Pulsed electron spin nutation spectroscopy for weakly exchange-coupled multi-spin molecular systems with nuclear hyperfine couplings: a general approach to bi- and triradicals and determination of their spin dipolar and exchange interactions

Abstract

Weakly exchange-coupled biradicals have attracted much attention in terms of their dynamic nuclear polarisation application in NMR spectroscopy for biological systems or the use of synthetic electron-spin qubits in quantum information processing/quantum-computing technology. Analogues multi-partite molecular systems are important in entering a new phase of the relevant fields. Many stable organic biradicals known so far have nitrogen nuclei at their electron spin sites, where singly occupied molecular orbitals are dominating and large hyperfine couplings occur. A salient feature of such weakly exchange-coupled molecular systems in terms of electronic spin structures is underlain by small zero-field splitting (ZFS) parameters comparable with nuclear hyperfine and/or exchange interactions. Pulse-based electron spin nutation (ESN) spectroscopy of weakly exchange-coupled biradicals, applicable to oriented or non-oriented media, has proven to be a useful and facile approach to the determination of ZFS parameters, which reflect relatively short distances between unpaired electron spins. In the present study, we first treat two-dimensional single-crystal ESN spectroscopy (Q-band) of a 15N-labelled weakly exchange-coupled biradical, showing the nuclear hyperfine effects on the ESN phenomena from both the experimental and theoretical side. ESN spectroscopy is transition moment spectroscopy, in which the nutation frequency as a function of the microwave irradiation strength ω1 (angular frequency) for any cases of weakly exchange-coupled systems can be treated. The results provide a testing ground for the simplified but general approach to the ESN analysis. In this study, we have invoked single-crystal electron-electron double resonance measurements on a typical biradical well incorporated in a diamagnetic host lattice and checked the accuracy of our ESN analysis for the spin dipolar tensor and exchange interaction. Next, we extend the general approach to analogues multi-partite molecular systems such as stable organic triradical, in which the exchange interaction can be governed by a significant amount of the delocalisation of three unpaired spins over the molecular frame of a triangular structure. The triangular structure maintains π-conjugation in which each spin-bearing nitroxide at the vertex participates and the exchange interaction is greatly controlled by the dihedral angle between the π-conjugation plane and nitroxide moiety at the vertex. In this context, the ZFS parameters do not correspond to spin distances (1.0 nm) in a straightforward manner, but reflect a salient electronic structure associated with both the π-electron network and the symmetry property of the triradical under study. Thus, both the D-value and exchange interaction J have been controlled in this study. In order to interpret the experimental ZFS parameters and exchange interaction, which is three-order of magnitude reduced in the present poly(methyl methacrylate) polymer matrix compared with that in the crystal, sophisticated quantum chemical calculations of the ZFS tensor and exchange interaction were carried out and reproduced the experimental values, concluding that the present triradical of the triangular structure undergoes significant twisting at the nitroxide sites in the polymer matrix. In this study, we observed electron spin resonance forbidden transitions between the Ms-manifolds belonging to the spin-doublet ground state and spin-quartet excited state. The observation enables us to derive the magnitude of the exchange coupling.