Improving the molecular spin qubit performance in zirconium MOF composites by mechanochemical dilution and fullerene encapsulation

Enlarging the quantum coherence times and gaining control over quantum effects in real systems are fundamental for developing quantum technologies. Molecular electron spin qubits are particularly promising candidates for realizing quantum information processing due to their modularity and tunability. Still, there is a constant search for tools to increase their quantum coherence times. Here we present how the mechanochemical introduction of active spin qubits in the form of 10% diluted copper(ii)-porphyrins in the diamagnetic PCN-223 and MOF-525 zirconium-MOF polymorph pair can be achieved. Furthermore, the encapsulation of fullerene during the MOF synthesis directs the process exclusively toward the rare PCN-223 framework with a controllable amount of fullerene in the framework channels. In addition to the templating role, the incorporation of fullerene increases the electron spin–lattice and phase-memory relaxation times, T1 and Tm. Besides decreasing the amount of nuclear spin-bearing solvent guests in the non-activated qubit frameworks, the observed improved relaxation times can be rationalized by modulating the phonon density of states upon fullerene encapsulation.


Contents
, and C 60 , respectively. The bands denoting the successful encapsulation of C 60 are marked with an asterisk (*). The spectral distortion visible in the spectrum of the C 60 can be ascribed to the Christiansen effect. 1 It is present in all the C 60 spectra taken, no matter the mode of collection ( 12 ] 2 ) and Zr 6 -methacrylate cluster (Zr 6 O 4 (OH) 4 -(C 2 H 3 CO 2 ) 12 ) were synthesized according to the literature methods. 6,7 5,10,15,20-Tetrakis(4-methoxycarbonylphenyl)porphyrin (TPPCOOMe) was prepared according to the literature. 8 1 H NMR and PXRD data were in accordance with previously published for these compounds.

List of Tables
Cu(II) meso-tetra(4-carboxyphenyl)porphine (CuTCPP) was synthesized according to the literature methods. 9,10 TPPCOOMe (100 mg, 0.118 mmol) and excess Cu(Cl) 2 x2H 2 O (250 mg, 1.47 mmol) were refluxed in DMF (20 mL) for 6h. The reaction mixture was cooled to room temperature and 20 mL of H 2 O was added to the mixture. Red precipitation was formed, filtered and followed by washing three times with H 2 O and dissolved in CH 3 Cl, washed three times with 1M HCl, and twice with H 2 O. The organic layer was dried over anhydrous magnesium sulfate and the organic solvent was evaporated to obtain the ester porphyrin complex, CuTPPCOOMe. To the THF-MeOH solution of CuTPPCOOMe, KOH (aq) (0.32 g KOH, 4 mL H 2 O) was added and refluxed for 12h. After the mixture was cooled to room temperature, organic solvents were evaporated, H 2 O was added to the water phase and the mixture was slightly heated until the solid was fully dissolved, then the homogeneous solution was acidified with 1 M HCl until no further precipitate was produced. The red solid was collected by filtration, washed with water and recrystallised from EtOH. PXRD and FTIR-ATR results are in good agreement with the literature data. Isolated: 60 mg (60%). Cu 1.0 -MOF-525 Zr 6 -methacrylate cluster (19.55 mg, 0.012 mmol), CuTCPP (20 mg, 0.0234), NaOAc (6 mg) and 30 µL DMF were placed into a Teflon jar (14 mL) with two zirconia balls (1.6 g each). The reaction mixture was milled using IST-500 (InSolido Technologies, Croatia) mixer mill at 30 Hz for 45 min. The resulting black powder was washed with DMF (3x4 mL) and analyzed by PXRD and FTIR-ATR. Isolated: 27 mg.

S1.4 Inductively Coupled Plasma Mass Spectrometry (ICP-MS)
ICP-MS was performed at the University of Zagreb on a Plasma ICP-MS (7900, Agilent Technologies, Singapore). Since we were limited with the revision time needed for the experiment, we were forced to give a Cu 1.0 -MOF-525 polymorph instead of the Cu 1.0 -PCN-223 because we were not able to prepare a phase-pure PCN-223 in this narrow time range. The two materials are polymorphs, therefore the ratio of the metals inside (Zr/Cu) is the same for both phases.

S1.5 Elemental analysis
The C, H, and N content was obtained using a Perkin Elmer 2400 Series II CHNS analyzer in an oxygen stream.

S1.6 TEM microscopy
Distribution of elements on the investigated samples were performed with energy dispersive X-ray spectroscopy (EDAX) using Jeol Centurio wide-area Silicon Drift Detector (SDD) system attached on a 200 kV cold field-emission gun (FEG) Cs-probe corrected transmission electron microscope (Jeol ARM 200 CF).

S1.7 Modeling
DFT. PCN-223 and C 60 @PCN-223 systems were assessed at the DFT/PBE-D3 level of theory using the VASP package 11 and projector augmented-wave method as implemented in the v5.5.4 code and the standard pseudopotentials provided along with the package. 12,13 The geometries were optimized in the G-point down to the maximal residual forces of 10 −4 eV/Å. DFTB. Classical MD employs the DFTB+ package 14 version 19.1 with initial geometries and in the unit cell as predicted by DFT theory. The systems were parameterized using MIO force fields with missing Zr parameters substituted by chemically closely related Ti and analyzed in-house python scripts. 15,16 The MD algorithm is driven by NVT (canonical ensemble, with Nose-Hoover thermostat) equation with T = 300 K. The overall trajectory for the C 60 @PCN-223 system was integrated for 100 ps with an integration time step of 1 fs. S1.8 Solid-state nuclear magnetic resonance (NMR) 1 H and 13 C MAS (Magic-Angle Spinning), 1 H-13 C CPMAS (Cross-Polarization Magic-Angle Spinning) and HETCOR (Heteronuclear Correlation) NMR spectra were recorded on a narrowbore 600 MHz Varian VNMRS spectrometer equipped with a 3.2 mm Varian CPMAS probe operating at 1 H Larmor frequency of 599.37 MHz and 13 C Larmor frequency of 150.71 MHz. Sample rotation frequency was 20 kHz. In one-dimensional (1D) NMR experiments the number of scans was 32 for 1 H MAS, 1500 for 13 C MAS measurements, and 1500 for 1 H-13 C CPMAS measurements while the repetition delays between scans were 1 s, 120 s, and 0.6 s, respectively. 1 H and 13 C MAS NMR spectra were measured using the Hahn-echo sequence with the echo delay of one rotation period. The 1 H and 13 C 90°pulses were 2.6 µs and 2.35 µs, respectively. 1 H-13 C CPMAS experiment employed RAMP 17 on proton channel during 1.0 ms CP block and high-power XiX proton decoupling 18,19 during acquisition. An additional CPMAS experiment was employed with a 50 µs CP block to elucidate the protonated 13 C signals. Two-dimensional (2D) 1 H-13 C HET-COR experiment was performed by first exciting the protons with a single pulse and letting the proton magnetization evolve in the absence of homo-/hetero-nuclear decoupling. In the next step the magnetization was transferred to carbon nuclei by RAMP CP block of 3.0 ms. 2D experiment was performed in a hypercomplex mode, 20 the number of increments along the indirectly detected dimension was 40 and 5000 scans per increment were accumulated. Tetramethylsilane was used as an external reference for both 1 H and 13 C frequency axes. The experiments were performed at 300 K.

S1.9 ESR spectroscopy
Continuous-wave (CW) and pulsed ESR experiments were performed using X-band (around 9.7 GHz) FT/CW Bruker ELEXSYS E580 spectrometer equipped with an Oxford Instruments temperature unit. CW ESR spectroscopy was performed applying modulation amplitude of 0.1 mT at 100 kHz modulation frequency from room down to liquid helium temperature.
Samples exhibiting 100% copper (II) concentration were analyzed only by CW ESR as the quantum coherence was too short to be detected due to the electron-electron spin dipolar interactions. For the pulsed ESR measurements the copper (II) concentration had to be lowered to 10%. Magnetization decay rates were followed in the temperature interval from 5-80 K using π/2 pulse duration of 16 ns. Two-pulse echo detected field-swept ESR spectra of MOFs at T = 80 K were recorded in order to define spectral positions for the relaxation rate measurements. Spin-lattice relaxation times, T 1 , were studied using inversion recovery (IR) pulse sequence with echo detection sequence, π −t − π/2 − τ − π − echo, where τ = 100 ns and variable t starting from the initial value of 400 ns. 21 T 1 was determined from a fit of the echo recovery amplitude to the mono (T > 40 K) and biexponential function (T < 40 K) to account for the spectral diffusion affecting IR sequence wherein the longer component was considered an approximation for T 1 . 22 The phase memory time, T m , was derived using two-pulse electron-spin-echo decay sequence, π/2 − τ − π − τ − echo, with τ = 100 ns and shots repetition time adjusted to accommodate complete spin-lattice relaxation. T m was estimated by fitting the echo signal to the mono-exponential decay function. 21 HYSCORE (Hyperfine Sublevel Correlation) experiment was performed using the sequence π/2 − τ − π/2−t 1 −π−t 2 −π/2 − τ − echo, τ = 100 ns and the starting values of t 1 = t 2 = 200 ns incremented by 16 ns in 150 steps. 21 Measurements of echo-detected Rabi oscillations were performed with the pulse sequence t p − T − π/2 − τ − π − τ − echo, where the nutation pulse length t p was varied, τ was 100 ns and T was 1000 ns. In specific, the time duration of the nutation pulse, t p , was incremented in such a way that its initial length (12 ns -28 ns), δt, was adjusted by choosing the proper microwave power attenuation (1 dB -8 dB) to account for maximal spin-echo signal (β = π/2) 21 and the field strength calculated from δt and β .   Figure S3: FTIR-ATR spectroscopy data for 1.0C 60 @Cu 0.1 -PCN-223, 0.2C 60 @Cu 0.1 -PCN-223, Cu 0.1 -PCN-223, DMF, and C 60 , respectively. The bands denoting the successful encapsulation of C 60 are marked with an asterisk (*). The spectral distortion visible in the spectrum of the C 60 can be ascribed to the Christiansen effect. 1 It is present in all the C 60 spectra taken, no matter the mode of collection (ATR or transmission in a KBr pastille).

S2.4 Solid-state CPMAS and CP-HETCOR NMR spectroscopy
The 1 H-13 C CPMAS spectra of Cu 0.1 -PCN-223 and C 60 @Cu 0.1 -PCN-223 are presented in Fig. S4. The assignment of 13 C peaks is supported by the analysis of CP-HETCOR spectrum of C 60 @Cu 0.1 -PCN-223 sample (Fig. S5). It can be noticed that the signals of DMF/DEF solvent are present in the NMR spectra of both samples. The 13 C signal of C 60 at ca. 138 ppm exhibits a narrow line indicative of fast motion of the fullerene in the MOF cavity. Figure S4: The 1 H-13 C CPMAS NMR spectra recorded for Cu 0.1 -PCN-223 and 1.0C 60 @Cu 0.1 -PCN-223 samples at 300 K. The blue color represents the CPMAS spectrum recorded at a very short mixing time, τ cp , of 50 µs which reveals the protonated 13 C signals of TCPP. The 13 C signal of C 60 at ca. 138 ppm is indicated by the arrow. The TCPP peaks indicated by numbers follow the notation of 1 H-13 C CP-HETCOR experiments shown in Fig. S5. Figure S5: The 1 H-13 C CP-HETCOR NMR spectrum of 1.0C 60 @Cu 0.1 -PCN-223 sample recorded at 300 K. The 13 C signal of C 60 at ca. 138 ppm is indicated in the figure.The TCPP peaks indicated by numbers follow the notation of 1 H-13 C CPMAS experiments shown in Fig. S4.

S2.5 CW ESR spectroscopy
Peak-to-peak linewidth W pp and g-value of fullerene-radical (FR) in 0.2C 60 @Cu 0.1 -PCN-223 sample show no significant change with temperature, as can be seen in Fig. S6. Figure S6: CW-ESR spectra of 0.2C 60 @Cu 0.1 -PCN-223 at indicated temperatures. Peak-to-peak linewidth W pp and g FR of fullerene-radical (FR) due to the defects in fullerene structure are given.
Experimental CW ESR spectra were simulated using EasySpin software package 4 and the obtained parameters are given in Table S1.
The analysis of porphyrin ring planar symmetry in various MOFs is presented in Table S2 according to Ref. 5. The tetrahedral distortion is checked by evaluating the ratio f = g ∥ /A Cu ∥ and isotropic A iso and g iso tensor values. The f value in the range (110-120) cm, A Cu iso = (75-90)10 −4 cm −1 and g iso = 2.06-2.11 are indicative for the copper complex with planar symmetry. 5

S2.6 Pulse ESR spectroscopy
The spin-lattice relaxation rate experimental data, 1/T 1 , were analysed according to 23,24 1/T 1 = aT + b T 9 where the first term denotes a direct one-phonon process while the second and third terms represent a two-phonon Raman and local-mode contribution processes, respectively. The best-fit parameters are given in Table 1 and with more statistical details in Table S3 while theoretical curves are presented in Fig. S7. The contribution of individual components i.e. direct, Raman and local modes are demonstrated in Fig. S8 referring to Cu 0.1 -PCN-223. Figure S7: Temperature dependence of the electron spin-lattice relaxation rate, 1/T 1 , in various MOFs as indicated in the legend for two spectral positions: a) g ∥ and b) g ⊥ . Full lines denote simulations of the experimental data according to the Eq. S1 with the parameters given in Table 1.  Figure S8: Temperature dependence of the electron spin-lattice relaxation rate, 1/T 1 , in Cu 0.1 -PCN-223 at g ∥ spectral position. Experimental data (symbols) were simulated (lines) according to the Eq. S1 with the parameters given in Table 1. Individual components of direct, Raman and local modes are presented as indicated in the legend.
The temperature dependence of phase-memory relaxation rate is presented in Fig. S9. Below 40 K there is no thermally activated processes while in the temperature interval from 40-80 K a thermally activated behavior can be noticed 25 with the activation energies increase in the presence of fullerene.  The contribution of different C atoms to superhyperfine interaction could be seen in Fig. S12 where 8 different Cu-C distances are indicated.