of this type would have Δ0 resonances above 1 T. On the basis of the magnetic field and the amplitude of the resonance, we have concluded that this resonance is due to 31P. The 31P hfc (\($$A_{^{31}{\rm P}}$$\)) was determined via Eq. 4 and is 127.54 ± 0.04 MHz at 298 K. Based on the muon and 31P hfcs, we have concluded that Mu regioselectively adds to the sp2-hybridized phosphorus in 1 leading to 1Mu (Fig. 4b). The relatively broad LCR signal (FWHM ~ 50 mT) might be due to the rotating CF3 units containing 19F nuclei of I = 1/239.

Other plausible positions of muoniation in 1, which are C2, C4, C8-11, and the 2,4,6-(CH3)3C6H2 aromatic ring, would provide the corresponding cyclohexadienyl radical upon muoniation and would display muon hfcs of 450 ~ 500 MHz. Therefore, muoniation at the aromatic rings in 1 is excluded.

Fig. 4
figure 4

(a) µLCR spectra of a 0.060 M solution of 1 in THF. The error bars are smaller than the data points. (b) Regioselective addition of muonium to the sp2-type phosphorus in 1, generating paramagnetic 1Mu.

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DFT calculations

The hyperfine parameters of 1Mu were obtained from DFT calculations and compared with experimentally measured Aµ and \($$A_{^{31}{\rm P}}$$\) parameters to draw some conclusions about the radical’s structure. The structure of 1Mu was first optimized at the UB3LYP/def2-SVP level. Hydrogen was used instead of Mu for the geometry optimization and the minimum energy structure is shown in Fig. 5a. The initial coplanar tetracyclic system is distorted to a saddle-type shape because of the CF3 group at the peri-position, and the CMes–C3···P (Mes = mesityl, 2,4,6-trimethylphenyl) and C3···P–Mu angles are 170.1 and 122.0°, respectively. The muon and 31P hfcs of the normally optimized structure of 1Mu are 211.4 and 148.2 MHz, respectively, and the calculated Aµ is significantly smaller than the experimentally determined value of 306.5 MHz. The DFT optimization using the H atom in place of Mu did not consider the light mass of the muon increasing zero-point energy, and accordingly, the structure in Fig. 5a should be corrected. In the muoniated cyclohexadienyl radical, the reduced muon hfc [Aµ’ = Aµ·(µp/µµ) = Aµ/3.1833, µp and µµ are magnetic moments of proton and muon, respectively] is 28% larger than the corresponding methylene Ap due to the approximately 4.9% longer C–Mu bond than C–H23,24,27,28,29. Such structural deviation into the energetically higher form is from the increased zero-point energy caused by the light mass of muon. Conventional structural modifications for the effects of muon were attempted by elongating the P–Mu(H) bond and scanning the angles around the phosphorus. However, these conventional methods were unsuccessful in simulating the experimental results (vide infra). Therefore, as we have previously done in the study of peri-trifluoromethylated 9-phosphaanthracene22, the structure of the muoniated radical 1Mu produced from the CF3-substituted phosphatetraphene (1) was optimized with the constraint that the tetracyclic molecular skeleton should be flat. This resulted in an alternative structure shown in Fig. 5b. The CMes–C3···P and C3···P–Mu angles are 175.8 and 94.6°, respectively, and the calculated muon hfc of 294.8 MHz is close to the experimental data. On the other hand, the simulated hfc value of 31P substantially deviated from the result of the µLCR. After some attempts, we found that changing the C3···P–Mu angle from 94.6° to 103° while increasing the total energy to 0.86 kcal/mol could simulate the comparable calculated muon and 31P hfc parameters of 304.5 and 128.3 MHz, respectively. The additional structural modifications for Fig. 5b via 4% elongation of P–Mu provided the larger muon hfcs such as 329 MHz (C3···P–Mu 94.6°) and 341 MHz (C3···P–Mu 103°) and were overestimated. Figure 5c displays a plot of the spin density distribution over the modified flat form obtained by altering the C3···P–Mu angle and indicates considerable delocalization over the tetracyclic skeleton. The delocalized spin density over the flat molecular framework would enhance the overlap with the P–Mu bond, corresponding to the increased muon hfc and the proportionally increased 31P hfc. Figure 5d displays a simulated µLCR spectrum for 1Mu of Fig. 5c using the program Quantum40,41 and is comparable with Fig. 4a showing the single, broad resonance around 750 mT. On the other hand, according to the Quantum calculations, the muoniation products at the C6 and C7 positions (C6-Mu and C7-Mu, Fig. 6) which would be possible to be produced (vide infra) should show several significant resonances at 1 ~ 1.8 T. Therefore, only 1Mu is compatible with the experimental µLCR spectra in Fig. 4a. Table 1 summarizes the experimental and DFT-estimated hyperfine constants and the energetic parameters for 1Mu. The normally optimized structure shown in Fig. 5a is incompatible with the experimental results even when the bond distance and angle around Mu(H) are modified (see Figure S6). Frequency analyses using the 0.1134 amu for muonium characterized the larger zero-point energies (ZPEs). On the other hand, the ΔEZPE(Mu-H) values comparing ZPE for each structure (1Mu_normal, 1Mu_flat, 1Mu_flat-modified) are proportional to the ΔEtotal data, which is consistent with the structural deviation by the muon isotope effect. The increased zero-point energy (ZPE) was estimated for each calculated structure using 0.1134 amu for muonium. Table S1 shows the parameters of C6-Mu and C7-Mu, which are not comparable with the experimental data discussed above. The increase of ZPE for C–Mu is larger compared with P–Mu.

Fig. 5
figure 5

(a) A normally optimized structure of 1Mu. Hydrogen was used instead of Mu at the UB3LYP/def2-SVP level. (b) The alternative structure of 1Mu maintains a flat tetracyclic system with an increased total energy of 1.59 kcal/mol. Modifying the C3···P–Mu(H) angle to 103° with increasing total energy (0.86 kcal/mol) provides the almost identical muon and 31P hfc constants of 304.5 and 128.3 MHz, respectively, to the experimentally determined Aµ (307 MHz) and \($$A_{^{31}{\rm P}}$$\) (128 MHz) values. (c) The spin density (iso = 0.006, blue: α spin, green: β spin) of the modified structure from (b) indicates the delocalization of the unpaired electron over the planar tetracyclic skeleton. (d) Simulated µLCR spectra for the DFT-calculated structures of 1Mu (c), C6-Mu, and C7-Mu (see Fig. 6).

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Table 1 Experimental and DFT-estimated hyperfine parameters of 1Mu.
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Fig. 6
figure 6

Distinguished coordinate reaction paths (ΔH, kcal/mol) for Mu addition to the sp2-phosphorus atom in 1 yielding 1Mu and Mu addition to the 6- and 7-positions in 1 yielding C6-Mu and C7-Mu. The inset shows an enlarged plot indicating the quite small barrier leading to C7-Mu. The structures of the resulting radicals are shown below.

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Figure 6 shows the distinguished coordinate reaction paths for Mu addition at different sites of 1 that produce 1Mu, C6-Mu, and C7-Mu. Muoniation affording 1Mu would proceed without activation energy, probably correlating with the instability of the P = C units. As indicated by the X-ray data, the C6 and C7 positions are relatively tolerant to muoniation because the 6-membered ring containing C6 and C7 lacks aromaticity as indicated by the small absolute value of Nucleus-Independent Chemical shift (NICS)42,43 at the ring center [NICS(0) = − 3.83]16. Muoniation leading to C6-Mu would require an obvious activation energy (Ea = 1.7 kcal/mol) and would be affected by steric effect. In the case of C7-Mu, a quite small (or negligible) activation energy of 0.006 kcal/mol was observed probably due to steric effect44. It is surprising that this radical was not observed. For reference, both C6-Mu and C7-Mu are thermodynamically unstable compared with 1Mu, which is correlated with the difference of stability between the P = C and C = C bonds. Both the experimental and theoretical µLCR spectra (Figs. 4a and 5d) are consistent with 1Mu.

Temperature effect and thermodynamic parameters of the muoniated 12-phosphatetraphene

Figure 7a and b show the temperature dependences of Aµ and \($$A_{^{31}{\rm P}}$$\) determined by TF-µSR and µLCR, respectively. Both hfcs values decrease as the temperature increases, indicating that a higher temperature promotes a more stable form by reducing the C3···P–Mu angle in the flat form (see the Supporting Information). The temperature dependence of Aµ in 1Mu is comparable to that in MuCH2-C·(CH3)245,46,47, and the deviation of \($$A_{^{31}{\rm P}}$$\) is proportional to that of Aµ. The small changes in hfcs would correlate with the considerable inversion barrier around phosphorus of ~ 30 kcal/mol. In contrast to the previous study on 9-phosphaanthracene22, 1 is a prochiral molecule, and thus the muoniation product 1Mu should be a mixture of chiral paramagnetic molecules48. When 1 could form distinguished chiral conformation, the muonium adducts should be diastereomeric and show two separate hfcs. In the case of 1, the TF-µSR and µLCR did not separate, and thus 1 would not form chiral structures in irradiation of muon beam in tetrahydrofuran.

Fig. 7
figure 7

(a) Temperature dependence of the muon hyperfine coupling constant of the Mu adduct of 1. (b) Temperature dependence of the 31P hyperfine coupling constant of the Mu adduct of 1.

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Conclusion

The reactions of a phosphorus congener of PAHs, peri-trifluoromethylated 12-phosphatetraphene 1, with Mu, arguably the simplest free radical, were investigated via µSR spectroscopy. Mu added exclusively to the phosphorus. This highly regioselective muoniation was promoted by the highly reactive sp2-hybridized phosphorus in 1. Notably, the paramagnetic signals of the muonium adduct were observed even when the dilute solution of 1 (0.060 M in THF) was used, in contrast to the µSR studies of 9-phosphaanthracene and most organic compounds. The hyperfine parameters of muon (Aµ) and 31P (\($$A_{^{31}{\rm P}}$$\)) included the effect of the muon increasing zero-point energy, which promoted the maintenance of the flat molecular framework of 12-phosphatetraphene and avoided the thermodynamically preferable saddle-type tetracyclic skeleton. The positive Aµ and \($$A_{^{31}{\rm P}}$$\) parameters decreased with increasing temperature, which was comparable with the cases of H2C = C(CH3)245,46,47 and biacetyl48,49. Additionally, the dynamics of muoniation to 1 were qualitatively discussed by using the relaxation parameters.

The results of this study strongly suggest that the π-extended phosphorus congener of a PAH, tetraphene, is useful for radical (spin) trapping on the basis of regioselective radical addition. Applications of 1 based on the basis of the findings from the µSR studies are now attempted. Additionally, other phosphorus congeners of PAHs such as phosphabenzotetraphenes and phosphatetracenes16 would be attractive. Subsequent µSR studies on other phosphorus congeners of PAHs are in due course.