First-principles investigation of hyperfine interactions for nuclear spin entanglement in photoexcited fullerenes

The study of hyperfine interactions in optically excited fullerenes has recently acquired importance within the context of nuclear spin entanglement for quantum-information technology. We here report a first-principles pseudopotential study of the hyperfine coupling parameters of optically excited fullerene derivatives as well as small organic radicals. The calculations are performed within the gauge-invariant projector-augmented wave method [C. Pickard and F. Mauri, Phys. Rev. B 63, 245101 (2001)]. In order to establish the accuracy of this methodology we compare our results with all-electron calculations and with experiment. In the case of fullerene derivatives we study the hyperfine coupling in the spin-triplet exciton state and compare our calculations with recent electron paramagnetic resonance measurements [M. Schaffry et al., Phys. Rev. Lett. 104, 200501 (2010)]. We discuss our results in light of a recent proposal for entangling remote nuclear spins in photoexcited chromophores.

Figure 1

(a) Ball-and-stick (left) and schematic (right) representations of the diethyl malonate (C${}_7$H${}_{12}$O${}_4$) C${}_{60}$ mono-adduct (M1). The bridging ${}^{13}$C atom carrying a nuclear spin is indicated. In the schematic representation the red bond indicates the anchoring point of the adduct on the fullerene cage. Atomic color code: C (grey), O (red/dark grey), H (white/light grey). (b) Schematic representations of three regioisomeric diethyl malonate fullerene bis-adducts (B1-B3).

Figure 2

Comparison between the HFI parameters calculated using PP-CP and AE methods and experimental data, from Tables and . (a) Fermi contact term of C atoms. (b) Fermi contact term of H atoms. (c) Dipolar coupling of C atoms. (d) Dipolar coupling of H atoms. If the calculations were able to predict experimental data exactly, then all the data points would fall on the diagonal solid line.

Figure 3

Spin density distribution in the lowest triplet excited state of the four fullerene derivatives M1 and B1–B3 considered in this work. The color code indicates the magnitude of the spin density (the density isosurface corresponds to an isovalue of 0.07 electron/Å${}^3$).

Figure 4

Ball-and-stick representation of the diethyl malonate adduct on a portion of the C${}_{60}$ fullerene (color code as in Fig. 1). The angles in all the systems considered M1 and B1–B3 differ by less than 1${}^{\circ }$: $\alpha$, ${\alpha }^{\prime }$ = 126${}^{\circ }$, $\beta$, ${\beta }^{\prime }$ = 245${}^{\circ }$, $\gamma$, ${\gamma }^{\prime }$ =  111${}^{\circ }$, $\delta$ = 112${}^{\circ }$, $\theta$ = 65${}^{\circ }$. The different C-C bond length $d1$ in the two adducts of B2 lifts the symmetry between the two isotopically labeled nuclei and results in different HFI parameters [cf. B2(1) and B2(2) in Table ].