Magneto-Structural Correlations in a Family of Fe^IIRe^IV(CN)₂ Single-Chain Magnets: Density Functional Theory and Ab Initio Calculations

Abstract

Until now, the expressions of the anisotropic energy barriers Δξ and ΔA, using the uniaxial magnetic anisotropy D, the intrachain coupling strength J, and the high-spin ground state S for single-chain magnets (SCMs) in the intermediate region between the Ising and the Heisenberg limits, were unknown. To explore this relationship, we used density functional theory and ab initio methods to obtain expressions of Δξ and ΔA in terms of D, J, and S of six R4Fe(II)-Re(IV)Cl4(CN)2 (R = diethylformamide (1), dibutylformamide (2), dimethylformamide (3), dimethylbutyramide (4), dimethylpropionamide (5), and diethylacetamide (6)) SCMs in the intermediate region. The ΔA value for compounds 1-3 was very similar to the magnetic anisotropic energy of a single Fe(II), while the value of Δξ was predicted using the exchange interaction of Fe(II) with the neighboring Re(IV), which could be expressed as 2JSReSFe. Similar to compounds 1-3, the anisotropy energy barrier ΔA of compounds 4 and 5 was also equal to (Di - Ei)SFe(2), but the correlation energy Δξ was closely equal to 2JSReSFe(cos 98.4 - cos 180) due to the reversal of the spins on the opposite Fe(II). For compound 6, one unit cell of Re(IV)Fe(II) was regarded as a domain wall since it had two different Re(IV)-Fe(II) couplings. Thus, the Δξ of compound 6 was expressed as 4J″SRe1Fe1SRe2Fe2, where J″ was the coupling constant of the neighboring unit cells of Re1Fe1 and Re2Fe2, and ΔA was equal to the anisotropic energy barrier of one domain wall given by DRe1Fe1(S(2)Re1Fe1 - 1/4).

Synthesis, Crystal Structure and Magnetic Properties of Heteropolynuclear ReIVMII Complexes Based on the Robust [ReCl5(pyzCOO)]2– Unit (pyzCOO = 2‐pyrazinecarboxylate)

“…In the light of these considerations, the magnetic data of 3 were analysed by using the Hamiltonian given in Equation (5): [34] (5) The first term corresponds to the isotropic exchange coupling between the S = 3/2 Re IV and Co II local spins. The second term takes into account the spin-orbit coupling between the S = 3/2 spin and the L = 1 effective angular moment of the 4 T 1g ground term of Co II , in which λ is the spin-orbit coupling parameter and α is an orbital reduction factor that includes the covalency of the metal-ligand bonds and the interaction that mixes the 4 T 1g ( 4 P) excited state into the ground state.…”

“…[2] Indeed, some of them were found to exhibit slow relaxation of the magnetization, for example, (NBu 4 ) 4 [Ni{ReCl 4 (ox)} 3 ] (NBu 4 = tetra-nbutylammonium cation, ox = oxalate dianion) [3] and [M(dmf ) 4 {ReCl 4 (CN) 2 }] n (M = Mn, Fe, Co, Ni; dmf = dimethylformamide), [4,5] being new examples of SMMs [6] and singlechain magnets (SCMs), [7] respectively. Rhenium(IV) is a 5d 3 ion that usually forms inert, relatively stable, octahedral complexes.…”

“…Besides the two examples mentioned in the first paragraph, several other di-, [15][16][17] tri- [18] and tetranuclear complexes [15b] as well as one-dimensional (1D) compounds [12,16,19,20] have also been described. Up to now, two heterobimetallic Re IV compounds with heavier 4d or 4f metals have also been synthesized, namely (PPh 4 ) 2 [21] and the pentanuclear (NBu 4 ) 5 [Gd III {Re IV Br 4 (μ-ox)} 4 (H 2 O)]·H 2 O. [22] Both ferro-and antiferromagnetic interactions have been observed, depending on the electronic structure of the M II/III ion and the coordination mode and bond lengths and angles of the bridge between the cations.…”

How to link theory and experiment for single-chain magnets beyond the Ising model: magnetic properties modeled fromab initiocalculations of molecular fragments

“…[41][42][43] Although a notable number of compounds with SCM behavior have been reported within the last few years, only a few have been investigated by ab initio quantum mechanical methods on the level of multi-reference methods. 23,24,[43][44][45][46][47] From our point of view this situation is unsatisfactory, since we are rmly convinced that synergies evolve wherever experimental and theoretical methods can be combined. However, ab initio quantum mechanical studies on the multi-reference level for 1D periodic systems like SCMs are challenging and computationally demanding.…”

Stepwise assembly of heterometallic 3d–4f chain exhibiting slow magnetic relaxation

“…Hitherto, current research mainly utilizes two effective approaches to build SCMs. The most common approach is serendipitous assembly between metal ions with large single-ion anisotropy such as Mn(III), Co(II), Fe(II) and Ln(III) ions [8][9][10][11] and suitable ligands that could efficiently mediate intrachain exchange interactions so as to get simultaneously isolate the chains to avoid interchain exchange interactions [12][13][14]. Although it is not easy to foresee the concrete bonding modes of the resultant products, the approach have been successfully utilized in many related systems.…”