  The coupling between electronic spins and lattice vibrations is fundamental
for driving relaxation in magnetic materials. The debate over the nature of
spin-phonon coupling dates back to the 40's, but the role of spin-spin,
spin-orbit and hyperfine interactions, has never been fully established. Here
we present a comprehensive study of the spin dynamics of a crystal of
Vanadyl-based molecular qubits by means of first-order perturbation theory and
first-principles calculations. We quantitatively determine the role of the
Zeeman, hyperfine and electronic spin dipolar interactions in the direct
mechanism of spin relaxation. We show that, in a high magnetic field regime,
the modulation of the Zeeman Hamiltonian by the intra-molecular components of
the acoustic phonons dominates the relaxation mechanism. In low fields,
hyperfine coupling takes over, with the role of spin-spin dipolar interaction
remaining the less important for the spin relaxation.
