Investigating the Interplay Between Spin-Vibrational Coupling and Blocking Temperature in Designing High-Performance Pseudo D5h Dy(III) Single Ion Magnets

At the cutting edge of high-performance single-molecule magnets (SMMs) lie lanthanide-based complexes, renowned for their potent magnetic anisotropy. The performance of the SMMs is measured generally via the barrier height for magnetization reversal (Ueff) and blocking temperature (TB), below which the magnetization is fully frozen. To enhance the Ueff and TB values in lanthanide-based SMMs, the static crystal field splitting of mJ levels has been effectively adjusted through ligand design, leveraging the oblate/prolate ground state 4f electron density shape. However, the maximum fine-tuning that can be achieved via ligand design called the axial limit is already reached in this class of compounds and demand new design principle to enhance the SMM characteristics to suit end-user applications. Among other avenues that can be explored to improve the SMM characteristics, a deeper understanding of spin-phonon coupling, critical to advancing TB values, offers numerous advantages. However, there are only a handful of examples where this is deciphered. In this work, using a combination of DFT and ab initio CASSCF calculations, we have performed spin-phonon calculations of five classes of pseudo D5h Dy(III) SIMs exhibiting TB value in the range of 4.5 K to 36 K ([Dy(bbpen)Br] (1, H2bbpen=N,N′-bis(2-hydroxybenzyl)-N,N′-bis(2-methylpyridyl)ethylenediamine), [Dy(OCMe3)Br(THF)5][BPh4] (2) [Dy(OSiMe3)Br(THF)5] [BPh4] (3), [Dy(LN5)(Ph3SiO)2](BPh4).CH2Cl2 (4) and [L2Dy(H2O)5][I]3.L2.H2O (5, L = tBuPO(NHiPr)2)). The approach provided here not only reduces the computational cost but also suggests chemical intuition to improve the performance of this class of compounds. Our calculations reveal that low-energy vibrational modes govern the magnetization relaxation in these SIMs. A flexible first coordination sphere found on some of the complexes was found to be responsible for low-energy vibrations that flip the magnetization reducing the TB values drastically (complexes 2 and 3).On the other hand, a rigid first coordination sphere and a stiff ligand framework move the spin-vibrational coupling that causes the relaxation to lie beyond the secondary coordination sphere resulting in the increase of TB values. Learning from this exercise, we have undertaken several in silico models based on these vibrations to improvise the TB values. Some of these predictions were correlated to literature precedents, offering confidence in the methodology employed. To this end, our comprehensive investigation, involving twenty-three molecules/models and five sets of geometries for the pseudo D5h Dy(III) single-ion magnets (SIMs), unveils a treasure trove of chemically sound design clues, poised to enhance the TB values in this fascinating molecular realm.