  Magnetic field effects (MFE) in certain chemical reactions have been well
established in the last five decades and are attributed to the evolution of
transient radical-pairs whose spin dynamics are determined by local and
external magnetic fields. The majority of existing experimental techniques used
to probe these reactions only provide ensemble averaged reaction parameters and
spin chemistry, hindering the observation of the potential presence of quantum
coherent phenomena at the single molecule scale. Here, considering a single
nitrogen vacancy (NV) centre as quantum sensor, we investigate the prospects
and requirements for detection of MFEs on the spin dynamics of radical-pairs at
the scale of single and small ensemble of molecules. We employ elaborate and
realistic models of radical-pairs, considering its coupling to the local spin
environment and the sensor. For two model systems, we derive signals of MFE
detectable even in the weak coupling regime between radical-pair and NV quantum
sensor, and observe that the dynamics of certain populations, as well as
coherence elements, of the density matrix of the radical pair are directly
detectable. Our investigations will provide important guidelines for potential
detection of spin chemistry of bio-molecules at the single molecule scale,
required to witness the hypothesised importance of quantum coherence in
biological processes.
