The photoexcitation of functionalized fullerenes to their paramagnetic triplet electronic state can be studied by pulsed electron paramagnetic resonance (EPR) spectroscopy, whereas the interactions of this state with the surrounding nuclear spins can be observed by a related technique: electron nuclear double resonance (ENDOR). In this study, we present EPR and ENDOR studies on a functionalized exohedral fullerene system, dimethyl[9-hydro (C60-Ih)[5,6]fulleren-1(9H)-yl]phosphonate (DMHFP), where the triplet electron spin has been used to hyperpolarize, couple and measure two nuclear spins. We go on to discuss the extension of these methods to study a new class of endohedral fullerenes filled with small molecules, such as H2@C60, and we relate the results to density functional calculations.
The photo-generated triplet state of organic chromophores has been extensively studied through pulsed electron paramagnetic resonance (EPR), time-resolved EPR (TR-EPR), time-resolved electron nuclear double resonance (TR-ENDOR) and optically detected magnetic resonance spectroscopy [1–4]. These techniques shed light on the photophysical properties of triplet states, their interactions, the exciton delocalization and the triplet exciton transfer . The first EPR experiment on photoexcited triplet states was conducted by Hutchison et al. , who measured the lifetime of the triplet state of naphthalene in a durene single-crystal host. Since then, many studies have been performed on molecular systems in their triplet state, motivated by applications in chemistry, biology and medicine, such as improving our understanding of photosynthesis, the binding of aromatic ligands to DNA and photodynamic therapy [7–11].
An important characteristic of certain triplet states that can be exploited for quantum information processing and dynamic nuclear polarization applications is the high yield of formation as well as the creation of large spin polarization. This triplet spin polarization can be transferred to nearby, coupled nuclear spins through continuous wave (CW) microwave illumination [12,13], via the dynamic nuclear polarization family of methods or by the application of microwave pulses . Even if the triplet state is not highly polarized upon formation, other properties such as a substantial difference in the decay rates of the triplet sublevels to the ground state can lead to spin polarization that can subsequently be transferred to a nuclear spin . The transient triplet electron spin has been proposed as a mediator to indirectly couple two nuclear spins, for example in a homonuclear fullerene system . In this scheme, the feasibility of high-power nuclear entangling gates depends critically on a combination of factors, including the triplet lifetime and the strength of the hyperfine interaction between the triplet and the nuclear spins. A related proposal, based on a heteronuclear system and exploiting the spinor nature of the triplet state, was experimentally applied to the fullerene dimethyl[9-hydro(C60-Ih)[5,6]fulleren-1(9H)-yl]phosphonate (DMHFP) molecule (figure 1a). In that work, ultrafast nuclear entangling gates were implemented on a time scale of hundreds of nanoseconds .
In §2, we give a brief background of the underlying physical mechanisms that give birth to the triplet state in fullerenes and we present detailed EPR studies at 10 GHz (X-band) and 34 GHz (Q-band) for the characterization of the DMHFP triplet state. In the second part of this work, we describe photoexcited EPR and ENDOR experiments performed on the H2@C60 molecule (figure 1b), relating the results to density functional theory (DFT) calculations.
2. The triplet-level system
In C60, the triplet state is typically created through the first excited singlet state via a mechanism called intersystem crossing (ISC), which originates from the spin–orbit coupling. In general, ISC rates vary from 104 to 1012 s−1, and are approximately 1010 s−1 for the fullerene C60. This process populates (unevenly, in general) the levels of the lowest triplet state, which are split by a zero field splitting (ZFS; figure 1c). Upon the application of a static magnetic field, the zero-field triplet levels mix in an orientation-dependent manner, resulting in the T0, T− and T+ electron spin states. These states may further split owing to hyperfine couplings between the triplet and any nearby nuclear spins. The triplet state decays to the ground singlet state directly, whereas spin lattice relaxation between the triplet sublevels can also be present especially at elevated temperatures. We use EPR spectroscopy to characterize the systems under investigation and determine all the interactions involved by extracting the terms of the spin Hamiltonian 2.1where B is the applied magnetic field, ge is the electron ge-factor tensor, μB is the Bohr magneton and D is the ZFS tensor for the S=1 triplet state. In the principal axis system, the ZFS term of the Hamiltonian SDS can be written alternatively as with D=3Dz/2 and E=(Dx−Dy)/2. A(i) is the hyperfine coupling tensor between the triplet and the nuclear spins i, J is the coupling between the nuclear spins and Ii,z is the projection of Ii along z which is defined by B0.
We synthesized the exohedral fullerene derivative DMHFP with two nuclear spins directly bonded to the cage (a proton, 1H, and a phosphorus, 31P), according to the procedure reported in . The sample of 4×10−4 M concentration in d8-toluene was deoxygenated using five freeze–pump–thaw cycles, flame sealed under vacuum and flash frozen in liquid nitrogen.
TR-EPR experiments of the photoexcited paramagnetic state of DMHFP were performed at 34 GHz (Q-band) on a Bruker Elexys 580 e spectrometer equipped with a low-temperature helium flow cryostat. Photoexcitation was performed using an optical parametric oscillator pumped by a Nd–YAG laser of variable repetition rate, with a pulse width of 7 ns and 10 mJ energy per pulse.
The contour plot shown in figure 2 illustrates the decay of the TR-EPR signal following the laser pulse, and a single spectrum is shown for reference in figure 3a. The EPR spectrum is broadened by the ZFS term (D), which causes the EPR transition frequencies to vary according to the orientation of the molecule with respect to the applied static magnetic field [2,19]. Therefore, each magnetic field position in the EPR spectrum corresponds to molecules with different orientations, and the four distinct peaks (named here as pairs: ‘inner’ and ‘outer’ peaks) reflect molecules with one of their three principal axes (x, y or z) parallel to the magnetic field. For example, the field positions marked with Z+ and Z− in the spectrum refer to molecules with their z-axes parallel to the magnetic field, and the superscripts refer to resonances situated at high and low magnetic fields, respectively. The molecular orientation selection achieved at all other field positions is not completely pure, as other non-canonical orientations also contribute to the signal intensity.
The EPR spectrum has an AAEE pattern (A, absorption; E, emission) and is symmetric in high and low fields. In general, a triplet EPR spectrum is a combination of an absorption and an emission component between pairs of levels with ΔMs=±1, as shown in figure 3b, and is not to be confused with the derivative line shape of an absorption spectrum seen in conventional field-modulated CW EPR methods. In figure 3c, we show for comparison the simulated spectrum assuming that the three triplet levels are thermally populated (as opposed to hyperpolarized), yielding a characteristic Pake pattern.
In order to extract the terms of the Hamiltonian and determine the polarization of the triplet state, we perform simulations of the Q-band TR-EPR spectrum using Easyspin  (figure 3a). From the fit, we extract the principal values of the g-tensor, gxx=2.00076, gyy=2.00224, gzz=2.00274 with an anisotropy of gzz−gxx=0.0019. The effect of this g-anisotropy in the spectrum would be more pronounced at even higher frequencies than the 34 GHz used here. The ZFS D is given by half the separation between the edges of the spectrum (marked with Z) and the central splitting in the spectrum provides an indication of the ZFS anisotropy.
The negative sign of the ZFS parameter from the fit D=−317 MHz is consistent with the negative D value of the fullerene C60, and the large E anisotropy of −53 MHz reveals a significant deviation from axial symmetry. The population ratio, |px−pz|/|py−pz|=0.32, indicates that the ISC populates mostly the Ty sublevel, considering that a negative D leads to a polarization pattern of |px,py|>pz. Previous studies at X-band reveal the same population ratio and a similar D-tensor .
Studies of the time evolution of the triplet signal were also performed using X-band EPR (9.7 GHz). We apply soft (selective) microwave pulses of 64 and 128 ns duration for the π/2 and the π pulses, respectively, and we extract series of electron spin echo-detected field sweep (ESE-FS) spectra in which the delay after the laser flash was varied up to 750 μs (figure 4). The quick decay of the outer peaks compared with the inner peaks indicates the presence of an anisotropic relaxation mechanism. The preservation of the symmetric shape of the spectra within this range shows that no substantial triplet relaxation between the triplet sublevels occurs. By performing an inversion recovery experiment at the field position ‘B’ (with respect to figure 4), we are able to extract the electron spin triplet T1 relaxation time by monitoring the decay of the echo after flipping the initial magnetization with an additional π pulse. From the fitting of this curve, it can be inferred that the T1 is longer than any of the observed triplet recombination times, the longest of which is 267 μs (figure 5a). By contrast, T2 at the same field is much shorter and was measured using a Hahn echo sequence to be approximately 3 μs (figure 5b). The field-swept spectrum was found to be temperature independent at temperatures from 5 to 50 K.
For the determination of the hyperfine coupling of the triplet to the 1H and 31P nuclear spins, we use the Davies ENDOR pulse sequence, and we apply microwave pulses of the same length as in the previous pulsed experiments and 12 μs radiofrequency (RF) pulses. Davies ENDOR spectra at four field positions (A, B, C, D, with respect to figure 5) are shown in figure 6a, indicating the nuclear spin resonance frequencies.
For each EPR transition joining two triplet sublevels (i.e. , or ), there are two measurable ENDOR resonance frequencies corresponding to the nuclear spin splitting in each sublevel. These frequencies are 3.1depending on whether the T+ or T− level is involved, where I is the nuclear spin, ω0 is the Larmor frequency and AH is the effective hyperfine splitting at a particular magnetic field orientation. In the ENDOR spectra, we observe two intense, narrow lines at ω0,H≈6 MHz and ω0,P≈15 MHz which correspond to the Larmor frequencies of 31P and 1H. The weakly resolved peak at around 3.8 MHz is the Larmor frequency of 13C present at low natural abundance in the fullerene cage or as impurities in the solvent.
In figure 6b, we plot separately the two ENDOR spectra at fields A, D, in order to demonstrate the effect of the RF excitation on the electron spin echo intensity in the ENDOR experiment, to extract the ENDOR efficiency. The high intensity of the Larmor frequency ENDOR peaks corresponds to an ENDOR efficiency of 90–100%. In the ENDOR spectrum at each magnetic field, we also observe two less intense peaks that show a much stronger magnetic field dependence (e.g. at ≈17 MHz and ≈21 MHz when measured at the A field position). These represent the hyperfine splittings in the T± subspace, and show substantially lower ENDOR efficiencies. Therefore, for high-fidelity control operations, it is better to use nuclear spin transitions within the T0 triplet subspace. The magnitude of the hyperfine splitting is directly obtained from the shift of the ENDOR lines compared with the Larmor frequency. The substantial magnetic field dependence of these peaks indicates anisotropic hyperfine interactions, whereas the width of these peaks arises from the presence of a spread of molecular orientations.
The assignment of these two peaks to the nuclear spins can be performed using equation (3.1), which indicates that ENDOR peaks should appear symmetrically around the Larmor frequency. For example, an ENDOR peak appears at about 21 MHz at A (338 mT) and at about 9 MHz at D (358 mT), shifted in each case by about 6 MHz from the 1H Larmor frequency at 15 MHz. Similarly, hyperfine peaks arising from the 31P appear at about 17 and 5 MHz, shifted by 11 MHz from the Larmor frequency of 6 MHz.
After assigning the hyperfine peaks to each of the two nuclear spins, we move on to simulate the ENDOR spectra and confirm those values. Fitting the ENDOR traces in all four different field lines, we determine the isotropic component hyperfine interaction of the 1H and 31P to be A(1H)=5.9 and A(31P)=11 MHz. The z-axis of the ZFS tensor coincides with the z-axis of the hyperfine tensor, so no additional orientations were required for fitting the spectra. The hyperfine tensor compares well with DFT studies .
Additional investigation of the ENDOR linewidth of the narrow 1H Larmor frequency line was performed by varying the length of the RFH pulse. According to the decay shown in figure 5a, there is a maximum window of the order of the recombination time (≈250 μs) for the application of an RF pulse. Using an RF π-pulse length of up to 230 μs, an ENDOR linewidth of about 4 kHz was observed (though still mostly limited by the excitation bandwidth of the RF pulse), indicating long nuclear spin T2 times.
Nuclear spins of molecules have been studied as potential quantum bits, or qubits, the building blocks of quantum computers [21,22]. Spin manipulation (e.g. by (ENDOR) or nuclear magnetic resonance (NMR)) can be used create single-qubit logical operations, whereas couplings between spins can be used for multiple-qubit operations. In order to explore the potential of a molecule to support high-fidelity quantum logic operations, it is necessary to fully characterize the spin Hamiltonian, as well as understand spin dynamics such as relaxation. We have combined X- and Q-band EPR studies to obtain a precise set of spin Hamiltonian parameters for the DMHFP system. The similarity between the ESE-FS spectrum at X-band (presented in ) and the TR-EPR Q-band spectrum (figure 3) reveals (i) the small impact of the T2 relaxation on the spectrum and (ii) the small g-anisotropy (ganiso (). From the ESE-FS experiments at X-band (figure 4), the fact that the spectrum remains symmetric as it decays following laser excitation indicates that triplet recombination, rather than spin–lattice relaxation, is the dominant decay mechanism . The large intensity of the ENDOR peak at the Larmor frequency indicates that high-fidelity spin manipulation can be achieved for nuclear spin transitions with no contribution from the hyperfine coupling (i.e. those which lie within the T0 subspace of the triplet). The above findings indicate that the heteronuclear DMHFP is a molecular system which could be used to implement basic nuclear spin entangling gates, as explored in detail in .
Recent years have seen an ongoing effort to gain a complete understanding of the properties of small-molecule endofullerenes. In these systems, one or more small molecules such as dihydrogen, H2, or water, H2O, are trapped inside fullerene cages [24,25]. In this section, we present EPR and ENDOR studies on the endohedral system H2@C60. The synthesis of these fullerenes is achieved by a technique called ‘molecular surgery’. This process involves the chemical creation of a stabilized hole in C60, followed by the application of high temperature and pressure which is increased gradually until the H2 is inserted in the fullerene. Reduction in the pressure and temperature stabilizes the H2 inside the fullerene and the ‘surgery’ is completed by chemically closing the hole and regenerating the pristine fullerene cage. A detailed description of these stages is given in .
The behaviour of the trapped molecules can be probed by interactions with microwave, infrared [26,27] and RF  radiation. According to the Pauli exclusion principle, H2 can exist in two distinct allotropic forms: the ortho-H2 with nuclear spin 1 and the para-H2 with nuclear spin 0. Ortho-to-para conversion is slow in the absence of a spin catalyst: at low temperature, the para-H2 has the lowest energy and the ortho-H2 is metastable with a lifetime of months. The ortho-to-para ratio is temperature dependent, and it is 3 : 1 at 300 K and 1 : 1 at 77 K and 2 : 1000 at 20 K.
Because the reported time scales required for the ortho–para ratio to reach equilibrium can be months, it is essential to find an effective spin catalyst in order to induce a fast interconversion between these two forms . Usually an electron or a nuclear spin that creates an effective magnetic field gradient across the positions of the two spins can serve this purpose [30,31]. For example, the ortho-to-para conversion can be driven by the photochemical formation of an electronic paramagnetic triplet state that is delocalized over the fullerene cage. This idea was put into practice in the work of Frunzi et al. , who reported the effect of photoexcitation of the fullerene triplet on the (room temperature) NMR spectra of H2@C60 and H2@C70. The ortho–para ratio was recorded before and after optical irradiation at 77 K, and whereas the H2@C60 signal showed no significant variation of the equilibrium composition at room temperature that of H2@C70 exhibited a reduction in the ortho-H2 signal which is compatible with the expected 1 : 1 ratio of the nuclear spin isomers of H2 at 77 K. The difference in the behaviour of H2@C60 and H2@C70 was attributed to the different triplet-state lifetimes of C60 and C70.
(b) EPR and ENDOR
In this work, we performed pulsed EPR experiments with laser excitation at 532 nm to study the properties and the dynamics of the photoexcited triplet H2@C60 at 20 K and identify the interactions of the ortho-H2 spins with the triplet state. It should be noted that the para-H2 does not interact with the triplet state since it has zero spin.
The ESE-FS spectrum of H2@C60 at 20 K is shown in figure 7 together with the triplet C60 spectrum for reference. The pulse lengths were 20 and 40 ns for π/2 and π pulses, respectively. Both spectra are almost identical and they are polarized in absorption in low fields and in emission in high fields. The resemblance of the two spectra shows the negligible impact of the presence of the H2 molecule in the line shape of the H2@C60 spectrum.
For the simulation, we adopt the g-tensor, gxx=1.9992, gyy=1.9992, gzz=2.0003 predicted in  by W-band spectroscopy at 1.5 K for C60, whereas the ZFS D and the anisotropy E determined initially by Wasielewski et al.  are D=|340| MHz and E=|15| MHz. We also adopted a negative D tensor as concluded later on by Heuvel et al. which reveals that the Tz sublevel has the highest energy. The population of the triplet sublevels is similar to that observed for the fullerene C60 [33–35] and the |px−pz|/|py−pz| population ratio is 1.2.
By taking a closer look at the fitting of the H2@C60 spectrum, we observe that the outer peaks are not accurately fitted despite using these well-established values. According to the literature the Jahn–Teller distorted triplet C60 spectrum is governed by pseudo-rotation effects, thus it cannot be simulated satisfactorily by considering a static model that incorporates Zeeman and ZFS interactions of one triplet state . Pseudo-rotation effects concern the rotation of the magnetic axes (ZFS axes) caused by the conversion of the distorted C60 between degenerate states, and affect significantly the shape of the EPR spectrum at different temperatures and delays after the laser pulse. This discrepancy is also observed here for the H2@C60 and a study of possible pseudo-rotation effects is currently under investigation.
A common characteristic in randomly oriented solutions is that the EPR spectrum lacks resolved hyperfine splittings mainly as a result of the anisotropy of the ZFS and the dipolar hyperfine broadenings. In order to resolve the hyperfine interaction between the triplet and the endohedral nuclear spins, we performed Mims ENDOR experiments at 20 K for H2@C60, as well as empty C60 as a control. Figure 8a–d shows ENDOR spectra at two magnetic field positions which correspond to the two innermost peaks of the EPR spectrum (marked C and F on figure 7). For both molecules, a peak at the Larmor frequency for 1H is observed, where the symmetric splittings are artefacts arising from the RF pulse applied. The existence of this peak for the empty C60 samples originates from residual protons in the deuterated-toluene solvent. However, an additional ENDOR peak is observed to the left and right of the Larmor frequency line in the case of H2@C60 (figure 8c–d), which arises from the hyperfine splitting of the H2 ortho-state, in the T± subspaces of the fullerene triplet.
Further H2 ENDOR spectra were recorded at different magnetic fields (A–H, with respect to figure 7) in order to extract the hyperfine coupling tensor (figure 8e). The magnetic field dependence of the peak arising from the hyperfine splitting indicates an anisotropic hyperfine tensor, whereas the slight frequency shift of the main Larmor frequency peak is as expected according to the 1H nuclear spin gyromagnetic ratio. As expected, the hyperfine peaks appear symmetrically around the Larmor frequency at different sides of the EPR spectra, and from the ENDOR spectra taken at fields A and H we can determine that the |Azz| component of the hyperfine interaction is ≈1 MHz. Fitting the ENDOR traces for all different magnetic fields, we determine the hyperfine tensor of the H2@C60 to be Axx=0.25, Ayy=0.75, Azz=−1.05 MHz (figure 8f). As the z-axis of the ZFS tensor coincides with the z-axis of the hyperfine tensor no additional orientations were required for fitting of the spectra. As we observe ortho-H2 in the ENDOR spectra at this temperature (20 K), we can infer that negligible ortho-to-para conversion has occurred for H2@C60, consistent with the result of . The hyperfine tensor is calculated in the following section using DFT and reveals a very good agreement with the experimental values.
After extracting the hyperfine tensor, we measure the ortho-H2 spin decoherence time by applying the pulse sequence shown in figure 9a. The sequence is based on Mims ENDOR with the difference that the RF π pulse is now replaced with a nuclear spin Hahn echo pulse sequence whose delay time τn is swept. We use a fixed time window of 320 μs to remove any effect of the triplet relaxation and we perform Rabi oscillations to manipulate coherently the nuclear spin by increasing gradually the length of the RF pulse and calibrate the measurement of nuclear spin coherence through electron spin echo intensity. For clarity, we also present the upper and lower levels of electron spin echo intensity arising from the absence and presence of the RF π pulse, using the same fixed time interval. The decay of the nuclear spin coherence was fitted to an exponential with T2=440 μs (figure 9b,c).
5. Density functional theory calculations of the hyperfine interaction
First-principles electronic-structure calculations are capable of predicting the parameters related to EPR and NMR spectroscopy [36–39]. Among these, those based on DFT offer the best scaling properties with respect to the increase in computational cost and resource usage. Hence, they are particularly suited to the purpose sought herein, because we are seeking to model molecules made of 60 carbon atoms.
Furthermore, modelling the system dealt with herein poses two major problems, i.e. the quantum motion of H2 within C60 and the weak interaction between them. In fact, an unsatisfactory performance of DFT is often observed when dealing with molecules (or parts thereof) that interact through weak dispersive forces. This issue is particularly sensitive here, because the H2 molecule is embedded within C60 (in whatever electronic state) but does not form any covalent bond with it; indeed, it precisely interacts with the interior of the C60 cage via dispersion. Therefore, all issues that involve an estimation of the energetics of H2/C60 interaction must face this problem. However, some modern density functionals (or modifications thereof) take dispersion into account; in this work, we have adopted a correction scheme proposed by Grimme et al.  to the BP86 functional.
Second, modelling H2 encapsulated in C60 may be hindered by the quantum nature of its internal dynamics . Even though a full description of the quantum roto-translational (RT) energy levels is available, that approach does not provide the electronic structure of the H2@C60 ensemble, required for predicting EPR parameters. Such calculations can be currently carried out only on fixed geometrical arrangements which treat RT motion classically. As mentioned above, this approach is questionable for H2@C60. Nevertheless, in a related work in this Theo Murphy Meeting Issue , we have demonstrated that, at least at room temperature, the error involved in treating the motion of H2 classically is negligible.
A final issue concerns the open-shell nature of the species. While the calculation of NMR properties of closed-shell, diamagnetic molecules is now widely used to aid structure determination [36–39,43], the corresponding computations for open-shell, paramagnetic species are comparatively less developed. Nevertheless, it has been shown that DFT methods can be used to predict NMR and EPR parameters for a variety of paramagnetic organic, organometallic and inorganic molecules [44–56].
In order to gain an atomic-level understanding of the endohedral H2@C60, determine the position of the H2 in the fullerene cage and extract the principal axis of the hyperfine tensor, we perform DFT calculations and we compare results with experimental values.
(a) Computational details
Density functional calculations were carried out with the ADF 2012 suite of programs  with the PBE0  hybrid exchange–correlation functional. Dispersion energies were modelled via Grimme's D3 correction . Triple-zeta basis sets made up of Slater functions with one (TZP) or two (TZ2P) sets of polarization functions were used for geometry optimization and properties, respectively. All calculations of triplet states were spin-unrestricted and run without symmetry (even though some arrangements have high symmetries), in order to ensure maximum flexibility and to avoid spurious constraints. Hyperfine couplings (A tensors) were computed at the optimized geometry with the PBE0-D3/TZ2P method.
(b) Density functional theory results
As a first approach to the electronic structure of singlet and triplet H2@C60, the H2 molecule was placed at the centre of the C60 cage, with the H–H axis aligned along a direction connecting two pentagonal faces (z-axis). Geometry optimization of the singlet state showed that H2@C60 preserves its spherical shape, while an elongation along the z-axis is observed in the triplet state (figure 10a). This picture is quite similar to what is observed for empty C60 in the triplet state where Jahn–Teller effects distort the cage. The spin density is distributed around the fullerene belt (figure 10b). In order to determine the average position of the H2 in the fullerene cage, we calculated the energetics of the displacement of H2 along x in the singlet and triplet states and along z in the triplet state (figure 11a). The plot of the energy of the structures in relation to the displacement is shown in figure 11b, which reveals that the most stable structures place the H2 in the centre of the fullerene cage. The energy minimum (at the centre) is somewhat more pronounced for triplet than for singlet C60; however, the direction of displacement is irrelevant. Small displacements (up to 0.6 Å) raise the energy by approximately 1.5 kcal mol−1.
Therefore, for practical purposes, one can assume that on average the encapsulated hydrogen molecule resides at the centre of C60. However, because the symmetry (and hence the spin density) of triplet C60 and H2@C60 is lower than in the singlet, it becomes interesting to probe into the effect caused by different H2 orientations within the cage, which seem energetically reachable as shown above.
Thus, we carried out further calculations with the H2 molecule initially arranged along the x- and y-axes, as well as the axes defined by the bisector of the xy, xz and yz planes in the positive and negative directions (±xy, ±xz and ±yz axes for short), for a total of nine orientations. Each calculation was run independently with the methods described above, and afforded energy, structure and hyperfine coupling.
Geometry optimization resulted in a H–H distance of 0.758 Å in all orientations, which is identical to the value for the singlet state. This distance is slightly longer than that calculated for H2 at the same level of theory (0.746 Å) or the experimental value (0.740 Å). Therefore, encapsulation into C60 (whether in the singlet or triplet state) results in an elongation of the H–H bond by approximately 0.1 Å. This finding may be relevant in connection with the rate of ortho–para conversion, which was shown to depend on that distance . Concerning the arrangement of encapsulated H2, geometry optimization invariably led to no change in its orientation with respect to the original one, indicating that the forces acting on the whole molecule are extremely small. This is consistent with a weak interaction between H2 and C60; however, we did not compute absolute interaction energies. All orientations have relative energies within 0.1 kcal mol−1 (z being most stable), which is smaller than the known accuracy of DFT methods; hence, all orientations can be considered energetically equivalent and equally populated.
The principal values of the hyperfine tensor which is axially symmetric are Axx=0.78, Ayy=0.78, Azz=−1.2 MHz for all orientations, whereas the isotropic value Aiso is 0.12 MHz. The calculated hyperfine tensor agrees well with the experiment.
Because the spin density is distributed across the belt as shown in figure 10b, one would not expect constant values of A for all arrangements of H2 inside. This is understood by examining the electronic structure of all orientations investigated (figure 12); contrary to expectation, the spin density is found to be quite mobile and is always located at the closest belt perpendicular to the H2 axis, so that the hydrogen nuclear spins experience a very similar density regardless of its orientation.
Photoexcitation of fullerenes and their derivatives can generate a hyperpolarized triplet state lasting for several hundreds of microseconds, allowing these systems to be probed by EPR and ENDOR spectroscopy for the study of dynamics and couplings between nuclear spins located within, or bonded to, the fullerene cage. We present characterization studies of the DMHFP molecule and discuss how the nuclear spins attached to the cage can be hyperpolarized and detected via the electron spin triplet state. We applied similar methodology to study endohedral H2@C60 and we extract the hyperfine tensor for coupling to endohedral ortho-H2. No appreciable ortho-to-para conversion was observed during the ENDOR experiments at 20 K for the H2@C60 molecule.
Understanding the interactions between the ortho-hydrogen and the electronic triplet state in H2@-fullerenes provides an important step in the design of systems where the para–ortho conversion can be controlled with the aim of inducing large polarization in the nuclear spins. Future experiments will extend these studies to other small-molecule endohedral fullerenes, such as H2@C70, in which the fullerene triplet state was found to catalyse ortho–para conversion .
This research is supported by the EPSRC through the Materials World Network (EP/ I035536/1), CAESR (EP/D048559/1) and a Basic Technology Grant ‘Molecular Spintronics’ (EP/F041349/1), as well as by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 279781. J.J.L.M. is supported by the Royal Society. EPR and ENDOR experiments were performed in CAESR, University of Oxford, and at University College London. Financial support from the University of Padova (PRAT CPDA103095) is gratefully acknowledged. Calculations were run on the Linux cluster of the Laboratorio Interdipartimentale di Chimica Computazionale (LICC) of the University of Padova.
One contribution of 13 to a Theo Murphy Meeting Issue ‘Nanolaboratories: physics and chemistry of small-molecule endofullerenes’.
- © 2013 The Author(s) Published by the Royal Society. All rights reserved.