Towards designing ^Mn₄ molecules with strong intramolecular exchange coupling

In this study, new distorted cubane ^{Mn 4+ Mn 3+} ₃ molecules were designed by rational variations in the μ₃-O, μ₃-Cl, ^O ₂ ^CMe, and dbm groups of the synthesized distorted cubane ^Mn ₄-dbm molecule.

The ^Mn ₄-dbm molecule contains three dbm groups [12]. Each dbm group, (^CH(^COC ₆ ^H ₅)₂), contains two ^C ₆ ^H ₅ rings, as depicted in figure 2(a). When replacing each ^C ₆ ^H ₅ ring with an isovalent H atom, i.e. substituting ^CH(^COC ₆ ^H ₅)₂ with ^CH(^CHO)₂ (a procedure also known as 'hydrogen saturation'), the ^Mn ₄-dbm molecule resizes to ^{Mn 4+ Mn 3+} ₃(μ₃-^{O 2−})₃(μ₃-^{Cl −})(^O ₂ ^CMe)⁻ ₃(^CH(^CHO)₂)⁻ ₃ (hereafter ^Mn ₄-^CH(^CHO)₂) molecule (see panel (b) of figure 2). Our calculated results show that, with this variation in the dbm groups, the geometric structure of the [^{Mn 4+ Mn 3+} ₃(μ₃-^{O 2−})₃(μ₃-^{Cl −})] core is nearly unchanged, especially the geometric structure of the ^{Mn 4+}–(μ₃-^{O 2−})–^{Mn 3+} exchange pathways, as shown in table 1. Also, the calculated magnetic moments at the ^{Mn 4+} (m ^_A ) and ^{Mn 3+} (m ^_B ) ions, as well as the exchange coupling between them (J ^_AB ), are nearly constant with this variation in the dbm group, as shown in table 2. These results demonstrate that variation in the outer part of dbm groups is not so much an influence on the magnetic properties of ^{Mn 4+ Mn 3+} ₃ molecules. This finding is very helpful, since the computational cost can be significantly reduced. Next, new distorted cubane ^{Mn 4+ Mn 3+} ₃ will be designed based on the ^Mn ₄–^CH(^CHO)₂ molecule instead of the Mn₄-dbm molecule.

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In the ^Mn ₄–^CH(^CHO)₂ molecule, the μ₃-O atoms form ^{Mn 4+}–(μ₃-^{O 2−})–^{Mn 3+} exchange pathways between the ^{Mn 4+} and ^{Mn 3+} ions, as shown in figure 3. Therefore, substituting μ₃-O with other ligands will be an effective way to tailor the geometric structure of exchange pathways between the ^{Mn 4+} and ^{Mn 3+} ions, as well as the exchange coupling between them. To preserve the distorted cubane geometry of the core of ^{Mn 4+ Mn 3+} ₃ molecules and the formal charges of Mn ions, ligands substituted for the core μ₃-O ligand should satisfy the following conditions: (i) to have the valence of 2; (ii) the ionic radius of these ligands should be not so different from that of ^{O 2−} ion. From these remarks, N based ligands, ^NR' (^R' = ^a radical), should be the best candidates. Moreover, by varying the ^R' group, the local electronic structure as well as electronegativity at the N site can be controlled. As a consequence, the Mn–N bond lengths and the ^{Mn 4+}–N–^{Mn 3+} angles (α), as well as delocalization of d ^{_{z 2}} electrons from the ^{Mn 3+} sites to the ^{Mn 4+} site and J ^_AB , are expected to be tailored. Also, by varying the core μ₃-Cl ligand and the ^O ₂ ^CMe ligands, the local electronic structures at the Mn sites are also changed. Therefore, combining variations in μ₃-O, μ₃-Cl and ^O ₂CMe ligands is expected to be an effective way to seek new superior ^{Mn 4+ Mn 3+} ₃ SMMs with strong J ^_AB , as well as to reveal magneto-structural correlations of ^{Mn 4+ Mn 3+} ₃ SMMs. By combining variations in μ₃-O, μ₃-Cl and ^O ₂ ^CMe ligands, forty two new ^{Mn 4+ Mn 3+} ₃ molecules have been designed. These molecules have a general chemical formula [^{Mn 4+ Mn 3+} ₃(μ₃-^{L 2−})₃(μ₃-^{X −})^{Z 3−}(^CH(^CHO)₂)⁻ ₃] (hereafter ^Mn ₄ ^L ₃ ^XZ) with ^L=^O, NH, ^NCH ₃, ^NCH ₂–^CH ₃, ^NCH=^CH ₂, ^NC≡^CH, or ^NC ₆ ^H ₅; ^X=^F, Cl, or Br; and ^Z=(^O ₂ ^CMe)₃ or ^MeC(^CH ₂–^NOCMe)₃. These 42 ^Mn ₄ ^L ₃ ^XZ molecules are labeled 1 to 42, and their chemical formulae are given in table 3.

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To determine exactly the magnetic ground state of Mn 4 L 3 XZ molecules, the same computational method as in our previous paper was used [5]. In this method, all possible spin configurations of Mn 4 L 3 XZ molecules are probed, which are imposed as an initial condition of the structural optimization procedure. The number of spin configurations should be considered depending on the charge state of manganese ions. In terms of the octahedral field, Mn 4+ ions could, in principle, have only the high-spin state with the configuration d3(t2g 3, e g 0), in which three d electrons occupy three different t2g orbitals. The possible spin states of the Mn 3+ ion are the high-spin (HS) state with configuration d4(t2g 3, e g 1) and the low-spin (LS) state with configuration d4(t2g 4, e g 0). Additionally, the magnetic coupling between the Mn 4+ ion at the A site and Mn 3+ ions at the B site can be ferromagnetic (FM) or antiferromagnetic (AFM). Therefore, there are four spin configurations that should be considered for each Mn 4 L 3 XZ molecule, including (i) AFM-HS, (ii) AFM-LS, (iii) FM-HS and (iv) FM-LS. Our calculated results show that the most magnetic stable state of all 42 Mn 4 L 3 XZ molecules is the AFM-HS. This means that the three Mn 3+ ions at the B sites exist in the HS state with configuration d4(t2g 3, e g 1), and the exchange coupling between the three Mn 3+ ions and the Mn 4+ ion is AFM, resulting in the ferrimagnetic structure in Mn 4 L 3 XZ molecules with the large S T of 9/2.

Note that the HS state with configuration d4(t2g 3, e g 1) relates to the appearance of Jahn–Teller distortions at Mn 3+ ions. Our calculated results confirm that each of three Mn 3+ sites is an elongated octahedron along the Mn 3+ O B axis. Here, the distortion factor of the B sites is measured by

where d ^_Z is the interatomic distance between the ^{Mn 3+} and ^{O _B} sites, as labeled in figure 3. The d_XY is the average interatomic distance between the ^{Mn 3+} site and the two O sites of the ^CH(^CHO)₂ group, as shown in figure 3. The value of f ^_dist is given in table 4, in which molecule 13 with [L, X, Z] = [^NCH ₃, F, (^O ₂ ^CMe)₃] has the highest value of f ^_dist =11.2%, the molecule 42 with [L, X, Z] = [^NC ₆ ^H ₅, Br, and MeC(^CH ₂−^NOCMe)₃] has the smallest value of f ^_dist =4.1%. The HS spin state as well as the elongated Jahn–Teller distortions at ^{Mn 3+} ions is known as one of the origins of the axial anisotropy in Mn SMMs [20–22]. These results demonstrate that all 42 ^Mn ₄ ^L ₃ ^XZ molecules must have axial anisotropy. Therefore, they are high-spin anisotropic molecules. Next, we will present in detail about the geometric structure and magnetic properties of these 42 ^Mn ₄ ^L ₃ ^XZ molecules. The geometric structures corresponding to the most stable states of these 42 ^Mn ₄ ^L ₃ ^XZ molecules are depicted in figure 4. Figure 4 also illustrates the development of geometric structure of ^Mn ₄ ^L ₃ ^XZ molecules by variations in L, X and Z ligands. Our calculations confirm that the C_3v symmetry of ^Mn ₄ ^L ₃ ^XZ molecules, with the C_3v axis passing through the A and X sites, is preserved even if the L, X and Z ligands are changed. Also, the distorted cubane geometry of the ^Mn ₄ ^L ₃ ^X core is preserved. However, their bond angles and interatomic distances are various, in which the exchange coupling angle (α) and the ^{Mn 3+}–^{Mn 4+} interatomic distance (d ^_AB ) are changed in the ranges of 88.84°–95.47° and 2.798–2.967 Å, respectively, as shown in table 4. As expected, the J ^_AB is also various, as shown in table 4. The calculated results confirm the expectation that J ^_AB tends to become stronger when the α reaches around 90°, as demonstrated in figure 5(a), due to the enhancement of hybridization between 3d orbitals at Mn sites and ligand orbitals at L sites. The molecule 22 with ^L=^NC ₂ ^H ₅ has the highest J ^_AB /k ^_B of −214.79 K, corresponding to α=89.69°. This value is about three times larger than that of molecules 1–6 with ^L=^O. Also, the J ^_AB tends to become stronger with a decrease in d ^_AB , which can be attributed to an increase in direct overlap between 3d orbitals at the A and B sites, as shown in figure 5(b).

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The α and d ^_AB dependence of J ^_AB demonstrates that, in the space of 88°⩽α⩽92° and d ^_AB ≤ 2.850 Å (hereafter the strong J ^_AB space), the J ^_AB of ^Mn ₄ ^L ₃ ^XZ molecules is at least about twice as strong as that of synthesized ^Mn ₄ SMMs (or Mn₄ molecules with ^L=^O). Here it is noted that, in the strong J ^_AB space, there are many ^Mn ₄ ^L ₃ ^XZ molecules with L being N-based ligands, such as ^L=^NCH ₃, ^NC ₂ ^H ₅ and ^NC ₆ ^H ₅, while ^Mn ₄ ^L ₃ ^XZ molecules with ^L=^O is far from this space. These results demonstrate the advantages of using N-based ligands instead of oxygen to form exchange pathways between Mn ions. N-based ligands give us possibilities of designing new superior ^{Mn 4+ Mn 3+} ₃ molecules with a strong J ^_AB .

As discussed above, J ^_AB can be described pretty well by the geometric parameters α and d ^_AB . However, as discussed in our previous paper [5], the basic mechanism of exchange coupling between the ^{Mn 4+} and ^{Mn 3+} ions in distorted cubane ^{Mn 4+ Mn 3+} ₃ molecules results from delocalization of the d_z² electrons from the ^{Mn 3+} ions to the ^{Mn 4+} ion, which can be evaluated by a difference between the formal magnetic moment and calculated magnetic moment of the ^{Mn 4+} ion, Δm ^_A =3– |m ^_A | (where m ^_A is the calculated magnetic moment of the ^{Mn 4+} ion). The values of Δm ^_A of 42 ^Mn ₄ ^L ₃ ^XZ molecules are given in table 4. It is expected that the larger Δm ^_A , the stronger J ^_AB . The Δm ^_A dependence of J ^_AB of ^Mn ₄ ^L ₃ ^XZ molecules, which is plotted in figure 5(c), confirms this expectation. As illustrated in figure 5(c), our calculated results demonstrate a very linear relation between Δm ^_A and J ^_AB ,

with the coefficient of determination R² =0.87. This finding suggests an effective way to predict J ^_AB of distorted cubane ^{Mn 4+ Mn 3+} ₃ molecules. A comparison among figures 5(a)−(c) shows that Δm ^_A is a much better parameter to describe J ^_AB than α and d ^_AB .