Theoretical Studies on Trinuclear {(Mn2GdIII)-Gd-III} and Tetranuclear {(Mn2Gd2III)-Gd-III} Clusters: Magnetic Exchange, Mechanism of Magnetic Coupling, Magnetocaloric Effect, and Magneto-Structural Correlations

Among various applications that are proposed for {3d-4f} clusters, magnetic refrigeration based on the principle of the magnetocaloric effect (MCE) is gaining attention in recent years due to the substantially large MCE values reported for these types of molecules. While various factors play a role in controlling the MCE values, understanding the structural parameters that control the magnetic exchange play a vital role in the development of novel molecules possessing attractive MCE characteristics. In this regard, theoretical tools based on density functional methods are indispensable. In this work, we have employed density functional methods to study the magnetic properties of six {(MnGdIII)-Gd-III} clusters. This comprises a trinuclear complex {(Mn2GdIII)-Gd-III}, [Mn2GdO (Piv)(2)(dmem)(2)(NO3)(3)] (dmem = 2-{[2-(dimethylamino)ethyl]methylamino}ethanol) (1), along with four tetranuclear {(Mn2Gd2III)-Gd-III} complexes, [Mn2Gd2O2(Piv)(8)(HO2CCMe3)(2)(MeOH)(2)] (Piv = 2,2-dimethylpropanoic acid) (2), [Mn2Gd2O2(Piv)(8)(HO2CCMe3)(4)] (3), [Mn2Gd2(OH)(2)(O2CPh)(4)(NO3)(2)(teaH)(2)] (tea = triethanolamine) (4), and [Mn2Gd2(O)(Piv)(2)(hep)(4)(NO3)(4)] (hep = 2-(2-hydroxyethyl)pyridine) (5), and a single-chain compound containing the {(Mn2Gd2III)-Gd-III} core, [Mn(2)Ln(2)(OH)(OMe)(hmp)(4)(NO3)(4)(O3SC6H4CH3)(2)](n) (hmp = 2-hydroxymethylpyridine) (6). Here we have evaluated the exchange interactions between Mn-III and Gd-III ions and Mn-III center dot center dot center dot Mn-III ions in trinuclear as well as tetranuclear complexes. Our DFT-computed exchange interaction (J) values reproduce the experimental susceptibility data well, offering confidence in the estimated J values. Our calculations yield a diverse set of J values among these complexes ranging from weak ferromagnetic to moderate antiferromagnetic {Mn-III center dot center dot center dot Gd-III} coupling. Using orbital overlap and NBO analysis, we have explored the mechanism of magnetic coupling and deciphered the origin of diverse J values noted among these complexes. Particularly, the importance of Jahn-Teller axes of the Mn-III ions and its orientation with respect to the nature of coupling is established using the qualitative mechanism derived. The {Mn-III center dot center dot center dot Mn-III} coupling in all complexes are estimated to be antiferromagnetic, and the consequence of this on the {Mn-III center dot center dot center dot Gd-III}J values and how this influences the ground-state S values are discussed in detail. Further, we have developed magneto-structural correlations to evaluate the importance of structural parameters that control the {Mn-III center dot center dot center dot Gd-III} coupling. Our results reveal that Mn-O-Gd bond angles and Mn-O-Gd-O dihedral angles hold the key to the sign and magnitude of the {Mn-III center dot center dot center dot Gd-III} J values. Further on, utilizing the computed J values, we have estimated the MCE values for these complexes and offer insight into how these two factors are correlated. To this end, our study reveals that the incorporation of anisotropic Mn-III ions in the cluster aggregation could lead to respectable MCE values if a suitable ligand design that offers a way to control the direction of the Jahn-Teller axes of Mn-III ions is presented