  We study the spin-phonon relaxation rate of both Kramers and non-Kramers
molecular magnets in strongly diluted samples at low temperature. Using the
"rotational" contribution to the spin-phonon Hamiltonian, universal formulae
for the relaxation rate are obtained. Intriguingly, these formulae are all
entirely expressed via measurable or \emph{ab initio} computable physical
quantities. Moreover, they are also independent of the energy gaps to excited
states involved in the relaxation process. These obtained expressions for
direct and Raman processes offer an easy way to determine the lowest limit of
the spin-phonon relaxation of any spin system based on magnetic properties of
the ground doublet only. In addition, some intriguing properties of Raman
process are also found. Particularly, Raman process in Kramers system is found
dependent on the magnetic field's orientation but independent of its magnitude,
meanwhile the same process in non-Kramers system is significantly reduced out
of resonance, i.e. for an applied external field. Interestingly, Raman process
is demonstrated to vary as $T^{9}$ for both systems. Application of the theory
to a recently investigated cobalt(II) complex shows that it can provide a
reasonably good description for the relaxation. Based on these findings, a
strategy in developing efficient single-molecule magnets by enhancing the
mechanical rigidity of the molecular unit is proposed.
