  Paramagnetic molecules can show long spin-coherence times, which make them
good candidates as quantum bits. Reducing the efficiency of the spin-phonon
interaction is the primary challenge towards achieving long coherence times
over a wide temperature range in soft molecular lattices. The lack of a
microscopic understanding about the role of vibrations in spin relaxation
strongly undermines the possibility to chemically design better performing
molecular qubits. Here we report a first-principles characterization of the
main mechanism contributing to the spin-phonon coupling for a class of
vanadium(IV) molecular qubits. Post Hartree Fock and Density Functional Theory
are used to determine the effect of both reticular and intra-molecular
vibrations on the modulation of the Zeeman energy for four molecules showing
different coordination geometries and ligands. This comparative study provides
the first insight into the role played by coordination geometry and ligand
field strength in determining the spin-lattice relaxation time of molecular
qubits, opening the avenue to a rational design of new compounds.
