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The unique electronic and magnetic properties of Lanthanides molecularcomplexes place them at the forefront of the race towards high-temperaturesingle-ion magnets and magnetic quantum bits. The design of compounds of thisclass has so far been almost exclusively driven by static crystal fieldconsiderations, with emphasis on increasing the magnetic anisotropy barrier.This guideline has now reached its maximum potential and new progress can onlycome from a deeper understanding of spin-phonon relaxation mechanisms. In thiswork we compute relaxation times fully ab initio and unveil the nature of allspin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in aprototypical Dy single-ion magnet. Computational predictions are in agreementwith the experimental determination of spin relaxation time and crystal fieldanisotropy, and show that Raman relaxation, dominating at low temperature, istriggered by low-energy phonons and little affected by further engineering ofcrystal field axiality. A comprehensive analysis of spin-phonon couplingmechanism reveals that molecular vibrations beyond the ion's first coordinationshell can also assume a prominent role in spin relaxation through anelectrostatic polarization effect. Therefore, this work shows the way forwardin the field by delivering a novel and complete set of chemically-sound designrules tackling every aspect of spin relaxation at any temperature

A complete ab initio view of Orbach and Raman spin-lattice relaxation in a Dysprosium coordination compound