We adapt the Monte-Carlo wavefunction (MCWF) approach to treat the
open-system spin dynamics of radical pairs subject to spin-selective
recombination reactions. For these systems, non-Lindbladian master equations
are widely employed, which account for recombination via the non
trace-preserving Haberkorn superoperator in combination with reaction-dependent
exchange and singlet-triplet dephasing terms. We show that this type of master
equation can be accommodated in the MCWF approach, by introducing a second type
of quantum jump that accounts for the reaction simply by suitably terminating
the propagation. In this way, we are able to evaluate approximate solutions to
the time-dependent radical pair survival probability for systems that have been
considered untreatable with the master equation approach until now. We
explicate the suggested approach with calculations for radical pair reactions
that have been suggested to be relevant for the quantum compass of birds and
related phenomena.

The Radical Pair Mechanism is a canonical model for the magnetosensitivity of
chemical reaction processes. The key ingredient of this model is the hyperfine
interaction that induces a coherent mixing of singlet and triplet electron spin
states in pairs of radicals, thereby facilitating magnetic field effects (MFEs)
on reaction yields through spin-selective reaction channels. We show that the
hyperfine interaction is not a categorical requirement to realize the
sensitivity of radical reactions to weak magnetic fields. We propose that, in
systems comprising three instead of two radicals, dipolar interactions provide
an alternative pathway for MFEs. By considering the role of symmetries and
energy level crossings, we present a model that demonstrates a directional
sensitivity to fields weaker than the geomagnetic field and remarkable spikes
in the reaction yield as a function of the magnetic field intensity; these
effects can moreover be tuned by the exchange interaction. Our results further
the current understanding of the effects of weak magnetic fields on chemical
reactions, could pave the way to a clearer understanding of the mysteries of
magnetoreception and other biological MFEs and motivate the design of quantum
sensors. Further still, this phenomenon will affect spin systems used in
quantum information processing in the solid state and may also be applicable to
spintronics.