Unravelling the role of spin-vibrational coupling in designing high-performance pentagonal bipyramidal Dy(iii) single...

At the cutting edge of high-performance single-molecule magnets (SMMs) lie lanthanide-based complexes, renowned for their potent magnetic anisotropy. SMMs containing one metal centre are defined as single-ion magnets (SIMs). The performance of SMMs is measured generally via the barrier height for magnetisation reversal (U_eff) and blocking temperature (T_B), below which the magnetisation is fully frozen. To enhance the U_eff and T_B values in lanthanide-based SMMs, the static crystal field splitting of m levels has been effectively adjusted through ligand design, leveraging the oblate/prolate ground state 4f electron density shape. However, the maximum fine-tuning achievable through ligand design, known as the axial limit, has already been reached in this class of compounds. This necessitates new design principles to enhance SMM characteristics to better suit end-user applications. Among other avenues that can be explored to improve SMM characteristics, a deeper understanding of spin-phonon coupling is critical to advancing T_B values. However, there are only a handful of examples where this has been deciphered. In this work, using a combination of DFT and ab initio CASSCF calculations, we have performed spin-phonon calculations on five classes of pentagonal bipyramidal Dy(iii) SIMs exhibiting T_B values 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(L^N5)(Ph₃SiO)₂](BPh₄)·CH₂Cl₂ (4) and [L₂Dy(H₂O)₅][I]₃·L₂·H₂O (5, L = BuPO(NHⁱPr)₂)). Unlike the method employed elsewhere for the calculation of spin-phonon coupling, in this work, we have employed a set of criteria and intuitively selected vibrational modes to perform the spin-phonon coupling analysis. The approach provided here not only reduces the computational cost significantly but also suggests chemical intuition to improve the performance of this class of compounds. Our calculations reveal that low-energy vibrational modes govern the magnetisation 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 magnetisation, reducing the T_B 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 an increase in T_B values. Our calculations also reveal that not only the atoms in the first coordination sphere but also those in the secondary coordination sphere affect the performance of the SMMs. Learning from this exercise, we have undertaken several in silico models based on these vibrations to improve the T_B values. Some of these predictions were correlated with 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 pentagonal bipyramidal Dy(iii) single-ion magnets (SIMs), unveils a treasure trove of chemically sound design clues, poised to enhance the T_B values in this fascinating molecular realm.