Synthesis of Nanometer Sized Bis- and Tris-trityl Model Compounds with Different Extent of Spin–Spin Coupling

Tris(2,3,5,6-tetrathiaaryl)methyl radicals, so-called trityl radicals, are emerging as spin labels for distance measurements in biological systems based on Electron Paramagnetic Resonance (EPR). Here, the synthesis and characterization of rigid model systems carrying either two or three trityl moieties is reported. The monofunctionalized trityl radicals are connected to the molecular bridging scaffold via an esterification reaction employing the Mukaiyama reagent 2-chloro-methylpyridinium iodide. The bis- and tris-trityl compounds exhibit different inter-spin distances, strength of electron–electron exchange and dipolar coupling and can give rise to multi-spin effects. They are to serve as benchmark systems in comparing EPR distance measurement methods.

The synthesis of 9 was carried out following a modified procedure by Valera et al. 1 Under an argon atmosphere, 6.78 mmol) was dissolved in dry tetrahydrofuran (THF, 20 ml) before PdCl 2 (PPh 3 ) 2 (79.1 mg, 110 µmol) and CuI (21.5 mg, 110 µmol) were added. The resulting yellow solution was degassed via three freeze-pumpthaw cycles. 1, 3.39 mmol) was added dropwise as a degassed solution in THF (5 ml). The reaction mixture was degassed once more before dropwise addition of an aqueous ammonia solution (0.5 M, 25 ml) which had been saturated with argon for 10 minutes. The mixture was stirred at room temperature for 40 hours and afterwards heated for 6 hours at 60 °C. The two phases were separated and the aqueous layer was extracted with ethyl acetate ester (EE) (2×20 ml). The combined organic layers were washed with 10% HCl (40 ml), water (40 ml) and brine (20 ml) before being dried over MgSO 4 .
Under an argon atmosphere, compound 1 • was dissolved in the degassed mixture of DCM and Et 3 N and stirred at room temperature for two hours to achieve complete deprotonation of the carboxylic acid groups. After addition of EtOH (135 µl, 2.32 mmol), the green reaction mixture was cooled down to 0 °C. CMPI and DMAP were added which resulted in a dark 1 • 5 • red color. The mixture was stirred at room temperature for 21 hours and then quenched with aqueous HCl (30 ml, 0.3 M). The organic layer was separated and the aqueous layer was extracted with DCM (3×20 ml). The combined organic layers were washed with brine (30 ml) and all solvents were removed under reduced pressure at 30 °C to give the crude product.

Synthesis of
Compound 6 • was synthesized following a modified procedure by Saigo et al. 2 Compound 1 • (562 mg, 562 µmol) as well as the reactants 2-chloromethylpyridinium iodide (CMPI, 351 mg, 1.38 mmol) and 55.4 mg,450 µmol) were dried under reduced pressure for two hours before starting the reaction.
Under an argon atmosphere, compound 1 • was dissolved in a mixture of dry tetrahydrofuran (THF, 7 ml) and triethylamine (Et 3 N, 390 µL, 2.81 mmol) and stirred at room temperature for three hours to achieve complete deprotonation of the carboxylic acid groups. After addition of MeOH (45.6 µl, 1.12 mmol), the green reaction mixture was cooled down to 0 °C. CMPI and DMAP were added which resulted in a dark red color.  2,6, benzo [1,2-d;4,5-d´]-bis [1,3]dithiol- 4-yl)mono (8-carboxyl-2,2,6,6-tetra methylbenzo [1,2-d;4,5-d´]-bis [1,3]dithiol- 4-yl) The organic layer was separated and the aqueous layer was extracted with DCM (3×20 ml). The combined organic layers were washed with brine (40 ml) and all solvents were removed under reduced pressure at 30 °C to give the crude product. MS-MALDI(+) analysis of the crude product indicated that the reaction had predominantly yielded a byproduct (m/z = 2081, see Figure S11), while the expected target compound signal was not visible at all. The 1 H-NMR spectrum ( Figure S12) of the isolated by-product showed strong paramagnetic contributions indicating that the by-product is a trityl radical containing compound. The by-product synthesis was presumably caused by an ethylene glycol contamination (from THF bottle packaging components or other), high resolution MS-APCI (atmospheric pressure chemical ionisation) gave a molecular formula which would be consistent with this hypothesis (see Figure S13 and Figure S14). A first purification step was performed by silica column chromatography using chloroform followed by 10% v/v acetonitrile in chloroform and finally 50% v/v methanol in chloroform as eluents. This step gave three fractions in the following order of mention: esterification reagents (fraction A), product and by-products (fraction B) and clean unreacted trityl 6 • (fraction C), the latter being thus easily regained for further usage. Fraction B was put to a second silica column chromatography procedure using a slowly increasing gradient of acetonitrile in chloroform. A third purification step consisted in a reversed phase middle pressure liquid chromatography (MPLC, see Figure S15) run using a water gradient in acetonitrile as eluent. After the collection of four impurity fractions, the column was rinsed with THF to collect the product containing fraction. The latter was purified by a final silica gel chromatography column using 1% v/v acetonitrile in chloroform as eluent.

Synthesis of
Product compound 2a •• was obtained as a brown solid (10.4 mg, 4.19 µmol, 12%). The compound´s purity was additionally assessed by MPLC (see Figure S17).  Figure S20) was followed by a second silica gel chromatography column using 1% v/v acetonitrile in chloroform to give product compound 2b •• as a brown solid (16.0 mg, 6.30 µmol, 17%). The compound´s purity was additionally assessed by MPLC (see Figure S22). Under an argon atmosphere, compound 6 • was dissolved in a mixture of dry THF (6 ml) with triethylamine (75.9 µL, 555 µmol), and stirred at room temperature for two hours to achieve complete deprotonation of the carboxylic acid groups. After addition of compound 10 (13.2 mg, 20.0 µmol), the reaction mixture was cooled down to 0 °C before CMPI and DMAP were added. The mixture was stirred at room temperature for 72 h. The reaction was quenched with aqueous HCl (20 ml, 0.2 M) and

MS
diluted with 80 ml of DCM. The organic layer was separated and the aqueous layer was extracted with DCM (3×20 ml). The combined organic layers were washed with brine (40 ml) and all solvents were removed under reduced pressure at 30 °C to give the crude product. Purification was performed by reversed phase MPLC using a water gradient in acetonitrile as eluent (see Figure S23). After the collection of unreacted educt compound 6 • and an impurity fraction, the column was rinsed with THF to collect the product compound in three fractions, one of which contained isolated target compound. Product compound 3a ••• was obtained as a brown solid (28.0 mg, 7.60 µmol, 38%). The compound´s purity was additionally assessed by MPLC (see Figure S25). diluted with 60 ml of DCM. The organic layer was separated and the aqueous layer was extracted with DCM (3×20 ml). The combined organic layers were washed with brine (40 ml) and all solvents were removed under reduced pressure at 30 °C to give the crude product. Purification was performed by reversed phase MPLC using a water gradient in acetonitrile as eluent (see Figure S28). After the collection of unreacted educt compound 6 • and an impurity fraction, the main product fraction (37 mg) was eluted at 10% v/v water in acetonitrile. MS-MALDI(+) showed that this fraction contained target compound 4a •• as well as sulfoxide derivatives thereof (Δ m/z = 16, see Figure S29). The column was rinsed with THF to collect small amounts of non-oxidized product compound in a mixture with two impurities. This mixture was put to silica gel column chromatography using 1% v/v acetonitrile in chloroform as eluent. Compound 4a •• was obtained as a brown solid (3.00 mg, 1.36 µmol, 6%). The compound´s purity was additionally assessed by MPLC (see Figure S31).

Isotropic interactions
The isotropic case is of importance for the treatment of the exchange interaction observed in the room temperature cw EPR spectra. There, the exchange coupling constant J can be obtained by measuring the effective isotropic hyperfine coupling constant of the 13 C satellites. This means that the molecules of interest contain one 13 C atom in one of the two trityl units ( Figure S37). Thus, the spin system consists of two electron spins and one nuclear spin.
As basis set, the product functions of the individual spins are considered -8) By definition, the nuclear spin is located on trityl 1 as depicted in Figure   S37. The spin Hamiltonian operator in frequency units for this system can be derived from eq. 1 in the main text and reads as -9) The terms in the operator represent the Zeeman effect for both spins, the isotropic hyperfine interaction, and the isotropic exchange interaction. For the latter two interactions, secular and pseudosecular interactions are taken into account in eq. S-9.
The corresponding Hamiltonian matrix for the functions |1> to |4> is given by -11) The matrix for the other functions is similar, only the signs of hyperfine terms have to be changed as these functions correspond to the other alignment of the nuclear spin. There is also no mixing between the first four functions (nuclear spin up) and the second four functions (nuclear spin down). Hence it is sufficient to discuss the functions and eigenvalues corresponding to one of the nuclear spin states. Importantly, functions |1> and |4> do not mix with any other function and are thus good wavefunctions regardless of the magnitude of J and the hyperfine coupling constant a. The eigenvalues of |1> and |4> can be read off directly from the matrix in eq. S-11. |2> and |3> are mixed to arrive at new wavefunctions |2'> and |3'> -13) with the orthonormality conditions -14) and The submatrix of involving |2> and |3> (eq. S-11) can be used to calculate the eigenvalues and mixing coefficients of the new wavefunctions |2'> and |3'>. For the eigenvalues, the determinant is considered: -18) where a/2 has been replaced by Δω in the last step and the upper sign before the square root refers to function |2'>. To obtain the eigenfunctions |2'> and |3'> to these eigenvalues, the secular equations have to be solved: -19) yielding together with the normalization condition (eq. S-14) Eqs. S-18, S-20, and S-21 show that the coefficients and energies of state |2'> and |3'> (upper and lower sign before Δω, respectively) depend in a complex manner on Δω and J. In the extreme case of |J| << |Δω| the functions |2'> and |3'> are identical to |2> and |3>, respectively (i.e. c 1 = 1 and c 2 = 0 in the case of |2'> and vice versa for |3'>). The eigenvalues of the resulting functions are identical to the diagonal elements in the matrix given in eq. S-11. In this weak coupling case, the molecule behaves like a real biradical, meaning that it is possible to selectively address either one of the electron spins spectroscopically. As a consequence, transitions in which a single electron spin is flipped are allowed in this regime, i.e. transitions |4> à |3>, |4> à |2>, |3> à |1>, and |2> à 1> with the transition frequencies -25) where the approximate result given at Their eigenvalues amount to -27) Importantly, transitions involving the singlet state function are forbidden in this regime. This leaves two allowed transitions between the triplet states with frequencies -29) Thus, in the strong coupling a pair of transitions is still observed, but with a splitting which is reduced by 50%. An example for this are the hyperfine coupling cosntants to the a-protons in 4a •• , which are lowered by 50% as compared to 2a •• and 3a ••• . The most complicated case is encountered when J is on the order of a. The transition frequencies in are then given by eqs. S-30 -S-33: -33) These equations have to be used for the ipso-and ortho-satellite lines.
Since cw EPR spectroscopy is usually conducted at constant MW frequency !" while the field values are swept it is sensible to rewrite the above equations to obtain the resonant field of all transitions: respectively. Note that it is not possible to extract the sign of J from the cw EPR spectra. However, the positive sign appears to be the right choice.
With the definition of the spin Hamiltonian operator given in eq. 1 in the main text this means that the spin system is antiferromagnetically coupled, which is also in agreement with the attachment of the spin centers in para positions of the diamagnetic bridging unit [4,5].

Dipolar, spectral broadening caused by one or two spins
As mentioned in the main text, the EPR spectrum of bistrityl 2a •• was found to be slightly broader than the EPR spectrum of the analogous monotrityl compound 1a • . Furthermore, the spectrum of tristrityl 3a ••• was found to be further broadened. The interaction with two electron spins instead of just one was mentioned as the origin of this additional broadening, which could be seen as manifestation of multi-spin effects [6][7][8] in cw EPR spectroscopy. Moreover, the situation was compared to the scenario of an electron spin coupling to either one or two nuclear spins. This interpretation is a different angle on multi-spin effects and is discussed here for better understanding. To that end, Figure S38 is considered, in which the orientations of the interspin vectors with respect to the external magnetic field are depicted for three different molecular orientations. Figure S38 also gives the expected coupling of spin A with the two other spins in multiples of the dipolar coupling constant D. These values can now be used to draw energy level schemes similar to those drawn in textbooks when discussing isotropic hyperfine interactions. This is shown in Figure S39 for a two-spin system AB and a three-spin system ABC. As can be seen by comparing the three-spin to the two-spin example depicted in Figure S39, the amount of transitions is larger in the three spin example, as there are also more different spin states. Each spin state is shifted from the position obtained by the Zeeman-splitting of spin A by the electron-electron dipole coupling. For the three-spin system, these shifts are just the sum of the individual couplings to spin B and C. This leads to a broadening of the cw EPR spectrum of a three-spin system as compared to a two-spin system. In addition, also the multi-spin effects observed in pulsed measurements can be related to the scheme shown in Figure S39. This is illustrated in Figure S40, which shows spectra obtained by numerical simulation of the couplings obtained for either a two-spin system or a three-spin system in a rigid, triangular system as shown in Figure 39. Note that the spectrum of the three-spin system has no obvious resemblance to a Pake pattern. Another important point to note is the high intensity of the spectrum at high absolute values above and below the frequencies at the singularities of the two spin system. This is a consequence of the occurrence of sum-and difference frequencies and in agreement with the experimental observations made on 2a •• and 3a ••• . Figure S40: Numerically simulated EPR spectra of the dipolar interaction for a two-spin or a three-spin system. The frequencies of the transitions discussed in Figure S39 are indicated by colored arrows, the color code is identical to the one used in Figure S39.