Conversion between two nuclear-spin isomers of water molecules has been extensively studied over many decades. A recent work on ${\mathrm{H}}_2\mathrm{O}@{\mathrm{C}}_{60}$ single-molecule transistors (SMTs) suggested that water molecules may exhibit ortho-para fluctuation in a short timescale, when conduction electrons pass the ${\mathrm{H}}_2\mathrm{O}@{\mathrm{C}}_{60}$ molecule. In this work, we have analyzed electron-tunneling spectra in ${\mathrm{H}}_2\mathrm{O}@{\mathrm{C}}_{60}$ SMTs. We consider the selection rule for the ortho-para conversion (OPC), taking into account the angular momentum exchange among tunneling electrons, nuclear spins, and molecular rotations. Due to stringent parity conservation of the system, six OPC processes are accompanied by molecular rotation, while a tunneling electron provides only the transition energies. Furthermore, angular momentum exchange among an electron spin, a molecular rotation, and a nuclear spin gives rise to six more conversion channels, representing unique processes in a single-electron-tunneling system. In the Coulomb stability diagram, most of the OPC lines appear very close to the excited state lines of molecular rotation, except for the excited state line at 9.3 meV. The expected OPC energies are in good agreement with experiment. The findings provide strong support for the electron-induced OPC, linking transport measurements with nuclear-spin dynamics.

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• Atomic & molecular structure
• Electronic structure
• Molecular junctions
• Single-electron transistors
• Inelastic electron tunneling spectroscopy